Theory

Chords, scales, harmony, melody, etc.
O.a
KVRer
1 posts since 15 Nov, 2019

Post Fri Nov 15, 2019 10:33 am

Hello everyone. I would like to ask some questions about music theory and would be happy to assist you.
1. An octave is divided into 12 half tones in western music. And in Arabic music at a smaller interval and what I wanted to know is whether these intervals are accurate, for example, a quarter-ton, an eighth-ton, are they really accurate or could be a little more or a little less.
  2. Suppose they are inaccurate. Where can I find the exact list of all characters and octaves and intervals and mqamim?
  3. If this is true and the intervals are correct, and the smallest interval is one-eighth tone, does that mean that the octave is divided into 48 sounds? And if there are 48 sounds, why does the cannon have more than 70 sounds in an octave?
  4. basically can I play any song even with one sound? It might not even sound like the song but can this sound add to the song?
5.If so then does that mean that with one octave meaning 12 sounds I can even sound good with any song and melody?
6. And in light of this question, what is the average number of octaves used in Western music? And what is the average amount of Arabic songs used? And how many octaves are used in Ethiopian songs. I mean each song separately.?

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Forgotten
KVRAF
5985 posts since 15 Apr, 2019 from Nowhere

Re: Theory

Post Fri Nov 15, 2019 10:48 am

Depends what you mean by “inaccurate” - equal temperament is inherently inaccurate in terms of harmonics, but it’s an established standard for most Western music.

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jancivil
KVRAF
19176 posts since 20 Oct, 2007 from No Location

Re: Theory

Post Fri Nov 15, 2019 2:23 pm

Traditionally, the Arabic intervals are derived by ratios to the central tone, basically a tonic. There is more than one system.
No, the idea is *not* to divide the octave into 1/8th tones, the idea of the intervals is expressive and the scales tend to be heptatonic.

An eg., 24-tET is actually anathema to the authentic music and such as "quarter tones" exists as a term as a simplification to begin with. The instruments are built for a music which generally uses a couple of possible 7-tone maqams - at 1 and at 4 - not 24-note scales at_all.

MadBrain
KVRian
971 posts since 1 Dec, 2004

Re: Theory

Post Fri Nov 15, 2019 11:41 pm

O.a wrote:
Fri Nov 15, 2019 10:33 am
Hello everyone. I would like to ask some questions about music theory and would be happy to assist you.
1. An octave is divided into 12 half tones in western music. And in Arabic music at a smaller interval and what I wanted to know is whether these intervals are accurate, for example, a quarter-ton, an eighth-ton, are they really accurate or could be a little more or a little less.
I'm not a any kind of Middle-Eastern musician, so I can only tell you about what I've read. It seems like varies regionally and from instrument to instrument. Some people do use the 24-equal tone division: there are Bağlamas that are fretted in 12-tone equal temperament, plus 5 half-flat frets (B-, E-, A-, F#-, C#-) that are exactly 50 cents lower, and Nassim Maalouf's Arabic trumpet has a 50-cent flat valve in addition to the 3 normal ones.

Inversely, some Turkish Saz's have more than 30 frets per octave, giving multiple options for just how flat or sharp you want your half-flats to be:
http://www.luthierhuseyinfirat.com/imag ... =329383863
  2. Suppose they are inaccurate. Where can I find the exact list of all characters and octaves and intervals and mqamim?
https://www.maqamworld.com/en/index.php has a bunch of Arabic Maqams.
http://www.channelingstudio.ru/texts/Mu ... Makams.pdf has a whole bunch of Turkish Makams.
https://www.oudforguitarists.com/arabic ... omparison/ compares Arabic Maqams with Persian equivalents.
  3. If this is true and the intervals are correct, and the smallest interval is one-eighth tone, does that mean that the octave is divided into 48 sounds? And if there are 48 sounds, why does the cannon have more than 70 sounds in an octave?
Generally, notes that aren't half-flat, and aren't raised or lowered by a comma are either on the Pythagorean scale (Turkish music theory, some Persian theories), or on the 12-tone equal temperament (Arabic theory, used in practice by some Western-influenced musicians).

The half-flattened notes are lower in Persian music, about in the middle for Arabic music, and sharper in Turkish music.

The raising and lowering of notes by a small amount (somewhere in the range of 0-15 cents) seems to be mostly used in tetrachords that have an augmented second, such as the Hijaz tetrachord D, Eb, F#, G: in that case, you would sharpen Eb a little, and flatten F# a little.

