111ed6: Difference between revisions

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{{Infobox ET}}
{{Infobox ET}}
'''[[Ed6|Division of the sixth harmonic]] into 111 equal parts''' (111ED6) is related to [[43edo|43 edo]] (meride tuning), but with the 6/1 rather than the 2/1 being just. The octave is about 1.66 cents stretched and the step size is 27.95 cents.
{{ED intro}}
 
111ED6 is related to [[43edo]] (meride tuning), but with the 6/1 rather than the 2/1 being just. This stretches the octave by about 1.66 cents.


Lookalikes: [[43edo]], [[68edt]], [[100ed5]], [[25edf]]
Lookalikes: [[43edo]], [[68edt]], [[100ed5]], [[25edf]]


==Harmonics==
== Harmonics ==
{{Harmonics in equal|111|6|1|intervals=prime}}
{{Harmonics in equal|111|6|1|intervals=prime}}
{{Harmonics in equal|111|6|1|intervals=prime|collapsed=1|start=12}}
{{Harmonics in equal|111|6|1|intervals=prime|collapsed=1|start=12}}

Revision as of 16:56, 21 January 2025

← 110ed6 111ed6 112ed6 →
Prime factorization 3 × 37
Step size 27.9455 ¢ 
Octave 43\111ed6 (1201.66 ¢)
Twelfth 68\111ed6 (1900.3 ¢)
Consistency limit 6
Distinct consistency limit 6

111 equal divisions of the 6th harmonic (abbreviated 111ed6) is a nonoctave tuning system that divides the interval of 6/1 into 111 equal parts of about 27.9 ¢ each. Each step represents a frequency ratio of 61/111, or the 111th root of 6.

111ED6 is related to 43edo (meride tuning), but with the 6/1 rather than the 2/1 being just. This stretches the octave by about 1.66 cents.

Lookalikes: 43edo, 68edt, 100ed5, 25edf

Harmonics

Approximation of prime harmonics in 111ed6
Harmonic 2 3 5 7 11 13 17 19 23 29 31
Error Absolute (¢) +1.7 -1.7 +8.2 +12.6 +12.6 +2.8 +13.5 -11.4 -6.8 +11.0 +7.4
Relative (%) +5.9 -5.9 +29.5 +45.0 +45.0 +10.1 +48.2 -40.9 -24.5 +39.5 +26.4
Steps
(reduced)
43
(43)
68
(68)
100
(100)
121
(10)
149
(38)
159
(48)
176
(65)
182
(71)
194
(83)
209
(98)
213
(102)
Approximation of prime harmonics in 111ed6
Harmonic 37 41 43 47 53 59 61 67 71 73 79
Error Absolute (¢) +8.5 -1.6 -0.2 +13.5 +1.1 +11.1 +9.2 -13.5 -2.1 +5.7 +8.7
Relative (%) +30.3 -5.7 -0.7 +48.2 +3.9 +39.5 +33.0 -48.2 -7.4 +20.5 +31.1
Steps
(reduced)
224
(2)
230
(8)
233
(11)
239
(17)
246
(24)
253
(31)
255
(33)
260
(38)
264
(42)
266
(44)
271
(49)


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