jdowning - 5-2-2014 at 06:32 AM
It is an established fact that musical instruments like ouds, lutes and guitars with soundholes behave like Helmholtz resonators - an essential
feature of instrument design that 'amplifies' the sound of the lower pitched strings due to the fundamental resonance mode of the air in the bowl
cavity.
Although this phenomenon has been known and used in ancient times, Herman Helmholtz in the 19th C (before the invention of fancy modern electronic
audio analytical equipment) used different sized spherical resonators to analyse the frequency of soundwaves - hence the name Helmholz Resonator. For
a smooth, non flexible, spherical resonator of volume V with a long vent of length L of cross sectional area A, the resonant frequency of a Helmholz
resonator is given by the speed of sound C divided by 6.28 multiplied by the square root ofthe product of A divided by V x L.
Unfortunately this straightforward equation cannot be used to accurately calculate the air resonance of a guitar, lute or oud as these instruments are
clearly not rigid spheres and do not have long vents - the typical soundhole vent being the thickness of the soundboard itself. To compensate, the
Helmholz equation is usually modifed by introducing an equivalent length L.equ representing the column of air oscillating through the soundhole where
L.equ is equal to the soundboard thickness h plus 1.7 times the soundhole radius.
However, due to the complexities of a musical instrument this equation still overestimates the resonant frequency (i.e. higher than it should be). In
particular, the flexibility of an instrument soundbox/bowl results in a lower resonant frequency than that predicted by the above equation.
Knowing little about instrument acoustics, in 2009 on this forum I ran some trials using a classical guitar as a test bed to gain a better
understanding of the relationship between the air volume of the guitar body and soundhole diameter as it affects resonant frequency as well as the
influence of a rosette pattern compared to an open soundhole. The procedure followed was reported here:
'Old Oud - New Project' starting on page 9.
http://www.mikeouds.com/messageboard/viewthread.php?tid=8488&pa...
The results of the test confirmed that a smaller soundhole diameter lowered the air resonant frequency, that the open soundhole of the test guitar
produced maximum amplification of the 5th (or A) string, that the Helmholtz equation overestimated the measured resonant frequency by about 25%. The
results also suggested that a rosette did not seem to significantly affect the measured air resonant frequency compared to an open soundhole of the
same diameter. In other words for a rosette it is the area A calculated with reference to the outer diameter of the rosette (i.e. as if it were an
open soundhole of that diameter) not the open areas of the rosette that might only constitute about a third of the open area in total. This
observation - if valid - would help simplify attempts to calculate the air resonance values of ouds and lutes.
Also - interestingly - it was observed that the presence of a rosette increased the sustain of the sound of the resonance compared to an open
soundhole by about 100%. This, together with the resonant frequency amplification might have been an important acoustical feature at a time when
duller sounding plain gut strings were used for the lower courses of a lute or oud.
More to follow!
jdowning - 5-4-2014 at 09:20 AM
My renewed interest in the acoustics of sound holes has come about after reading, a few days ago, the research paper 'Acoustic Function of Sound Hole
Design in Musical Instruments' by Hadi Tavakoli Nia submitted as a partial requirement for the degree of M.Sc. in Mechanical Engineering, M.I.T.
A free to download copy of the paper is available on line here :
http://dspace.mit.edu/bitstream/handle/1721.1/61924/707340180.pdf?s...
Of particular interest is the attention given by the author to investigating the influence that complex soundhole designs, found in ouds and lutes,
might have in affecting the acoustic response of an instrument. The approach to the subject is both theoretical and experimental. As my knowledge of
fluid flow, gas thermodynamics, calculus and all of that good stuff (such as it was) is now a dim and distant memory of 50 years ago, I am unable to
follow or usefully comment upon most of the theoretical work presented. Of greater interest are the reported observations of the experimental work
which - if I understand correctly - include:
- The complexity of rosette design has no significance on the air resonant frequency of an oud or lute.
- The oscillating air mass through a circular sound hole at resonant frequency is concentrated close to the outer edges of a sound hole.
- The inner part of a sound hole, having little influence in the resonance response, may be blocked in completely without significantly affecting
acoustic response.
- For purposes of calculating the air resonance frequency, the total open area of a rosette (about 0.3 to 0.45 of the total rosette area) does not
provide the correct frequency whereas the total rosette area will (to a lesser degree of error). In other words - for the purposes of calculation -
any influence that a rosette might have can be ignored.
Interestingly the latter observation confirms my conclusions based upon my earlier trials on the guitar test bed reported in the previous post.
The research paper is of necessity a summary of the experimental work so there appears to be a few missing details necessary for my complete
understanding of the results. With this in mind I thought that it would be interesting to undertake some experimental work of my own in the hope of
discovering a greater understanding of the subject.
Preliminary trials with my low cost experimental apparatus have already provided some promising results so to start the ball rolling I shall next
describe my acoustic chamber apparatus and methodology for the information of all those interested.
jdowning - 5-7-2014 at 04:47 AM
The resonance chamber that will be used for part of these trials is a scrap welded steel pressure tank from a domestic water system (I never throw
anything away that looks as if it might have a useful future purpose!).
The tank has a convenient mounting flange at one end with an outlet measuring 9.9 cm (3.9 inches) in diameter and a small hole at the other end (once
used to hold a valve - part of the original system to pressurise the tank). The tank measures about 25 cm (10 inches) in diameter and about 35 cm (14
inches) overall length - almost custom made for the job! The small hole in the tank has been sealed with a bolt and washer and the exact volume of the
tank determined by filling with water. The measured volume of water is 17,500 cc.
The tank is secured to a wooden cradle with a hose clamp and mounted in a vice to minimise any movement. Test sound holes made from 3 mm thick fibre
board are mounted over the tank outlet flange with strong spring clamps.
After several trials, the air in the resonance chamber was simply set in motion with a pressure pulse generated by tapping the end of the tank with a
rubber mallet.The resulting sound wave pattern was then recorded on an H2 Zoom digital recorder placed 10 cm distance from the sound hole and the
sound recording subject to a spectrum analysis to determine the fundamental resonant frequency using a computer and the excellent 'Audacity' (free)
software.
After a few more tests to determine the optimum position of the recorder in front of the test sound holes. A series of sound holes of different
diameters will be subject to test and analysis - the results to be reported next.
[file]31328[/file] [file]31326[/file]
[file]31330[/file]
jdowning - 5-7-2014 at 11:13 AM
The open circular sound hole trial has been undertaken with sound hole diameters of 3.2 cm, 3.9 cm, 7.1 cm, 8.7 cm and 9.9 cm (open resonator vent)
giving peak air resonance frequencies (Audacity Spectrum Analysis) of 67 Hz, 75 Hz, 88 Hz, 105 Hz, 114 Hz and 124 Hz respectively. Sound hole areas
are 8 cm², 11.6 cm², 20.4 cm², 39.6 cm², 59.4 cm² and 77 cm² respectively. Ratio of sound hole areas relative to the open resonator vent are
10%, 15%, 27%, 51%, and 77% respectively.
See attached image of the spectrum analysis for the 7.1 cm diameter sound hole. Lots of higher frequency acoustic 'noise' but the fundamental air
frequency at 105 Hertz (cycles per second) is clear enough. The spectrum plot is loudness (in decibels) against frequency
For open circular sound holes of short length (thickness of test pieces is 0.3 cm) an end correction must be applied to determine the equivalent
length (Lequ) of the slug of air oscillating through the sound hole. The empirical value of the correction factor has been determined by others to be
1.7 x sound hole radius. See here for more detail.
http://www.phys.unsw.edu.au/jw/Helmholtz.html
For comparison, calculating the air resonance frequency using 1.7R as the correction factor added to the test piece thicknesses of 0.3 cm for the
above sound hole diameters works out as 66.4 Hz, 73.6 Hz, 85.6 Hz, 102.0 Hz, 113.4 Hz and 121.4 Hz (for the resonator vent) respectively. All in
pretty close agreement so confirming the validity of correction factor for this particular experimental set up. The speed of sound in air was
corrected for air temperature of 13 °C but not for relative humidity.
The attached sheet shows the method of calculating the resonant frequency using the Helmholz formula modified for sound hole end correction. Note that
if the thickness of the sound hole is ignored in the end correction (it being small compared to the sound hole radius) then - as the volume of the
resonance chamber is constant and if the speed of sound at room temperature is taken as constant then the resonant frequency is proportional to the
square root of the sound hole diameter or is equal to 39.2 X squ. rt. of the diameter.
So, ignoring the sound hole thicknes for the above sound hole diameters gives calculated resonant frequencies of 70 Hz, 76.9 Hz, 88.5 Hz, 104.5 Hz
115.7 Hz and 123.6 Hz (for the open resonator vent). It can be seen that these values are even closer in agreement with some of the recorded values
above (all within 3 Hz or less.
These tests confirm what is already well known - that for a fixed volume of resonance chamber - reducing the sound hole diameter (and so area) reduces
the resonant frequency.
Next to use the rig to measure the resonance frequency of a 'real' historical lute rosette compared to an open sound hole of the same outside
diameter.
(Posting revised 09 May 2014)
[file]31332[/file]
[file]31351[/file]
antekboodzik - 5-9-2014 at 12:04 AM
May I add something?
What your setup resembles to me, is an udu 
African Udu is an almost "purest" Helmholtz resonator - has chamber and neck with hole. Tapping with open hand on the other hole "pushses" air into
chamber forcing it to vibrate.
Some time ago I picked this cheap, about 30cm height jug and drilled an extra hole (but the jug is still usable for flowers) to produce simple udu
While not really best udu in the world, it allowed me to do some
observations:
- it is somehow fragile and has too high sound (compared to professional ones) - probably neck lenght/width not matched to produce good sound,
- covering (reducing it intersection) the neckhole drastically lowers the sound (a fifth max or more), the sound can be adjusted,
- it also works when you cover mid-hole, but there the sound is slightly higher, and can be also "adjusted" by covering by hand,
- the mid-hole must be covered (partially) just from the edge. I mean, if you simply keep something in the mid-hole "goalmouth", it doesn't change the
sound (?!). This trick - keeping something in the neck - actually works.
It looks like the like the mid-hole must be covered, as if it is a kind of "elongation" walls of the jug. I think that this observation applies to
rosettes of lutes. It is mentioned in that MIT thesis, something jus like the vibrating air travels just near outer edge of soundhole.
I can remember, once one violin luthier said to me, that edges of the f-holes of the violin must be definitely straight (vertically), and have nice,
sharp corners (may not be rounded). I think it creates even very small, but present, "necks" of the resonator. It is not mentioned in the thesis. Also
- do it apply (and how much) to thin "walls" around lute rosette?
I haven't got a stuff to record even sound of this udu for a now, but would try to find some and demonstrate it a little.
[file]31349[/file]
jdowning - 5-9-2014 at 05:20 AM
The ancient ceramic 'flute' - the ocarina - works the same way but has more vent holes to adjust the resonant frequencies to enable production of a
tune.
The MIT paper does go into a lot of detail concerning violin sound holes and how and why they appear to have developed from circular sound holes to
the current narrow 'vertical' f holes. They also derive a more precise formula for calculation of the violin family sound hole (confirmed by
experiment) that takes into account the narrow sound hole geometry and includes the resonance edge effects, increased bandwidth and the improved sound
radiation due to the narrowness of the sound holes running roughly parallel to the sound board vertical axis that results in increased sound board
vibrating area.
jdowning - 5-9-2014 at 11:54 AM
The next trial is to test a lute rosette taken from a scrapped soundboard. This is from a copy of a lute by Giovanni Hieber, Venice, circa 1570 that I
made some years ago. The rosette complete with bracing has been cut from the soundboard and clamped to the resonance chamber. The rosette measures 8.7
cm in diameter (to the outer edges of the holes or voids in the rosette pattern) and is about 1.5 mm thick across the rosette.
The resonance frequency of the rosette on test is 108 Hz. This compares with the measured resonance frequency of an open test sound hole of 8.7 cm
diameter of 3mm thickness of 115 Hz - so is about a semitone lower than the resonant frequency of the open sound hole. Nevertheless pretty close.
This is not quite as near to being the same frequency as the open sound hole as expected but may be explained by the fact that the open area or void
area of this rosette pattern is estimated to be only about 17% of the open sound hole area - much more congested than the rosettes under test by the
MIT project that range in void area from 31% to 45% of an equivalent open sound hole.
However, this does support the MIT conclusions that confirm that the using the void area of a rosette to calculate the resonant frequency is not valid
- the maximum diameter of the rosette must be used and treated as if it were an open sound hole of the same diameter - agreeing with my observations
on the guitar test in 2009.
In this case calculating the equivalent frequency for an open sound hole of 8.7 cm diameter 1.5 mm thick gives a resonance frequency of 113.6 Hz - a
little closer than the measured experimental value.
It was also observed from the Audacity wave form that the measured sustain of this rosette pattern was about 60% less than that of the open sound hole
- contrary to the observations made on the guitar test bed back in 2009 where the sustain of the rosette pattern tested was about twice that of the
open sound hole. However, it must be remembered that the geometry of the resonance chamber used for these trials is quite different from that of a
guitar body so is likely to provide somewhat different results for resonant frequency under comparative test conditions.
[file]31359[/file]
jdowning - 5-9-2014 at 04:07 PM
An observation expressed in the MIT paper and confirmed both theoretically and experimentally is that most of the air mass oscillating through a
circular sound hole - with or without rosette - is concentrated around the outer edge so that resonance frequency changes less than a semitone with
the central area of a sound hole completely blocked by 50% - a steep drop in resonance frequency occurring only when the blocked diameter exceeds 80%
of the sound hole diameter.
I presume that the experimental results reported in the MIT paper result from tests of an open sound hole blocked at various inner diameters but am
not sure. So two tests are next to be carried out the first with the Hieber rosette and secondly with an open sound hole both blocked with various
inner diameters to compare results.
To block the Hieber rosette thin tinplate discs of relative diameter to the rosette outer diameter (d/D) were bolted to the rosette and the resonant
frequency measured on the test rig. Disc relative diameters were 0.5, 0.6, 0.7, 0.8 and 0.9.
