9ed5/3: Difference between revisions
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Created page with "'''9ED5/3''' is the equal division of the just major sixth into sixteen parts of 98.2621 cents each, corresponding to 12.2122 edo. It is very closely rel..." Tags: Mobile edit Mobile web edit |
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''' | {{Infobox ET}} | ||
'''9ed5/3''' is the [[Ed5/3|equal division of the just major sixth]] into nine parts of 98.2621 [[cent]]s each, corresponding to 12.2122[[edo]]. It is very closely related to the [[Passion family#Passion|passion temperament]]. | |||
[[ | ==Intervals== | ||
{| class="wikitable right-2 center-3" | |||
|+ | |||
!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 == | |||
{{Harmonics in equal|9|5|3}} | |||
{{Harmonics in equal|9|5|3|collapsed=1|start=12}} | |||
{{todo|inline=1|improve synopsis|expand}} | |||
[[Category:Nonoctave]] | [[Category:Nonoctave]] | ||
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 |