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Created page with "'''Division of the 7th harmonic into 25 equal parts''' (25ed7) is related to 9 edo, but with the 7/1 rather than the 2/1 being just. The step size is about 13..." Tags: Mobile edit Mobile web edit |
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'''[[Ed7|Division of the 7th harmonic]] into 25 equal parts''' (25ed7) is related to [[9edo | {{Infobox ET}} | ||
'''[[Ed7|Division of the 7th harmonic]] into 25 equal parts''' (25ed7) is related to [[9edo]], but with the 7/1 rather than the 2/1 being just. The octave is about 12.7773 cents stretched and the step size is about 134.7530 cents. | |||
{| class="wikitable" | == Intervals == | ||
{| class="wikitable mw-collapsible" | |||
|+ Intervals of 25ed7 | |||
|- | |- | ||
! | degree | ! | degree | ||
| Line 15: | Line 18: | ||
| | 1 | | | 1 | ||
| | 134.7530 | | | 134.7530 | ||
| | [[27/25]] | | | ([[27/25]]), [[13/12]] | ||
| | | | | | ||
|- | |- | ||
| Line 40: | Line 43: | ||
| | 6 | | | 6 | ||
| | 808.5182 | | | 808.5182 | ||
| | | | | (147/92) | ||
| | | | | | ||
|- | |- | ||
| Line 55: | Line 58: | ||
| | 9 | | | 9 | ||
| | 1212.7773 | | | 1212.7773 | ||
| | | | | 161/80 | ||
| | | | | | ||
|- | |- | ||
| Line 90: | Line 93: | ||
| | 16 | | | 16 | ||
| | 2156.0486 | | | 2156.0486 | ||
| | | | | 80/23 | ||
| | | | | | ||
|- | |- | ||
| Line 105: | Line 108: | ||
| | 19 | | | 19 | ||
| | 2560.3077 | | | 2560.3077 | ||
| | | | | (92/21) | ||
| | | | | | ||
|- | |- | ||
| Line 130: | Line 133: | ||
| | 24 | | | 24 | ||
| | 3234.0729 | | | 3234.0729 | ||
| | 175/27 | | | 84/13, (175/27) | ||
| | | | | | ||
|- | |- | ||
| Line 139: | Line 142: | ||
|} | |} | ||
[[ | == Harmonics == | ||
[[ | {{Harmonics in equal|25|7|1|intervals=prime}} | ||
{{Harmonics in equal|25|7|1|intervals=prime|collapsed=1|start=12}} | |||
==25ed7 as a generator== | |||
25ed7 can also be thought of as a [[generator]] of the 23-limit temperament which tempers out 169/168, 176/175, 208/207, 221/220, 247/245, 256/255, and 361/360, which is a [[cluster temperament]] with nine clusters of notes in an octave. This temperament is supported by [[9edo]], [[71edo]] (using 71d val), [[80edo]], and [[89edo]] among others. | |||
{{todo|expand}} | |||
Latest revision as of 19:21, 1 August 2025
| ← 24ed7 | 25ed7 | 26ed7 → |
Division of the 7th harmonic into 25 equal parts (25ed7) is related to 9edo, but with the 7/1 rather than the 2/1 being just. The octave is about 12.7773 cents stretched and the step size is about 134.7530 cents.
Intervals
| degree | cents value | corresponding JI intervals |
comments |
|---|---|---|---|
| 0 | 0.0000 | exact 1/1 | |
| 1 | 134.7530 | (27/25), 13/12 | |
| 2 | 269.5061 | 7/6 | |
| 3 | 404.2591 | 24/19, 91/72 | |
| 4 | 539.0121 | 15/11 | |
| 5 | 673.7652 | 28/19 | |
| 6 | 808.5182 | (147/92) | |
| 7 | 943.2713 | 19/11 | |
| 8 | 1078.0243 | 28/15 | |
| 9 | 1212.7773 | 161/80 | |
| 10 | 1347.5304 | 24/11 | |
| 11 | 1482.2834 | 40/17 | |
| 12 | 1617.0364 | 28/11 | |
| 13 | 1751.7895 | 11/4 | |
| 14 | 1886.5425 | 119/40 | |
| 15 | 2021.2955 | 77/24 | |
| 16 | 2156.0486 | 80/23 | |
| 17 | 2290.8016 | 15/4 | |
| 18 | 2425.5547 | 77/19 | |
| 19 | 2560.3077 | (92/21) | |
| 20 | 2695.0607 | 19/4 | |
| 21 | 2829.8138 | 77/15 | |
| 22 | 2964.5668 | 72/13, 133/24 | |
| 23 | 3099.3198 | 6/1 | |
| 24 | 3234.0729 | 84/13, (175/27) | |
| 25 | 3368.8259 | exact 7/1 | harmonic seventh plus two octaves |
Harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +12.8 | -15.4 | +43.5 | +0.0 | +26.0 | +6.3 | -53.8 | +23.1 | -38.2 | -35.2 | -15.9 |
| Relative (%) | +9.5 | -11.4 | +32.3 | +0.0 | +19.3 | +4.7 | -40.0 | +17.1 | -28.3 | -26.1 | -11.8 | |
| Steps (reduced) |
9 (9) |
14 (14) |
21 (21) |
25 (0) |
31 (6) |
33 (8) |
36 (11) |
38 (13) |
40 (15) |
43 (18) |
44 (19) | |
| Harmonic | 37 | 41 | 43 | 47 | 53 | 59 | 61 | 67 | 71 | 73 | 79 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -52.7 | +39.1 | -43.4 | -62.6 | -1.1 | -52.0 | +25.0 | -2.6 | +31.7 | -16.4 | -18.4 |
| Relative (%) | -39.1 | +29.0 | -32.2 | -46.5 | -0.8 | -38.6 | +18.6 | -2.0 | +23.5 | -12.1 | -13.6 | |
| Steps (reduced) |
46 (21) |
48 (23) |
48 (23) |
49 (24) |
51 (1) |
52 (2) |
53 (3) |
54 (4) |
55 (5) |
55 (5) |
56 (6) | |
25ed7 as a generator
25ed7 can also be thought of as a generator of the 23-limit temperament which tempers out 169/168, 176/175, 208/207, 221/220, 247/245, 256/255, and 361/360, which is a cluster temperament with nine clusters of notes in an octave. This temperament is supported by 9edo, 71edo (using 71d val), 80edo, and 89edo among others.