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Author: Subject: Oud Strings, Calculations and Tuning.
jdowning
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[*] posted on 7-18-2012 at 12:23 PM
Oud Strings, Calculations and Tuning.


Thanks to Yaron Naor and Yair Dalal, I recently had the opportunity to examine some old gut and wound copper on silk core oud string fragments (see the topic 'Repairing a "Nahhat" Oud' on this forum).

In order to determine the physical characteristics of each string fragment, it was necessary not only to accurately measure the string outside diameters and the diameters of the windings (as well as confirming the materials of construction) but to undertake some basic calculations to determine string tensions and operating limits of pitch dictated by string breakage (upper limits) and inharmonicity (lower limits) for varying pitch standards (A440, A415 and A 392). This exercise confirmed that the strings (six double courses) were originally probably tuned to Arabic tuning CEAdgc'.

Forum members Alfarabi and Brian Prunka made the interesting observation that the old ouds (made before 1950 when gut and wound silk strings were the norm) generally are considered sound 'better' when tuned a semitone or a full tone lower than A440 pitch standard yet there seemed to be no reason given in the literature as to why this should be.

The answer - as far as the European gut strung lute is concerned - is that string breakage of the first course is the limiting factor. So, for example, one of my lutes - a copy of an historical original - with a string length of 60 cm, if strung with plain gut, can be taken no higher in pitch than f' if the top string is to last more than an hour or two before breaking. A lute of this string length is generally designated as tuned in nominal G tuning i.e. with the top string at g' which is possible with gut but not really practical due to the potentially short string life. With modern plastic strings it is possible to take the top string to g' without string breakage problems. However I have found that on this lute - although strung with modern strings - sounds more resonant and responsive when tuned a full tone below G tuning.

However, this is not the case with an oud of the same string length where the top string (Arabic tuning) is at a lower pitch of c' - no breakage limitations here. So, why do the old ouds fitted with modern strings sound better when tuned down a semitone or a full tone below standard A440 pitch?
I don't claim to know the answer - but I have a suspicion and would be interested in ideas that other members might have.

In the meantime, I thought it might be useful and of general interest, to go through - in detail - the procedures and tools that I used to calculate the string properties of the old oud string fragments (comparing gut with modern nylon stringing) so that anyone with a pocket calculator and readily available special slide rules might be able to undertake their own string calculations without having to delve into and understand all of the complexities of string design theory.

So that's the challenge - lets see how it goes!
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[*] posted on 7-18-2012 at 12:28 PM


One possibility is tuning lower allows for thicker strings which sound warmer. This is particularly relevant if using lower tension. A related possibility is materials like nylgut or PVF develop a distinct twang at lower tensions which are made more practical at lower tuning; to my ear using nylgut or PVF at higher tensions makes them sound a bit choked and lifeless.
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[*] posted on 7-18-2012 at 02:05 PM


Is it possible that older ouds sound better at lower pitch due to factors involving the wood, the neck angle, the resonating cavity, and other non-string factors? I am remembering my 1965 Khalife oud. I got it new in 66 or 67. For the first 25 years it sounded good at standard pitch Arabic tuning with the first course at cc. I used LaBella oud strings or different brands of classic guitar strings at appropriate gauges. No matter what strings I used the oud responded well at standard pitch. Occasionally circumstances dictated that it needed to be tuned a bit higher. No problem. But then, starting in about 1998 this oud not only sounded better at lower pitch but it if left unplayed for several days it would drift down between a half step and a step in pitch. The oud would be pretty well in tune with itself, just lower than where I left it. This oud simply wanted to sing lower. It's scale was 61cm by the way. I think that changes in the soundboard and neck angle might have been a factor.Once the oud began to show its preference for lower tuning if I would tune it up to standard pitch it responded less readily than when the strings were just a bit slacker.
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[*] posted on 7-18-2012 at 02:14 PM


Interesting thought. Both the 2006 Sukar 213 I used to own and the 2011 Michael Moussa GamilGeorges replica I currently own resonate better at certain lower tunings e.g. the Sukar was great at anything below standard where as if you tune the Moussa anything more than a halfstep down the third course sounds unusually dead. So I think you could say the Moussa likes lower tuning a little bit less. What's interesting is both ouds' tuning will drift downwards but the relative tuning of each course will be correct and the strings in each course will almost always be perfectly in tune with one another. I never calculated the neck angle of either oud but they feel relatively similar for whatever that's worth.
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[*] posted on 7-19-2012 at 03:02 AM


