9ed5/3: Difference between revisions
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==Intervals== | ==Intervals== | ||
{| class="wikitable" | {| class="wikitable right-2 center-3" | ||
|+ | |+ | ||
!Degrees | !Degrees | ||
! | !Cents | ||
! | !5/3.4/3.7/3 interpretation | ||
|- | |- | ||
|1 | |1 | ||
|98.2621 | |98.2621 | ||
|[[16/15]], [[21/20]] | |||
|- | |- | ||
|2 | |2 | ||
|196.5241 | |196.5241 | ||
|[[28/25]] | |||
|- | |- | ||
|3 | |3 | ||
|294.7862 | |294.7862 | ||
|[[25/21]] | |||
|- | |- | ||
|4 | |4 | ||
|393.0483 | |393.0483 | ||
|[[5/4]] | |||
|- | |- | ||
|5 | |5 | ||
|491.3104 | |491.3104 | ||
|[[4/3]] | |||
|- | |- | ||
|6 | |6 | ||
|589.5725 | |589.5725 | ||
|[[7/5]] | |||
|- | |- | ||
|7 | |7 | ||
|687.83455 | |687.83455 | ||
|[[112/75]] | |||
|- | |- | ||
|8 | |8 | ||
|786.0966 | |786.0966 | ||
|[[25/16]], [[80/63]] | |||
|- | |- | ||
|9 | |'''9''' | ||
|884. | |'''884.3587''' | ||
| | |'''[[5/3]] (just)''' | ||
|- | |- | ||
|10 | |10 | ||
|982.6207 | |982.6207 | ||
|[[7/4]], [[16/9]] | |||
|- | |- | ||
|11 | |11 | ||
|1080.8828 | |1080.8828 | ||
|[[28/15]] | |||
|- | |- | ||
|12 | |12 | ||
|1179.14495 | |1179.14495 | ||
|[[49/25]] | |||
|- | |- | ||
|13 | |13 | ||
|1277.407 | |1277.407 | ||
|[[25/12]] | |||
|- | |- | ||
|14 | |14 | ||
|1375.6691 | |1375.6691 | ||
|[[20/9]] | |||
|- | |- | ||
|15 | |15 | ||
|1473.9312 | |1473.9312 | ||
|[[7/3]] | |||
|} | |} | ||
The interval interpretations listed belong to the generator chain of [[septimal passion]] without octaves. | |||
== Harmonics == | == Harmonics == | ||
Latest revision as of 14:20, 24 April 2025
| ← 8ed5/3 | 9ed5/3 | 10ed5/3 → |
9ed5/3 is the equal division of the just major sixth into nine parts of 98.2621 cents each, corresponding to 12.2122edo. It is very closely related to the passion temperament.
Intervals
| Degrees | Cents | 5/3.4/3.7/3 interpretation |
|---|---|---|
| 1 | 98.2621 | 16/15, 21/20 |
| 2 | 196.5241 | 28/25 |
| 3 | 294.7862 | 25/21 |
| 4 | 393.0483 | 5/4 |
| 5 | 491.3104 | 4/3 |
| 6 | 589.5725 | 7/5 |
| 7 | 687.83455 | 112/75 |
| 8 | 786.0966 | 25/16, 80/63 |
| 9 | 884.3587 | 5/3 (just) |
| 10 | 982.6207 | 7/4, 16/9 |
| 11 | 1080.8828 | 28/15 |
| 12 | 1179.14495 | 49/25 |
| 13 | 1277.407 | 25/12 |
| 14 | 1375.6691 | 20/9 |
| 15 | 1473.9312 | 7/3 |
The interval interpretations listed belong to the generator chain of septimal passion without octaves.
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -20.9 | -35.0 | -41.7 | -35.0 | +42.4 | -27.9 | +35.7 | +28.3 | +42.4 | -24.3 | +21.6 |
| Relative (%) | -21.2 | -35.6 | -42.4 | -35.6 | +43.2 | -28.4 | +36.3 | +28.8 | +43.2 | -24.7 | +22.0 | |
| Steps (reduced) |
12 (3) |
19 (1) |
24 (6) |
28 (1) |
32 (5) |
34 (7) |
37 (1) |
39 (3) |
41 (5) |
42 (6) |
44 (8) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -18.7 | -48.8 | +28.3 | +14.8 | +8.1 | +7.5 | +12.1 | +21.6 | +35.4 | -45.2 | -23.9 |
| Relative (%) | -19.1 | -49.6 | +28.8 | +15.1 | +8.3 | +7.6 | +12.3 | +22.0 | +36.0 | -46.0 | -24.3 | |
| Steps (reduced) |
45 (0) |
46 (1) |
48 (3) |
49 (4) |
50 (5) |
51 (6) |
52 (7) |
53 (8) |
54 (0) |
54 (0) |
55 (1) | |
|
Todo: improve synopsis , expand |