Mike's Oud Forums

Turkish interval system: tone breakdown and its usage

SV_T_oud - 11-16-2014 at 09:30 AM

I'm getting more familiar with Turkish music system but I'm still far from complete understanding of its organization. There are bits and pieces all over the Internet but not much information clearly presented in one place.

One of the questions I have is why out of 9 comas making up one whole tone only the 1, 4, 5 and 8 coma values get practical application in Turkish Art Music?

I understand the choice of 4 and 5 comas: they are located in the middle between the base tones and both can logicaly represent half-tone with little deviation from it which for some can be hardly noticeable.

However why the 1 and 8 comas instead of 2 and 7? If it were 2 and 7 they would quite reasobably represent quarter tones. In comparison 1 and 8 look (please note I don't say 'sound') more like errors rather than intentional displacements from the core base tones.

SV_T_oud - 11-16-2014 at 09:57 AM

I just realized that I probably asked a wrong question in respect to the application of the Turkish comas.
My question assumes the whole tones are a mainstay and comas are deviations from the mainstay. That would be correct if we were deriving the chromatic notes from the Turkish system of intervals.

However as far as I understand there are no such things as chromatic intervals in Turkish music. Am I going in the wrong direction again? Sometimes I feel like I confuse myself with incorrect usage of the terms.

So, I just realized the comas are not deviations from the mainstay but they themselve constitute the mainstays. Does it make sense?
In that case the 1 and 8 coma locations are more clear for me although I can't judge yet how good those choices are.

Anyway, what about chromatic notes in the Turkish music. Can the comas be applied just like chromatic deviations?
Sorry... I'm getting more and more confused.

abc123xyz - 11-16-2014 at 10:30 AM

The intervals used in music, Turkish and otherwise, are based upon mathematical ratios that, in certain combinations and sequences, affect the pattern-recognizing regions of the brain in a way we call musical.

When these intervals get laid down in order on a piece of paper for examination, as frets on the neck of a lute, etc. they don't necessarily produce an evenly spaced pattern, nor do they need to.

Western equal temperament, which does produce such an equal spacing, is an artificial creation, an expedient to allow for standardized design and tuning of musical instruments and western orchestration, and none of its intervals, except the octave, correspond to the natural intervals based upon the simplest ratios.

The Turkish comma system is actually an artificial creation itself, created by theorists, and also an approximation to the natural system. Although, as you'd expect, with a larger number of divisions it can more closely approximate the natural tones than Western equal temperament can.

So we shouldn't expect an even or symmetrical use of every comma location available.

David

Brian Prunka - 11-16-2014 at 10:49 AM

Just think of the 1 and 8 cent versions the same way you though of the 4 and 5 cent version, but just in reference to the other notes in the scale, rather than 0 and 9.

C D E = 0 9 18
C D Eb = 0 9 13 (i.e., Eb=18-5)
C Dd Eb = 0 8 13 (i.e., Dd=9-1)
C Db Eb = 0 4 13 (i.e., Db=9-5)

Make sense?

DavidJE - 11-16-2014 at 01:53 PM

Wow, I just wrote a long and detailed response to this and accidentally hit the back button and erased it all!

So, I think I understand your questions and issues here. Briefer this time...

The comma system is a theoretical system that does not represent actual practice/performance. I assume the theorists decided to limit notation to only one comma flat or sharp of any whole or half tone to avoid having accidentals for 1 comma flat, 1.5 commas flat, 2 commas flat, 2.5 commas flat, etc. In practice/performance different intervals are used. For example:

The note named buselik is written as a "B". The note named segah is written as a "B-one-comma-flat", but it is most definitely not always played as one-comma-flat. In the makam Ussak it is probably 2 or even 2.5 commas flat on average. In the makam Rast it's probably between 1 and 2 commas flat. However, even within a makam like Rast or Ussak there is no fixed position for segah. The flatness of the note changes depending on whether you are going up or down, what notes are prominent before and after, etc.. This leads to a richness in sound, and even a richness in personal playing style. Different players might play segah more or less flat in different situations. Sometimes segah is closer to dik kurdi than it is to buselik, and sometimes vice versa.

Does that make sense?

Think of 1 and 8 as just meaning "sharper" and "flatter". When you see 1 and 8 in NOTATION or THEORY, it really could be 2 and 7 in PERFORMANCE. 1 and 8 just means "sharper" and "flatter".

This is why it's VERY useful to have someone with a lot of experience as a teacher. I don't think anyone who isn't an experienced musician will recognize if something is "one comma flat" or not, if it is indeed only one comma flat, and especially within the context of a quickly moving piece of music. HOWEVER, I do think there is a subtle difference in the sound/feeling of the music due to these small variations. I do think they add a richness to the music.

SV_T_oud - 11-16-2014 at 05:06 PM

All is fine with comas - makes sense. However what about "chromatics" in Turkish makams? For instance where you have a whole tone of 9 comas can you put an accidental at 4 or 5 or... let's go right in the middle in Western style: 4.5 ?
I assume 'NOT' bacause it would ruin the particular makam. Correct?

So, it other words, when you play a certain makam, let's say the Cargah (Chargah) which according to L.Signel is the most close makam to the Western major scale (9949994 in comas), do you have a freedom to split any of the 9's in half or are you limited to only the "diatonic" tones? Sorry about diatonic - of course it has not much meaning here but it's the best definition I could find because I didn't want to call the notes 'fixed' since they are not.

SV_T_oud - 11-16-2014 at 05:14 PM

Quote: Originally posted by DavidJE  
Wow, I just wrote a long and detailed response to this and accidentally hit the back button and erased it all!
....


I get very frustrated when it happens. I remeber when I had that happening two times in a row maybe in the course of a few days I started to copy the message post before hitting the 'Post' button. You know those forums with a short timeout logout?
However once it doesn't happen for awhile I forget to copy and then.... AGAIN!

SV_T_oud - 11-16-2014 at 05:46 PM

One more question if you don't mind. Not exactly on the subject but very related.

When on Turkish tanbur (the long necked lute) the fret positions are identified as Makam names, i.e. Yegah-Asiran-Irak-Rast-etc. starting from the nut (Yegah) is it safe to say we can relate that fret position to the makam it names and develop our taqsim in the corresponding makam from that fret?
I'm not sure the makams can be transposed on the tanbur neck with fixed fret positions or... can they?