Quote: Originally posted by Jody Stecher  
Is it possible that older ouds sound better at lower pitch due to factors involving the wood, the neck angle, the resonating cavity, and other non-string factors? I am remembering my 1965 Khalife oud. I got it new in 66 or 67. For the first 25 years it sounded good at standard pitch Arabic tuning with the first course at cc. I used LaBella oud strings or different brands of classic guitar strings at appropriate gauges. No matter what strings I used the oud responded well at standard pitch. Occasionally circumstances dictated that it needed to be tuned a bit higher. No problem. But then, starting in about 1998 this oud not only sounded better at lower pitch but it if left unplayed for several days it would drift down between a half step and a step in pitch. The oud would be pretty well in tune with itself, just lower than where I left it. This oud simply wanted to sing lower. It's scale was 61cm by the way. I think that changes in the soundboard and neck angle might have been a factor.Once the oud began to show its preference for lower tuning if I would tune it up to standard pitch it responded less readily than when the strings were just a bit slacker.


I was directed to this thread by Alfarby with these remarks "There's a hanging question in the forum about this issue here, : http://www.mikeouds.com/messageboard/viewthread.php?tid=13176 that has not been concluded yet. Please Master, tell us there what do you think about this issue.
Waiting to learn more about this question"

To me this issue is highly complicated. But I suppose there is one answer to be near the mark: We all know that inner force vectors of a construction at the shape of a dome are in the direction to the edges of the dome thus a dome is the most stable construction. You can not break an egg squizing it in your palm in the direction of the long axis.
As the oud gets aged a dome-like shape starts to buil up in front of the bridge and at the back of it. These areas traverse when the instrument is plucked and are dominantly responsible for the sound characteristics of the instrument. Having become dome-like these areas are now more stable than before. This is associated with a shift of the resonant areas. Formerly these back and front areas were more resonant against the fundamental frequencies of the higher pitche strings likewise of the higher pitche sounds but now they became more resonant against the second, third and fourth harmonics of the lower pitche strings likewise of the lower pitche sounds .
This is only a proposition to handle the issue and understand what is going on with the aged instruments. I think this approach of mine is worth to be discussed.




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[*] posted on 7-19-2012 at 05:12 AM


These are some interesting comments. I can confirm that the observation that ouds seem to automatically find their optimum pitch level has also been observed in lutes. This suggests that the instruments over time adjust to overstress due to string loading - local stresses that are relieved or redistributed not only in wood movement/distortion but also in glued joints temporarily relaxing slightly - particularly under conditions of high temperature and humidity.

Too high a stress may also result in an instrument sounding 'tight' or less free in its response as noticed by ameer. It is interesting that ouds are strung with heavier plain strings in the upper courses (compared to lutes) and no doubt this is to help give a 'warmer' sonority - thicker strings having less upper harmonics that are in tune with the fundamental. However, due to this inharmonicity, there is a limit as to how far one can go before a string becomes unacceptably dull in sound. This lower limit is dependent upon a number of factors - personal preference, the way a string is sounded, acoustic performance of the instrument etc. For a plain gut strung lute of 61 cm string length for example, with the strings sounded with the soft fingertips, the lower limit is around B at A440 standard pitch. For an oud this limit may be a bit lower due to the strings being plucked with a risha that increases somewhat the range of upper harmonics sounding.
Therefore, for an oud of 61 cm string length and Arabic tuning, plain gut trebles should serve for the first three courses (although they would likely not sound as bright to modern ears as modern plastic string equivalents).
The lower limitation may be increased by making a string more elastic (a higher degree of twist or use of roped construction) or by use of composite (wound) strings that are thinner and more dense than plain strings.
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[*] posted on 7-19-2012 at 05:29 AM


This thread makes me want to try gut strings.
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[*] posted on 7-19-2012 at 11:51 AM


Very interesting . I knew we could count on Mr. Downing :)

I wrote to Master Faruk in his Jamil George's thread that:

"I have had tens of Arabic ouds during the last 35 years I've been in the oud world. Some were very old and some were newly born, Syrian, Egyptian, Iraqi, Moroccan, Palestinian .... Every single one of them sounded better to my ear when tuned F instead of G. This of course might be a subjective preference, not a scientific conclusion. "

Well, it's not only old ouds respond "better" in low pitch. All ouds, not only Arabic, resonate in a mellow & soft mode when tuned a whole step lower. even a Manol 1904 sounded even greater on F instead of G.