The measured resonant frequencies were - uncovered rosette 8.7 cm diameter, 108 Hz and 105 Hz, 103 Hz, 101 Hz, and 97 Hz respectively. The frequency
for the 0.9 d/D measurement was difficult to be certain about as at this point the open area remaining was small - almost completely blocked. The most
prominent lower frequency resonance - albeit small in amplitude - was 71 Hz. The attached plot of frequency f/fo normalised for maximum resonance of
108 Hz against d/D ratios of 0.5, 0.6, 0.7, 0.8, and 0.9 - follows the presentation of this data in the MIT report for direct comparison.
Although the MIT experimental apparatus was more sophisticated, it can be seen that the results obtained here are quite similar and also confirm that
frequency drop remains at about a semitone or less with 50% of the rosette area blocked (d/D = 0.7).
One other interesting observation is that the rosette design incorporates a ring that measures about 0.65 d/D - an indication perhaps that the early
luthiers knew more about sound holes and air resonance that might be first imagined?
I have also noticed similar central rings in the rosettes of ouds. I must check out the lute rosette patterns that I have on file to find more
examples for examination.
Revised 22 July 2015. The Hierber rosette curve does not match the MIT resonance chamber curve exactly because my carving of the rosette pattern is
not as fine as on the original so that at d/D of 0.9 there is very little open air space remaining.
[file]31361[/file]
[file]35964[/file]
narciso - 5-10-2014 at 12:11 AM
I was a bit sceptical that the pronounced peak in the spectrumof your figure is indeed the Helmholtz resonance without further ado.
But I checked the numbers you give and they look plausibly in the right ballpark. Some more extensive data for error analysis would be nice, but
otherwise this is really a very nice demonstration you have achieved here!
Reading through the interesting Nia preprint you are focusing on (thanks for the link), it looks as if for the case of a lute the 1/C term of his Eqn
(2.3) will always dominate over the the h/A term (since h/R<<1 for rosettes)
So perhaps of the several directions you could now take with the data you have, one avenue would be to drop the h/A contribution, and focus instead
on improving the C=2R approximation
My suggestion would be to try to fit an empirical scaling dependence on the void density n,
i.e.
C=f(n)R with f(n)=const x n^exponent
jdowning - 5-10-2014 at 05:22 AM
Thanks for your observations and suggestions narciso.
I hope - albeit with this very basic resonance chamber test rig and essentially quick preliminary testing just to get a feel for what is going on - to
eventually be able to fine tune the empirical side on the basis of more extensive data if all looks promising enough to warrant the extra effort
involved.
The problem with the empirical adjustments to sound hole end corrections is that they likely vary quite a bit on a case by case basis (i.e. from
instrument to instrument) making it problematic to develop an accurate formula for luthiers to use in order to refine their instrument design.
However, it may turn out that if the resonance predictions for an oud or lute can be limited within say, a couple of semitones accuracy, together with
the frequency tolerance (band width) on either side of the peak resonance, this might be perfectly adequate for a luthier to come close enough to
predicting - by straightforward calculation - the optimum value of sound hole diameter to bowl air volume.
The MIT results suggest that this approach may well be possible provided the proper value for sound hole area is chosen e.g. based on the maximum
diameter of a rosette and not the total area of the holes in a rosette.
The air resonant curve (with the aid of the cursor in the Audacity Spectrum analysis) can be used to determine frequency bandwidth at 3dB less than
peak resonance. This is the point of half maximum loudness (on a logarithmic scale) that I understand is the loudness limit that can be determined by
the human ear. So the bandwidth (frequency range) measured on either side of the resonance curve at this point gives the frequency tolerance. Nia of
MIT uses the minus 3dB in his paper as well as the minus 10dB level (100% reduction in volume?) that he applies to the violin family sound hole
resonances - perhaps because violins are naturally much louder instruments than lutes?
I have just completed tests on ring sound holes (also part of the MIT study) and appear to have quite consistent results in comparison. To be reported
next on this thread.
There is, of course, a significance difference between resonance values obtained on a Helmholtz type resonator compared to a real instrument like an
oud, lute or guitar - requiring comparative studies to be undertaken if some kind of reasonably valid general empirical formula can be developed.
The MIT paper reports on trials to determine the air resonance peak of a 17th C lute but unfortunately did not try to estimate the air volume of the
bowl in order to predict how close the calculated value might be.
Later in this thread I plan to estimate the bowl air volume of this lute (as well other lutes that I have to hand) and measure the air resonant
frequency of my lutes to try to determine the validity or otherwise of empirical calculation in predicting the resonant frequency.
jdowning - 5-10-2014 at 12:09 PM
The open 'ring' sound hole arrangement was tested this morning to see if the MIT results could be more closely replicated without the presence of the
rosette (see previous tests).
The test arrangement was an open sound hole made from 3 mm thick fibreboard and 8.7 cm diameter (same as that of the rosette previously tested) with a
wooden bar glued across the opening for the mounting of central discs with d/D ratios of 0.5, 0.6, 0.7, 0.8 and 0.9.
The measured resonance frequencies at 17°C ambient temperature were 115 Hz (open soundhole) and 113 Hz, 112 Hz, 109 Hz, 105 Hz and 95 Hz
respectively. The resonant peaks in the Audacity spectrum analysis were clear throughout.
Plotting the frequency ratios against d/D it can be seen that the results agree quite closely with the MIT data. It will be useful to make a d/D disc
= 0.95 to obtain a reading for the region where the resonance frequency drops dramatically dramatically. So quite happy with these results so far.
Lute rosettes were standardised - printed on paper for distribution to the luthier trade in the 16th and 17th C. Luthiers might use the full rosette
pattern or a reduced diameter rosette made by only cutting the inner circle of the pattern. On some of the very large lutes, the sound hole area might
be increased by cutting extra 'holes' around the outside of the standard rosette pattern.
I have never seen a lute or oud with the centre section filled in completely (covering up to 50% of the sound hole area) which would increase the
total area of the sound board and total sound radiation. I wonder if at one time this was the practice among luthiers so that the open inner rings
seen in rosette patterns today were at one time completely filled in?
There are a number of examples of this type of lute rosette (with inner rings in the pattern). Attached is an example of a similar oud rosette of this
kind.
So luthiers, if you want to add a fancy engraved central solid plate to your rosette just go ahead - it will not significantly affect air frequency
response of the instrument provided the d/D ratio is not more than 0.7.
[file]31369[/file] [file]31371[/file]
jdowning - 5-11-2014 at 12:04 PM
Here are another two 16th C full size lute rosette patterns that I have on file - both with inner circles incorporated into the design.
The earliest rosette (circa 1530) on a lute by Laux Maler measures 86 mm diameter. The smallest inner ring measures 44 mm outside diameter and the
largest ring measures 80 mm outside diameter. So if the smallest ring was 'filled in' (solid), d/D ratio is 0.51 and for the large ring d/D is 0.93.
These also might be guides to allow a luthier to make smaller diameter 'cut down' rosettes measuring either 80 mm diameter or 45 mm diameter.
The second example by Michielle Harton 1599 measures 92 mm diameter with inner ring outside diameter of 45 mm - d/D being 0.49.
This basic rosette has been enlarged (not shown here) by the addition of small square holes cut around the perimeter of the rosette increasing the
diameter to 100 mm modifying the d/D ratio of the inner ring to 0.45.
[file]31373[/file] [file]31375[/file]
jdowning - 5-13-2014 at 11:56 AM
Part of the MIT study includes testing the bowl air resonance response of a surviving original 11 course lute (converted later to 13 courses) of the
late 17th C by Andreas Berr in the Fine Arts Museum, Boston here:
http://www.mfa.org/collections/object/lute-51267
Unfortunately, it was not possible for the experimenter to directly measure the volume of the bowl in order to determine how close the calculated air
resonance was to the measured value. The paper therefore only reports the measured resonance frequency (124 Hz) as well as the recorded plot of the
normalised sound level against frequency. The rosette diameter of this lute is only 59 mm
I thought that it would be an interesting exercise to estimate bowl volume in order to calculate the air resonance frequency for comparison with the
measured value.
The lute in question started life as an 11 course 'French' style lute, similar to the lute depicted in this portrait of the famous French lutenist
Charles Mouton. Note the relatively small diameter rosette.
The rosette on the Berr lute is another example of a rosette cut down from the central part of a larger diameter design as shown in the attached
example typical of the late 17th C early 18th C period. The cut down rosette measures about 60% of the larger diameter rosette design.
For comparison an image of the Berr rosette is posted on the Boston Museum website.
[file]31404[/file]
[file]31406[/file]
jdowning - 5-14-2014 at 12:05 PM
I do not have a full size drawing of the Berr lute bowl or precise details of the bowl sections. From a full face image (but of rather low resolution)
of the lute I was able to draw a reasonably accurate sound board profile. Knowing that the bowl is of slightly 'flattened' cross section, a volume was
calculated by dividing the bowl into 1 cm thick slices of semicircular section and adding together the volume of each slice. An adjustment was then
made for the flattening by deducting the volume of a wedge shaped section of the bowl (again determined by adding the volume of individual strips
together). See attached image.
Making allowances for sound board, rib and neck block thickness, total air volume of the bowl was estimated to be around 8,000 cc
Assuming an air temperature of 15° C (museum conditions?) when the lute was tested gives a speed of sound - corrected for temperature = 340.4 m/sec
Sound hole area at 5.9 mm diameter is 27.3 cm² - i.e open sound hole ignoring the rosette.
Assuming a sound hole thickness of 1.5 mm the end correction factor is 1.7R plus thickness and so equals 5.17 cm.
Plugging these numbers in to the established corrected formula for the air resonance frequency gives 139 Hz compared to the measured frequency of 124
Hz. However the frequency response curve included in the MIT paper shows a band width of about 26 Hz at the 50% normalised sound level (i.e. at minus
3dB) so the tolerance on each side of the peak frequency of 124 Hz is about 13 Hz within which range the human ear can not distinguish a change in
sound level from the peak value (if I understand things correctly!).
Therefore , the maximum value of the frequency response might be taken as 137 Hz - close enough to the calculated value of 139 Hz. The minimum value
would then be about 111 Hz.
At A392 pitch standard (an historically appropriate two semitones below modern concert pitch standard of A440) eflat tone is 139 Hz and B is 110
Hz.
There are a number of possible tunings for this lute in both the 11 course and current 13 course configuration.
For both Baroque 11 and 13 course lutes, a tuning (Dminor) of A' B' C D E F G A d f a d' f' ( at A440 standard pitch) would be appropriate for the
string length of 651 mm (gut stringing throughout). So it can be seen that the air resonance frequency would reinforce primarily the pitch of the
fifth course and (partially) the sixth course - just as might be expected.
Next to test other instruments that I have for measured compared to calculated air resonance frequency response.
[file]31422[/file]
narciso - 5-15-2014 at 02:06 AM
Inspirational stuff! Amazing that you are able to reverse engineer this sort of fundamental technical info using just museum exhibits and paintings!
As regards the volume calculation of the type you have here, rather than doing it longhand, I can recommend from agreeable experience the general
purpose maths packages like Mathematica, Matlab etc.
You can use them to fit a cubic spline to profiles like the one you have drawn. then computationally integrating over the volume swept out by
revolution is a doddle.
I am a bit unclear on where your bowl profile came from. Is it from the Charles Mouton portrait? Or were you able to photograph the Berr under glass
in Boston?
Anyway it certainly looks more or less frontal in the Mouton jpeg you show. So I had a go at matching your plan to the portrait with the help of the
Lute design program discussed elsewhere in this forum
(http://www.mikeouds.com/messageboard/viewthread.php?tid=13881).
In the attachments I show my reconstruction superimposed against your Berr bowl profile, along with the 3d visualisation as it looks when superimposed
over the portrait.
The program calculates 10,400 cc for the volume of this reconstruction, so a bit more than your estimate; but this probably does not qualitatively
change the conclusions you reach.
[file]31424[/file] [file]31426[/file] [file]31428[/file]
[file]31430[/file]
jdowning - 5-15-2014 at 05:38 AM
Thanks narciso for your helpful constructive comments and calcs.
The image that I used to create the profile of the Berr lute is posted in several locations on the Internet but I am not sure of the original source.
See attached.
I will take a closer look at the programs that you mention that may save my current long winded 'macro integral calculus' approach to determine lute
(or oud) bowl volumes. Note that few if any surviving lute bowls are perfectly semicircular (or elliptical) in cross section as can be seen from my
current thread on this forum 'Old Oud compared to Old Lute Geometry'. They are either flatter or deeper than a semicircle which, of course affects the
precise volume calculation compared to that calculated if a semicircle section is assumed.
However, for all practical luthier purposes this may not be a critical consideration - the volume contribution being the square root of the reciprocal
of air volume for the purposes of calculating resonant air frequency.
It is not possible to tell if the bowl of the Mouton portrait lute is the same size as the Berr lute. It may be proportionally larger with a longer
string length.However, if a volume of 10,400 cc is assumed then the calculated value of resonance air frequency is 122 Hz so - as you say this
difference in estimated volume (8000cc compared to 10400 cc) should not significantly affect the practical outcome - both being in the same 'ball
park' given the bandwidth frequency tolerance. So for a peak frequency of 122 Hz the bandwidth tolerance range would be from about 109 Hz to 135
Hz.
I have a number of full size drawings of original lutes on file so it would be interesting to see what the calculated resonant air frequencies for
those might be. It would not, of course, be possible for me to verify the results with measured values on the original instruments but could be
compared with the known tuning of the instruments with gut strings.
[file]31431[/file]
jdowning - 5-16-2014 at 04:35 AM
My interest in ancient technologies unfortunately also extends to modern computer systems! My two PC's of 2004 vintage with on board graphics and
32bit processors do not work with the Linux Ubuntu version of the Sharpitor Lute CAD software requiring a 64 bit processing capability. I still use
Windows XP as an alternative operating system but since support for XP ended last month I only use XP for off line work. The Sharpitor version that
works with Windows 32 bit systems also requires on line communication with the Sharpitor site in order to function so that alternative is now not an
option. In any case, in my recent communications with Nick Braun - the developer of the Lute CAD program - it turns out that my computer's graphics
capabilities are also inadequate for the job (needing 'power of two' dimensional capability such as 256x512, 512x512 etc.) so although I can take
advantage of the volume calculation facility introduced in version 1.8 I could not (when last tested in April) create the required image overlay of an
original lute sound board profile for analysis.