By the way, since the tanbur frets are somewhat "fixed" and cannot be moved on the fly is tanbur playing considered more limited compared to oud in this respect?

Brian Prunka - 11-16-2014 at 06:02 PM

Quote: Originally posted by SV_T_oud  
All is fine with comas - makes sense. However what about "chromatics" in Turkish makams? For instance where you have a whole tone of 9 comas can you put an accidental at 4 or 5 or... let's go right in the middle in Western style: 4.5 ?
I assume 'NOT' bacause it would ruin the particular makam. Correct?

So, it other words, when you play a certain makam, let's say the Cargah (Chargah) which according to L.Signel is the most close makam to the Western major scale (9949994 in comas), do you have a freedom to split any of the 9's in half or are you limited to only the "diatonic" tones? Sorry about diatonic - of course it has not much meaning here but it's the best definition I could find because I didn't want to call the notes 'fixed' since they are not.


Traditionally, chromatic playing like that is not typical for traditional music, but it has become more common, probably due to Western influence. It wasn't even that common in Western music until the adoption of Equal Temperament because a succession of more than a couple of unequal semitones sounds a little weird (one or two are fine but if you heard a non-equal chromatic scale it is a little strange),

So yes, you can use chromatic passing tones.
It does detract from the maqam somewhat; it is a more modern affectation but at this point it's an accepted practice. It pretty much only occurs where you have a whole tone. Note that the minor whole tone is 8/9 so you can actually divide it in half. The major whole tone cannot be divided in half using the comma system.
If you have any thing less than a whole step, you can't really use a passing tone.


A Western major scale, by the way, I think would actually be 9 8 5 9 8 9 5. The ET version is only an approximation.

Diatonic and chromatic mean the same thing here as in western music, it's just that we have more alterations to choose from.

Diatonic = belonging to the scale
Chromatic = non-diatonic

So if you have, say, Husayni: A Bd C D E F+ G A, those are the diatonic notes. Anything else would be chromatic.



Theory is a follower to practice—this stuff should come from listening. Trying to square it with theory is a waste of time, IMO.

As David notes, the music doesn't really follow the theory anyway, even in the basic makams.

Brian Prunka - 11-16-2014 at 06:07 PM

Quote: Originally posted by SV_T_oud  
One more question if you don't mind. Not exactly on the subject but very related.

When on Turkish tanbur (the long necked lute) the fret positions are identified as Makam names, i.e. Yegah-Asiran-Irak-Rast-etc. starting from the nut (Yegah) is it safe to say we can relate that fret position to the makam it names and develop our taqsim in the corresponding makam from that fret?
I'm not sure the makams can be transposed on the tanbur neck with fixed fret positions or... can they?

By the way, since the tanbur frets are somewhat "fixed" and cannot be moved on the fly is tanbur playing considered more limited compared to oud in this respect?


The makams are named after the notes, not the other way around. The makam can be named after the tonic, a prominent note, starting note or just by the note that distinguishes it. So Kurd is actually the second note of the makam Kurd, not the tonic. It's just the prominent feature of that makam. Hicaz is the third note of hicaz maqam, etc.

Some makams can be transposed with fixed frets, it just depends on how many frets you have and whether those notes are there.

Yes, I would say that any fretted instrument is somewhat more limited than a fretless instrument.

Jody Stecher - 11-16-2014 at 07:30 PM

I can add two small things to Brian's 99.9% complete answer.

1) One of the meanings of "maqam" in Arabic is *position* or *station*, and this may shed light on the names of the frets and the pitches they produce.

2) The oud and other fretless instruments provide unlimited opportunities to play out-of-tune in ever new ways!

and one Big Thing: yes yes yes; theory describes existing music. Or tries to do this. When and where theory prescribes, the resultant music suffers. And so do the listeners.

SV_T_oud - 11-17-2014 at 03:10 AM

Quote: Originally posted by Brian Prunka  

... As David notes, the music doesn't really follow the theory anyway, even in the basic makams.


Brian - thanks a lot for you help and here are a few comments:

I agree but often one needs to understand initial set of rules in order to proceed with practice. For instance you mentioned about naming makams after prominent notes, not tonics. Without knowing that I would assume the latter and having had developed good ear I would have hard time struggling with recordings trying to match them to tanbur neck diagrams with fret names.

That's a very specific example but I knew people who gave up playing piano because they didn't learn about whole and half steps first. That may sound silly but the lack of that fundamental knowledge gave then troubles in related, still simple but higher level steps they've tried to take in order to progress. Of course they weren't good ear players but not everyone has to be.
Bill Evans, the great Jazz pianist (sorry, you know of course who he is) used to say that because he had not so good ear he had to break down everything to pieces and then assimilate and only then implement in his music. He could be modest of course but I doubt he would mention that if he didn't face that problem of some degree.

If you didn't tell me that 'Maqam note' not= tonic of the maqam I wouldn't know that! It's not in the book of L.Signel or if it's there I overlooked it.

I've tried to go without this forum but I found that many specific Internet resources on Mid-East music don't consider the basics.

SV_T_oud - 11-17-2014 at 03:14 AM

Quote: Originally posted by Jody Stecher  
...
and one Big Thing: yes yes yes; theory describes existing music. Or tries to do this. When and where theory prescribes, the resultant music suffers. And so do the listeners.


I agree again but someone envented that theory for some less initiated to get started. Also, bigs thanks to them because it helped to preserve precious music over the centuries.

hans - 11-17-2014 at 04:15 AM

Theory helps western ears to make sense of what they hear :-)

Jody Stecher - 11-17-2014 at 05:51 AM

Quote: Originally posted by SV_T_oud  
Quote: Originally posted by Jody Stecher  
...
and one Big Thing: yes yes yes; theory describes existing music. Or tries to do this. When and where theory prescribes, the resultant music suffers. And so do the listeners.


I agree again but someone envented that theory for some less initiated to get started. Also, bigs thanks to them because it helped to preserve precious music over the centuries.


