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jdowning
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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]
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jdowning
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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.
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jdowning
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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]
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jdowning
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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.
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jdowning
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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]
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narciso
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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
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jdowning
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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]
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antekboodzik
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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]
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jdowning
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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]
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jdowning
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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]
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jdowning
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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).
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antekboodzik
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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
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jdowning
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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]
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antekboodzik
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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]
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antekboodzik
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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.
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jdowning
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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]
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jdowning
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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.
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jdowning
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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...
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antekboodzik
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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]
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jdowning
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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.
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jdowning
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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]
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jdowning
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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
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jdowning
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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.
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jdowning
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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]
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antekboodzik
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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.
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