It should be noted that the Lute CAD program will not precisely give the volume of a lute bowl as most if not all lutes are not semicircular in cross
section. The program also does not take account of volume taken up by internal bracing, sound board and rib thickness (although these factors can be
estimated and deducted from the initial volume given by the program). Nevertheless - as has just been demonstrated - the volume based on a
semicircular section and the outside sound board profile provided by the Lute CAD software should be close enough for all practical purposes in
calculating resonance air frequencies and so in determination of the optimum sound hole diameter versus bowl air volume.
The alternative to using the Lute CAD program for me would be to adapt a CAD program for the purpose (I have several of these that will work off line
on Windows XP). However, as I do not have the time or willpower required to learn even the basics of these programs, I shall for now stick to my more
tedious ancient technology for estimating bowl volume which is probably not a bad thing as the method it is easily understood and requires only basic
mathematical/geometrical knowledge to implement, so may be used by most luthiers - which is part of the objective of this topic.
Next to test the resonant air frequency of the classical guitar that was subject of the trials reported on this forum over four years ago (see link
previously posted) to determine if the calculated resonant air frequency (based upon the formula that works with my experimental resonance chamber) is
valid in predicting the measured frequency.
jdowning - 5-16-2014 at 11:42 AM
In Sept 2009 I carried out tests on a guitar and established that the sound hole diameter/air volume resonance coincided with the fifth string tone at
A 110 Hz pitch. However, the calculated value for resonance frequency (applying the same formula used here for the resonance chamber trials - modified
for end correction) was way off - 136 Hz compared to 110 Hz - nearly four semitones. I thought at the time that this was because the guitar was not a
perfect Helmholtz resonator having - among other things - a flexible body that would reduce the 'spring' effect of the trapped air and result in a
lower frequency than calculated. I suggested that - according to theory - the sound hole should have measured only 5.7 cm in diameter compared to 8.7
cm but could not otherwise understand what might account for the significant difference between the measured and calculated results. Clue - note that
in this case the ratio of d/D is 5.7/8.7 = 0.66. Sound familiar?!
Re-testing the guitar yesterday with all of the strings damped against vibration with a cloth and recording the pressure wave at the sound hole with
the recorder held about 10 cm distance while tapping the end of the bridge to initiate resonance, a peak frequency of 103 Hz was measured using
Audacity Spectrum analysis.
The calculated value, however, was 135 Hz - again way off by over 4 semitones.
The answer to this discrepancy may have been provided by Nia in his MIT research project in demonstrating that most of the air flow activity at
resonance occurs at the perimeter of a circular sound hole and that much of the central area (d/D = 0.7) contributes little and so might be ignored.
Tests with my resonance chamber, reported earlier in this thread, support this finding.
Instead of using the entire sound hole area to calculate resonant frequency what happens if only the area out side the d/D = 0.65 'dead zone' is used?
The open sound hole area D at 8.7 cm diameter is 59.5 cm² and the 'dead zone' area diameter d = 5.7 cm is 25.1 cm².
59.5 minus 25.1 gives an 'active' area at the perimeter of the sound hole measuring 34.4 cm².
If this area 34.4 cm² is used to calculate the air resonance frequency instead of 59.5 cm² for the open sound hole then the calculated resonant
frequency is 103 Hz - spot on!
Why is the formula valid for the test resonance chamber using the full open sound hole area and not for the guitar? Probably because my resonance
chamber - made from steel with dome shaped end is much closer to being a true Helmholtz resonator than the guitar.
The other interesting observation is that for the Berr lute previously reported I had estimated that the rosette diameter had been cut down to 0.6 of
the diameter of the original pattern used. I also observed earlier that the Hieber model rosette subject to testing on the test rig has an inner ring
incorporated in the rosette pattern measuring d/D = 0.6+.
So that is one test on a real instrument so let's next test one of my lutes to see if the results might be reasonably consistent.
narciso - 5-16-2014 at 12:23 PM
I'm attaching a couple of equationsI've written out to help with the bowl volume calculation, taking the flattening into account.
Hope they come in handy!
[file]31435[/file]
jdowning - 5-17-2014 at 04:34 AM
I have no plans to use integral calculus as a tool in this investigation but I have no doubt that it would be possible to define the entire bowl
geometry using integral calculus - given that the geometry of lute and oud sound board profiles were once created from conjunct arcs of circles (using
dividers, straight edge and 'divine' proportions).
In the meantime my estimate of lute bowl volumes will be undertaken working with full size museum drawings of original lutes and calculating volume
'slice by slice'. This approach is likely to produce accurate enough results free of scaling errors inherent in the Sharpitor Lute CAD approach and/or
when working from small sized images that may also be subject to optical distortions.
I would be interested to know, for comparison, the estimated volume of the Berr lute bowl that you now arrive at, narcisco, by applying your derived
calculus formula to the full face Berr lute image.
Adding to the observations about the possible 'hidden' importance to luthiers of rosettes with inner circles incorporated in the design, similar inner
circles can be found in some traditional oud rosettes. For example the attached image of a Nahat (?) rosette from an old oud recently restored by
Yaron Naor has such an inner circle. However - unlike the lute rosettes where d/D seems to be between 0.6 and 0.7 - the outside diameter of this oud
rosette inner ring measures d/D = 0.44. This oud has a single sound hole but many ouds have a triple soundhole arrangement - one large diameter and
two small (unlike any surviving lute that I know of). The MIT paper addresses the question of air resonance with triple sound hole arrangements. I
have yet to look into the implications but it is interesting to note that a 'typical' relative size of the small sound hole diameter to large sound
hole diameter used in the MIT investigation is d/D = 0.4.
For comparison, measuring the relative sound hole diameters on my old Egyptian oud I find that d/D = 0.42.
Too early to say without more data but could it be that this type of oud rosette design incorporates the proper proportions as a guide for a luthier
to create a triple sound hole design as an alternative to a single sound hole - for whatever the reason might be?
As an aside for luthiers - note that Yaron, in rebuilding the damaged rosette, has incorporated a slot in the outer perimeter of the rosette. This
useful feature allows the rosette to be installed or removed without need to remove the sound board.
narciso - 5-19-2014 at 05:14 AM
Thanks for posting above the Boston museum frontal image of the Berr lute I asked about
I found another slightly rotated view of the same original instrument on the web which I used to visually tweak the flattening, again using the
LuteCAD program.
The revised result calculated by the program for the Berr volume is 10,300 cc
I probably ought to clarify by the way (since I suspect that there was a misunderstnading) that my equations posted above were intended as a basis
for computational calculation, not as a purely analytical alternative.
ie., I wasn't implying these equations would lead to significantly different results from the existing LuteCAD approach
just that the Pappus-Guldinus theorem gives a neat way to think about the flattening correction
[file]31466[/file]
jdowning - 5-21-2014 at 10:14 AM
We are both working from the same low resolution image of the Berr lute narcisco yet our bowl air volume calculations are so far apart - mine about
8000 cc and yours, using the LuteCAD program, about 10,000 cc. I have rechecked my measurements and calculations and arrive at a total volume -
excluding the neck block volume but without flattening compensation etc. of about 8,800 cc which reduces to about 8,000 cc with flattening for the air
volume of the bowl (and we want air volume not the exterior volume of the bowl.
As I understand it the LuteCAD program calculates the volume by rotating the lute half sound board profile 180° around a central axis to generate the
bowl volume - which is the exterior volume of a semicircular bowl without flattening - presumably including the volume of the neck block and part of
the neck?. This will overestimate the air volume unless appropriate manual corrections/deductions are made.
When I look at the tabulation of dimensions that you posted for the initial volume calculation using LuteCAD, the bowl width used is 30.2 cm and bowl
depth is 14.3 cm whereas the maximum width of the Berr lute is 28.3 cm and depth 13.5 cm - the latter being the dimensions that I used as the starting
point for my calculations.
Perhaps this dimensional error might account for the difference in our bowl volume calculations?
jdowning - 5-21-2014 at 10:37 AM
Before leaving the Berr lute I thought that it would be interesting to make a preliminary attempt at predicting the original geometry of the sound
board - albeit based upon a low resolution image of the lute. The attached image of the proposed geometry - created using dividers and 'finger' units
- is largely self explanatory and follows the geometrical proportions found in other surviving lutes that I have examined to date.
Note that the finger unit in this case measured the equivalent of about 17.5 mm which may be the actual index finger width of A. Berr measured just
below the finger nail (if so he had more slender fingers than an average male).
Note that the sound hole diameter is a quarter of the sound board width measured at the sound hole centre position. This may be an important
proportion in lute design. Arnault de Zwolle in the 15th C gave the same proportion of sound hole diameter to sound board width as 1/3 - found on some
surviving lutes. It is unlikely that early luthiers used mathematics to calculate air resonance but may have used rule of thumb methods of which the
sound hole to sound board width may have been a part.
The easiest way to accurately determine the air volume of a finished bowl before fitting the sound board is to fill it with seed and measure the dry
volume. Interestingly there is a connection with the ancient volume measures and finger units that were based upon equal sided cubes with sides
measuring 15, 16, 17 or 18 finger units - all related according to the material being measured - water (16), wheat (17) or barley (18) all being of
equivalent weight. Could the old luthiers have used these old measures as part of some empirical method to arrive at the correct sound hole diameter
for a bowl volume measured according to these ancient standards? Just a thought!
[file]31477[/file]
jdowning - 5-22-2014 at 12:15 PM
The first lute to be tested is one that I built 25 years ago a 'copy' of a seven course lute by Giovanni Hieber (circa last quarter 16th C) - from a
full size working drawing of the instrument. String length is 60 cm.
My version of the lute has been repaired (after being dropped on a concrete floor!) and the sound board (that later split under dry winter conditions)
replaced with a new one with a slightly larger rosette design than on the original (8.9 cm diameter compared to 8.6 cm). There currently exists a
small variation in sound board profile compared to the original lute but the estimated bowl air volume based both upon the working drawing and the
lute copy are the same at about 10,000 cc. ('slice by slice' method of calculation)
With the lute up to full string tension the strings were damped with felt strips and the air resonance recorded (tapping on the end of the bridge to
set things in motion). The Audacity spectrum analysis gave a peak resonance reading of 133 Hz. I am not sure how (or if it is possible) to accurately
measure the band width tolerance at half loudness (minus 3dB) of the response curve using Audacity but if a value of 10 Hz either side of peak
frequency is assumed to be reasonable, then the tolerance range would be from 123 Hz to 143 Hz.
With modern nylon strings this size of lute could be tuned to G tuning at A440 pitch standard i.e. g' d' a f c G D. However with all gut stringing the
original lute would have been tuned a semitone or tone lower in pitch to avoid frequent top string breakage. So the fifth course pitch at A440
standard would be c = 131 Hz and a semitone lower 124 Hz or full tone lower 117 Hz.
Calculating air resonance frequency - assuming that the full sound hole area (diameter 8.9 cm) is used in the calculation - gives an air frequency of
156Hz - 3 semitones too high.
However, if the 0.6 D sound hole 'dead zone' area is deducted in the calculation (to give an 'active' area of 39.9 cm²) the calculated resonant
frequency is 125 Hz.
Time out more to follow in conclusion.
jdowning - 5-22-2014 at 03:40 PM
...... calculating the air resonance frequency from the original lute dimensions - active rosette area = 37.1 cm² - gives an air resonance frequency
of 123 Hz. Both calculated frequencies are just within the lower bandwidth tolerance of the measured frequency for the fifth course (123 Hz to 143
Hz)
Interestingly - although the measured air resonance frequency of 133 Hz appears to favour the lute being tuned in G tuning (at A440 standard), to my
ear, the lute sounds best (somehow less stressed) tuned a full tone below using modern plastic strings rather than gut - i.e. with the fifth course at
about 117 Hz.
On the other hand if the diameter of the rosette 'dead zone' is taken to be 0.66D (2/3) the active area of the original lute rosette is then 32.7 cm²
and the calculated air resonant frequency is 115Hz.
Next to test another of my lutes.
[file]31483[/file]
[file]31485[/file] [file]31487[/file]
jdowning - 5-23-2014 at 12:09 PM
The next test is on a six course lute that I made in 1979 as a research project based upon a lute sound board fragment by renowned 16th C luthier Laux
Maler - Cat# M1.54 in the Germanisches Nationalmuseum Nürnberg. I still have the mold used for the construction so this will be a convenient way to
measure and estimate air volume of the bowl. As information about the geometry of the original 9 ribbed lute bowl was not available 25 years ago I
assumed a semicircular bowl profile.
More recently I shortened the neck to give a string length of 67.5 cm that I speculate may have been the original string length - with seven frets on
the neck and an unusually very low bridge position that may also be original.
The rosette diameter measures 7.7 cm
With the strings damped with felt strips, the air resonance was initiated by tapping the end of the bridge and the recorded sound file (at the sound
hole) analysed using Audacity giving a clear resonance frequency of 110 Hz or A (at A440 Hz standard)
From experience gained so far I would anticipate that the estimated bowl air volume would measure around 10,000 cc. Let's see if it does - using the
'slice by slice' method!
[file]31507[/file] [file]31509[/file] [file]31511[/file] [file]31513[/file]
jdowning - 5-24-2014 at 05:37 AM
The calculated air volume of the Maler lute bowl - assuming a smooth semicircular bowl section and deducting the volume of the bracing - is about
10,600 cc. The actual air volume is likely to be somewhat less than this due to the wide ribs of the bowl requiring the luthier to cut flats in the
mold for construction of the bowl (see previously posted image of my mold). Therefore, 10,000 cc will be taken as the air volume as a close enough
best estimate.
A 16th C gut strung lute of 67.5 cm string length might be tuned between e' b g d A E and d' a e c G D the pitch of the fifth courses being 110Hz to
98 Hz (at A440 pitch standard) and a semitone in between 104 Hz
The measured air resonance frequency is 110 Hz. If a minus 3dB bandwidth of ± 10Hz is assumed then the resonant frequency tolerance range would be
from 100 Hz to 120 Hz.