The various theorists in the Ottoman and post-Ottoman world and also in the lands of Arab music(s), created their theories for various reasons. Some reasons were intellectual/philosophical, some were political, some mathematical, but to the best of my knowledge, helping the novice was not a motive.

In the worlds of maqam music and beyond I cannot think of a single example of theorists and their theories helping to preserve music. It has always been those who do the singing and playing who do the preservation. My pointing this out does not mean that I am against theory or theorists or that I am not interested in theory. It does mean, in part, that I could not properly hear and understand maqam music until I realized that maqam theories were neat and tidy systems that dealt insufficiently with the music of living musicians or of real musicians of the past whose musical style was to some extent in living memory of present musicians. Maqam theories, ancient and modern, tend to describe ideal Plantonic models where everything fits neatly. I could not square what my ears heard with what my eyes read. Once I realized that what I was hearing was maqam music and what I was reading was Beautiful Ideas, I was able to begin making sense of the music.

SV_T_oud - 11-17-2014 at 07:22 AM

Sure it reminds me of one quite hot thread on the AllAboutJazz forum with the fight mostly between two persons:

- One was insisting that music theory in Jazz is useless and everything should be played by ear. That one was very objetive and somewhat rude in his opinions. "Ear!!! - everything else is crap!" That was his point.
- Another one (Jerry Engelbach http://www.engelbachmusic.com/) was defending his point of view through his own experience. He admitted that before he could improvise by ear he spent years playing standards from the fake books. He is a well respected musician and quite modest and gentle in his judgements.

Many more well respected forum members in that thread admitted that majority can't play MODERN Jazz exclusively by ear: there are so many theoretical things embedded into that music that they cannot be picked up straight from recordings and appriciated as is by majority of the developing musicians. I emphasized 'majority' - makes sense? 'Developing musicians' also is a key word here.

Well, Jazz is not Mid-East music, it's much more complicated in some aspects. But as you can see there are people in the Jazz World who try to prove their point through ignorance. I'm not relating any of this to any of the previous posts in this thread, mind you! I just want to say that EVERYONE has his own way of obtainig knowledge. Some are natural ear players, others approach the destination through theory and practice and everything else in between.

I'm neither insisting that music theory should define practical performance but it's there to help especially to those, who are less gifted but still want to play music.

Jody Stecher - 11-17-2014 at 07:56 AM

Yes, there many ways of learning and several paths to musical competence and understanding.

Certainly the various conflicting maqam theories can serve as a door. That was true for me as well. But how can a "system" that prescribes 24 equal divisions of the octave help a novice musician to understand and perform music that does not make use of these artificial divisions? Arabic music before the era of the 24 tone accordion used a different set of microtones than the theory presents. According to my still developing and not perfected ears, today's better maqam musicians adhere to that, with a certain flexibility that allows for adjustment according to the type of music and the variations that exist in regional and personal styles.

In my opinion the relationship between theory and practice is entirely different in jazz. Jazz developed its harmonic ideas "in harmony" with theory, in accord with theory. As you say, the theory is embedded in the music. But Western chord theory is not a misfit with jazz. And there are not conflicting theoretical schools in "western music". In maqam music there exist conflicting and incompatible theories all of which adequately describe some aspects of the music and all of which ignore the inconvenient parts.

I think it is possible that we mean different things by "theory". I am not talking about tetrachords and the names of each maqam and the body of knowledge that describes typical modulations to another jins and I am not dissing traditional models of seyir (melodic pathways). I am recommending skepticism toward theoretical models that that exist apart from actual music.

SV_T_oud - 11-17-2014 at 09:56 AM

Oh, no, I also wasn't suggesting that if I understand how comas make up a makam it's all I need. It's just a *useful approximation* in order "to get into" the Turkish makam world but only on the surface for a start. If there is no better way to describe something we use what we have even if it's not perfect. And once again, if I had good a discriminating ear, I would be less interested in comas and makam names, etc. I would probably even wouldn't like to know what kind of music that is: I would pick it up by ear and play.

Someone hearing me play would say: "Oh, you play such a wonderful Turkish taqsim on this oud"!
And I would reply: "What oud? Ah, you mean this oval guitar with a short neck I got on a flea market yesterday? So you say it's Turkish music? I don't know - I just picked it up on the radio. Maybe it's Turkish, I don't care, I just like how it sounds."
- "Yes - but you play such beautiful music intervals, so nice 8-coma whole notes and so heart-touching 4-coma flats!"
- "Would you please stop insulting me! I just pluck these thin ropes and you hear what you hear - I don't care about... what you just said? - intervals? Not sure what you mean..."
:)

Brian Prunka - 11-17-2014 at 10:29 AM



It depends by what you mean by "theory" and by "ear" . . . some people call reading music "theory," which is not what we're talking about here. Yes, some amount of theory is necessary to even be able to communicate ideas but you are asking a specific question about microtonal intervals and the real answer is that these intervals are now and always have been learned and understood aurally and not through the theory. I still answered the question according to your parameters, but there is no way I can conscientiously answer the question without pointing out that the comma system does not match reality.

To some extent the theory attempts to provide guidelines for fret placement (Al Farabi, for example was explicit about this). However, in my experience, pro musicians typically end up refining the fret locations by ear if the instrument maker placed them according to the theoretical positions.

There are a number of practical things that are part of the tradition that are unlikely to be learned just from listening: aesthetic principles, formal concepts, etc. The mental categories we construct influence our perceptions in significant ways. If you are coming from a Western background, you already have a mental structure built that parses music through a system of 12 note categories. So it is very helpful to study the theory as a stepping-stone to increasing the number of perceptual categories you have access to. However, the simple fact is that the theory in this case does not actually match practice and the correct intervals can be learned only by ear.

No one here is opposed to theory, we are just saying don't get too caught up in it because it is only a guideline and is often rather idealized with respect to the actual music practice. There are people who argue against ever even using sheet music for anything, a position I find ridiculous. Still, I end up learning most things by ear because there is a ton of information that can't be conveyed by sheet music.