Does this remind of viola tuning compared with violin tuning ? Is there any similarity between the two cases ? I don't really know how to tune a viola nor a violin, but the warm sound of the first just crossed my mind, so excuse me if this question does not fit in. Just an idea/question !

To make this even more complicated: Why is a Turkish oud tuned a whole tone higher ?!
Oh yea, WHY ? Are we allowed to Turkish-tune an Arabic oud without replacing the strings ? This involves another issue: strings. The lower you go, the thicker you choose & vice versa !! Does this make any sense or am I just distracted/ing ?

Yours indeed
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[*] posted on 7-19-2012 at 01:39 PM


Tuning an Arabic oud to Turkish tuning (with appropriate considerations to tension of course) can be quite interesting. Two very different examples that come to mind are Amir Amouri's performances with Sabbah Fakhri where they use Turkish tuning and the recording of Farid El Atrash and Muhammad Abdel Wahab where they use Turkish tuning without the high D.
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[*] posted on 7-19-2012 at 11:39 PM


To those contemplating different tunings, tuning an Arabic oud up two half-steps to Turkish tuning WILL develop more tension than on an Arabic tuning, that's obvious. Normal tension on an oud string is around 2.5-3.5 kg (on a Spanish guitar, stronger in build, double that is customary - roughly the same strings are pulled to higher pitch on a longer scale). Whether this is OK depends on the string set and the oud. If the oud has a relatively short scale, below 600 mm, it can be fine. But if the strings are relatively thick, or the scale is longer, or both, the tension (over 4 kg) may well damage the instrument. It is said that ouds cannot tolerate tensions over 5kg per string. But 4 kg is already a lot. Specifically what happens is that the tension will 1) stress the bracing and soundboard, braces may come unglued, the soundboard may distort/buckle 2) pop the bridge, which is normally just glued onto the soundboard. The higher the bridge, the more stress develops under tension (leverage). If the glue "gives" in a slingshot moment, the bridge goes flying. It's a disturbing event, but a simple repair. If the glue is very strong (Aliphatic glues are not a good idea for the bridge) and the tension very high, part of the soundboard can come off with the bridge. Catastrophic.

So, Alfaraby, we ARE allowed to tune a Turkish short scale oud either Turkish or Arabic. It may sound weaker down-tuned Arabic, or it could sound great. But it's a generally a very bad idea to tune an Arabic (longer scale) oud up to Turkish unless the string gauges are thinner than normal. In any case it takes some study and caution.

As to WHY Turkish ouds are tuned that way, it could be because the shorter scale Turkish ouds sound better with Arabic strings pulled up to the same tension (as on an Arabic longer scale oud) by raising the pitch, but they could have used thicker strings, so that's not much of an argument. That's like the theory that it's because their demented notation has confused them. Could it be because other Turkish instruments prefer to make D = Rast and not C?

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[*] posted on 7-20-2012 at 02:49 AM


Quote: Originally posted by ameer  
Farid El Atrash and Muhammad Abdel Wahab where they use Turkish tuning without the high D

Without the high D, it would be AEBGD instead of CGDAF. This means 1.5 tone lower than A440 ! Sunbaty also played on this tuning, as much as I can recall, in several recordings.
Is this right ?

Yours indeed
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[*] posted on 7-20-2012 at 04:15 AM


You're right that it is 1.5 tones down from A440. As for Sunbati I'm not aware of him using this tuning but given that Qassabgy, Abdel Wahab, etc tried it it wouldn't surprise me.
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[*] posted on 7-20-2012 at 03:39 PM


Well, ouds (and lutes) may sound better at a lower pitch as they age but human beings may not hear better as time passes. Perhaps this is a reason why an instrument is perceived to 'improve' with time but at a lower pitch than original?
Loss of hearing (Presbycusis) - particularly of the higher frequencies - is an inevitable and irreversible part of the aging process which may be 'amplified' (!) by genetics,gender, race and ill health as well as exposure to loud noise (rock concerts and other over- amplified music etc.). The loss of hearing starts at about the age of 8 years and slowly becomes measurable by the age of 60+.

