25edt: Difference between revisions
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{{Infobox ET}} | {{Infobox ET}} | ||
'''25EDT''' is the [[Edt|equal division of the third harmonic]] into 25 parts of 76.0782 [[cent|cents]] each, corresponding to 15.7732 [[edo]] (stretched version of [[16edo]]). | '''25EDT''' is the [[Edt|equal division of the third harmonic]] into 25 parts of 76.0782 [[cent|cents]] each, corresponding to 15.7732 [[edo]] (stretched version of [[16edo]]). | ||
This scale coincidentally turns out to be 16 equal divisions of a stretched octave (1217.25 cents) and a tritave twin of the Armodue/Hornbostel flat third-tone system: | This scale coincidentally turns out to be 16 equal divisions of a stretched octave (1217.25 cents) and a tritave twin of the Armodue/Hornbostel flat third-tone system: | ||
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* fourth power = 2358.425 cents = 456.47 cents | * fourth power = 2358.425 cents = 456.47 cents | ||
== Intervals == | |||
{| class="wikitable" | {| class="wikitable" | ||
|- | |- | ||
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| | 1 | | | 1 | ||
|} | |} | ||
== Harmonics == | |||
{{Harmonics in equal | |||
| steps = 25 | |||
| num = 3 | |||
| denom = 1 | |||
| intervals = prime | |||
}} | |||
{{Harmonics in equal | |||
| steps = 25 | |||
| num = 3 | |||
| denom = 1 | |||
| start = 12 | |||
| collapsed = 1 | |||
| intervals = prime | |||
}} | |||
[[Category:Armodue]] | [[Category:Armodue]] | ||
[[Category:Edt]] | [[Category:Edt]] | ||
[[Category:Edonoi]] | [[Category:Edonoi]] | ||
Revision as of 06:46, 6 October 2024
| ← 24edt | 25edt | 26edt → |
25EDT is the equal division of the third harmonic into 25 parts of 76.0782 cents each, corresponding to 15.7732 edo (stretched version of 16edo).
This scale coincidentally turns out to be 16 equal divisions of a stretched octave (1217.25 cents) and a tritave twin of the Armodue/Hornbostel flat third-tone system:
- 6th = 1065.095 cents
- squared = 2130.19 cents = 228.235 cents
- cubed = 1293.33 cents
- fourth power = 2358.425 cents = 456.47 cents
Intervals
| Degree | cents | hekts | Armodue name |
|---|---|---|---|
| 1 | 76.08 | 52 | 1#/2bb |
| 2 | 152.16 | 104 | 1x/2b |
| 3 | 228.235 | 156 | 2 |
| 4 | 304.31 | 208 | 2#/3bb |
| 5 | 380.39 | 260 | 2x/3b |
| 6 | 456.47 | 312 | 3 |
| 7 | 532.55 | 364 | 3#/4b |
| 8 | 608.625 | 416 | 4 |
| 9 | 684.70 | 468 | 4#/5bb |
| 10 | 760.78 | 520 | 4x/5b |
| 11 | 836.86 | 572 | 5 |
| 12 | 912.94 | 624 | 5#/6bb |
| 13 | 989.02 | 676 | 5x/6b |
| 14 | 1065.095 | 728 | 6 |
| 15 | 1141.17 | 780 | 6#/7bb |
| 16 | 1217.25 | 832 | 6x/7b |
| 17 | 1293.33 | 884 | 7 |
| 18 | 1369.41 | 936 | 7#/8b |
| 19 | 1445.485 | 988 | 8 |
| 20 | 1521.56 | 1040 | 8#/9bb |
| 21 | 1597.64 | 1092 | 8x/9b |
| 22 | 1673.72 | 1144 | 9 |
| 23 | 1749.80 | 1196 | 9#/1bb |
| 24 | 1825.88 | 1248 | 9x/1b |
| 25 | 1901.955 | 1300 | 1 |
Harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +17.3 | +0.0 | +28.6 | -21.4 | +33.0 | -28.0 | -36.0 | -0.3 | -26.7 | +28.4 | -10.9 |
| Relative (%) | +22.7 | +0.0 | +37.6 | -28.1 | +43.4 | -36.8 | -47.3 | -0.4 | -35.1 | +37.4 | -14.4 | |
| Steps (reduced) |
16 (16) |
25 (0) |
37 (12) |
44 (19) |
55 (5) |
58 (8) |
64 (14) |
67 (17) |
71 (21) |
77 (2) |
78 (3) | |
| Harmonic | 37 | 41 | 43 | 47 | 53 | 59 | 61 | 67 | 71 | 73 | 79 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -12.9 | +37.6 | +31.2 | +29.4 | -26.5 | +16.1 | +34.5 | +24.2 | -0.1 | +27.9 | -32.8 |
| Relative (%) | -17.0 | +49.4 | +41.0 | +38.6 | -34.8 | +21.2 | +45.3 | +31.8 | -0.1 | +36.6 | -43.1 | |
| Steps (reduced) |
82 (7) |
85 (10) |
86 (11) |
88 (13) |
90 (15) |
93 (18) |
94 (19) |
96 (21) |
97 (22) |
98 (23) |
99 (24) | |