I was probably involved in the AAJ discussion you reference; my position has always been similar to Jerry's—different things work for different people at different times and we should use all the available tools. But that said, many people use theory as a crutch to avoid developing their ears, and that is never OK. Also, the way much theory is taught encourages certain limiting ways of approaching music. Theory is great, but take it with a grain of salt and always always confirm with your ears. I stopped participating there because. unlike here, the environment gets pretty toxic and there are a lot of competing egos—it ended up feeling like a waste of time. Nice to see you here!

Brian Prunka - 11-17-2014 at 10:32 AM

By the way, the Turkish word is "koma" but it in English it is "comma," just like the punctuation. You can use either, but a "coma" will put you in the hospital :D

Brian Prunka - 11-17-2014 at 10:42 AM

Quote: Originally posted by SV_T_oud  
Quote: Originally posted by Brian Prunka  

... As David notes, the music doesn't really follow the theory anyway, even in the basic makams.


Brian - thanks a lot for you help and here are a few comments:

I agree but often one needs to understand initial set of rules in order to proceed with practice. For instance you mentioned about naming makams after prominent notes, not tonics. Without knowing that I would assume the latter and having had developed good ear I would have hard time struggling with recordings trying to match them to tanbur neck diagrams with fret names.


Sure, which is why I pointed out that you shouldn't expect the theory to match what you hear.
Quote:

That's a very specific example but I knew people who gave up playing piano because they didn't learn about whole and half steps first. That may sound silly but the lack of that fundamental knowledge gave then troubles in related, still simple but higher level steps they've tried to take in order to progress. Of course they weren't good ear players but not everyone has to be.


Early on I gave up on singing because I was always out of tune with the piano. It was only later that I learned that it is actually the piano that is out of tune with how we naturally hear and was able to learn how to sing (not professionally but well enough) and develop my ears more deeply. For a long time, I wondered why no one explained that the piano could really throw off your voice if you tried to match it.
Quote:

Bill Evans, the great Jazz pianist (sorry, you know of course who he is) used to say that because he had not so good ear he had to break down everything to pieces and then assimilate and only then implement in his music. He could be modest of course but I doubt he would mention that if he didn't face that problem of some degree.

Sure, I am not an opponent of music theory.
Quote:

If you didn't tell me that 'Maqam note' not= tonic of the maqam I wouldn't know that! It's not in the book of L.Signel or if it's there I overlooked it.

I've tried to go without this forum but I found that many specific Internet resources on Mid-East music don't consider the basics.


There is a lot of useful theory, but there are some things that it is important to know by ear and that theory is somewhat inaccurate or vague on. I think you are misinterpreting our comments about a specific area of theory (intonation and comma values) with a general condemnation of theory; I assure you this is not the case.

SV_T_oud - 11-17-2014 at 11:43 AM

Brian, I don't care about the theory of this word :D
I picked it up by ear!
Quote: Originally posted by Brian Prunka  
By the way, the Turkish word is "koma" but it in English it is "comma," just like the punctuation. You can use either, but a "coma" will put you in the hospital :D

SV_T_oud - 11-17-2014 at 11:52 AM

Quote: Originally posted by Brian Prunka  

... pro musicians typically end up refining the fret locations by ear...


Brian, that thing in bold would explain almost everything.
I'm an amateur musician without particular gift in music but I play a variety of instruments and gradually improve.

When I started five years ago I couldn't tell the fifth from the fourth by ear. Now I can and I can do many more things with music I couldn't do a year ago.

I'll never be at the level of a pro musician but it doesn't distract me from learning everything music, includinh history, theory and after all, how it sounds :)

SV_T_oud - 11-17-2014 at 12:01 PM

Quote: Originally posted by Brian Prunka  
... I think you are misinterpreting our comments about a specific area of theory (intonation and comma values) with a general condemnation of theory; I assure you this is not the case.


That's quite possible. Honestly I rarely think of what is more theory and what is more practice in music. I approach learning music with whatever means I have with what little gift I've got for music.

By the way, if I'm out of tune with piano, I tune up to the piano. That's my level.
Piano is a very forgiving instrument. You press a key and it's always "in tune" with itself. The rest is your technique and soul.

There are people who hear guitar as an out of tune instrument as well. I don't. However there are many people who I know who can't properly tune up a guitar without a tuner. I can!
But once again, my level of hearing intervals is way below any pro musician.

SV_T_oud - 11-18-2014 at 10:50 AM

One more question I'd like to ask my more knowledgeable forum mates is about the difference in intervalic relationships between Turkish and Arabic makams, maqams. Do they follow the same scheme or are there noticeable differences?
Take for instance Rast (that's one of a few I know by name): is Turkish version the same as Arabic and maybe even Persian versions?

In couple years from now I might be able to tell the difference (if any) by ear but for now please share with me your observations.

I ask because I'm mostly interested in Turkish music but majority of the instructional material is for Arabic music.

DavidJE - 11-18-2014 at 02:21 PM

Yes, there are differences in the intervalic relationships between Turkish and Arabic makams, among other differences. With Rast for example, the 3rd and 7th degrees are played a bit flatter in Arabic playing than in Turkish playing, I believe. It SEEMS to me (but I'm not actually very qualified to say!) that Arabic players tend to play closer to the "quarter tone", that the standardization of the theory has had a little more impact on performance. Or, maybe the Arabic quarter tone theory happened to match performance more? I don't know.

Brian Prunka - 11-18-2014 at 07:50 PM

The Arabic quarter tone varies geographically, but I don't think it is so much the "quarter tone" idea that is the cause. It's hard to know, but going by Farabi's calculations you are not far off from the sikah that is used today, so I think that it just happened to match the practice more rather than it being an influence. I think this is more about a general trend of how people feel about theoretical descriptions; in my experience, people from the Arabic tradition are not especially concerned with verbal descriptions and names—the music is just what it is. A kind of minimalist approach to theory, which works well in a mentor-protege type relationship. It is much more challenging for an academic setting or for self-study.
Quote: Originally posted by SV_T_oud  
One more question I'd like to ask my more knowledgeable forum mates is about the difference in intervalic relationships between Turkish and Arabic makams, maqams. Do they follow the same scheme or are there noticeable differences?
Take for instance Rast (that's one of a few I know by name): is Turkish version the same as Arabic and maybe even Persian versions?

In couple years from now I might be able to tell the difference (if any) by ear but for now please share with me your observations.