Interestingly the trend in lutes from the late 16th C was to add more bass courses to the nominal 6 or 7 course lute of the
16th C culminating in larger solo lutes with 13 or 14 courses by the mid 18th C at which time the lute went out of fashion in Europe. Yet the development of the oud never appears to have exceeded 7 courses throughout its history - perhaps compensating in some cases by working with relatively thicker strings and lower tunings than found on lutes with the same string lengths?

So when an oud appears to sound better at a lower pitch after a period of 25 years or so, is this due to physical changes within the instrument itself or due to a slow deterioration of the hearing ability of its owner the auditor?

So we will all suffer from this ailment to a greater or lesser extent as we age but - hopefully - not to the extent experienced by poor English lutenist Thomas Mace (Musick's Monument, 1676) who in 1672 at the age of about 59 found it necessary to invent a new, louder lute (the Lute Dyphone) with 50 courses so that he could continue to play despite a serious hearing loss. Even then his affliction was so severe that he could only hear all that he played by holding the edge of the sound board in his teeth - the sound being transmitted satisfactorily to his brain in that manner!! Now there is a dedicated musician!
Nevertheless the Dyphon never did 'catch on'.

Mace 1 (600 x 344).jpg - 103kB Mace 2 (600 x 323).jpg - 48kB
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[*] posted on 7-20-2012 at 05:03 PM


In my case it had nothing to do with hearing loss. Since the time I acquired that oud any number of string instruments of all vintages passed through my hands and none of them tuned themselves down to where they sounded better and none of them sounded better when I deliberately tuned them down. This was true for instruments that were both older and newer than this particular oud. Had it been a matter of subjective perception surely it would have applied to my guitars etc.

And since typical hearing loss is of high frequencies why would a lower pitch appear to provide the missing highs? I suppose one could argue that a lower fundamental creates lower harmonics and the upper partials become more audible when a string has a lower tension and therefore a lower fundamental. But I think the issue here is not string behavior but the behavior of the resonating box called oud.

Quote: Originally posted by jdowning  




So when an oud appears to sound better at a lower pitch after a period of 25 years or so, is this due to physical changes within the instrument itself or due to a slow deterioration of the hearing ability of its owner the auditor?


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[*] posted on 7-20-2012 at 05:58 PM


My thought here was only another general theory to add to the others already expressed on this thread and was not intended to be directed at you personally Jody Stecher.
Rightly or wrongly my thought is that the lower pitch does not provide the missing upper harmonics - only that lower frequency harmonics remain audible.

Incidentally there are audio tests available online to check for the incidence of hearing loss over time for those curious about how well (or not) they can hear. One website even suggests that it is musicians who are most likely to suffer greatest from this ailment - not sure why.

So it was only the oud - among all of the other instruments that passed through your hands - that auto-tuned itself downwards to sing better at an optimum pitch level? Could it be that this phenomenon is only to be observed in ouds and other related instruments like the lute? If so, I wonder why?
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[*] posted on 7-20-2012 at 06:37 PM


Hi jdowning,

I put my responses in italics between your lines in the quote box below. Hmmm, probably not an optimum way to respond to individual points. Oh well, I'll give it a whirl this one time.

Quote: Originally posted by jdowning  
My thought here was only another general theory to add to the others already expressed on this thread and was not intended to be directed at you personally Jody Stecher.

Sure, I understood that.

Rightly or wrongly my thought is that the lower pitch does not provide the missing upper harmonics - only that lower frequency harmonics remain audible.

that's what I meant

Incidentally there are audio tests available online to check for the incidence of hearing loss over time for those curious about how well (or not) they can hear. One website even suggests that it is musicians who are most likely to suffer greatest from this ailment - not sure why.

perhaps they equate "musician" with "rock musician". In the latter category, hearing loss is a common occupational hazard


So it was only the oud - among all of the other instruments that passed through your hands - that auto-tuned itself downwards to sing better at an optimum pitch level?

yes

Could it be that this phenomenon is only to be observed in ouds and other related instruments like the lute? If so, I wonder why?

that's what we're all trying to find out here.
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[*] posted on 7-21-2012 at 04:21 AM


Your system of relating quote and answer seems to work well enough. Happy that we are all working on the same page!

I guess that they were referring not only to 'rock musicians' but also to all those who regularly listen to or play over amplified music. This of course is a fairly recent occupational hazard for musicians and music lovers of all stripes. However even if one manages to steer clear of occupational sustained high noise levels (by wearing adequate ear protection in a commercial woodworking shop environment or when operating heavy machinery for example) - the hearing loss due to aging for everyone would seem to be inevitable to a greater or lesser degree dependent upon a number of factors already mentioned - and would likely be the same (or worse) for a person living in earlier times.
Just a thought.