When notes do get half-flat or adjusted, the amount that it's lowered or raised varies from region to region, from style to style, between Maqams, if the melody is going up or down etc. Which is why some Qanuns can have lots of mandals, to select which level of lowering/raising is stylistically appropriate.
  4. basically can I play any song even with one sound? It might not even sound like the song but can this sound add to the song?
5.If so then does that mean that with one octave meaning 12 sounds I can even sound good with any song and melody?
I guess melodies on the Rast, Bayati or Sikah family of Maqams would have to be modified to fit equal temperament, which could change their character a lot. Though you might be able to get away with some weird compromises such as using half-flats in the melody, but western 12-tone temperament in the accompaniment and bass.
6. And in light of this question, what is the average number of octaves used in Western music? And what is the average amount of Arabic songs used? And how many octaves are used in Ethiopian songs. I mean each song separately.?
Western music uses roughly 8 octaves: the piano has 88 notes (a few notes over 7 octaves). Arabic, Turkic and Persian music tend to put vocal music to the forefront, so they tend to emphasize the middle octaves more.
Last edited by MadBrain on Sat Nov 16, 2019 8:27 am, edited 1 time in total.

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jancivil
KVRAF
19176 posts since 20 Oct, 2007 from No Location

Re: Theory

Post Sat Nov 16, 2019 8:24 am

where's the edit button, another fail
Last edited by jancivil on Sat Nov 16, 2019 8:28 am, edited 1 time in total.

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jancivil
KVRAF
19176 posts since 20 Oct, 2007 from No Location

Re: Theory

Post Sat Nov 16, 2019 8:27 am

"Generally, notes that aren't half-flat, and aren't raised or lowered by a comma are either on the Pythagorean scale (Turkish music theory, some Persian theories) on the 12-tone equal temperament (Arabic theory)..."
Whose theory, what theory? This is a nonsense.

Pythagorean is a specific name for a specific set of tones. IE/EG: Al Farabi is not that thing, the baglama gamut I cite below is not that thing, neither of these are the things you confuse in this statement.

Your statement asserts there are but two, and only the one rational system. No.
It really is an absurd assertion the way you wrote it, as you actually state by it that it isn't systematic.*
The notes which aren't "half-flat" are "Pythagorean" ratios. No, this is not how it works. This does not form any general truism, it's a confusion on your part. You seem to be doing exactly what one editor at Wiki did**, a blank quote presented
out-of-context .

And I'm going to stand by 'anathema per the traditional music'; Maalouf's approach cannot be reduced to the notion that a 4th valve half the length of the 2nd valve equals 50¢ difference.

Maalouf credits his father, the renowned Lebanese classical trumpeter Nassim Maalouf, with the innovation.

"This trumpet that he invented is really pure genius. He invented the only Arabic instrument in which you blow, that allows you to play all modes, all scales, in all the tonalities," Maalouf says. "This does not exist in Arabic music. It's not only a trumpet that makes you play quarter-tones. He invented a way to blow in the instrument. He invented a new way to play the trumpet."

Maalouf says there are many links between Arabic and Western music. He says when he's playing jazz, he can incorporate Arabic scales thanks to one specific similarity.

"There's this note that we actually call 'the blue note' and I believe it's a heritage from African music," Maalouf says. "Those notes that are right in the middle, between a note and another note, those are 'blue notes' that you bend with the lips.


https://www.npr.org/2013/03/31/17559822 ... instrument

The intervals, again, differ greatly than 12tET for an aesthetic value, and cannot be extricated from the intonation of speech and the way sounds are formed in the voice, to begin with. It's an ethnic expressivity which was sought to be codified ultimately.

**: https://en.wikipedia.org/wiki/Talk:Arab_tone_system
"Everything on this page is wrong."
2. at the cairo conference in 1932, they tested the 24-tone theory by tuning a qanun to those equal tuned notes, and then played musical examples for arab musicians. all agreed it was out of tune.

3. in actual practice, there are more notes in between a half-tone than 1. there are more on the order of 12-20 different notes in use in between a standard half step. the so-called "quarter tones" differ in their intonation from maqam to maqam; there are also several differently tuned varieties of "natural" and "flat."


*To be fair to this argument, there are numerous things in traditional practice in a given maqam so close to a quarter tone there is no real tell. EG: 36:35 is 1.23 cents flat compared with a 50 cents from tonic. I can possibly tell but I wouldn't ask it. It's like the 11th partial gives a note appx that close to halfway between 11 and #11 in 12tET, a cent diff.