I ask because I'm mostly interested in Turkish music but majority of the instructional material is for Arabic music.

I find it strange that you say the majority of instructional material is for Arabic music. I know of almost no real instructional materials for Arabic music (in English, anyway), while there are tons of resources for Turkish music.

What I will say is this: while the concept of seyir does exist in the Arab maqam, it is not taught and verbalized as it is in Turkish music, and it is not as rigid. In Turkish music, the same scale with a different seyir is considered a different maqam. In Arabic music it's not, usually. It's more like "here's one kind of Rast, and then there is this other way that goes like this." It would seem from old sources that this used to be somewhat different in Arabic music, but over time the conception became somewhat simplified.

There are differences in the intonation of the maqamat. Overall they are similar enough that Turkish and Arab musicians can play together, but there are some noticeable discrepancies and the musicians have to come to agreement . . .

The biggest one that stands out to me is that in Turkish music, the third of hicaz is the same interval as the third of Rast. In Arabic music, that is not the case. This causes an interesting issue when you modulate to sikah from hijaz . . . in Turkish music it is no problem (hicaz to segah) but in Arabic music it is not "real sikah". Sami Abu Shumays coined the term "pseudo sikah"—it acts like sikah in every way, but it is higher than the Arabic version of sikah. Sometimes, a modulation to Rast in a Turkish piece is considered a modulation to ‘Ajam (Acem) by Arab musicians, since Turkish rast is so close to ‘ajam (if it was learned by ear, rather than from sheet music).

SV_T_oud - 11-19-2014 at 06:00 AM

Quote: Originally posted by Brian Prunka  
...I find it strange that you say the majority of instructional material is for Arabic music.


Brian, first of all - thanks much again for your detailed and critical answer! I appreciate your help as always.

Regarding your comment above that I quoted. Let me explain what I mean. Imagine I want to get into my ear and ingrain into my mind the sound of some common makams, let's say 10.

For that the best way to go I think is to get some books with audio examples clearly demonstrating the sound of these makams.

I found these books/DVDs that I think would serve the purpose:
- Cameron Powers, Arabic-Musical-Scales-Basic-Maqam-Teachings available at:
http://www.maqam.com/store/p/19-Arabic-Musical-Scales-Basic-Maqam-T...
- Learn Maqamat on the OUD (VERSION 2) available on eBay:
http://www.ebay.com/itm/251707033501

Both are for Arabic version of makamat. Although the 'Learn Maqamat on the OUD' mentions some Turkish content present I understand the creator comes from the Arabic tradition anyway.

I didn't find any similar books/DVDs currently readily available for Turkish version. If you pointed me to such books/DVDs etc. I would send you my big thanks.

SV_T_oud - 11-19-2014 at 06:04 AM

David, thank you for your input also.
Quote: Originally posted by DavidJE  
Yes, there are differences in the intervalic relationships between Turkish and Arabic makams, among other differences. With Rast for example, the 3rd and 7th degrees are played a bit flatter in Arabic playing than in Turkish playing, I believe. It SEEMS to me (but I'm not actually very qualified to say!) that Arabic players tend to play closer to the "quarter tone", that the standardization of the theory has had a little more impact on performance. Or, maybe the Arabic quarter tone theory happened to match performance more? I don't know.

Brian Prunka - 11-19-2014 at 01:00 PM

Quote: Originally posted by SV_T_oud  

Regarding your comment above that I quoted. Let me explain what I mean. Imagine I want to get into my ear and ingrain into my mind the sound of some common makams, let's say 10.

For that the best way to go I think is to get some books with audio examples clearly demonstrating the sound of these makams.

I found these books/DVDs that I think would serve the purpose:
- Cameron Powers, Arabic-Musical-Scales-Basic-Maqam-Teachings available at:
http://www.maqam.com/store/p/19-Arabic-Musical-Scales-Basic-Maqam-T...
- Learn Maqamat on the OUD (VERSION 2) available on eBay:
http://www.ebay.com/itm/251707033501

Both are for Arabic version of makamat. Although the 'Learn Maqamat on the OUD' mentions some Turkish content present I understand the creator comes from the Arabic tradition anyway.

I didn't find any similar books/DVDs currently readily available for Turkish version. If you pointed me to such books/DVDs etc. I would send you my big thanks.


Here is one for Turkish makamlar: http://www.ortav.com/sunshop/index.php?l=product_detail&p=415

Really, the sound of the makam should simply be learned from recordings, there are plenty of examples of taksim in various makams on CDs . . . it's true that these will have modulations that deviate from the essential notes of the makam, but I don't consider that a big deal. I was really thinking of actual detailed instructional materials, of which there is an abundance in Turkish music and a relative paucity for Arabic music. The Signell book is very detailed also, though it doesn't include recordings. There are numerous Turkish oud method books as well.

The main thing is to understand the jins concept in the construction of the maqam . . . if you know rast, bayati/ussak, nahawand/buselik, kurd, hijaz, nikriz, ajam, saba, sikah, then you know all the sounds, you just need to learn which combinations produce which maqam.

SV_T_oud - 11-19-2014 at 01:09 PM

Thank you Brian for the link and useful tips!

DavidJE - 11-19-2014 at 02:13 PM

The book Brian recommended is excellent...highly recommended.

SV_T_oud - 11-20-2014 at 04:28 AM

However, it's out of stock. Maybe even out of print...
Quote: Originally posted by DavidJE  
The book Brian recommended is excellent...highly recommended.

Gocauo - 11-20-2014 at 10:04 AM

It does not appear to be out of print, but you may have trouble finding it with the CDs.

This is the ISBN 0974588245

SV_T_oud - 11-20-2014 at 11:42 AM

Quote: Originally posted by Gocauo  
...but you may have trouble finding it with the CDs...


... which are the most valuable part of it...

Gocauo - 11-20-2014 at 11:57 AM

Quote: Originally posted by SV_T_oud  
Quote: Originally posted by Gocauo  
...but you may have trouble finding it with the CDs...


... which are the most valuable part of it...


Agreed....

SV_T_oud - 11-21-2014 at 06:23 AM

I'd like to expand my question a little bit into the theoretical direction if you don't mind. It's still related to Turkish music though.

