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jdowning
Oud Junkie
Posts: 3485
Registered: 8-2-2006
Location: Ontario, Canada
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Here are the first of the 12 test results: All strings are round (silver plated) copper wire on nylon filament core. String length 61 cm. Equivalent
diameter calculated for nylon core material derived from measurements of string outside diameter and wire diameter according to the basic formula for
close wound strings previously posted.
Note that tensions on the Pyramid calculator are in Newtons so have been converted to Kilograms force (9.8 Newtons = 1 Kg)
Some strings tested are used (but not worn) others are new.
Pyramid #906 at f pitch (175 Hz) - used string
Calculated equivalent diameter = 0.88 mm.
Tension Arto Wickla calculator = 2.93 Kg
Tension Pyramid calculator = 2.96 Kg
Tension Pyramid tables = 3.04 Kg
Tension test rig = 3.09 Kg
Range 2.9 Kg to 3.1 Kg
Pyramid #908 at e pitch (165 Hz) - new string
Equivalent diameter = 1.01mm
Tension A.W. calculator = 3.37 Kg
Tension Pyramid calculator = 3.27 Kg
Tension Pyramid tables = not available
Tension test rig = 3.47Kg
Range 3.3 Kg to 3.5 Kg
Pyramid # 1010 at c pitch (132 Hz) - used string
Equivalent diameter = 1.15 mm
Tension A.W. calculator = 2.80 Kg
Tension Pyramid calculator = 2.96 Kg
Tension Pyramid tables = 2.90 Kg
Tension test rig = 2.92 Kg
Range 2.8 Kg to 3.0 Kg
Pyramid #1011 at B pitch (124 Hz) - used string.
Equivalent diameter = 1.18 mm
Tension A.W. calculator = 2.63 Kg
Tension Pyramid calculator = 2.91 Kg
Tension Pyramid tables = 2.80 Kg
Tension test rig = 2.90 Kg
Range 2.6 Kg to 2.9 Kg
Pyramid #1012 at B pitch (124 Hz) - new string.
Equivalent diameter = 1.27 mm
Tension A.W. calculator = 3.05 Kg
Tension Pyramid calculator = 3.27 Kg
Tension Pyramid tables = 3.04 Kg
Tension test rig = 3.29 Kg
Range 3.0 Kg to 3.3 Kg
Pyramid #1013 at B pitch (124 Hz) - new string
Equivalent diameter = 1.29 mm
Tension A.W. calculator = 3.14 Kg
Tension Pyramid calculator = 3.47 Kg
Tension Pyramid tables = 3.30 Kg
Tension test rig = 3.50 Kg
Range 3.1 Kg to 3.5 Kg
Pyramid # 1016 at G pitch (98 Hz) - new string
Equivalent diameter = 1.49 mm
Tension A.W. calculator = 2.64 Kg
Tension Pyramid calculator = 2.76 Kg
Tension Pyramid tables = 2.77 Kg
Tension test rig = 2.61 Kg
Range 2.6 Kg to 2.8 Kg
More to follow.
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jdowning
Oud Junkie
Posts: 3485
Registered: 8-2-2006
Location: Ontario, Canada
Member Is Offline
Mood: No Mood
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Pyramid #1017 at G pitch (98 Hz) - new string
Equivalent diameter = 1.55 mm
Tension A.W. calculator = 2.86 Kg
Tension Pyramid calculator = 3.01 Kg
Tension Pyramid tables = 2.87 Kg
Tension test rig = 3.03 Kg
Range 2.9 Kg to 3.0 Kg
Pyramid #1020 at F pitch (87 Hz) - new string
Equivalent diameter = 1.71 mm
Tension A.W. calculator = 2.76 Kg
Tension Pyramid calculator = 2.83 Kg
Tension Pyramid tables = 2.79 Kg
Tension test rig = 2.81 Kg
Range 2.8 Kg
Pyramid #1023 at E pitch (82 Hz) - new string
Equivalent diameter = 1.81 mm
Tension A.W. calculator = 2.76 Kg
Tension Pyramid calculator = 3.06 Kg
Tension Pyramid tables = 2.91 Kg
Tension test rig = 2.98 Kg
Range 2.8 Kg to 3.1 Kg
Pyramid #1025 at D pitch (73 Hz) - new string
Equivalent diameter = 1.95 mm
Tension A.W. calculator = 2.54 Kg
Tension Pyramid calculator = 2.60 Kg
Tension Pyramid tables 2.62 Kg
Tension test rig = 2.71 Kg
Range 2.5 Kg to 2.7 Kg
Pyramid #1027 at D pitch (73 Hz) - used string
Equivalent diameter = 2.08 mm
Tension A.W. calculator = 2.89 Kg
Tension Pyramid calculator = 2.96 Kg
Tension Pyramid tables = 2.86 Kg
Tension test rig = 2.83 Kg
Range 2.8 Kg to 3.0 Kg
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jdowning
Oud Junkie
Posts: 3485
Registered: 8-2-2006
Location: Ontario, Canada
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Taking a closer look at the results there appears to be quite a reasonable consistency between comparison of tensions from the four sources.
