User:Hotcrystal0/27edo: Difference between revisions
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Hotcrystal0 (talk | contribs) Created page with "'''27edo''', or 27 equal divisions of the octave, is the equal tuning featuring steps of (1200/27) ~= 44.44 cents, 27 of which stack to the perfect octave 2/1. ==Theory== ===JI approximation=== {{Harmonics in ED|27|31|0}} ===Edostep interpretations=== 27edo's edostep has the following interpretations in the 2.3.5.7.13 subgroup: * WIP ===Chords=== {{WIP}} ===Scales=== {{WIP}} == Multiples == === 54edo === {{Harmonics in ED|54|31|0}} === 81edo === {{Harmonics..." |
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== Multiples == | == Multiples == | ||
=== 54edo === | === 54edo === | ||
{{Harmonics in ED|54|31|0}} | {{Harmonics in ED|54|31|0}} | ||
=== 81edo === | === 81edo === | ||
{{Harmonics in ED|81|31|0}} | {{Harmonics in ED|81|31|0}} | ||
=== 270edo === | |||
{{Harmonics in ED|270|31|0}} | |||
{{navbox EDO}} | {{navbox EDO}} | ||
{{Cat|edos}} | {{Cat|edos}} | ||
Revision as of 00:46, 23 April 2026
27edo, or 27 equal divisions of the octave, is the equal tuning featuring steps of (1200/27) ~= 44.44 cents, 27 of which stack to the perfect octave 2/1.
Theory
JI approximation
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | 0.0 | +9.2 | +13.7 | +9.0 | -18.0 | +3.9 | -16.1 | +13.6 | -6.1 | -7.4 | +10.5 |
| Relative (%) | 0.0 | +20.6 | +30.8 | +20.1 | -40.5 | +8.8 | -36.1 | +30.6 | -13.6 | -16.5 | +23.7 | |
| Steps
(reduced) |
27
(0) |
43
(16) |
63
(9) |
76
(22) |
93
(12) |
100
(19) |
110
(2) |
115
(7) |
122
(14) |
131
(23) |
134
(26) | |
Edostep interpretations
27edo's edostep has the following interpretations in the 2.3.5.7.13 subgroup:
- WIP
Chords
This page or section is a work in progress. It may lack sufficient justification, content, or organization, and is subject to future overhaul.
Scales
This page or section is a work in progress. It may lack sufficient justification, content, or organization, and is subject to future overhaul.
Multiples
54edo
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | 0.0 | +9.2 | -8.5 | +9.0 | +4.2 | +3.9 | +6.2 | -8.6 | -6.1 | -7.4 | +10.5 |
| Relative (%) | 0.0 | +41.2 | -38.4 | +40.3 | +19.1 | +17.6 | +27.7 | -38.8 | -27.2 | -33.1 | +47.3 | |
| Steps
(reduced) |
54
(0) |
86
(32) |
125
(17) |
152
(44) |
187
(25) |
200
(38) |
221
(5) |
229
(13) |
244
(28) |
262
(46) |
268
(52) | |
81edo
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | 0.0 | -5.7 | -1.1 | -5.9 | -3.2 | +3.9 | -1.3 | -1.2 | -6.1 | -7.4 | -4.3 |
| Relative (%) | 0.0 | -38.2 | -7.6 | -39.6 | -21.4 | +26.4 | -8.4 | -8.2 | -40.9 | -49.6 | -29.0 | |
| Steps
(reduced) |
81
(0) |
128
(47) |
188
(26) |
227
(65) |
280
(37) |
300
(57) |
331
(7) |
344
(20) |
366
(42) |
393
(69) |
401
(77) | |
270edo
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | 0.0 | +0.3 | +0.4 | +0.1 | -0.2 | -0.5 | +1.7 | +0.3 | -1.6 | +1.5 | +1.6 |
| Relative (%) | 0.0 | +6.0 | +7.9 | +1.4 | -4.7 | -11.9 | +38.5 | +6.0 | -36.2 | +34.5 | +36.7 | |
| Steps
(reduced) |
270
(0) |
428
(158) |
627
(87) |
758
(218) |
934
(124) |
999
(189) |
1104
(24) |
1147
(67) |
1221
(141) |
1312
(232) |
1338
(258) | |