BUT, this supposed system is theoretical. It appears to have gotten started when...
The invention of the scale is attributed to Mikhail Mishaqa whose work Essay on the Art of Music for the Emir Shihāb (al-Risāla al-shihābiyya fi 'l-ṣināʿa al-mūsīqiyya) is devoted to the topic but also makes clear his teacher Sheikh Muhammad al-Attar (1764–1828) was one of many already familiar with the concept.[10]

On a solid factual grounding, here's this for one example:
https://en.wikipedia.org/wiki/Ba%C4%9Fl ... lama_scale
The musical scale of the bağlama differs from that of many western instruments – such as the guitar – in that it features ratios that are close to quarter tones. The traditional ratios for bağlama frets are listed by Yalçın Tura [3]:
Fret 1: 18/17
Fret 2: 12/11
Fret 3: 9/8
Fret 4: 81/68
Fret 5: 27/22
Fret 6: 81/64
Fret 7: 4/3
Fret 8: 24/17
Fret 9: 16/11
Fret 10: 3/2
Fret 11: 27/17
Fret 12: 18/11
Fret 13: 27/16
Fret 14: 16/9
Fret 15: 32/17
Fret 16: 64/33
Fret 17: 2/1

[3] = Yalçın Tura, "Türk Musikisinin Mes'eleleri". İstanbul, Pan Yayıncılık, 1988, og 159

like the 22 Sruti thing in India, this is in service of smaller scales, most commonly here 7 notes. Running the gamut like a scale would be exceedingly rare I think. What it actually is is optional intonations for 'minor second' and minor third/mixed third/major third etc. 27:22 is the actual idea of this "355" interval (in fact 354.547).
Interestingly here, the major 2nd, which is 3:2 squared, is fixed like 3:2 or 4:3.
Pythagorean keeps multiplying 3:2 and corrects with 'commas', Arab scholars expounded significantly on that kind of thought. 3:2, 9:8, 27:16, 81:64... This doesn't use the Pythagorean 'minor third' or appx 3 semitones, for instance.
https://en.xen.wiki/w/Gallery_of_just_intervals

MadBrain
KVRian
971 posts since 1 Dec, 2004

Re: Theory

Post Sun Nov 17, 2019 2:03 am

jancivil wrote:
Sat Nov 16, 2019 8:27 am
"Generally, notes that aren't half-flat, and aren't raised or lowered by a comma are either on the Pythagorean scale (Turkish music theory, some Persian theories) on the 12-tone equal temperament (Arabic theory)..."
Whose theory, what theory? This is a nonsense.
For Persian music, the theories I've read about come from this paper, from page 7: https://www.theseus.fi/bitstream/handle ... sAllowed=y
It lists 3 theories for Persian intonation:
- "4.1 The 24 quarter tone scale " (equal temperament, "quarter-tones" are 50 cents flat/sharp)
- "4.2 The 22 tone scale" (pythagorean intonation, "quarter-tones" are flattened or sharpened by a 24-cent pythagorean comma)
- "4.3 The theory of flexible intervals" (pythagorean intonation, "quarter-tones" are flexible and flattened or sharpened by about 45-cents)

For Turkish music:
- The 53-comma theory (essentially pythagorean intonation) is used by the various sources talking about Turkish music (such as the Oud book I've previously linked to: http://www.channelingstudio.ru/texts/Mu ... Makams.pdf).
- Apparently, some Turkish Kanuns are built with mandals based on 72-tone equal temperament (source: https://en.wikipedia.org/wiki/Qanun_(in ... emperament), which creates a system that's 12-tone equal temperament plus "quarter-tones" (and just-intoned notes) that can be 16, 33 or 50 cents flat/sharp.

For Arabic music:
- There's the controversial 24-tone equal temperament system of course.
- Historically, there are theory proposals such as Urmavi's 17-tone system that are based on an idealized pythagorean intonation (with "quarter tones" that are flattened by a 24-cent pythagorean comma... unfortunately I can't find a good paper about this anymore).
- I can't find a good paper on Al Farabi's system but it seems to be made out of Pythagorean intervals (256/243, 9/8, 32/27, 81/64, 4/3..), plus intervals that seem to be relatively close to equal temperament (18/17, 81/68), plus roughly half-flat intervals of various sizes (162/149 and the slightly higher 54/49; 27/22). The Bağlama fretting you've listed seems to be closest to this system.

---

Ok. Now, maybe some guy has taken a strobe tuner through the Lebanese countryside and has proven that all these "pythagorean intonation plus many more notes" theories and all these "12-tone equal temperament plus many more notes" theories are all bananas and the actual practice is quite different. If so, I want to see it.

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jancivil
KVRAF
19176 posts since 20 Oct, 2007 from No Location

Re: Theory

Post Sun Nov 17, 2019 9:12 am

I've seen this from you from years back. You have some reason to want 50¢ to govern which is a side issue (programming) and we're just going to get this ad culum circular to the premise. It's not the basis, it's theory qua theory. I see it with some frequency looking around, people want this to be true but a real examination of the whys and wherefores shows quite something else.

When it's *not* literal quarter tones, it's Pythagorean. Well, this could be confounding that term for 'ratio-based intonation', I don't know.
But moving right along...