First, please consider me ignorant in this field for the ease of conversation and do not assume I possess any deep knowledge in the area of Musical Temperament systems.

There are quite a few temperament systems according to information available on the Internet. Here is a good example of the web site making an attempt on categorization of the temperaments:
http://leware.net/temper/temper.htm#_nr_308

Apparently there are a few competing systems offering their "best" ratios based on scientific calculations.

Just Intonation, Pythagorean Tuning, a few Regular and Irregular Temperament schools, you name it. All in all I think there are at least 10 commonly accepted temperament versions including the notorious Equal Temperament which is the basis of the Western Music. And the latter is ironic.

Well, what I'm getting at you may ask? Here we go.

First, how do you know which version of the temperament out of ten is correct? For instance one musician's ear will be fond of the scale coming from the Pythagorean tuning and other's will favor the Kirnberger's temperament of the Irregular school of thought.
Is it correct to say that there is no "correct" temperament in Nature and there are only preferences?

Second, if the above is not ultimately true which of the temperaments is considered most "natural" by good ear players?

Finally, which of the scientifically justified temperaments most closely matches the temperamet used in the Turkish koma system and why?

By the way, I remember reading somewhere else in the Wikipedia (actually here):

http://en.wikipedia.org/wiki/Pythagorean_tuning

that the shortcoming of the Pythagorean tuning is in accumulating an error when superimposing the stack of pure fiffths with the 3:2 ratio over a stack of octaves with the 2:1 ratio.
It's said that over the span of 7 octaves the error resulting from superimposing two stacks is approximately a 1/4-th of a semitone.

As far as I can imagine the 1/8-th of a tone Pythagorean comma is somehow related to the 1/9-th of a tone Turkish koma.
Exactly how and why?

Brian Prunka - 11-21-2014 at 03:51 PM

I wrote a detailed answer and lost it. maybe i'll try gain later.
short answer: pythagorean tuning and just intonation are not temperaments, because the intervals are not modified (tempered)

pythagorean comma is in between 1/8 and 1/9 of a tone, and closer to 1/9 than 1/8. Probably the Turkish theorists picked the nearest simple ratio, which may explain somewhat why the theory doesn't match how people actually play.
1/8 = ~25.49¢
Pythagorean comma = ~23.46¢
1/9 = ~22.66¢

Brian Prunka - 11-21-2014 at 04:33 PM

Quote: Originally posted by SV_T_oud  
I
Just Intonation, Pythagorean Tuning, a few Regular and Irregular Temperament schools, you name it. All in all I think there are at least 10 commonly accepted temperament versions including the notorious Equal Temperament which is the basis of the Western Music. And the latter is ironic.


ET is not the 'basis' for Western music, the basis is 5-limit Just Intonation, but the spread of ET in the 1800s led to musical developments that have become essentially intertwined with Western musical styles. All of the temperaments are attempts to balance the best sound (Just Intonation) with the widest musical possibilities in the areas of modulation, modal interchange and chromatic development. JI generally sounds the most "in-tune" if you stick to one basic key, but sounds the worst if do a lot of modulating (unless you have infinite note possibilities, such as in choral music).
Quote:

First, how do you know which version of the temperament out of ten is correct? For instance one musician's ear will be fond of the scale coming from the Pythagorean tuning and other's will favor the Kirnberger's temperament of the Irregular school of thought.
Is it correct to say that there is no "correct" temperament in Nature and there are only preferences?


No, it is not correct, because the first 12 notes of the harmonic series, representing simple vibrational ratios (1/1, 2/1, 3/1, 4/1, etc) are unassailably in tune.

Quote:
which of the temperaments is considered most "natural" by good ear players?


This gets more complicated because while there is a simple physical basis for tuning, culturally we learn to identify with various sounds in a somewhat arbitrary way. The more complex the reference ratio, the more we seem to accept culturally determined or ambiguous tuning cues. For example, nearly everyone agrees that 1/1 unisons and 2/1 octaves are ideal. 3/2 fifths and 4/3 fourths likewise are nearly universally desirable. 5/4 major thirds are a little less universal, but still very widely considered ideal (largely dependent on the degree to which third-based harmony is stylistically desirable, or possibly the other way around). Beyond that, there is a lot of variability.

However, when you consider music that employs the sounding of many simultaneous tones, it becomes quite clear that (5-limit) Just Intonation is most widely considered ideal. That is, we can accept a lot of tuning variation melodically that we cannot accept harmonically.
Vocalists and instruments with flexible pitch most naturally gravitate toward this tuning most of the time.
Quote:

Finally, which of the scientifically justified temperaments most closely matches the temperamet used in the Turkish koma system and why?


53 tone equal temperament is essentially identical to the Turkish 1/9 tone system.

53tET results in a division being ~22.64¢, compared to the theoretical turkish comma of 22.66¢ if we are going by 1/9 of the pythagorean whole tone. Considering that the size of a "whole tone" is arguably not fixed, I think this difference is a computational error of some kind. Or put another way, they figured out that if you divide the octave equally into 53 parts, 9 of those parts is a rounding error with respect to a pure pythagorean whole tone (remember that we can't really hear discrepancies less than 2¢ in most cases, this is 203.91¢ for a Pythagorean WT, compared to 203.77¢ for 53tET WT).

None of the traditional Western temperaments approximate the Koma system because they were devised for different purposes entirely.
Quote:

the shortcoming of the Pythagorean tuning is in accumulating an error when superimposing the stack of pure fiffths with the 3:2 ratio over a stack of octaves with the 2:1 ratio.


This is not really the problem, Pythagorean tuning is perfectly usable, as long as you stay in one key. The real problem with it is that major thirds and minor sixths, and to a lesser extent minor thirds and major sixths sound pretty terrible, which is why music composed in this system (medieval Western music like Gregorian chant, etc.) shies away from using those intervals harmonically (or treats them as dissonances rather than consonances).
Quote:
It's said that over the span of 7 octaves the error resulting from superimposing two stacks is approximately a 1/4-th of a semitone.

this is the basis of the Pythagorean comma, however, note that the situation where you would notice this doesn't necessarily come up in non-modulating music.