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[*] posted on 7-24-2012 at 12:21 PM


Out of the multitude and variety of Arabic tunings I am curious about the origin of the Arabic tuning F A d g c' f' (or F2 A2 D3 G3 C4 F4 in American nomenclature). I assume that the first course here is tuned to F above middle C - i.e frequency 349 Hertz and not down an octave (re-entrant tuning found on some of the longer string length European lutes)?

Does anyone know when this tuning first appeared historically? Does it only go back as far as the 1950's (Bashir style ouds) or is the history more ancient?
For a string length of 61 cm, f' would be the upper practical limit of a gut first course if frequent string breakage is to be avoided.

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[*] posted on 7-24-2012 at 12:49 PM


You can hear that George Michel has a high f string on the oud he used on a 1960s LP recording "Authentic Instrumental Music by the Most Famous Arab Artists". This is certainly a fixed bridge oud. It seems to be a 7 course oud since low C is sounded several times.



Quote: Originally posted by jdowning  
Out of the multitude and variety of Arabic tunings I am curious about the origin of the Arabic tuning F A d g c' f' (or F2 A2 D3 G3 C4 F4 in American nomenclature). I assume that the first course here is tuned to F above middle C - i.e frequency 349 Hertz and not down an octave (re-entrant tuning found on some of the longer string length European lutes)?

Does anyone know when this tuning first appeared historically? Does it only go back as far as the 1950's (Bashir style ouds) or is the history more ancient?
For a string length of 61 cm, f' would be the upper practical limit of a gut first course if frequent string breakage is to be avoided.







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[*] posted on 7-24-2012 at 01:12 PM


Whoops, I posted before finishing my thought. Apologies if the following is too obvious:
My idea, which is meant to be descriptive, not historical, is that a high F course added to the tuning C F A d g c' yields C F A d g c' f.' And then dropping the low C yields F A d g c' f'.
Looked at another way it is simply moving up by an interval of a 4th the tuning of C E A d g c'. But perhaps by "origin" you mean "who did it first"? My guess would be that it was someone with access to nylon strings.
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[*] posted on 7-24-2012 at 01:16 PM


According to Simon Shaheen Qassabgy introduced the high F some time around the middle of the century. I can't find the interview link, but it was the Afropop interview in 2003 I think.
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[*] posted on 7-24-2012 at 05:51 PM


Thanks Jody Stecher and ameer. Interesting.
Yes I am curious to know when this tuning may have first been introduced. So far around 1950 would seem to be the case?

For a 'standard' Arabic style oud of around 61 - 62 cm string length, this tuning would still be feasible with plain gut trebles so might still have been used before nylon strings became generally available for the oud.
The 'rule of thumb' upper practical limit for low twist plain gut strings (based upon frequency of breakage) is that the product of tone frequency (Hz) X string length (metres) should not exceed a value of about 210 (source E. Segerman, N.R.I. Instruments) So if a 61 cm long first course is tuned to f' - i.e. 349 Hz at A440 standard - then 210 X 0.61 = 213 or just about good enough. The string pitch can be increased above this limit but string life might then be only a matter of minutes or hours before breakage occurs.

Whoever introduced this high f' tuning was presumably seeking a brighter tonality - a move away from the traditional deeper, darker sound of the Arabic oud so another indication that this might have been a mid 20th C innovation perhaps - or does this tuning have its origins during a much earlier period for different reasons?

For the European 6 course gut strung lute f' first course tuning would have been the norm for a nominal tuning of G c f a d' g' i.e. tuned down a full tone. The top string was tuned as high as possible to help make the thicker, lower plain gut strings sound better (with the help of octave strings to brighten the sound or by employing greater string twist to improve string elasticity - that is before wound strings as we know them today (late 19th C) were invented). For a plain gut string 61 cm long this lowest acceptable limit (due to inharmonicity - out of tune upper harmonics causing the string to sound dull) is around B 98 Hz perhaps slightly lower for a string sounded with a risha.
So one has to wonder, therefore, what type of bass strings were used on five or six course ouds prior to the 19th C and what was the pitch of the first course as a consequence.
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[*] posted on 7-24-2012 at 06:24 PM


In listening to the Qassabgy taqsims on this site you can hear him using a high F by 1939. See http://www.mikeouds.com/audio/qassab/qassab_taqsim_hijaz_kar_kurd_1...
Note that it is hard to determine the natural pitch of these recordings do the quality of the initial transfers, but given the time period and other Qassabgy recordings it is likely that he tuned a wholestep down making it a high Eb rather than F.
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[*] posted on 7-25-2012 at 05:51 AM


In addition to plain gut strings it is likely the oud was also fitted with wound basses - copper wire on silk filament core - giving a brighter more balanced sound overall.

