42edt: Difference between revisions

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{{Infobox ET}}
{{Infobox ET}}
'''42EDT''' is the [[Edt|equal division of the third harmonic]] into 42 parts of 45.2846 [[cent|cents]] each, corresponding to 26.4990 [[edo]]. It is [[contorted]] in the no-twos 17-limit, tempering out 77/75, 119/117, 147/143, 169/165, and 245/243. Using the patent val, it tempers out 363/361 in the 19-limit; 117/115, 119/115, 255/253, 299/297, and 391/375 in the 23-limit (no-twos subgroup). It entirely misses 2/1, but nails the "double octave" 4/1, so it strongly resembles the scale with generator 2\53 of an octave.
'''42EDT''' is the [[Edt|equal division of the third harmonic]] into 42 parts of 45.2846 [[cent|cents]] each, corresponding to 26.4990 [[edo]]. It is [[contorted]] in the no-twos 17-limit, tempering out 77/75, 119/117, 147/143, 169/165, and 245/243. Using the patent val, it tempers out 363/361 in the 19-limit; 117/115, 119/115, 255/253, 299/297, and 391/375 in the 23-limit (no-twos subgroup). It entirely misses 2/1, but nails the "double octave" 4/1, so it strongly resembles the scale with generator 2\53 of an octave.
{{Harmonics in equal|42|3|1|intervals=prime|columns=15}}


Lookalikes: [[53ed4|53ED4]]
Lookalikes: [[53ed4|53ED4]]

Revision as of 19:00, 30 September 2024

← 41edt 42edt 43edt →
Prime factorization 2 × 3 × 7
Step size 45.2846 ¢ 
Octave 26\42edt (1177.4 ¢) (→ 13\21edt)
Consistency limit 3
Distinct consistency limit 3

42EDT is the equal division of the third harmonic into 42 parts of 45.2846 cents each, corresponding to 26.4990 edo. It is contorted in the no-twos 17-limit, tempering out 77/75, 119/117, 147/143, 169/165, and 245/243. Using the patent val, it tempers out 363/361 in the 19-limit; 117/115, 119/115, 255/253, 299/297, and 391/375 in the 23-limit (no-twos subgroup). It entirely misses 2/1, but nails the "double octave" 4/1, so it strongly resembles the scale with generator 2\53 of an octave.


Approximation of prime harmonics in 42edt
Harmonic 2 3 5 7 11 13 17 19 23 29 31 37 41 43 47
Error Absolute (¢) -22.6 +0.0 +21.3 -17.8 +14.9 -2.6 -14.2 +19.7 +5.9 +12.1 -12.7 -2.1 +1.4 +9.5 -8.7
Relative (%) -49.9 +0.0 +47.1 -39.2 +32.8 -5.8 -31.4 +43.4 +13.0 +26.8 -28.1 -4.6 +3.0 +20.9 -19.1
Steps
(reduced)
26
(26)
42
(0)
62
(20)
74
(32)
92
(8)
98
(14)
108
(24)
113
(29)
120
(36)
129
(3)
131
(5)
138
(12)
142
(16)
144
(18)
147
(21)

Lookalikes: 53ED4