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jdowning
Oud Junkie
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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.
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jdowning
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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]
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jdowning
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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]
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jdowning
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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]
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jdowning
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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.
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jdowning
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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]
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jdowning
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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.
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jdowning
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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?
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jdowning
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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.
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jdowning
Oud Junkie
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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.
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jdowning
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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.
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jdowning
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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]
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jdowning
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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.
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jdowning
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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]
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jdowning
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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]
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jdowning
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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]
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jdowning
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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.
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jdowning
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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.
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jdowning
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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.
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jdowning
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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.
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jdowning
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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!
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jdowning
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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.
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jdowning
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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]
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jdowning
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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.
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jdowning
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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]
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