The calculated air resonant frequency - assuming the full rosette diameter (D = 7.7 cm) is used to calculate sound hole area (46.6 cm²) - is 144 Hz ,
over 4 semi tones too high. Further confirmation that using full sound hole area to calculate air resonance frequency (for a lute with a single
circular rosette sound hole) is an invalid assumption.
Assuming a 'dead zone' of 0.6D (area + 16.8 cm²) is deducted from the total sound hole area the resultant 'live' area of the sound hole (29.8 cm²)
gives a calculated air resonance frequency of 115Hz. For a 'dead zone' of 0.67D the air resonance frequency becomes 107 Hz. Both these results are
within the measured resonance frequency tolerance range - the 2/3D 'dead zone' area deduction giving the closest result to 104 Hz.
jdowning - 5-24-2014 at 12:07 PM
For clarity, the attached basic formula for predicting instrument air resonance frequency appears to work quite well based on limited tests so far on
'real' instruments with single round sound holes - with or without rosettes. The important feature is the 'active' area of a sound hole which is the
total area of a sound hole (diameter D) minus the central 'dead zone' area of diameter 2/3D that does not contribute significantly to the air
resonance phenomenon (as reported in the MIT paper and demonstrated here in previous posts).
Using the entire area of a sound hole of diameter D does not appear to provide valid results for instruments (as it does for a resonance chamber that
is physically similar to a true Helmholtz resonator) - the calculated resonance frequency being several semitones too high. Musical instruments have
relatively flexible air chambers that result in measured air resonance frequencies that are lower than those calculated for a more rigid resonator
chamber.
For a practical application, a luthier might be able to accurately determine the optimum sound hole diameter for lute, oud or guitar (for an
unfinished sound board) - using this formula - by first measuring the volume of the completed bowl (filling with seed and measuring the dry volume).
[file]31517[/file]
jdowning - 5-26-2014 at 04:35 AM
During construction of a lute or oud bowl the last outer ribs are left oversize to allow for trimming to size and levelling of the sound board to bowl
joint surface. If a luthier wanted to adjust bowl volume at this stage this can easily be achieved by trimming material from the sides of the bowl.
Perhaps this is why some of the surviving lutes from the late 16th C have a 'flattened' semi circular cross section?
Having determined bowl volume, how does a luthier next calculate optimum sound hole diameter. The air volume formula previously posted may be further
simplified to facilitate calculation. The area of the 'active portion of the sound hole is proportional to the sound hole diameter squared (D²). The
Lcorr element equivalent to h + 1.7R or h + 1.7D/2 can be simplified by ignoring h the sound board thickness of about 0.2 cm. In this case Lcorr is
proportional to D.
If the speed of sound is assumed to be constant for the purposes of calculation (at 20°C standard) then the air resonance frequency formula for D is
simply D = K V f² ( f² being f x f) where K is a constant, V is the measured bowl air volume in cubic centimetres and f is the resonance frequency
in Hertz (cycles per second).
Calculating the constant for centimetre units taking the diameter of the sound hole 'dead zone' as 2/3D and the Lcorr correction factor as 1.64 gives
K = 6.3 x 10-8 or 0.000000063 (Note that some (MIT) use 1.6 as a correction factor others 1.7).
The resonant frequency value chosen may be any value desired but for six course lutes, ouds or guitars the target value appears to be the frequency of
the tone of the fifth course which in turn depends upon the instrument tuning used. So for a modern classical guitar, for example, the fifth string is
tuned to A110 Hz at A440 pitch standard which might be the target value chosen. However, testing the modified formula against the instruments subject
so far to these trials it is observed that using a resonance frequency a half step or semi tone lower gives reasonably accurate results. So for the
guitar tested, the frequency value a semi tone lower is 17/18 x 110 = 104Hz giving D = 8.8 cm (compared to 8.7 cm actual sound hole diameter).
Likewise for the original Hieber lute, D calculated is 8.65 cm compared to 8.6 cm actual and for the Maler lute 7.6 cm calculated compared to 7.7 cm
actual.
For lutes with more than six courses (of equal string length) the chosen frequency may be lowered to say the sixth course tone frequency. So for the
11 course Berr lute the chosen frequency may be that of the sixth course A110 down a semitone to 104 Hz giving a calculated D = 5.5 cm compared to
actual D = 5.9. (for comparison using A110 Hz in the calculation gives a calculated diameter of 6.1).
Early days yet so more tests need to be done to confirm the validity (or otherwise) of the modified formula as it now stands.
jdowning - 5-26-2014 at 11:46 AM
I thought that it would be interesting to test the modified formula on the 14th C 'Urmawi' oud that I recently tried to replicate from the original
manuscript drawing and reported on this forum. The drawing quite accurately represents the geometry of the oud profile - drawn by the scribe using
compasses to a 'vesica pisces' construction.
This is essentially the same geometry used later by Arnault de Zwolle in his 15th C drawing of a lute - the difference being that the oud has two
small sound holes whereas the lute has a single large sound hole. The diameter of the latter is given by de Zwolle as 1/3 the width of the sound board
at the sound hole centre position - the sound hole centre being placed midway between the top of the bowl and the front of the bridge.
Prior to fitting the sound board, I took the opportunity to precisely measure the bowl air volume of the replica oud by filling the bowl with corn
seed and measuring the dry volume of the seed. The measured volume is 12,000 cubic centimetres.
The string length of the replica oud is 56 cm so when originally strung with silk or gut the maximum pitch of the top string would have been g' at
A440 standard. Tuned in fourths the bottom fifth course would have been B124 Hz.
Taking the target air resonance frequency as a semitone lower f = 17/18 x 124 = 117 Hz
Using the modified formula previously posted, the calculated diameter of a single sound hole (replacing the original two small soundholes of the
Urmawi oud) would be:
D = 6.3 X10-8 V f² = 6.3x10-8 x 12,000 x 117 x 117 = 10.34 cm.
Referring to my original full size working drawing of the project oud, the sound board width is 31.3 cm at the sound hole centre position specified by
Arnault de Zwolle so sound hole diameter would be 31.3/3 = 10.35 cm.!
Next to test the 'Urmawi' replica oud to see if the the measured air resonance frequency matches the calculated frequency.
[file]31571[/file] [file]31567[/file] [file]31569[/file]
narciso - 5-26-2014 at 11:23 PM
My understanding of one of your remarks above is that flattened bowl geometries might historically have been achieved in practice by a final 'shaving'
stage after rib assembly on a semicircular mould
I wondered are there any specific instances you are aware of which show the kind visual evidence one would expect to see in this event? i.e. wider
thanexpected spacing of lines at the more heavily shaved (back) end ?
Although I suppose when a clasp is present, this effect would be obscured
---------
This a wonderful forum thread you have created here. But one very slight misgiving I have overall is that you are tacitly promoting the view (via
terminology such as 'chosen frequency') that historical lute builders would have worked with a fairly precise frequency-defined notion of musical
pitch similar to that of the present day.
Do you think there is a case for a converse argument that the soundhole dimension was in fact chosen more or less randomly, the associated Helmholtz
resonance then determining tuning/frequencies, rather than the other way round
Even if the resonance was not very carefully controlled by the instrument builder, by tuning up using the resonance for reference the player would
nevertheless be afforded a pitch consistency useful at least for solo playin
jdowning - 5-27-2014 at 11:36 AM
The bowl shaving proposal is just food for thought - a procedure that might have been used by some luthiers to fine tune the bowl air volume? Some of
the late 16th C Venetian lute bowls appear to be semicircular in section and flattened by removal of a wedge shaped section (viewed in the bowl side
view) tapering from zero at the neck block to maximum depth at the clasp end. Not all surviving 16th C lutes have semicircular or flattened sections
however.
Attached is an image of the end of a lute bowl by Wendelin Tieffenbrucker dated 1571. The section is a semicircle that has been 'flattened'
geometrically by removal of a longitudinal wedge section. There is a lot of optical and perspective distortion of the image in the photo but it is
clear nevertheless that the rib ends meet at a point above the plane of the sound board.
I do not believe that any part of an historical lute (or oud) design was ever random but created according to harmonic ratios and proportioned
literally according to 'rule of thumb' (or 'rule of finger' equivalent - Turkish or Persian). The earliest accounts about the oud (Ikhwan al Safa and
others) describe the dimensions of the instrument and its strings proportionally as well as referencing dimensions measured in 'finger' units. As
mentioned in my previous post Arnault de Zwolle gives the diameter of the sound hole as a proportion related to the geometry of the lute he
describes.
Instruments of the 16th C such as the lute and vihuela were sometimes made in different sizes (e.g. descant, treble, tenor and bass) as matched sets
to be played together in consorts of up to four instruments. So the luthiers must have had a pretty good grasp of the important aspects of acoustic
design of the instruments in order to ensure optimum performance of each one in a matched set - all being tuned to the same 'pitch standard' (whatever
that may have been).
The early luthiers would have known well enough how the pitch of a vibrating string related to length, tension and diameter (string material being
plain gut or silk would be more or less constant in density) - so may have used monochords to define frequency by some precise measure (without having
a clue about how many cycles per second the frequency might be) - string length and diameter perhaps - string tension being dictated by the breaking
limit of gut or silk?
[file]31573[/file]
antekboodzik - 5-27-2014 at 02:25 PM
Edited 28.05.2014
Hope You will forgive if I vouchsafe some of my oppinions.
I couldn't resist temptation to do some basic tests at my own, using a lute I built myself, tuned in G at 440 Hz. At first I have measured main body
air resonance frequency by "humming" a tone close to front of an instrument kept in hands (don't do this if your woman is close, may think you're
mad), having an eye to electronic tuner (applicatin on smartphone). Resonance could be felt pretty well at "sound" between 114 and 120 Hz. Then I
recorded some tapping (again with a smartphone), do spectral analysis in Audacity, and in several trials I got first significant peak at 110 Hz, and
top main resonance frequency about two times greater. Not bad at all.
Second trial was estimating body air volume. I have the mold the lute was constructed on, so I wrapped it acccurately with stretch-foil, taped up to
get consistient shape (not shown on the picture) and dipped it into water For
that I managed to prepare a setup of baby bathtub arranged in a way that all displaced water could be collected to another plastic tub. It gave me the
volume of 10 800 cc, but this value is overestimated for sure as my mold has its baseplate edge lower that finished bowl top ribs, and also space for
neckblock was partially included. Anyway, I didn't ever see how much water was displaced during immersion, and only very little water got into "bowl",
so no self-suggestion was made, and I think it is good approximation of air volume.
I had also calculated air volume in a way of numerical quadrature (correct term?). It produced me volume of 9990 cc. I think this value, in opposite
to water measurement, was underestimated, as "curved" objects has allways greater volume than "canted" ones of similar size. And a sum of "slices" is
a sum of that "canted" objects.
These measured values meets pretty well those presented here by jdowning (coincidence? or I made not so bad instrument by chance?). Giving these
values with the dimension of rosette (7.2 cm) and with average thickness of top there (0.2 cm, at first I took 2cm by a mistake) to
the presented formula makes 103Hz.
Some more things:
solid moulds involves measuring volume with immersing in water by natural
frame-molds can probably be "filled" temporairly with montage foam, and excesses cut down to size - it should make more accurate measures,
at the stage where lute bowl is fully assembled but not closed with top, it could be possible to line its interior with something non-stickable
and use foam too. Who would be so brave
if a lute has semicircular section, it consist of odd number of identical longitudal "slices" with ribs at the top of each. It might be more
practical to measure only one section (or even have it modelled in CAD or Blender)?)
original lute rosettes vere cut in thinned down area of soundboards (?), and had edges carved. Do its imply to any formulas here? As I remember
in the mentioned paper rosettes vere cut in 3mm ply with laser, so should have straight, vertical edges.
Edited 28.05.2014
[file]31575[/file] [file]31577[/file] [file]31579[/file] [file]31581[/file] [file]31583[/file]
jdowning - 5-27-2014 at 04:16 PM
In my version of the Urmawi oud, I added a small sound hole (fenestrum) at the neck block end of the sound board to conform with similar sound hole
arrangements seen in the iconography.
String length is 56 cm and measured bowl air volume V = 12000 cc. The two large sound hole diameters measure D = 6.85 cm and the small d = 4.4 cm.
The measured air resonance frequency was recorded with the small sound hole blocked with a piece of card taped in place (to simulate the two sound
hole original) and with the three sound holes open.
For the three sound hole test, the air resonance frequency was recorded first at the main sound holes and secondly at the small sound hole. No
difference in the resonance frequency was seen in the Audacity spectrum analysis.
Measured resonance frequency for three sound holes f3 = 163 Hz and for two f2 = 145 Hz.
The modified formula previously posted should predict the air resonance frequency a semi tone below measured frequency i.e. f3 = 17/18 x 163 = 154 Hz
and f2 = 137 Hz.
How should a 2 or 3 sound hole arrangement be calculated? The MIT paper found that if the sound holes are well separated the air resonance frequency
may be approximated by linear superposition - that I take to be mathematical jargon to mean additive. Otherwise triple sound holes found on ouds,
large lutes require application of the developed method mentioned in the MIT paper (but not sure what that is at present).
So let's assume that simply adding the effects of each sound hole separately will give reasonably accurate calculated results.
Reworking the modified formula D = 6.3x10-8. V. f² to find f :
f = (D/6.3x10-8 . V)½
So for the three sound hole test f3 calculated = 156 Hz and for two sound holes f2 calculated = 135 Hz. So the additional sound hole does make a
difference. These results are quite close to the measured resonance frequencies taken down by a semi tone i.e. 156 Hz compared to 154 Hz and 135
compared to 137 Hz respectively.
For comparison a gut first course of string length 56 cm might be tuned to g' at A440 pitch standard without frequent breakage. This equates to a
fifth course tuned to B124 Hz. So the measured resonance frequency for the original two sound hole Urmawi arrangement at 145 Hz is higher than the
target value of 124 Hz. However, assuming a minus 3dB bandwidth tolerance of ± 1 semitone the lower target value is 137Hz (as noted above) and the
calculated value is 135 Hz. which is just over a semitone higher than 124 Hz.