Brian Prunka - 11-21-2014 at 05:55 PM

Warning Okay, this is going to get nerdy:

The degree to which Pythagorean tuning is usable (leaving aside the issue of harmony using thirds and 6ths), depends largely on the extent to which the scale is devised of contiguous 5ths.

Consider, any mode of the major scale can be constructed entirely of contiguous 5ths:

Dorian:
F C G D A E B

Originating tone is in the center.

Mixolydian:
F C G D A E B

Originating tone is slightly off center

Ionian:
F C G D A E B

originating tone fairly off center

Lydian:
F C G D A E B

originating tone is the lowest.

Aeolian:
F C G D A E B

originating tone slightly off-center above

Phrygian:
F C G D A E B

originating tone fairly off-center above

Locrian:
F C G D A E B
originating tone extremely off-center above


All else being equal, notes below the tonic and intervals farther away from the tonic (based on the harmonic relationships) are harder to hear. This would point to Dorian or Mixolydian being the easiest to hear in Pythagorean tuning, and Locrian and Phrygian as the hardest to hear.

Dorian's hardest note to hear is F; it's 3 fifths away in the downward direction.
Mixolydian's hardest note to hear is B, it's 4 fifths away in the upward direction.

Lydian's hardest note is B, it's 6 fifths away in the upward direction. Compare to Phrygian, which has the F located 5 fifths away in the downward direction.

As a rough estimate, lets assign difficulty this way: 3 points for each fifth in the upward direction, 4 points for each fifth in the downward direction.
As presumably the most difficult, let's consider Locrian as the reference for 100% difficulty:
Locrian: F(24) C(20) G(16) D(12) A(8) E(4) B(0), total difficulty: 84 (100%)

Dorian: F(12) C(8) G(4) D(0) A(3) E(6) B(9), total difficulty: 42 (50%)
Mixolydian: F(8) C(4) G(0) D(3) A(6) E(9) B(12), total difficulty: 42 (50%)
Ionian: F(4) C(0) G(3) D(6) A(9) E(12) B(15), total difficulty: 49 (58%)
Aeolian: F(16) C(12) G(8) D(4) A(0) E(3) B(6), total difficulty: 49 (58%)
Lydian: F(0) C(3) G(6) D(9) A(12) E(15) B(18), total difficulty: 63 (75%)
Phrygian: F(20) C(16) G(12) D(8) A(4) E(0) B(3), total difficulty: 63 (75%)

Now let's look at what happens if you use five limit JI and assume that 3rds above are 4 points and 3rds below are 5 points:
Dorian: F(8) C(8) G(4) D(0) A(3) E(6) B(8), total difficulty: 37 (44%)
Mixolydian: F(8) C(4) G(0) D(3) A(6) E(8) B(4), total difficulty: 33 (39%)
Major: F(4) C(0) G(3) D(6) A(8) E(4) B(7), total difficulty: 32 (38%)
Minor: F(5) C(8) G(8) D(4) A(0) E(3) B(6), total difficulty: 34 (40%)
Lydian: F(0) C(3) G(6) D(9) A(4) E(7) B(10), total difficulty: 39 (46%)
Phrygian: F(9) C(5) G(8) D(8) A(4) E(0) B(3), total difficulty: 37 (44%)

So we can see that in the case of Dorian and Mixolydian, it is not a big difference to use Pythagorean tuning, but in the case of Major, Minor, Lydian and Phrygian, it makes it much easier to use Just Intonation.
Of course, my point assignments are a bit arbitrary, just to get a rough sense of how far removed each scale note is from the tonic. In reality, I would say that fourths (that is, 5ths below) are slightly harder than 3rds above, and 3rds below slightly harder still, so maybe better values would be 6, 8, 7 and 9.

This yields: Dorian (difficulty 50% Pythagorean, 43% JI), Mixolydian (50% Pythagorean, 38% JI), Lydian (75% Pythagorean, 45% JI), Phrygian (75% Pythagorean, 42% JI) etc.

Again this is just to get a rough sense of how our intuition works regarding how easy intervals are to hear (note this works both ways: it is harder to hear it to get it in tune, but as a listener we are also more forgiving of variation)

TL;DR: I am a nerd

SamirCanada - 11-21-2014 at 06:20 PM

:cool: = Brian

Just missing a peice of white tape in the middle of the glasses

SV_T_oud - 11-22-2014 at 04:29 AM

Brian, great job!
A few of my miserable comments follow.
Quote: Originally posted by Brian Prunka  
No, it is not correct, because the first 12 notes of the harmonic series, representing simple vibrational ratios (1/1, 2/1, 3/1, 4/1, etc) are unassailably in tune.


This is interesting. What is essentially "in tune"?
Is this something you have to believe or is there a scientific definition of this term that makes it unassailably true?
Or is it the thing-in-itself, the self-defining substance? That is: because this is the natural harmonic series the notes coming out of the series are considered "unassailably in tune"?

It's interesting also because before I used to believe that natural harmonics of the brass instruments (I play some trumpet) are "out of tune" and only today I noticed the following in the commonly used description: "Some harmonics are 'out of tune', meaning that they don't lie close to notes on the familiar, equal-tempered scale."
Quote: Originally posted by Brian Prunka  
ET is not the 'basis' for Western music, the basis is 5-limit Just Intonation, but the spread of ET in the 1800s led to musical developments that have become essentially intertwined with Western musical styles.


Did I have to say "...basis of the modern Western music" to be accepted?

Otherwsie, Brian, thanks again and I need couple weeks to digest your dissertation.

SV_T_oud - 11-22-2014 at 04:43 AM

Quote: Originally posted by SamirCanada  
:cool: = Brian

Just missing a peice of white tape in the middle of the glasses


That sounds "cool", but what's the humor? I want to understand...
Sort of "stays cool all the time" with the tape between the glasses or anything else? I'm not that good at English idiomatic thinking.

SV_T_oud - 11-22-2014 at 05:05 AM

Brian, please help me with one more thing.
When cents are used to estimate the intervals, how are they calculated?

For instance when you say: "...53tET results in a division being ~22.64¢, compared to the theoretical turkish comma of 22.66¢..." how do we get 22.64 cents per a fraction when deviding the whole (octave) into 53 bits? In other words 22.64 cents of what?