Comparing tension results:
The test rig results compared to the Arto Wickla values calculated from equivalent diameter agree within in a range from 0.03 Kg to 0.36Kg maximum.
The tensions from the Pyramid calculator compared to the A.W. calculated values agree within the range 0.03 Kg to 0.33Kg - quite consistent with the
results from the test rig.
Tensions from the Pyramid tension tables compared to the A.W. calculated values agree within the range 0.01 Kg to 0.17 kg
Tensions from the test rig compared to the Pyramid tables (presumably measured on a similar test rig) agree within the range 0.02 Kg to 0.25 Kg.
Comparing tensions between the Pyramid Calculator and the Pyramid tension tables agree within the range 0.02 Kg to 0.23 Kg
So it can be seen that there is even some degree of discrepancy of values between the Pyramid data - probably due to manufacturing tolerances of
dimensions and material densities in the string manufacture.
For all practical purposes tensions may be quoted to the first decimal place it being pointless to assume any greater degree of accuracy given the
normal variables.
The results of these test confirm that application of the basic equivalent diameter formula can provide a pretty accurate assessment of string
tensions based upon accurate diameter measurements of string outside diameter and winding wire (using only a well made and accurate Chinese micrometer
costing under $20).
For copper wire wound on nylon filament core - densities within the range of 1.4 gm/cc to 1.8 gm/cc for the nylon filament and 9.8 to 9.9 gm/cc would
appear to be acceptable. For gut and silk filament cores assume a density of 1.3 gm/cc.
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jdowning
Oud Junkie
Posts: 3485
Registered: 8-2-2006
Location: Ontario, Canada
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Found three low cost unused wound guitar strings from times past so measured the strings to see if they might be be viable for a 61 cm string length
oud in Arabic tuning.
The string makes are unknown so there are no convenient manufacturer's tension tables to refer to. The cores are nylon filament with silver plated
copper wire winding.
String #1
Outside diameter = 1.07mm
Wire diameter = 0.28 mm
Calculated equivalent diameter = 2.478 mm
Tension for oud 6th course C (65 Hz) tuning - Arto Wikla = 3.3 kg
String #2
Outside diameter = 1.17 mm
Wire diameter = 0.28 mm
Calculated equivalent diameter = 2.645 mm
Tension for oud 6th course C (65 Hz) tuning - Arto Wickla = 3.7 Kg
String #3
Outside diameter = 0.89 mm
Wire diameter = 0.019 mm
Calculated equivalent diameter = 1.95 mm
Tension for oud 5th course G pitch (98 Hz) tuning - Arto Wikla =4.5 Kg
Tension for oud 5th course F pitch (87 Hz) tuning - Arto Wickla = 3.6 Kg
Tension for oud 5th course E pitch (82 Hz) tuning - Arto Wickla = 3.2 Kg
Verifying string tensions directly using the string test rig gave the following results:
String #1 - 3.3 Kg
String #2 - 3.8 Kg
String #3 - G - 4.8 Kg
F - 3.8 Kg
E - 3.4 Kg
So again these tests confirm that the equivalent diameter calculation gives reasonably accurate results for close wound string tensions - in the
absence of any manufacturers string data whatsoever - given only the measured string outside diameter and the winding wire diameter (and knowing the
core and wire densities within a reasonable tolerance).