The basis for the Arabian Tone System is intervals, confer 10th century Al Farabi's 25.
Screen Shot 2019-11-17 at 8.57.06 AM.png
(6 of the 10 are part of the Pythagorean gamut)
The work was defining intervals suitable for a music and in a holistic sense with culture and identity, Al Farabi being a serious polymath and scholar. Whence this 168¢?

Al Farabi additionally recommended this heptatonic basis for Rast:
1:1
9:8 (major 2nd), 203.91¢
27:22 for a half-third, 355 cumulative ¢
4:3 (P4)
3:2 (P5)
18:11 for a 'middle' 6, 853 cumulative ¢
19:9, 996 cumulative ¢

Now perhaps we are to believe the system is trying to replicate 'quarter tones' in this era (via time travel?). The reality, of course is that certain of these rational intervals find a close correspondence with 12tET, which comes centuries later. Or 24tET which gets going in the 19th century really.


An interesting thing I found is a paper where certain of these intervals are objected to as 'this doesn't really happen', a good instance of that is "17:14": if you deconstruct this acoustically we have an imaginary fundamental derived as though from a 14th partial and the interval derived from a 17th partial of that, so essentially an Occam's Razor sort of objection.

In my own research, which I did towards understanding what would be needed to build a fingerboard and/or fretboard off of rational systems like these, I found a lot of strain towards formulating the intervals qua intervals, which led to a fair amount of arithmetic and intellectualizing as well.

But reasons for ratios...

Zalzal (8th c) hypothesized that the “neutral third” (the third in
between the major and minor third in size) had a frequency ratio of 27/22, which seems a bit
complex until we realize that its inverse in the perfect fifth is 11/9 (27/22 * 11/9 = 3/2), the ratio
between the 11th and 9th partials of a tone. Such an explanation fits within the theoretical
requirement, taken originally from the ancient Greeks...
Fuzzy Boundaries_Maqam Intonation

It's so clear that "355 cumulative cents" is a coincidence.


24tET is not only not foundational here, it's not needed.
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MadBrain
KVRian
971 posts since 1 Dec, 2004

Re: Theory

Post Sun Nov 17, 2019 10:51 am

Dude, I've never said that the "quarter-tone" intervals were supposed to be 50 cents. I've merely said that it's *one* of the *dozens* of realizations of this family of intervals that has been theorized, built into instruments and played in Middle-Eastern music. That's why I've listed systems where the "quarter-tone" is:
- 16-cents (72-tone Kanun system using a 1-comma half-flat)
- 24-cents (Persian 22-tone system, Turkish 53-tone system in theory, Urmavi's 17-tone system)
- 33-cents (72-tone Kanun system using a 2-comma half-flat)
- 36-cents (Al Farabi's 54/49 interval)
- 45-cents (Persian flexible interval system, Turkish 53-tone system in practice with a 2-comma half-flat)
- 50-cents (24-tone equal temperament, 72-tone Kanun using a 3-comma half-flat)
- 53-cents (Al Farabi's 27/22 interval)
- 60-cents (Al Farabi's 162/145 interval)
- 67-cents (72-tone Kanun using a 4-comma half-flat)
- 70-cents (frets on the Pesian Setar, flexible interval system, Turkish 53-tone 3-comma half-flat)
- 83-cents (72-tone Kanun using a 5-comma half-flat)
- 90-cents (Persian 22-tone system, Turkish 53-tone system using a 4-comma half-flat)

I've never for one second implied that 24-tet was foundational, and I've listed a whole bunch of other systems where there are no 50-cent intervals whatsoever in order to make this clear. No doubt performers are playing a whole spectrum of intervals in practice, which is why Kanuns have so many mandals and Turkish Tamburs have so many frets.
Last edited by MadBrain on Sun Nov 17, 2019 11:09 am, edited 1 time in total.

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vurt
addled muppet weed
54759 posts since 26 Jan, 2003 from through the looking glass

Re: Theory

Post Sun Nov 17, 2019 10:56 am

fiddy cent governing?
no worse than any current political figure!

:hihi:
sorry, resistance was futile. and i did try.

mguerrero90
KVRist
55 posts since 8 May, 2019

Re: Theory

Post Tue Dec 03, 2019 2:57 am

Music is more language than math, as in, the only way to really learn is not by learning all the math and theory, but by just practicing and having fun with what sounds natural to you. The goal isnt to hit a set of metrics, the goal is to give an impression or a feeling to the listener. Harmony is an effect you can achieve if you follow certain rules, it is not a goal, though it can be. Tunnings are never perfect but that hardly matters. For example, the invention of modal jazz and more modern classical music post debussy is about a focus on these aspects, if you want to delve into some listening. They get effect from the music not by following strick rules, but by using shape, rhythm, and creative solutions to come up with unique ways to naturally express things to listeners. Debussy for example often goes deep in and out of harmony in a piece, and in some way, all pieces do.

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