37edt: Difference between revisions

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{{Infobox ET}}
{{Infobox ET}}
'''37EDT''' is the [[Edt|equal division of the third harmonic]] into 37 parts of  51.4042 [[cent|cents]] each, corresponding to 23.4355 [[edo]]. The tunings supplied by [[111edt|111EDT]] (or 70edo) cannot be used for all low-limit just intervals, but they can be used on the 17-limit 8.3.100.70.22.52.68 just intonation subgroup, tempering out 289/288, 325/324, 352/351, 385/384, 561/560, 595/594, 625/624, 676/675, 1089/1088, 1156/1155, 1225/1224, and 1331/1326.
'''37EDT''' is the [[Edt|equal division of the third harmonic]] into 37 parts of  51.4042 [[cent|cents]] each, corresponding to 23.4355 [[edo]]. The tunings supplied by [[111edt|111EDT]] (or 70edo) cannot be used for all low-limit just intervals, but they can be used on the 17-limit 8.3.100.70.22.52.68 just intonation subgroup, tempering out 289/288, 325/324, 352/351, 385/384, 561/560, 595/594, 625/624, 676/675, 1089/1088, 1156/1155, 1225/1224, and 1331/1326.
{{Harmonics in equal|37|3|1|intervals=prime|columns=15}}


[[Category:Edt]]
[[Category:Edt]]
[[Category:Edonoi]]
[[Category:Edonoi]]

Revision as of 18:59, 30 September 2024

← 36edt 37edt 38edt →
Prime factorization 37 (prime)
Step size 51.4042 ¢ 
Octave 23\37edt (1182.3 ¢)
Consistency limit 3
Distinct consistency limit 3

37EDT is the equal division of the third harmonic into 37 parts of 51.4042 cents each, corresponding to 23.4355 edo. The tunings supplied by 111EDT (or 70edo) cannot be used for all low-limit just intervals, but they can be used on the 17-limit 8.3.100.70.22.52.68 just intonation subgroup, tempering out 289/288, 325/324, 352/351, 385/384, 561/560, 595/594, 625/624, 676/675, 1089/1088, 1156/1155, 1225/1224, and 1331/1326.


Approximation of prime harmonics in 37edt
Harmonic 2 3 5 7 11 13 17 19 23 29 31 37 41 43 47
Error Absolute (¢) -17.7 +0.0 -10.5 +23.9 +12.4 -19.8 -21.6 -8.5 +20.6 -20.9 +17.9 +20.0 -3.5 +16.8 +17.0
Relative (%) -34.4 +0.0 -20.4 +46.4 +24.2 -38.5 -41.9 -16.5 +40.0 -40.7 +34.7 +38.8 -6.9 +32.7 +33.1
Steps
(reduced)
23
(23)
37
(0)
54
(17)
66
(29)
81
(7)
86
(12)
95
(21)
99
(25)
106
(32)
113
(2)
116
(5)
122
(11)
125
(14)
127
(16)
130
(19)