11ed6: Difference between revisions
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==Related temperament== | == Theory == | ||
===2.3.11 subgroup 17& | 11ed6 corresponds to 4.2554…[[edo]]. It is related to the temperaments which temper out [[28561/28512]] and [[85293/85184]] in the [[13-limit]], which is [[support]]ed by edos {{EDOs| 17, 149, 166, 183, 200, 217, and 234}}. | ||
=== Harmonics === | |||
{{Harmonics in equal|11|6|1|intervals=integer|columns=11}} | |||
{{Harmonics in equal|11|6|1|intervals=integer|columns=12|start=12|collapsed=true|Approximation of harmonics in 11ed6 (continued)}} | |||
== Intervals == | |||
{{Interval table}} | |||
== Related temperament == | |||
=== 2.3.11 subgroup 17 & 183 === | |||
Comma: |-19 36 0 0 -11> | Comma: |-19 36 0 0 -11> | ||
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EDOs: {{EDOs|17, 34, 166, 183, 200, 217, 366, 383, 400, 566}} | EDOs: {{EDOs|17, 34, 166, 183, 200, 217, 366, 383, 400, 566}} | ||
===2.3.11.13 subgroup 17& | === 2.3.11.13 subgroup 17 & 183 === | ||
Commas: 28561/28512, 85293/85184 | Commas: 28561/28512, 85293/85184 | ||
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EDOs: {{EDOs|17, 34, 149, 166, 183, 200, 217, 234, 366}} | EDOs: {{EDOs|17, 34, 149, 166, 183, 200, 217, 234, 366}} | ||
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Revision as of 13:06, 23 May 2025
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Template:Niche is deprecated. Please use Template:Mathematical interest instead. |
| ← 10ed6 | 11ed6 | 12ed6 → |
11 equal divisions of the 6th harmonic (abbreviated 11ed6) is a nonoctave tuning system that divides the interval of 6/1 into 11 equal parts of about 282 ¢ each. Each step represents a frequency ratio of 61/11, or the 11th root of 6.
Theory
11ed6 corresponds to 4.2554…edo. It is related to the temperaments which temper out 28561/28512 and 85293/85184 in the 13-limit, which is supported by edos 17, 149, 166, 183, 200, 217, and 234.
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -72 | +72 | +138 | +34 | +0 | +15 | +66 | -138 | -38 | +79 | -72 |
| Relative (%) | -25.5 | +25.5 | +48.9 | +11.9 | +0.0 | +5.4 | +23.4 | -48.9 | -13.6 | +27.9 | -25.5 | |
| Steps (reduced) |
4 (4) |
7 (7) |
9 (9) |
10 (10) |
11 (0) |
12 (1) |
13 (2) |
13 (2) |
14 (3) |
15 (4) |
15 (4) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +71 | -57 | +106 | -6 | -111 | +72 | -22 | -110 | +87 | +7 | -70 | +138 |
| Relative (%) | +25.3 | -20.2 | +37.5 | -2.2 | -39.4 | +25.5 | -7.7 | -39.1 | +30.9 | +2.3 | -24.9 | +48.9 | |
| Steps (reduced) |
16 (5) |
16 (5) |
17 (6) |
17 (6) |
17 (6) |
18 (7) |
18 (7) |
18 (7) |
19 (8) |
19 (8) |
19 (8) |
20 (9) | |
Intervals
| Steps | Cents | Approximate ratios |
|---|---|---|
| 0 | 0 | 1/1 |
| 1 | 282 | 7/6, 13/11, 20/17, 22/19 |
| 2 | 564 | 7/5, 15/11, 18/13 |
| 3 | 846 | 18/11, 21/13 |
| 4 | 1128 | 19/10, 21/11 |
| 5 | 1410 | |
| 6 | 1692 | |
| 7 | 1974 | 19/6, 22/7 |
| 8 | 2256 | 11/3 |
| 9 | 2538 | 13/3, 22/5 |
| 10 | 2820 | |
| 11 | 3102 | 6/1 |
Related temperament
2.3.11 subgroup 17 & 183
Comma: |-19 36 0 0 -11>
POTE generator: ~|7 -13 0 0 4> = 281.9832
Mapping: [<1 -1 -5|, <0 11 36|]
EDOs: 17, 34, 166, 183, 200, 217, 366, 383, 400, 566
2.3.11.13 subgroup 17 & 183
Commas: 28561/28512, 85293/85184
POTE generator: ~286/243 = 281.9821
Mapping: [<1 -1 -5 -1|, <0 11 36 20|]