Four commonly referenced Western tuning systems are Pythagorean tuning, just intonation, equal temperament, and meantone temperament.

From Music, Language, and the Brain, I recently learned there are a wide diversity of tunings that do not follow these systems. However, from what I could tell, although there may or may not be a “logic” to how the ratios in other cultures are picked, all the tuning systems referenced in the book still are built upon dividing an octave, implying that after a few distinct pitch classes, the octave recurs.

Are there people with tuning patterns or systems that don’t involve repeating the octave?

  • My guess would be yes, but I can't back that up with any evidence. Nice name. – user45266 Sep 19 '18 at 19:50
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    You may be interested in Category:Non–octave-repeating scales, but the scales described may not relate to a 'culture' in the sense that you mean it. – topo morto Sep 19 '18 at 20:02

There are a few patterns in Arabic or Persian music that don't have true octave repetition. For example (I don't remember the exact patterns), one pattern looks a bit like: C-D-E-F-G-A-B-C-D-Eb-F-G; the lower octave and upper octave o melodies a slightly different. Of course, the tunes come first; one gets "scales" by sorting notes by frequency.

There are some commas computed by other than octave division. The Pythagorean comma is the difference between 12 fifths and 7 octaves; the syntonic comma is the difference between a Pythagorean major third and the just major third. All these commas can be rewritten as octave-based (though not necessarily the most natural way to look at them.) The Syntonic comma occurs in Guitar tuning also: A guitar is tuned to 4 fourths and a major third which is equivalent to two octaves: 4/3*4/3*4/3*5/4*4/3 spans the guitar strings the ratio is 80/81 (the guitar cannot be exactly tuned to just intervals thus forcing some tempering.)

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