6ed6: Difference between revisions
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{{Harmonics in equal|6|6|1|intervals=integer|columns=11}} | {{Harmonics in equal|6|6|1|intervals=integer|columns=11}} | ||
{{Harmonics in equal|6|6|1|intervals=integer|columns=12|start=12|collapsed=true}} | {{Harmonics in equal|6|6|1|intervals=integer|columns=12|start=12|collapsed=true}} | ||
=== Subsets and supersets === | |||
Since 6 factors into primes as {{nowrap| 2 × 3 }}, 6ed6 contains [[2ed6]] and [[3ed6]] as subset ed6's. | |||
== Intervals == | == Intervals == | ||
{{Interval table}} | {{Interval table}} | ||
Revision as of 13:02, 23 May 2025
| ← 5ed6 | 6ed6 | 7ed6 → |
6 equal divisions of the 6th harmonic (abbreviated 6ed6) is a nonoctave tuning system that divides the interval of 6/1 into 6 equal parts of about 517 ¢ each. Each step represents a frequency ratio of 61/6, or the 6th root of 6.
Theory
6ed6 corresponds to 2.3211…edo. It is the generator chain for the harry temperament.
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -166 | +166 | +185 | -201 | +0 | +250 | +19 | -185 | +150 | -15 | -166 |
| Relative (%) | -32.1 | +32.1 | +35.8 | -38.9 | +0.0 | +48.4 | +3.7 | -35.8 | +28.9 | -3.0 | -32.1 | |
| Steps (reduced) |
2 (2) |
4 (4) |
5 (5) |
5 (5) |
6 (0) |
7 (1) |
7 (1) |
7 (1) |
8 (2) |
8 (2) |
8 (2) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +212 | +84 | -35 | -147 | -252 | +166 | +72 | -16 | -101 | -181 | -258 | +185 |
| Relative (%) | +41.1 | +16.3 | -6.8 | -28.4 | -48.7 | +32.1 | +14.0 | -3.2 | -19.5 | -35.1 | -50.0 | +35.8 | |
| Steps (reduced) |
9 (3) |
9 (3) |
9 (3) |
9 (3) |
9 (3) |
10 (4) |
10 (4) |
10 (4) |
10 (4) |
10 (4) |
10 (4) |
11 (5) | |
Subsets and supersets
Since 6 factors into primes as 2 × 3, 6ed6 contains 2ed6 and 3ed6 as subset ed6's.
Intervals
| Steps | Cents | Approximate ratios |
|---|---|---|
| 0 | 0 | 1/1 |
| 1 | 517 | 15/11, 18/13, 19/14 |
| 2 | 1034 | 11/6, 13/7 |
| 3 | 1551 | 5/2, 12/5 |
| 4 | 2068 | 17/5 |
| 5 | 2585 | 13/3 |
| 6 | 3102 | 6/1 |