On the string technology front I should mention that the useful frequency X string length product used for judging the upper limit of gut due to string breakage (210 or less) can also be used to determine the lower limit of a plain gut string the product f X L being equal to or above about 80 before the sound is so dull that a change to wound strings is necessary. This lower limit value is subjective and depends upon the how a string is sounded (plucked or bowed), the acoustic quality of an instrument and the tolerance of a listener to the sound quality.
The same limits apply to plain plastic strings except that they can be taken to a higher pitch limit than gut (the limit for nylon, for example, is about four semitones higher). At the other end of the scale, however, plain gut can be taken down to a lower pitch than plain nylon (about three semitones lower).

Gut strings can be taken to a lower pitch if they are made more elastic by providing more twist to a string or by making the string like a cord or rope by combining two or more threads together. By this means a plain gut string with higher twist,
61 cm long can be taken down to F and a roped gut string down to C (source E. Segerman, NRI). The downside is that the more highly twisted strings will break at a lower tension than those of low twist so should not be considered for use in the upper courses. Whether or not ouds in the 15th or 16th C used the same string technology as the European lute is, of course, not known (it is not perfectly clear in the case of lutes either).

The other possible historical method for bass string design is to add weight uniformly to a string without increasing the string diameter (achieved today by means of wound string design). Mimmo Peruffo of Aquila Strings has experimented with this possibility by adding metal powders or salts to gut strings pointing to evidence for weighted strings in the iconography (coloured strings - possibly loaded with mercury or iron salts/powders) and in the small diameter string holes measured in original lute bridges - too small to accommodate strings made from untreated gut.

I have never tried it but a few years ago some lute players advocated twisting plain nylon strings to improve elasticity. This was achieved by mounting a string on a lute, threading the string though a peghole and applying the required amount of twist before wrapping the string around the peg and bringing it up to tension. I suppose that these days the availability of denser PVF strings now makes this practice unnecessary. I must try it some time on my string test rig just to see how well (or not) it might work.

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jdowning
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[*] posted on 7-26-2012 at 12:21 PM


Given the upper and lower tonal limitations of gut strings, the way to go for greatest tonal range - given all gut stringing (i.e. prior to availability of close wound bass strings) - is to increase string length (to extend the lower range) and to pitch the top string as high as it will go practically.

Some of my recent studies of early oud and lute geometries (see 'Old Oud compared to Old Lute Geometry, page 2) suggest that the string lengths of some ouds (Al-Kindi, Kanz al-Tuhaf and Ibn al-Tahhan) and lutes (Laux Maler) dating from the 9th to 16th C may have had string lengths consistently measuring 67.5 cm in length - dependent upon the ancient standard of measure chosen (a 'finger' unit ranging in value from 1.875 cm (Egyptian) to about 2.25 cm (Persian). For a plain gut first course this would give a maximum practical pitch at A440 standard of about e' (330 Hz) or f' (349Hz) at A415 standard.

So this might suggest that the Arabic tuning F A d g c' f' historically came well before (centuries before) the current C F A d g c' with its lower pitched darker tonalities - achieved by adding the lower C and removing the upper f' - only made possible on a shorter 61 cm string length oud by the invention of close wound silk filament bass strings first available in the late 19th C?
If so, a 14th C 67.5 string length, gut strung 5 course oud might have been tuned A d g c' f' (i.e. in fourths) by eliminating the low F course - the A course then just about being the lowest pitch limit for a plain low twist gut string (at A415 standard) or a pitch easily achieved with a higher twist plain gut string (lowest pitch limit about E). So the next step historically from a five course low twist gut strung oud tuned A d g c' f' to six course F A d g c' f' would have been made possible by simply increasing the degree of twist of a gut string from about 25° (low twist) to about 45° or so (high twist).

Note that historically both plain gut and silk strings were used on ouds - silk being about the same density as gut but a bit stronger.
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