However, if the oud were to be strung in silk strung - as once was common practice - this discrepancy might be eliminated, silk strings being capable
of being tuned to a higher pitch than gut ("the strings of the top courses require a taughtness, on account of their high pitch, which one or two
strands of gut are not capable of sustaining". Al- Kindi 9th C - G.H. Farmer translation).
So, on this basis, my three sound hole arrangement was not a good idea the original two sound hole arrangement being best for optimum air resonance
frequency!
[file]31589[/file] [file]31591[/file] [file]31593[/file]
jdowning - 5-28-2014 at 06:52 AM
Although the outlet of my resonance chamber is limited in diameter, a triple sound hole test has been undertaken just to see what the results might
be. The three sound holes each measure 3.2 cm in diameter, area 8 cm² arranged with their centres equally spaced.
The measured resonance frequency is 100 Hz
The calculated frequency approximated by linear superposition of the total sound hole area (3 x 8 = 24 cm²) with a 1.7 correction factor is 118 Hz -
about three semitones too high.
Assuming a 0.67D 'dead zone' for each sound hole (active area 4.4 cm² per sound hole, total area 13.2 cm²) the calculated resonance frequency is 88
Hz - too low by about 2 semi tones.
Recalculating assuming a 'dead zone' diameter of 0.5D gives a resonance frequency of 102 Hz - close enough to the measured value.
So perhaps the difficulty with triple sound hole arrangements observed in the MIT report may be simply resolved by empirically adjusting the 'dead
zone' diameter of each sound hole (the adjustment factor 0.67D, 0.5D - or whatever - perhaps dependent upon sound hole diameter? - to be established
by experiment) and then calculating the resonance frequency assuming linear superposition of the adjusted active areas? This heuristic approach may be
perfectly valid and accurate enough from a practical perspective.
If it works by simple arithmetical calculation who would care about a more sophisticated alternative solution requiring a knowledge of higher
mathematics, the physics of gas dynamics etc - certainly not the 16th C luthiers nor, I suspect, their modern day equivalent?
Further tests are planned to verify the modified resonance frequency formulae using dimensions taken from full scale museum drawings of surviving
lutes - as time permits.
[file]31595[/file]
jdowning - 5-28-2014 at 12:16 PM
Somehow I missed your posting antekboodzik! I would encourage others to follow your example.
I suspect that reasonable results might also be possible by recording the sound on low cost digital voice recorders? No need for costly apparatus!
Would it be possible for you to post an image the Audacity spectrum analysis for comparison at a lower sample size say 2048 0r 4096 so that the air
resonance frequency is more clearly shown?
No need to line a bowl with plastic to measure volume - just use grass seed, wheat or the like to measure the dry volume (but not sand!).
The sound board thickness at the rosette on lutes can be around 1 mm thick but as the MIT paper confirms (as have my tests) - the rosette does not
significantly alter the measured air resonance frequency compared to that of an an open sound hole of the same diameter. The thickness of the rosette
h be it 0.1cm or 0.3cm is accounted for in the L corrected factor = h + 1.7R (or h + .85D).
antekboodzik - 5-29-2014 at 11:10 AM
Thanks! Here are few more. Sound clip was the same, but I chose different single "knocks" (or group of them).
Using grass seeds seems to be the most environmental friendly method, as they can be simply disposed wherever outside
jdowning - 5-29-2014 at 04:36 PM
Here for comparison are the Audacity spectrum analyses images for my Maler lute (similar in size to your lute antekboodzik). Peak air resonance
frequency at 109 Hz for sample sizes of 2048, 16384 and 8192. The resonant peak is distinct in each case.
As I understand it, smartphones incorporate a filter that cuts off bass frequencies lower than 300 Hz - so interesting that you obtained results in
the 110 Hz region. A feature of the Audacity Fast Fourier Transform computation perhaps?
[file]31610[/file] [file]31612[/file] [file]31614[/file]
antekboodzik - 5-30-2014 at 11:08 AM
Ok, I've borrowed some stuff and quickly got some results
In my oppinion, comparing result of FFT of one fragment using different size samples doesn't make a sense. Of course, in theory, no matter which size
of samples you take, you should get the same "spectrum".
But in real situation, (when there's background noise, vibration aren't perfectly harmonic, recording hardware and analyzing software has its
limitations) taking too few samples may lead to false results. Too widely spreaded samples may pass over significant properities of signal, and
exaggerate parts that would be normally diminished.
Here are pictures of the stuff used for next recording, and one fragment of recorded "knock" sound and analysis at different sample size. At low
sample size (rather numbers of samples, but anyway Audacity calls it so) distortion and enormous amount of noise can be seen.
So I think that every time size sample should be set to maximum available value. Higher sample size = narrower "bands" of frequencies = more accurate
results.
And I guess, that filtering low frequencies by smartpones appears only when making calls. It is probably connected with limiting "window" of
frequencies to those necessary to understand speaking only, and also compressing voice. In other applications the only limit is general quality of the
phone. And so on, 115 Hz isn't very low tune, and many tuner software works at least at usable level - you can tune musical instruments with them
quite well.
[file]31626[/file] [file]31628[/file] [file]31624[/file]
[file]31630[/file]
antekboodzik - 5-30-2014 at 11:30 AM
What makes sense to me is comparing different samples of sound, to see for similarities.
I did some more tests. I hadn't got a "silent" recording device, and I needed to use my pc, which added a lot of noise to the recording for sure. I
have recorded three "sets" of knocks (produced by rubber on a toothpick) tapping on the bridge area of my lute, of course with strings damped at two
points (not allowing to hear a harmonic) with small cloths. Sets differs by the distance to the microphone, and thus by volume.
I randomly took few "knocks", selected each time roughly a size to see 8192 sample size and did analyze. You can see them selected in the background
of window with plot. Results vary by 1 Hz up and down from mentioned value of 115 Hz. Is it a lot or no? There were no cooking, selected "knocks"
weren't chosen by fitting to the theory. In fact, "knocks" that vary more than few Hz are hard to find, and different selection of any sound sample
may change results slightly.
jdowning - 5-30-2014 at 11:53 AM
Interesting to make these comparisons.
My Zoom H2 recorder has a low pass filter function (to eliminate low frequency wind noise etc. when recording outside). I shall repeat the test on my
Maler lute tomorrow - with the low pass filter engaged - just to see what the Audacity spectrum analysis might look like - just for comparison and
information.
Attached is the frequency response of the built in microphones of the Zoom H2 showing a steep fall in dB below about 90 Hz.
[file]31642[/file]
jdowning - 5-31-2014 at 05:29 AM
Here, for comparison, is the Audacity spectrum analysis from signals recorded from my Maler lute with the lo-cut filter employed and tapping the end
of the bridge with my finger tip. The peak resonance at 107 Hz (compared to 109 Hz without the filter) is still clear enough - which is the objective
of these tests. Sample size is 8192 and 'window' is Hanning.
The Fast Fourier Transform represents the frequency composition of the time based signal - assuming that the signal components are sinusoidal. As most
signals are composed of random data that is not periodic, window functions are applied to correct errors ('leakage') introduced. There are a number of
window functions to choose from each having its strengths and weaknesses. the Hanning window is the best choice for random signals having good
frequency resolution and spectral leakage correction but only fair amplitude accuracy.
For measuring the air resonant frequency of an instrument a one or two Hertz variation in the measurement is of no consequence.
Hopefully even the use of relatively low cost low end recording equipment (such as a smartphone or digital voice recorder) will still provide
acceptable results for a modern day luthier to usefully employ in optimising instrument performance - at least as far as air resonance is
concerned.
jdowning - 5-31-2014 at 12:07 PM
By adjusting the sound hole diameter relative to bowl air volume a luthier may adjust the air resonance frequency to emphasise any string pitch
desired. For a six course lute, oud or guitar the favoured resonance pitch appears to be around the 5th course pitch. For lutes with more than six
courses the air resonance frequency may be lowered to say the pitch of the sixth course (?). For instruments with fewer courses the pitch may be
raised to match the pitch of the higher courses (yet to be investigated).
So, what about those long necked small bodied instruments like the Saz or Colascione or the tiny soprano mandolino lutes. Where would a luthier try to
place the air resonant frequency for best acoustic effect?
I currently have an interest in the 17th C Italian Colascione and have examined and measured a surviving example so this might be a good start to
predict the air resonance using the modified formula.
Here is some forum discussion about this instrument:
http://www.mikeouds.com/messageboard/viewthread.php?tid=7096#pid438...
antekboodzik - 5-31-2014 at 01:01 PM
Very interesting and informative topic, I have learned a lot analyzing thoughts presented here, really. Thanks jdowning
But could you say if there are at least partial conclusions derrived from these a few "real" examples? As I understand, you lute after Hieber math the
theory quite well, but another (Mahler) lute does not. And I think, my lute is much more close to you Hieber one (600mm string lenght).
Shortly before you started this topic I was reading a little about so-called "tornavoz" device used by Torres. Much to say about it - I would just
mention two interesting websites. One is showing, that special "contra" classical guitars (tuned an octave below) meet big improvement in sound, when
adopting even improvised tornavoz. Just hear presendet egzamples:
http://www.hago.org.uk/faqs/contrabass/construction.php
And the other was a topic on another forum:
http://www.classicalguitardelcamp.com/viewtopic.php?f=11&t=8284...
As I understand, todays classical guitar luthiers construct their instruments rather in a way to favore main air frequency around 100Hz (G~G#, about
third fret on sixth string). It is in fact not far from fifth course, but perform better for todays demands, giving great bass fundamental to the tone
of the instrument. I have tried to measure main air frequency in ways presented on that forum - both with singing to the instrument, and recording it
with a smartphone. I measured that way my luthier made classical guitar (2007y., regarded not only by me as very good quality concert instrument), and
got the same result (100Hz on the plot, 97-98 Hz when singing), like presented there...
And interestingly, measured values for my lute meets the "rule" of 3rd-4th fret on lowest string (115 Hz is roughly about B flat). Maybe it is another
key to understand lute acoustic?
The main air frequency for my guitar is clearly seen on the plot. As I understand renaissance lute acoustic, its "ladder" type barring was for maximum
"damping" lowest parts of spectrum, and promoting higher harmonic parts. With this, I wasn't surprized, that there is much more difficult both to feel
resonance when singing to a lute, and see it on an graph... Does my suppositions make sense? Should be lute rather different than guitars in that way,
shouldn't it?
And for last, I think most of us vere first engaged in guitars, and later came to be interested in lutes. Do You remember your first time when hearing
a lute (live or from a records)? I must admit, I was used to hear classical guitar, and I was quite astonish hearing rather thin, with almost no bass
(at least renaissance lute), "punchy", but not loud sound of a lute. Weren't you too?
[file]31650[/file]
jdowning - 6-1-2014 at 04:41 AM
I stopped playing classical guitar in the early 1970's after switching over to the lute and now rarely listen to performances on that instrument so am
out of touch with developments and efforts aimed at improving the modern guitar acoustically. It is all a matter of taste and preference but I do not
like the booming bass or the harsh brittle sound of strings being struck with fingernnails close to the bridge on the modern classical guitar -
particularly when performing transcriptions of music originally written for lute or vihuela. When I first took an interest in the lute the only
available instruments were essentially heavily strung instruments - lute shaped guitars - that required a classical guitar technique. It was only
until about the mid 70's that lightly built 'authentic' lutes (copies of original surviving lutes) became generally available and guitarists who had
changed over to the lute switched to the proper right hand technique for lute (and some brave souls even began using authentic gut stringing). This
made a huge difference acoustically but in all of the many live concerts I have attended over the years I do not recall any difficulties with the
abilities of the performers to achieve adequate sound volume and projection from their lutes. Of course, listening to recordings can be misleading -
sound engineers can (and do) manipulate the recorded sound to best effect (in their judgement).
Presumably modern classical guitar makers achieve their favoured air resonance frequency by adjusting sound hole diameter to air volume accordingly?
The tornavos device experimented with by Torres was not a success so has not prevailed as far as I know (for whatever reason). But why use such a
device when reducing the sound hole diameter would presumably achieve the same result?
My 'Maler' lute calculated air resonance frequency does match the measured frequency according to the proposed modified equation that uses the
'active' area of the sound hole rather than the whole area. The measured frequency is 110 Hz at 20°C. The rosette sound hole diameter D is 7.7 cm and
calculated air volume is 10,000 cc. The active sound hole area is calculated by subtracting the area of the 'dead zone' diameter 0.67D = 21 cm² from
the total sound hole area = 47 cm². So the active area = 26 cm².
Then the calculated resonant air frequency (speed of sound at 20°C) is 108 Hz, close enough to the measured frequency particularly if the bandwidth
tolerance of the measured frequency is taken into account (measured at minus 3dB on the resonance curve - say ± a semitone (?) i.e. from 104 Hz to
116 Hz).
A lute of string length 67.5 cm fitted originally with plain gut strung would have the first course pitch as e' (A440 standard) - an absolute maximum
to avoid frequent breakage. The fifth course would then be A110 Hz (at A440 standard).
Or tuned down a semitone (top string at e'flat) to put less stress on the first course, the pitch of the fifth course would then be 104 Hz at A440
standard.
jdowning - 6-2-2014 at 12:04 PM
The next instrument to be studied is a 16/17th C Italian long necked lute or colascione - of interest because of its relatively small body compared to
string length. This is an example in Dean Castle, Scotland that I examined and measured some years ago.
Generally regarded as a folk instrument although some - like this example - were made from ivory and exotic woods so were originally destined for a
higher place in society than the streets. Nevertheless little is known about the instrument and the only known surviving music is in parody
compositions for lute and keyboard.
The colascione was a fretted bass instrument, played monophonically (equivalent to a modern electric bass guitar) with two, three or four single
strings - most often 3 strings. Tuning was variable but Marin Mersenne in the 17th C gives a common tuning of C-c-g that is an octave and a fifth.
Strings were gut or metal. They came in various sizes - mezzo size apparently being of string length 70 -100 cm and the larger instruments with string
length up to 160cm (but museums tend to report instrument sizes as overall length just to confuse things!).