For string fragments too short (a centimeter or so in length) to allow direct measurement of string tension on the rig the calculated results are, of
course, just as accurate as for a complete string.
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jdowning
Oud Junkie
Posts: 3485
Registered: 8-2-2006
Location: Ontario, Canada
Member Is Offline
Mood: No Mood
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As 'classical' guitar strings the previously tested wound strings at guitar pitch gave a tension on the test rig (at 61 cm string length) as
follows:
String #1 - low E, sixth string - tension = 5.3 Kg
String #2 - low E, sixth string - tension = 6.1 Kg
String #3 - fifth string, A pitch - tension = 6.0 Kg
I am not familiar with classical guitar tensions (they usually are vaguely designated as 'light', 'medium', 'heavy' tension etc) but assume that the
above tensions are not out of line.
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jdowning
Oud Junkie
Posts: 3485
Registered: 8-2-2006
Location: Ontario, Canada
Member Is Offline
Mood: No Mood
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Interesting to speculate here (on the basis of the tests on the three guitar strings) that oud players of the late 19th early 20th C may have switched
to using European guitar strings (then gut trebles and close wound copper on silk filament - later nylon trebles and copper wound on nylon filament)
from the all gut/silk strings of earlier times. This would allow use of an oud design with a more convenient shorter string length of say 60 to 63 cm
and enable a lowering of the pitch to the current Arabic tuning of say C E A d g c' (rather than high f' gut tuning) still in general use today. If
this is the case then the ouds of this string length and size seen today may be a relatively 'modern' innovation (late 19th C).
Indeed, forum member Jameel reported in the topic 'Oud or lute?' on this forum that kanun player Dr George Sawa once told him that "all old ouds
before the turn of the 20th C had this (elongated) shape and that the wider bigger ouds are relatively new."
The large old oud - subject of the discussion on the topic 'Oud or lute?' - is currently owned by Richard Hankey awaiting restoration. The sound board
is missing but it may be speculated the dimensions conform to a string length of about 67.5 cm which fits nicely with the estimated size of both early
(gut strung) ouds and lutes. The extra string length was necessary to provide adequate performance of the gut basses but in turn limited the highest
pitch of the gut or silk trebles to about f' (A440 pitch standard).
As mentioned earlier in this thread little is known about the early gut basses and there is much speculation about how the strings were made so that a
lute of the 17th C (10 or 11 courses) could have a range of the open strings of 2 1/2 octaves without adding extra weight to the strings or making
them like little ropes when writers of the period makes no mention of the strings being other than just being plainly twisted in construction.
Marin Mersenne in his monumental theoretical work 'L'Harmonie Universelle', Paris, 1636 in book three page 167 writes that "le son des grosses cordes
de luth est appercue de l'oreille durant la sixiesme partie ou le tiers d'une minute". As if to confirm performance to future doubting readers of the
21 st century, Mersenne goes on to state that " ... c'est à dire pendant que artere (?) du poux d'un homme sain,& sans emotion bat dix , ou vingt
fois".
(.. that the sound of the largest (diameter) strings of a lute is perceived by the ear to last for a sixth or a third (part) of a minute - that is to
say while the pulse of a calm healthy man beats ten or twenty times.)
Here Mersenne confirms that the gut bass strings of his day had a performance that no modern made gut string can come close to matching (as well as
confirming that a healthy Parisian male had a pulse rate of 60 beats per minute). Indeed, string sustain of the previously tested wound strings (61 cm
string length) has been measured to be between 15 seconds and 20 seconds on the string test rig - similar to Mersennes gut basses!
No wonder that there was a general switch from plain gut to wound basses as these strings became more generally available. We have some idea as to
where some of the early lute strings in the European centres were made but what about oud strings? I suspect that many of the early gut and silk oud
strings were made in the Moorish controlled Iberian Peninsula where silk and wool production were the primary agricultural industry (until destroyed
by punitive measures in the late 16th C after the Christian conquests). Persia - an early centre of the silk trade may also have been a candidate.
But what about the wound strings? Were these made in the Middle Eastern regions or just conveniently imported as guitar strings from Europe? If the
strings were not imported where were they made and by whom? Is there any information out there about this?
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