19ed7: Difference between revisions
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'''[[Ed7|Division of the 7th harmonic]] into 19 equal parts''' (19ed7) is related to the 11-limit [[Tetracot family|wollemia temperament]], which is a [[cluster temperament]] with seven clusters of notes in an octave. The step size is about 177.3066 cents, corresponding to 6.7679 [[edo]]. | '''[[Ed7|Division of the 7th harmonic]] into 19 equal parts''' (19ed7) is related to the 11-limit [[Tetracot family|wollemia temperament]], which is a [[cluster temperament]] with seven clusters of notes in an octave. The step size is about 177.3066 cents, corresponding to 6.7679 [[edo]]. | ||
==Intervals== | |||
{| class="wikitable" | {| class="wikitable" | ||
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==Harmonics== | |||
{{Harmonics in equal | |||
| steps = 19 | |||
| num = 7 | |||
| denom = 1 | |||
}} | |||
{{Harmonics in equal | |||
| steps = 19 | |||
| num = 7 | |||
| denom = 1 | |||
| start = 12 | |||
| collapsed = 1 | |||
}} | |||
{{stub}} | |||
Latest revision as of 19:20, 1 August 2025
| ← 18ed7 | 19ed7 | 20ed7 → |
Division of the 7th harmonic into 19 equal parts (19ed7) is related to the 11-limit wollemia temperament, which is a cluster temperament with seven clusters of notes in an octave. The step size is about 177.3066 cents, corresponding to 6.7679 edo.
Intervals
| degree | cents value | corresponding JI intervals |
comments |
|---|---|---|---|
| 0 | 0.0000 | exact 1/1 | |
| 1 | 177.3066 | 10/9 | |
| 2 | 354.6133 | 11/9, 60/49, 49/40, 27/22 | |
| 3 | 531.9199 | 49/36, 15/11 | |
| 4 | 709.2265 | 3/2 | |
| 5 | 886.5331 | 5/3 | |
| 6 | 1063.8398 | 13/7 | |
| 7 | 1241.1464 | 49/24, 45/22 | |
| 8 | 1418.4530 | 25/11, 91/40 | |
| 9 | 1595.7596 | 98/39 | |
| 10 | 1773.0663 | 39/14 | |
| 11 | 1950.3729 | 40/13, 77/25 | |
| 12 | 2127.6795 | 24/7 | |
| 13 | 2304.9861 | 49/13 | |
| 14 | 2482.2928 | 21/5 | |
| 15 | 2659.5994 | 14/3 | |
| 16 | 2836.9060 | 77/15, 36/7 | |
| 17 | 3014.2127 | 154/27, 40/7, 63/11 | |
| 18 | 3191.5193 | 63/10 | |
| 19 | 3368.8259 | exact 7/1 | harmonic seventh plus two octaves |
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +41.1 | +48.4 | +82.3 | +50.6 | -87.7 | +0.0 | -53.9 | -80.5 | -85.6 | -73.3 | -46.6 |
| Relative (%) | +23.2 | +27.3 | +46.4 | +28.5 | -49.5 | +0.0 | -30.4 | -45.4 | -48.3 | -41.3 | -26.3 | |
| Steps (reduced) |
7 (7) |
11 (11) |
14 (14) |
16 (16) |
17 (17) |
19 (0) |
20 (1) |
21 (2) |
22 (3) |
23 (4) |
24 (5) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -7.9 | +41.1 | -78.3 | -12.7 | +59.6 | -39.3 | +44.4 | -44.4 | +48.4 | -32.1 | +68.2 |
| Relative (%) | -4.4 | +23.2 | -44.2 | -7.2 | +33.6 | -22.2 | +25.0 | -25.1 | +27.3 | -18.1 | +38.5 | |
| Steps (reduced) |
25 (6) |
26 (7) |
26 (7) |
27 (8) |
28 (9) |
28 (9) |
29 (10) |
29 (10) |
30 (11) |
30 (11) |
31 (12) | |
|
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