The Dean Castle instrument appears to be original with a string length of 76 cm and three strings. Overall length is about 94 cm. Sound board width is
211 mm and the ivory/ebony bowl section is deeper than a semicircle - similar to bowl of 19th C Neopolitan mandolins. Sound hole diameter is 7.5 cm
The attached sketch is a proposed geometry of the colascione for information. Note that this is the geometry for constructing the mould - i.e. the
internal dimensions of the bowl. Interesting that the unit equivalent of 12.9 mm is not that of a 'finger' but of half a 'thumb' (or half an inch) -
an inch then being equivalent to 25.8 mm. Both 'finger' and 'inch' units seem to have been used by luthiers in 16th/17th C Italy.
According to Vincenzo Schisano, in Naples the large Colascione was also called the Tiorba a Taccone. There was also a smaller version of the
Colascione that was about a metre in length called the Colasciontino or Mezzo Colascione. This had 2 or 3 strings and was tuned an octave above the
larger instrument and was built with finer materials such as ivory, ebony. In Naples the instrument was considered to be a folk instrument used as
bass continuo in instrumental groups.
So the Dean Castle instrument may be a Neapolitan Colasciontino.
Edited 4th June 2014
[file]31676[/file] [file]31678[/file] [file]31680[/file]
jdowning - 6-2-2014 at 03:16 PM
Here is the sound of a colascione from Rolf Lislevand's arrangement of the 16th C Spanish song 'La Perra Mora' - the first soloist is the colascione
(0.36 minutes into the recording) - followed by triple harp and lute. Non 16th C audio effects added - Renaissance jazz!
http://www.youtube.com/watch?v=qWT2kAsZVKs
.... and Klaus Mader and Andreas Nachstheim baroque guitar and Colascione - Canarios by 17th C Spanish guitarist Gaspar Sanz.
http://vimeo.com/74817415
jdowning - 6-3-2014 at 09:53 AM
Estimating the bowl air volume of the Dean Castle colascione using a full size drawing and the the 'slice by slice' gives a volume of 3,473 cc that I
have rounded up to 3,500 cc. Assuming the modified 'active sound hole area' formula is valid, the sound hole area (D= 7.5 cm) is 44.2 cm² and the
area of the 'dead zone' diameter 0.67D is 19.8 cm². The active area of the sound hole is therefore 44.2 - 19.8 = 24.4 cm². The end correction for
the sound hole is 0.3 +1.64x3.75 = 6.45.
The calculated air resonant frequency at 20°C is therefore f = 180 Hz.
The highest pitch of a 76 cm string length instrument strung in plain gut is d' 294Hz at A440 pitch standard and the lowest is G 98Hz.
Therefore this colascione when originally gut strung would have been tuned G 98 Hz - g 196 Hz - d' 294 Hz (octave and a fifth intervals). (So the
tuning C - c - g given by Mersenne, previously posted, is for a larger colascione - about 112 cm string length).
Interesting that the physical range of plain gut strings is an octave plus a fifth.
So it can be seen that the calculated air resonance frequency for the Dean Castle colascione is below the pitch of the middle string by just over a
semitone at A440 pitch standard which seems reasonable.
I will now have to build a replica of the Dean Castle instrument to verify the theory!
Next to look at the other end of the spectrum and examine one of the tiny mandolino lutes of the 18th C to determine its calculated air resonance
frequency.
jdowning - 6-5-2014 at 05:24 AM
The MIT paper includes the measured air resonance frequency spectrum of the Berr lute (Figure A-15). Peak resonance is 124 Hz. The resonance curve - a
plot of normalized loudness against frequency in Hz - is not symmetrical due to sound reflections from the walls of the room where the resonance was
measured.
To gain a better understanding of 'bandwidth' and by way of illustration, attached is an idealised sketch of the Berr resonance curve that is drawn
symmetrically about the peak resonance frequency. The normalised loudness is the loudness at each frequency point on the curve (measured in dB)
divided by the maximum loudness at 124 Hz. The half maximum loudness level (0.5 Normalised) is equivalent to 3dB below the peak loudness at 124 Hz - a
point at which the human ear can just distinguish a change in the loudness of a sound. Measuring the width of the resonance curve at this point gives
the bandwidth at minus 3dB which - in this case - ranges from about 116 Hz to 132Hz on either side of the peak resonance of 124 Hz or about ± 1
semitone. (This is a narrower bandwidth than previously assumed for the Berr lute earlier in this thread).
In other words, to a listener, the air resonance frequency might be anywhere between 116 Hz to 132 Hz or just over a full tone. This is what I have
referred to earlier in this thread as the 'band width tolerance' and have assumed a band width of ± 1 semitone - for want of better data - applied to
measured air resonance frequencies reported in this thread. Hopefully this 'rule of thumb' measure will be close enough for practical purposes.
The Audacity software does not appear to have facility to accurately determine bandwidth of the resonant curve at low frequencies?
Hope that I understand all of this correctly!
[file]31696[/file]
antekboodzik - 6-5-2014 at 03:23 PM
Well, it's going to be too much complicated...
I have a little different understanding of "3dB bandwith". Let me clear a few things:
1. What we really did, was checking impulse response of a lute.
http://en.wikipedia.org/wiki/Impulse_response
DIfferent ways to measure it can slightly modify results.
2. Lute can be treatened as an acoustic filter. In this case we look for frequencies, of which lute (as an independent unit) acts like bandpass filter
for its own resonant frequency.
http://en.wikipedia.org/wiki/Cutoff_frequencies
3. It is generally true that human ear can distinguish differences about 3 dB at most frequencies and amplitudes of sound. But this "volume"
resolution of ear vary, and it is spoken, that for range of frequencies we usually talk AND volume about 40-60 dB, which is typical volume of human
speaking, we can distinguish subtle differences of less than 0,5 dB...
4. So 3dB bandwith is rather that lute would resonant well at range of frequencies at this bandwith, but most at particular one frequency. I think
that usually it is good, that resonant frequency of a lute or guitar is not a particular note that can be played (it is just in a middle between some
two). If not, this note (and its higher harmonics) would be much more louder, and would be a wolf-note. This is often clearly seen, or heard, with
cheap guitars, where G, G# or A are extremely loud compared to other notes, makig succesful bass line leading hard.
5. For this reason main air resonance pick of good instruments is rather thin, so 3dB bandwith "window" is not wide. It is important of not mixing
ludness and projection of a sound of an instrument with its resonance.
6. Nobody hears lute resonance At least I have never. What we hear, is acoustic
response, and/or resonance phenomenon at some tones.
jdowning - 6-6-2014 at 04:39 AM
I was simply trying to get a better understanding of what Hadi Tavakoli Nia, author of the MIT paper, was proposing when talking about band width
associated with the air resonance frequency of instruments with complex sound holes (i.e. the lute, oud and violin - he does not mention modern
concert guitars). In his introduction Hadi proposes that an increase in band width (observed in the development of the violin sound hole) "enhances a
wider range of frequencies at the low frequency region of the spectrum .... which is favourable to the instrument maker by giving more tolerance in
placing the air resonance". He also illustrates what is meant by the resonance band width (as I have done in my previous post) at minus 3dB in Fig.
A-5 of his paper.
Minus 3dB is the point where human hearing just starts to notice a change in loudness from the level at the resonance frequency. Minus 10 dB - also
indicated on Fig A-5 - is the point at which the human hearing perceives that the loudness is half that of the level at resonance frequency.
The minus 3dB point in turn equates to a 50% radiated sound energy reduction and the minus 10dB point to a 90% reduction in the radiated sound
energy.
Although the MIT research reveals important information about sound hole design that can be used to better predict the air resonance frequency through
a modification of the established Helmholtz resonance formula, what is missing is the verification of the developed formula through the testing of
surviving lutes and ouds. The resonance test on the Berr lute determined the air resonance frequency and approximate band width tolerance (from a
distorted resonance curve) but - because the air volume of the bowl was not measured - the developed formula could not be verified.
An attempt to approximately verify the developed formula for the Berr lute by estimating the air volume of the bowl from scaled images of the lute was
undertaken and reported earlier in this thread.
The task currently in hand is to test the modified formula by estimating the air volume of a number of surviving lutes (of varying size) from full
scale museum drawings and measurements that I have on file and then calculating the air resonance frequency knowing the sound hole dimensions. The
calculated air resonance frequency may then be compared to the pitches of the strings of each instrument (known string length, tuning, and highest
workable pitch of the gut first course) to see if there is some consistency in the placement of the air resonance frequency in lutes. This will take
some time!
My current resonance chamber is not wide enough to accommodate triple sound hole arrangements found on some ouds and lutes so further trials on these
sound hole arrangements will be undertaken later as I have found another larger steel domestic water tank measuring 25 cm (9 3/4 inches) in diameter
that might be easily pressed into service as an alternative resonance chamber.
jdowning - 6-7-2014 at 12:02 PM
The resonance test chamber to be used for testing triple sound holes is a steel tank already cut in half (left over from another project) - by chance
it happens to be about the same volume and diameter as the current resonance test chamber. Inside diameter is 25 mm (9 3/4 inches) so should cover
investigation of lute sized triple sound holes (of equal diameter) as well as oud arbi and possibly the smaller sized oud large/ two small sound hole
arrangement.
If this tank is too small then I have yet another scrap water pressure tank measuring 38 cm (15 inches) in diameter that can be cut in half and
converted into a resonance chamber - although with the larger volume I am not sure if the Audacity spectrum analysis and my recording apparatus will
be sensitive enough to clearly resolve the air resonance frequencies of the sound hole configurations under test.
The first step is to cut and fit an outlet flange. The mounting flange is made from 3/4 inch thick (19 mm) plywood that will be glued into place with
epoxy cement once finally fitted. When finished the test chamber will be spray painted blue - just to look nice!
[file]31719[/file] [file]31721[/file]
jdowning - 6-19-2014 at 11:54 AM
The wooden mounting flange has been fitted and glued to the new resonance test chamber. While waiting for the paint to dry some work has been done to
prepare a device for initiating the air resonance acoustic signal of the chamber.
On the original test chamber, the relatively thin steel walls are flexible enough so that the air resonance pulse can be initiated by simply hitting
the closed end of the chamber with a rubber mallet.
The new chamber has thicker steel walls and is more rigid so an alternative method to set the air resonance in motion is to be tested. This will be to
inject a small volume of compressed air into the chamber using a spring air gun via a convenient port already installed on the chamber side wall.
Rather than spend time making a gun in metal, a plastic toy air gun was purchased from a local store for a couple of dollars. The toy is designed to
safely shoot foam plastic projectiles - but should provide sufficient air pulse for these experiments. The gun was easily dis-assembled to access and
modify by installing a screwed hollow tube (a standard electrical light fitting) at the end of the spring chamber. This will in turn be mounted in a
standard screwed plumbing fitting (using rubber tubing) for attaching to the test chamber. The trigger operation of the gun will be a convenience for
the trials.
This device has already been tested on the original test chamber so should work. Time will tell!
[file]31824[/file] [file]31820[/file] [file]31822[/file]
jdowning - 6-27-2014 at 12:00 PM
The more sophisticated apparatus used for the MIT experiments was sensitive to signal distortion due to sound wave reflection from the surrounding
walls when measured in a confined space - as was the case when recording the air resonance frequency of the Berr lute - the sound pressure wave
travelling uniformly in all directions at about 345 metres per second (or 1132 feet/second). The solution was to conduct the experiments outside in a
wide open space late at night (to avoid traffic noise etc).
I was not sure if my simpler experimental apparatus and method would be similarly affected so a test was conducted in an open field on my property
using the test resonance chamber mounted vertically facing the heavens - just to see if a better defined recorded resonance signal would be the
result. Two sound hole diameters (32 mm and 71 mm) were tested with the air gun used to initiate air resonance of the chamber. The open space is about
an acre in area and is surrounded by trees. Nevertheless a distinct reflected sound echo can be heard following a sound impulse.
The Audacity spectrum analysis results obtained were compared with the original test results that were measured in an enclosed space. No significant
differences in the air resonance frequencies were apparent. This is good because conducting the experiments outside is inconvenient to say the
least.
[file]31929[/file]
jdowning - 6-28-2014 at 04:39 AM
For the apparatus and method used in these trials the air resonance must be mechanically initiated.
For the steel resonance chamber three methods have been tested all providing consistent measured air resonance frequency results:
1) striking the end of the chamber with a rubber mallet.
2) injecting a pulse into the end of the chamber with an air gun.
3) injecting a pulse directly through the test sound hole with an air gun (i.e. no contact with the chamber walls)
For the instrument trials both tapping the sound board (with strings damped) and injecting a pulse directly through the soundhole with an air gun
provide measured air resonance frequency results consistent within one or two Hertz even with the main area of the sound board damped with a
cushion.
The difference between the resonance chamber and instrument test results - as already reported - is that the calculated frequency for the resonance
chamber, based upon the full open area of the sound hole, agrees with the measured resonance frequency whereas for the instrument tests a calculated
frequency based upon only the 'active' sound hole area at the sound hole perimeter agrees with the measured air resonance frequency. The 'active' area
in this case is the area of the open sound hole (diameter D) less the area of the central 'dead zone' of 0.67D diameter.
Why the calculated resonance frequency, based upon the full open soundhole area, applies only to the resonance chamber results has yet to be
explained as the resonance chamber tests have already demonstrated that the air flow passing through a circular sound hole at resonance is
concentrated at the sound hole perimeter - little if any flow passing through the central area of a sound hole.
See Fig A-13 and Fig A-23 of the MIT paper for a graphical representation of air flux distribution through lute and oud sound holes. Not sure how
these images were produced - the MIT paper does not explain.
jdowning - 7-1-2014 at 11:53 AM
The second resonance test chamber is now complete and ready for action. The outlet flange internal diameter measures 24.6 mm - so will provide ample
space for testing traditional triple sound hole geometries of both lutes and ouds. The measured resonance chamber volume is 17,000 cc so is close to
that of the original chamber.
The chamber is set up to operate vertically.
Before running a series of tests on triple sound holes - a single sound hole arrangement with deep braces on each side (as found typically on
surviving lutes) will be tested to find out if the presence and depth of these braces might significantly influence the air resonance frequency.
