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From what I remember of music theory, all music (at least Western music) boils down to scales that revolve around the 12 notes (circle of fourths/fifths). I know there are scales in different regions that have different combinations of those notes (many scales have 5 or 7 notes, some have 8, others like the chromatic have all 12, etc.).

But there are many more possible sounds than just those 12 notes (and the octaves created from those 12 notes). I don't know how many more sounds than notes, but it's probably a lot. So I'm wondering, if there are any musical scales / traditions / references on non-12-note musical systems. Say a musical system that has 13 notes before an octave is reached, or 100 notes, etc.

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Almost "all Western music" before the early 20th century is based on 12 note scales, but music elsewhere in the world and some later western music is not.

The earliest theoretical written description of the Arabic 17-note scale dates back to the 13th century, though more modern Arabic music uses the "quarter-tone" scale with 24 notes which divide each Western semitone in half, and is therefore more compatible with western musical instruments.

The theoretical basis of classical Indian music is complicated, but some of it can be considered to use a 22-note scale - though individual pieces would only use a subset of the 22 notes.

In the baroque era, before equal temperament tuning had become the default standard in western music, notes like D sharp and E flat did not share the same pitch. Some keyboard instrument makers designed and built instruments with more than 12 notes per octave (often 19) but they were intended more for playing several unequally-tuned 12-note scales without having to retune the instrument, rather than as a 19-note scale.

In the 20th century Western music started to use the 24-note quarter-tone scale as well, and some composers have experimented with other scales - for example Harry Partch used a 43-note scale, and built musical instruments to perform his own music.

  • wondering why " (often 19) ", would be interested to see more on that. Assuming you mean this. – Lance Pollard Jun 20 '18 at 10:44
  • Yes, that is the "logical" layout of the keyboard, but the early ones were not necessarily tuned in 19 equal steps. The reason for 19 was a practical compromise between making something that could be played by humans, and the range of keys that could be included - for example it excludes double-sharps and double-flats (if C sharp is not the same pitch as D flat, then C double sharp is unlikely to be the same pitch as D natural!) Physically, the "black keys" were often split "front and back" rather than "side to side" as in the picture in your link. – user19146 Jun 20 '18 at 11:29
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First of all the 12 note concept emerges from equal tempered tuning. Older European systems based on just tuning are still mostly based on the diatonic scale but, for example, G# and Ab are not the exact same frequency.

Equal temperament is based on constraining the half step to be a 12th root of 2, an irrational number that cannot be exactly replicated.

Traditional Turkish music contains quarter steps in the music but not a full 24 quarter tones, just one or two placed in the scale. Classical Indian ragas also contain fractions of a western half step.

From a mathematical point of view you can create an equal tempered set of N steps between an octave by the Nth root of 2 as a definition of the "step". But this may not sound good or even be audible.

Human pitch discrimination is not great. Blues players bend by quarter tones all the time and if you play on a guitar you can definitely distinguish 1/4 tones by bending. However there is a limit to what a human can distinguish.

Frequency changes are continuous on many instruments (fret less string instruments for example) and we hear glissando, but that doesn't mean that when presented with two distinct tones an 1/8 step apart, at different times, that the average person would be able to tell the difference. So a good deal of what has evolved in western music is based on cultural preference, what sounds good to the western ear.

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    Exactly. I don't subscribe to the idea that most Western music has much to do with 12edo tuning; it has mostly to do with diatonic tonality and adds chromatic notes that happen to be renderable in 12edo. Only some works build so firmly on chromaticism that it's fair to say they are based on the 12 notes. – leftaroundabout Jun 20 '18 at 13:06
  • What do you mean by replicating in cannot be exactly replicated? – JiK Jun 20 '18 at 22:30
  • You cannot have a finite decimal representation to the twelfth root of 2 as that number is irrational. Its decimal representation will truncated and or rounded. I should have used the word "represented". – ggcg Jun 20 '18 at 22:36
  • @ggcg Why is a decimal representation important? You can't have a finite decimal representation (in base 10) of 4/3 either but I don't see why that would matter in any musical context. – JiK Jun 21 '18 at 11:54
  • So if an octave is divided into more or less than twelve equal tempered semitones, then are the semitones each still equivalent to 100 cents logarithmically? Take the pelog scale, e.g., which is based on an equal tempered 9-note octave: would the octave then be equal to 900 cents? – Udon Joe Apr 30 at 22:49
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There are many. (Wiki gives some.) The continuants of the continued fraction for Log(3)/Log(2) give one things like 31-note and 53-note octave divisions. https://en.wikipedia.org/wiki/53_equal_temperament These and similar ones have been known for more that 2000 years in theory.

Harry Partch used a 43 note scale derived from a reversed Monzo lattice. It's like "just intonation" but uses ratios with divisors of 7 and 11 in addition to 2, 3, and 5. https://en.wikipedia.org/wiki/53_equal_temperament

Partch's stuff sounds better than it reads.

  • 31edo and 53edo were known for more than 2000 years? That's news to me, who described them back then? I always associate 31edo with Christiaan Huygens. – leftaroundabout Jun 20 '18 at 13:01
  • Maybe you could point to a good part to listen to in that video, not sure where to begin. – Lance Pollard Jun 20 '18 at 13:12
  • I just poked around various of Partch's stuff. I don't recall any specific place. It all sounded pretty good, but not the contrast I'd like. (This seems a problem with most "non-standard" music.) – ttw Jun 20 '18 at 19:35
  • Ching Fang circa 59BC is one who knew it. Newton also. – ttw Jun 20 '18 at 19:37
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Hi there is Indian classical concept called Shruti

It has 22 notes which is loosly translated as "what is heard".

It is considered as almost all sounds can be written in forms of Shruti.

  • This answer needs a lot more explanation to be good. – Tim Jun 20 '18 at 13:41

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