29th-octave temperaments

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29edo is notable for being the first equal division to have a more precise 3/2 than 12edo, and the first tuning to be consistent in the 15-odd-limit. 29th-octave temperaments occur naturally when temperament-merging edos whose greatest common divisor is 29.

Temperaments discussed elsewhere include:

Mystery is notable for having a separate page.

Copper

Copper temperament is derived from a 5-limit comma called copper comma, because it is constructed the same way towards 29edo as Kirnberger's atom is towards 12edo. A fifth of each of these tunings is modified by a tiny amount, then a circle of these fifths is set to close eventually at the octave.

Surprisingly, despite 29edo's fifth being closer to 3/2 than 12edo's, copper has a higher TE error than atomic and is not a very high accuracy temperament.

Subgroup: 2.3.5

Comma list: [-481 261 29

Mapping: [29 0 481], 0 1 -9]]

Mapping generators: ~[-199 12 108 = 1\29, ~3/2 = 701.905

Optimal tuning (CTE): ~3/2 = 701.905

Supporting ETs: 23, 754, 783, 812, 1566, 1537, 2320, 3103, 3132, ...