[file]31962[/file]
jdowning - 7-2-2014 at 12:08 PM
The first preliminary test with the new resonance chamber gave a measured air resonance frequency of 123 Hz for a circular sound hole measuring 94 mm
in diameter, 3 mm thick. Speed of sound in air corrected for an ambient temperature of 26 °C was 347 metres/sec. Corrected equivalent length of the
sound hole = 0.3 + 1.7X sound hole radius = 8.29 cm. Resonance chamber volume is 17,000 cc. The total open area of the sound hole is 69.4 cm².
Therefore, the calculated air resonance frequency based upon the full open area of the sound hole = 122.6 Hz or 123 Hz rounded up to the first whole
number. So this again confirms that for my test resonance chambers the calculated resonance agrees with the measured air resonance based upon the open
sound hole area of diameter D not the whole area less the inactive central area (measuring 0.67D in diameter) as seems to be the case for lutes, ouds
and guitars. Why would this be?
Clearly the geometry of an instrument - lute or guitar - is different from a resonance chamber the latter being deep and narrow whereas the instrument
bodies are relatively shallow and wide (and a lot more flexible). So, for example, a guitar body might be around 10 cm in depth so the slug of air
oscillating through a sound hole of the above diameter would be over 4cm deep within the guitar body which might have some significant effect on air
flux through the sound hole - the pressure pulse travelling sideways (rather than vertically in the case of the resonance chambers). Not only that but
both lute and guitar have deep braces on either side of the sound hole that may also significantly affect air flow - creating perhaps an increased
equivalent sound hole depth?
Next to test if brace depth influences the air resonance frequency braces of depth 3.5 cm will be glued on each side of the 94 mm diameter sound hole
extending to the sides of the test chamber. The resonance frequency will be measured for this arrangement and then with brace heights reduced in steps
of 5 mm - 3 cm, 2.5 cm, 2 cm and 1.5 cm.
jdowning - 7-3-2014 at 11:53 AM
It is perhaps also worth noting that within the limit of the chamber maximum volume (17,000 cc) the volume may be infinitely varied by adding measured
amounts of water to the chamber positioned vertically (it was - after all - once a water tank). This would require initiating air volume resonance
with the air gun firing an air pulse directly through the test sound holes from outside the chamber. In fact a test earlier today confirmed that this
convenient method gives a better well defined resonance peak in the Audacity FFT spectrum analysis than with the gun attached to the chamber by the
side port. In this method the gun fires the compressed air pulse directed at an angle (about 45° or so) into the sound hole positioned along side the
H2 Zoom digital recorder (that is in turn positioned directly above the sound hole at a distance of about 10 cm).
The facility to easily vary the tank volume may be useful (time permitting!) as it will allow more data to be collected for given sound hole
arrangements and shallower tank geometries - the latter perhaps better representing actual musical instruments?
jdowning - 7-7-2014 at 11:38 AM
To test if brace depth might affect the air resonance frequency two braces 3.5 cm deep were glued on either side of a test sound hole measuring 94 mm
in diameter. The ends of the braces were trimmed to fit closely against the side of the resonance chamber - essentially 'boxing in' the sound hole
with the braces as it would be on a lute or oud.
By filling the resonance chamber with water in stages the air resonance signal was recorded for chamber air volumes of 17,000 cc (i.e. empty), 10,000
cc, 8,000 cc, 6,000 cc and 4,000 cc. For the latter smallest air volume, the distance between the water level in the chamber and sound hole was 9.5
cm.
The air resonance frequencies determined from the Audacity FFT frequency analysis were 121 Hz, 162 Hz, 183 Hz 210 Hz and 256 Hz respectively.
The calculated air resonance frequencies based upon the full sound hole open area (69.4 cm²) and Le = 0.3 + 1.7 x sound hole radius = 8.29 cm were
all within 2% to 3% of the measured frequencies. Even closer agreement was obtained using an Le correction factor of 1.62 instead of 1.7.
So, it is concluded that (for this test chamber arrangement at least) the proximity of the braces at the edge of a sound hole and their depth does not
significantly affect the air resonance frequency.
jdowning - 7-8-2014 at 12:14 PM
Looking for other instrument sized resonant boxes that might yield more comparative data, the air resonance frequency of the sound box on my string
testing rig was measured.
The sound box is rectangular long, narrow and shallow (51.7 cm x 11 cm wide x 6 cm deep) with a relatively small diameter sound hole. Construction is
wood with thick rigid sides and back - with a 2 mm thick Spruce sound board. The sound hole diameter D is 4.1 cm supported on each side by two
braces.
The measured air resonance frequency, determined by the Audacity spectrum analysis, is a clear peak at 154 Hz.
Total volume of the box is 3412 cc, sound hole area is 13.2 cm², and radius 2.05 cm Corrected sound hole length Le = 0.2 + 1.62 x 2.05 = 3.52 cm.
Calculated air resonance frequency based upon the full open sound hole area is 183 Hz - three semitones above the measured frequency - so not
valid.
Calculated air resonance frequency based upon the open area less a 'dead zone' area of 0.67 (active area = 8.45 cm²) is 146 Hz - about a semitone too
low.
Assuming a dead area of diameter 0.55D gives a calculated air resonance frequency of 153 Hz - close enough to the measured value.
This trial is interesting in confirming that the calculated resonance based upon the full open sound hole area - while it applies to a relatively
deep, rigid steel resonance chamber - is not valid for a relatively shallow sound box with one surface that is flexible (a sound board). Not only that
but it suggests that for a calculated frequency based upon a sound hole active area, the diameter of the 'dead zone' may reduce as relative sound hole
diameter diminishes. This observation was previously noted in the case of the Berr lute that has quite a small sound hole diameter.
It is also interesting to note that Figure A-23 of the MIT paper - that shows the normalised air flux distribution in a 3 sound hole oud configuration
- appears to confirm the above - the flux distribution being more concentrated across the entire diameter of the small diameter sound holes than it is
for the large sound hole.
jdowning - 7-12-2014 at 12:10 PM
The formula given in the MIT paper and by others for calculating the air resonance frequency of a guitar, lute or oud with a single circular sound
hole - referred to earlier in this thread is :
Frequency = c/6.28 (A/V. Le)½
Note that ( )½ is the square root value of the product within the brackets.
Where
C= speed of sound in air
A= Area of the open sound hole of radius R
V = Air volume of the instrument body.
Le = corrected thickness (h) of the sound hole
where Le = h + K. R where K ranges from 1.6 (MIT value) to 1.7 (others).
However, although this calculated value of the air resonance frequency seems to work well for a rigid steel resonance chamber it would appear to over
estimate the air resonance frequency by several semitones (i.e. higher than measured) if applied to a musical instrument so is not valid for the
latter (unless a very wide bandwidth tolerance is assumed).
It has been proposed so far in this thread that better agreement between calculated and measured values for instruments may be achieved by assuming a
value of A that is equivalent to the total area less the area of the central 'dead zone' of a sound hole. (This may just be fortuitous - a
coincidence - and is not proposed by the MIT author).
The diameter of this 'dead zone' may vary according, possibly, to a number of factors such as sound hole diameter, resonance chamber volume and
geometry etc. - factors that have yet to be determined by experiment.
jdowning - 7-13-2014 at 05:18 AM
From the test data on the resonance box of my string testing rig previously reported, the measured and calculated air resonance frequency were in
close agreement if the assumed area of the sound hole (diameter D) used to calculate frequency is the total area less a 'dead zone' area of diameter
0.55D.
For comparison a sound hole of the same diameter (41 mm) was tested on the new resonance chamber (air volume 17,000 cc). The sound hole was cut into a
3mm thick piece of fibreboard ('Masonite') stiffened with two braces - quite a rigid arrangement compared to an instrument sound board.
The measured air resonance frequency was 78 Hz. Calculating the air frequency assuming the full sound hole area and an Le correction constant K of 1.7
gives a frequency of 78.6 Hz - close enough to the measured value.
On the other hand, if the calculated value is based upon the full sound hole area less 'dead zone' areas of 0.67D diameter and 0.5D diameter the
frequency is 58 Hz and 68 Hz respectively.
This again confirms that the calculated air resonance formula that works for a rigid steel resonance chamber does not appear to accurately predict the
resonance frequency of a wooden musical instrument.
Clearly my new resonance test chamber is different not only in material but in geometry and air volume from the string test rig resonance box. Could
these be significant factors that might somehow explain the discrepancy between the calculated and measured frequencies?
Next to examine the effect of air volume reduction by testing the 41mm sound hole with the resonance chamber volume reduced to that of the string test
rig resonance box (3412 cc).
[file]32071[/file] [file]32073[/file]
jdowning - 7-13-2014 at 11:57 AM
The air volume of the resonance chamber was reduced to 3565 cc by filling with water and the 41 mm diameter sound hole retested. The depth from water
level to the test sound hole was 7.5 cm.
The measured air resonance frequency was 170 Hz
Calculating the resonance frequency assuming full sound hole area and Le factor K = 1.7 gave a frequency of 171 Hz - close enough.
Calculations based upon the full sound hole area less 'dead zone' areas of diameter 0.67D and 0.5D gave resonance frequencies of 127 Hz and 148 Hz
respectively.
So this again confirms that the calculated air resonance frequency based upon the full sound hole area is valid only for a rigid symmetrical
resonance chamber and that volume change for a given sound hole diameter - as expected - proportionally alters the resonance frequency - smaller
volume = higher frequency and vice versa. Fine if we want to predict the air resonance frequency of a rigid Helmholtz resonator fitted with a thin
rigid sound hole but not for a musical instrument like an oud, lute or guitar it would seem.
Next to see what happens if the resonance chamber is fitted with a flexible 'sound board' and a 41 mm sound hole.
jdowning - 7-21-2014 at 03:25 PM
To test the effect on the air resonance frequency of a flexible surface on the otherwise rigid test chamber three tests have been undertaken using a
low cost material that replicates an instrument sound board physical characteristics - corrugated cardboard. This material is a familiar commonly used
packing material - for making cardboard boxes - and like an instrument sound board of wood is stiff in one direction and less so 'across the grain'.
Not to suggest that corrugated card board might serve as a material for oud, lute or guitar sound boards!
The three tests are:
1) with no sound hole - chamber volume 17,000 cc and 3565 cc.
2) with 43 mm diameter sound hole - chamber volumes 17,000cc and 3565 cc.
3) with 43 mm sound hole braced on each side with 2 cm deep spruce braces - chamber volumes 17,000cc and 3565 cc.
The latter test (3) is to compare with the results from the sound box on my string test rig previously reported as well as to determine the effect of
changing the chamber geometry from a deep to shallow depth.
Test 1) - with the resonance chamber sealed with the flexible sound board (i.e.equivalent to a drum and so no air resonance effect), the measured
frequency response on tapping the sound board was 211Hz at a volume of 17,000cc and 281 Hz at the smaller volume of 3565 cc. The smaller chamber
volume was achieved by filling the chamber with water leaving a depth of 7.5 cm from the water surface to the sound board.
Next for test 2) results.
[file]32116[/file]
jdowning - 7-22-2014 at 02:42 PM
Out of curiosity and for information a second test #1b with the sound board in place was to remove the plug in the body of the resonance chamber to
determine how much that might affect the measured resonance of the sound board (now including an air resonance 'Helmholtz' component). Resonance
chamber volume was 17,000 cc.
The threaded connection was lined with a piece of thin sheet metal 2.6 cm in length and 2.8 cm internal diameter to make a smooth air vent to the
chamber. Based upon a rigid Helmholtz resonance chamber, the calculated resonance frequency should be about 60 Hz.
However, with a flexible diaphragm ('sound board') in place at one end of the chamber, the measured resonance frequency was 205 Hz which, corrected
for temperature, compares to the previously posted frequency of 211 Hz for the chamber (with the vent sealed).
Not surprisingly the dominant resonance frequency was lowered but not by much - the flexibility of the 'sound board' being the main factor it would
seem?
Next to test the sound board with the test chamber vent sealed and with a 4.3 cm sound hole cut in the 'sound board'.
[file]32125[/file] [file]32127[/file]
jdowning - 7-23-2014 at 11:58 AM
Test 2 is to cut a sound hole in the card sound board and measure air resonance. The sound hole diameter D - cut with craft knife - is 43 mm, as close
as I could get to the sound hole diameter of the string test rig sound box at 41 mm - for comparison purposes. The open cavities at the edges of the
card sound hole were sealed with glue.
Two measurements were taken with the resonance chamber air volume at 17,000 cc and 3565 cc (i.e. the latter as close to the volume of the string test
rig sound box as I could get - for comparison purposes).
For a volume of 17,000 cc the measured air resonance was 72 Hz and for a volume of 3565 cc 112 Hz
Calculating the air resonance frequency for the 17,000 cc volume case based upon the full sound hole area A and Le correction factor K =1.7 gives a
value of 83 Hz - too high. Based upon an active sound hole area of A less the area of a dead zone of diameter 0.5D gives a calculated frequency value
of 72 Hz - in agreement with the measured value.
On the other hand for the 3565 cc case calculated frequency only agreed with measured frequency for an active sound hole area of A less the area of a
dead zone of diameter 0.78D.
This suggests that the geometry of the air chamber (deep vs shallow) as well as the flexibility of the sound board (acting as a diaphragm) has a
strong influence on the air resonance frequency.
This test still may not represent the condition of musical instruments such as oud, lute or guitar where the sound boards are stiffened in the area of
the sound hole with deep braces placed on each side of the sound hole.
Test 3 - with braces glued onto the card soundboard on either side of the sound hole - to follow
Note that currently tests on this relatively small sound hole diameter may provide some useful data in future tests when oud triple sound hole
arrangements are to be examined.
[file]32129[/file]
jdowning - 7-27-2014 at 11:54 AM
For test #3 two braces, 2 cm deep and extending the full diameter of the chamber, were glued on either side of the sound hole and the tests repeated.
The corrugated card 'sound board' was cut from an old box that once contained a coffee maker - hence the printing on the underside seen in the
attached image!
The measured air resonce frequency at a volume of 17000 cc was 77 Hz and for a volume of 3565 cc was 147 Hz. This compares with the un-braced sound
board frequencies of 72 Hz and 112 Hz respectively previously reported.
So - as expected - the consequence of stiffening the sound board (reducing its flexibility) is to increase the air resonance frequency (i.e. the
spring effect of the air trapped in the resonance chamber has been increased - i.e. made stiffer).