I actually never understood "cents" widely used in English texts compared to what we use in our country which are "percents". If I interpreted the 22.64 cents as our "percents" applied to an octave I would get something between 1/4 and 1/5 of an octave.

And one more thing. You say about "equal division" of an octave into 53 tones. Is it literally equal, that is if we take the Western tone A and calculate the frequency increment per a microtone over an octave we get: 880-440 Hz = 440 Hz / 53 = 8.3 Hz per microtone over an octave? Of course that value will vary when applied to different octaves, ie. 440-220 Hz = 220 / 53 = 4.1 Hz per microtone in that octave. It would make no sense.

Or does "equal" means "equal logarithmic" increment? I vote for the latter but who knows?
Brian knows!

I would appreciate if you gave me a small example in cents and Hz applied to an octave of A = 440 Hz. Just a few first values, please like:

A + 0/53 = 440 Hz, x cents
A + 1/53 = ...
A + 2/53 = ...
the rest will be self explanatory if the formula is known.

Thanks in advance!

Brian Prunka - 11-22-2014 at 06:47 AM

Calculating cents from Hz is difficult and calculating Equal Temperaments in Hz is based on logarithmic increments.

"Cents" is a system of measurements that takes into account the logarithmic scale of frequency and is based on Equal Temperament. It is convenient because it simply expresses the way we hear (ratios do this as well, but only for integer relationships, while cents can express irrational numbers). 100 cents = an ET half step. "Cent" just means hundred or hundredth. "Percent" is actually a compound word from "per cent", meaning "out of a hundred", so 100% just means "100 out of 100". In this case "100" is a half step, not an octave. An octave is 1200 cents (12 half steps).


Here is a calculator for converting between Hz and ¢

(It also shows the formula)

Brian Prunka - 11-22-2014 at 06:48 AM

Quote: Originally posted by SV_T_oud  
Quote: Originally posted by SamirCanada  
:cool: = Brian

Just missing a peice of white tape in the middle of the glasses


That sounds "cool", but what's the humor? I want to understand...
Sort of "stays cool all the time" with the tape between the glasses or anything else? I'm not that good at English idiomatic thinking.


It's just a stereotypical image of a nerd or geeky scientist type.

Brian Prunka - 11-22-2014 at 07:05 AM

Quote: Originally posted by SV_T_oud  

For instance when you say: "...53tET results in a division being ~22.64¢, compared to the theoretical turkish comma of 22.66¢..." how do we get 22.64 cents per a fraction when deviding the whole (octave) into 53 bits? In other words 22.64 cents of what?


Hopefully it is clear from my post above, but an octave is 1200 cents, so 1200/53 = ~22.64
Quote:

And one more thing. You say about "equal division" of an octave into 53 tones. Is it literally equal, that is if we take the Western tone A and calculate the frequency increment per a microtone over an octave we get: 880-440 Hz = 440 Hz / 53 = 8.3 Hz per microtone over an octave? Of course that value will vary when applied to different octaves, ie. 440-220 Hz = 220 / 53 = 4.1 Hz per microtone in that octave. It would make no sense.


"Equal" in this case would mean perceptually equal, which is based on a logarithmic scale; it would be equal ratios, not equal frequency increments.
Think of it this way:
A is 110 Hz. To get to the next A we double it, adding another 110 Hz, so the next A is 220 Hz. If we added another 110 Hz, we would have 330 Hz. This isn't A, it is E. Since every octave requires a proportional doubling, going by equal frequency increments isn't equal at all.
Quote:

I would appreciate if you gave me a small example in cents and Hz applied to an octave of A = 440 Hz. Just a few first values, please like:

A + 0/53 = 440 Hz, x cents
A + 1/53 = ...
A + 2/53 = ...
the rest will be self explanatory if the formula is known.

Thanks in advance!


You can't express Hz in cents because cents measures a ratio, not a frequency. If you said Just Intonation, A(440Hz) to E (660Hz), you could calculate the 3/2 ratio as being 701.955 cents. An ET fifth, we can simply count up 7 half steps and get 700 cents.

The calculator from the site below gives me ~1.013164/1 as the ratio of succeeding intervals in 53tET. So in your example:

440Hz +1/53 = 440Hz*1.013164 = 445.79216Hz
440Hz +2/53 = 440Hz(1.013164^2) = 451.66057Hz
440Hz +3/53 = 440Hz(1.013164^3) = 457.60623Hz
etc.

From this site (which has more calculation options than the one above):
Quote:

Formula for converting the interval frequency ratio f2 / f1 to cents (c or ¢).
¢ or c = 1200 × log2 (f2 / f1)
log 2 = 0.301029995
This formula employs a log 2, or logarithm base 2 function. This formula can also be
written using a log 10 function, available on most scientific calculators via the log button:
c = 1200 × 3.322038403 log10 (f2 / f1)
1/log 2 = 1/0.301029995 = 3.322038403
The formula expressed using log10 rather than log 2.
3.322038403 is a conversion factor that converts base 2 logarithms to base 10 logarithms.
1 Cent = 2(1/1200) = 1.0005777895065548592967925757932
One cent is thus the number that multiplied by itself 1200 times results in the number 2.
The cent is an interval which is calculated from the interval frequency ratio as follows:
(In of the interval frequency ratio / ln 2)×1200 = cents value of the interval.
An interval of a halftone is equivalent to: 2(1/12) = 1,0594630943592952645618252949463.
That is: [ln (2(1/12)) / ln (2)]×1200 cent = 100 cent.

The Pythagorean comma is the frequency ratio (3 / 2)12 / 27 =
312 / 219 = 531441 / 524288 = 1.0136432647705078125.
The resulting is converted to 23.460010384649013 cent.
Twelve perfect fifths (3 / 2) reveals 8423.46 cents and
seven octaves, however, reveals only 8400 cents.


I am not about to do that math, so I use the handy calculator provided (and also some rule-of-thumb estimates based on simpler math).

SV_T_oud - 11-22-2014 at 07:43 AM

Thanks Brian, I of course could be more persistent in finding all that info myself, especially the 100 cents for 1/2 step but sometimes the amount of information given on the realted web sites is overwhelming and I get lost before finding the answers.
Big thanks for all your teaching!