144edo: Difference between revisions
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== Theory == | == Theory == | ||
144edo is the | 144edo is closely related to [[72edo]], but the [[patent val]]s differ on the mapping for 13 and 17. It is [[contorted]] in the 11-limit, tempering out [[225/224]], [[243/242]], [[385/384]], [[441/440]], and [[4000/3993]]. Using the patent val, it tempers out [[847/845]], [[1188/1183]], 1701/1690, 1875/1859, and [[4225/4224]] in the 13-limit; [[273/272]], [[715/714]], [[833/832]], 875/867, 891/884, and [[1275/1274]] in the 17-limit; 210/209, 325/323, [[343/342]], [[363/361]], [[400/399]], [[513/512]], and 665/663 in the 19-limit. | ||
The 144gh val is a tuning for semihemisecordite temperament, while 144eff val is a tuning for hemimiracle. 144ee is a tuning for oracle. 144cf val supports necromanteion. | |||
=== Approximation to φ === | |||
144edo is the 12th Fibonacci edo, and the square of world-dominant [[12edo]]. As a consequence of being a Fibonacci EDO, it can produce extremely precise approximation of the [[Logarithmic phi|logarithmic golden ratio]] at 89 steps. In addition, it ''also'' excellently represents the [[Acoustic phi|acoustic golden ratio]] by 100 steps. | |||
== Music == | == Music == | ||
* [https://www.youtube.com/watch?v=p71oF-A9gF8 Like an endless uphill] by 5 hideya | * [https://www.youtube.com/watch?v=p71oF-A9gF8 ''Like an endless uphill''] by [[5 hideya]] | ||
Revision as of 11:37, 2 September 2023
| ← 143edo | 144edo | 145edo → |
Theory
144edo is closely related to 72edo, but the patent vals differ on the mapping for 13 and 17. It is contorted in the 11-limit, tempering out 225/224, 243/242, 385/384, 441/440, and 4000/3993. Using the patent val, it tempers out 847/845, 1188/1183, 1701/1690, 1875/1859, and 4225/4224 in the 13-limit; 273/272, 715/714, 833/832, 875/867, 891/884, and 1275/1274 in the 17-limit; 210/209, 325/323, 343/342, 363/361, 400/399, 513/512, and 665/663 in the 19-limit.
The 144gh val is a tuning for semihemisecordite temperament, while 144eff val is a tuning for hemimiracle. 144ee is a tuning for oracle. 144cf val supports necromanteion.
Approximation to φ
144edo is the 12th Fibonacci edo, and the square of world-dominant 12edo. As a consequence of being a Fibonacci EDO, it can produce extremely precise approximation of the logarithmic golden ratio at 89 steps. In addition, it also excellently represents the acoustic golden ratio by 100 steps.