This effect is more pronounced with the smaller air volume (3565 cc) than it is at the maximum volume (17,000 cc) of the test chamber. So at maximum
volume, the calculated resonance frequency based upon full sound hole area is 80 Hz - less than a semitone higher than measured whereas for the
smaller, shallower air volume the calculated air resonance based upon sound hole area less the area of a 'dead zone' of diameter 0.55D gave a
frequency of 146 Hz in agreement with the measured frequency. (Note that 0.55D was the dead zone diameter that gave the 'right answer' in comparing
measured and calculated resonance frequencies for the string test rig sound box previously reported).
This last test with braced soundhole and shallow air volume should be more representative of an oud, lute or guitar than that of the former deep air
volume (17000 cc) test.
jdowning - 7-29-2014 at 12:07 PM
In order to collect more data on 'real' instruments, for comparison, tests have been undertaken on 3 classical guitars that I own that have been
gathering dust for years. These are an 'Aria' - a Vincente Tatay, Valencia, Spain and a copy of a mid 19th C Torres guitar by J. Downing. The latter
was the first instrument that I made during the summer of 1963 in order to relax after graduating in engineering.
The 'Aria' guitar was picked up for $20 at a local flea market - purchased because the unstrung instrument vibrated in my hands when a motor cycle
went past nearby.
Tests on this guitar were reported earlier in this thread but have been repeated here for comparison.
By coincidence, all three guitars have a sound hole diameter of 8.7 cm but differ in the air volume of their bodies - the 'Aria' being the largest
volume.
To measure the air volume of the guitars they were filled with Indian corn seed (low cost from a local store - and to be fed later to our geese). The
volume of the corn was measured using a kitchen liquid measure.
To ensure reasonable accuracy the guitar volume was measured, with the guitar in the vertical position, in two stages - volumes of the top and bottom
bouts were each filled with corn seed to the edge of the sound hole. The remainder of the volume, at the sound hole, was then calculated from sound
hole diameter, depth of the body and mean width at the guitar waist.
For the 'Aria ' guitar the measured volume is 13,052 cc compared to an estimated 'slice by slice' calculated volume of 12,957 cc. The volume of the
guitar body - splitting the difference is, therefore, taken as 13,000 cc.
The results of the trials is to be reported next.
jdowning - 8-3-2014 at 12:12 PM
For all three guitars - the sound hole diameters (D) are equal at 8.7 cm so the corrected equivalent length Le of the sound holes for determination of
the calculated value of the air resonance frequencies is 0.2 + 1.7 x 4.35 = 7.6.
Calculated resonance frequency = c/6.28 (A/V x Le)½ where c is speed of sound in air, A is area of sound hole, V is air volume of guitar body and Le
= 7.6 in this case. Note that ( )½ is the square root of the product within the brackets.
Aria guitar - volume = 13,000 cc, measured air resonance frequency = 104 Hz @ 24°C
Tatay guitar - volume = 10,250 cc, measured air resonance frequency = 93 Hz @ 22°C
'Torres' guitar - volume = 10,800 cc, measured air resonance frequency = 99 Hz @ 22°C
Calculated air resonance frequencies based upon the full open sound hole area (59.5 cm²) corrected for air temperature are:
Aria = 135 Hz (5 semitones high)
Tatay = 152 Hz (8 semitones high)
Torres = 148 Hz (7 semitones high)
So calculated air resonance based upon full sound hole area is not valid
Active sound hole areas for the calculated resonance values to equal measured values are :
Aria = 34.5 cm² ( equivalent sound hole 'dead zone' diameter = 0.65D)
Tatay = 23.3 cm² ('dead zone' diameter = 0.78D)
Torres = 26.1 cm² ('dead zone' diameter = 0.75D)
As I had to hand a reduced sound hole diameter fitting (D=3.4 cm, area 9.1 cm²) for the Aria guitar (from earlier experiments in 2009), this was
taped to the sound hole and the air resonance frequency measured as 68 Hz @ 24°C. Calculated air resonance frequency - corrected for temperature - is
83 Hz or 3 semitones high.
Active sound hole area for the calculated resonance value to equal measured value = 6.3 cm² ('dead zone' diameter 0.55D).
For comparison the pitch of the fifth string of a modern concert guitar at (A440 standard pitch) is A110 Hz and the sixth string is E82 Hz so the
measured air resonance frequency of all the guitars tested is just below the pitch of the fifth string.
jdowning - 8-5-2014 at 12:15 PM
To summarise the position judging from the limited test results obtained so far from resonance chamber #2.
1) If the test plate with sound hole is rigid - regardless of sound hole diameter or resonance chamber air volume - the calculated frequency, based
upon the full open sound hole area and length correction factor of 1.7R, will closely predict the measured air resonance frequency. This arrangement
is not valid for a musical instrument with a braced sound hole in a flexible sound board.
2) If the test plate with a braced sound hole is flexible, so representing an instrument sound board, then the geometry of the resonance chamber air
volume appears to affect the air resonance frequency. For a relatively deep resonance chamber geometry, calculated frequency based upon the full open
sound hole area will predict the measured air resonance frequency. However for a relatively shallow chamber, a calculated frequency based upon the
full sound hole area significantly over estimates the air resonance frequency by several semitones so is not valid for instruments with relatively
shallow sound box depths (compared to sound board area) like ouds, lutes, guitars etc.
3) For instruments, calculated air resonance frequencies based upon the 'active' area of sound hole (A-Ad with 'dead zone' diameters ranging from
about 0.5D to 0.8D - in turn dependent upon relative sound hole diameter) may provide empirically valid results in predicting air resonance
frequency.
The objective here is to find valid, empirical relationships that will allow a luthier - who is not a 'rocket scientist' - to easily calculate sound
hole diameter in order to obtain an optimum air resonance frequency for the sound box of an instrument under construction.
jdowning - 8-9-2014 at 12:07 PM
So far, the limited tests on lutes and guitars reported in this thread suggest that the air resonance frequency of the instrument bodies more or less
coincide with the pitch of the fifth course so reinforcing the bass response of the instrument. Although tests have yet to be undertaken on ouds it is
expected that the sound hole acoustics will be similar to that of a lute.
Between the years 1660 to 1672 Mary Burwell - who was being taught to play the 11 course lute - made a manuscript copy of the lessons provided by her
teacher (who may have been Englishman John Rogers). The manuscript contains much valuable information about performance and practice of the French
Baroque lute as well as practical guidance on such matters as choosing strings, fretting and tuning etc.
The A. Berr lute, reported earlier in this thread, is an example - in its original condition - of an 11 course French lute
Burwell notes that a lute has a natural pitch so must not be tuned too high or too low (beyond that pitch) to avoid spoiling the acoustic response of
even an otherwise excellent lute.
Interestingly, she also states that "For the tuning of the lute you must begin with the fifth (course). String it in a pitch proportional to the lute
then from that course you shall tune all the others by thirds or fourths as the tuning requires".
There is, of course, no mention of pitch standards so the implication here (it would seem) is that the lutenist must first set the pitch of the fifth
course (by ear) to coincide with the air resonance frequency of the lute. This optimum pitch will vary somewhat from instrument to instrument but for
the 11 course lute this lack of a defined pitch standard would not have presented a problem as this style of lute - according to Burwell - was
strictly a serious, high art solo instrument not used for accompaniment of singers, or for playing country dances and certainly not for playing in
taverns or otherwise for drunken ranting or serenading in the streets!
jdowning - 8-11-2014 at 12:11 PM
I should add that until the comment by Burwell to begin tuning an 11 course lute at the fifth course, earlier instructions for tuning a lute (16th C)
began with the first course that was tuned to a pitch as high as it would go without frequent breakage. The reason for this was to give the thicker
bass strings of the 5th or 6th courses (then of plain gut or silk) the best chance of sounding reasonably well - even with octave tuned string pairs
which was once standard practice.
Clearly, by the late 17th C string technology had developed to the point where the open bass strings of an 11 course lute (still octave tuned pairs)
sounded well enough. Indeed Burwell notes that the sound of the 11th course was so overpowering that its use has been discontinued by the masters. How
these strings were made to be so acoustically effective - comparable to modern metal wound strings - we do not know.
jdowning - 8-7-2015 at 11:54 AM
The original MIT research paper on soundhole acoustics by Hadi T. Nia (link at start of this topic) covered a range of trials using resonance chambers
and actual instruments (violin, lute, oud) with some interesting results. Unable to follow the dynamic flow mathematics presented in the paper (long
since forgotten after having left behind my University studies in engineering over 50 years ago) I have attempted in this thread to verify some of the
results of particular interest obtained by the MIT research using basic low cost apparatus.
I have yet to work on measurements for mutiple sound hole arrangements due to lack of a suitable large diameter resonance chamber. I have obtained a
scrap domestic pressure water tank from a friend that should do the job. Currently sitting in my metal working shop it is 40 cm in diameter and will
be cut in half with support legs welded to the shell so that it can stand with the dome end at the bottom. Air volume will be varied for the trials by
adding/subtracting water. Work on this resonance chamber will need to be completed before the cold weather sets in.
The latest research paper from MIT by Hadi T. Nia et. al. appears to be an extension of the original research that investigated violin soundholes and
their effect on air resonance power efficiency. Summary here:
https://newsoffice.mit.edu/2015/violin-acoustic-power-0210
The paper is available from the Royal Society publishing for about $50 for a 30 day read. Too costly for my pocket and I am not partcularly interested
in the air resonance phenomenon in violins anyway - only plucked stringed instruments (lute, oud and guitar) where the air resonance may be of greater
importance in the overall instrument acoustics than for a violin.
Of interest is the reported air resonance power increase with change in sound hole shape from round, to semicircular, to ring type - configurations
that I am currently testing on a long necked lute here:
http://www.mikeouds.com/messageboard/viewthread.php?tid=15437&p...
Some shapes have already been tested and analysed so before dismantling the experimental set up on the instrument the additional shapes (semicircular
and half ring) will also be tested.
[file]36192[/file]
jdowning - 8-7-2015 at 03:42 PM
Worth mentioning perhaps that the latest MIT paper about air resonance power efficiency in violins was not well received by the violin luthier
fraternity - if this forum is anything to go by
http://www.maestronet.com/forum/index.php?/topic/332056-new-researc...
The problem is that the MIT authors go beyond their interesting scientific experimental results by treading on speculative thin ice to suggest
discovery of a 'secret' (a perceived sound hole development over the centuries) about why Stradivarius violins sounded so good - a certain provocation
for violin experts who have heard it all before. The consequent negative comments on the Maestronet forum do, however, contain one or two useful
observations.
jdowning - 8-10-2015 at 06:45 AM
The water tank was cut open this morning as a start to making resonance test chamber #3. I know that the tank was last used as a domestic water
pressure vessel but nevertheless the tank was first filled with water as an extra precaution. Never cut into an enclosed vessel with spark generating
abrasive tools if the contents previously contained are unknown - good way to kill or injure oneself if there are combustble residues inside that may
be ignited.
To cut the tank I used a metal cutting abrasive disc mounted in a power saw to complete the job quickly and smoothly - the wide cutting disc acting as
a guide to produce a straight level cut.
Although there is some external corrosion and pitting of the steel, the interior - being ceramic (glass) lined is in good shape. The wall thickness of
the tank is about 2 mm. This will make a perfect test chamber fitted with a plywood mounting flange at the open end. The whole thing when complete
will be painted (to make it look more serious scientifically!).
The other half of the tank with its concave base will eventually be made into a small blacksmith's forge - as time and motivation permits.
[file]36251[/file] [file]36253[/file]
jdowning - 8-20-2015 at 11:43 AM
In the meantime.
The latest MIT paper on the air resonance power efficiency in violins has a supplementary paper freely available here:
http://rspa.royalsocietypublishing.org/content/royprsa/suppl/2015/0...
... and includes a diagram at the beginning comparing the air resonance frequencies of a long, narrow S shaped violin soundhole with a round
soundhole of the same area and a round soundhole of the same peripheral length. Not surprisingly - all else being equal, same air volume, resonance
chamber stiffness etc. - the larger diameter soundhole (same peripheral length) results in a higher air resonance frequency than the smaller diameter
soundhole (same area).
The MIT results show an air resonance frequency for the violin S shaped soundhole falling between the round soundhole max/min values.
Using my #1 resonance chamber, I plan to run a series of trials to compare the measured air resonant frequencies of a simple long, narrow rectangular
soundhole (of variable length) with round soundholes of equivalent area and peripheral length - just to see if similar comparable results might be
obtained. See attached sketch - soundholes drawn to the same scale.
jdowning - 9-16-2015 at 02:36 PM
An update on resonance test chamber #3.
A 2cm (3/4 inch) thick plywood flange or rim has been cut, fitted and glued to the chamber with waterproof construction adhesive (polyurethane). This
will allow the test sound boards to be clamped to the chamber.
The chamber exterior has been spray painted for cosmetic reasons - green colour because that is what I had available in stock!
A water drain valve has been added to the bottom of the chamber for convenience as water will be used to vary the chamber air volume for the
trials.
I found a welded steel support frame - made for another project - that has been sitting outside for a few years so is pretty well rusted but will
serve the purpose with some wooden blocks added to fit the chamber. I might even wire brush and paint the frame to look pretty - although not
essential.
All components and materials have been found in stock so there has been no expenditure apart from a little of my time.
The air volume of the chamber empty works out to be a maximum 36,825 ml (cc) with an internal diameter at the flange of 40.2 cm. The volume was
accurately determined by filling the difficult to calculate dome end with a measured amount of water (8,650 ml) and then by calculating the volume of
the cylindrical portion from measured diameter and height.
This larger diameter chamber is to investigate the air resonance frequency responses of multiple sound hole geometries - particularly the large/small
diameter configurations typically found on ouds and on some types of historical lutes represented in the iconography (but not in surviving examples).
The testing will be more complicated than single sound hole acoustic testing due to the increased number of variables - multiple sound hole diameters
and spacings with different air volumes.
I will likely simplify test parameters by focussing first on single large sound hole/single small sound hole configurations - just to see where that
might lead.
Not a top priority project for me at the present time, however.