User:MisterShafXen/6ed9/7: Difference between revisions
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Prime factorization
2 × 3 (highly composite)
Step size
72.514 ¢
Octave
17\6ed9/7 (1232.74 ¢)
Twelfth
26\6ed9/7 (1885.36 ¢) (→ 13\3ed9/7)
Consistency limit
2
Distinct consistency limit
2
Created page with "{{ED intro}} ==Harmonics== {{Harmonics in equal | num = 9 | denom = 7 | steps = 6 | columns = 20}}" Tags: Visual edit Mobile edit Mobile web edit |
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{{ED intro}} | {{Infobox ET|6ed9/7|debug=true}} | ||
{{ED intro}} | |||
== Theory == | |||
This tuning tempers out [[21/20]] in the [[7-limit]], [[55/54]] in the [[11-limit]], [[27/26]], [[55/52]], and [[16/13]] in the [[13-limit]], [[17/16]] and [[17/13]] in the [[17-limit]], and [[38/33]] in the [[19-limit]]. | |||
==Harmonics== | ==Harmonics== | ||
{{Harmonics in equal | {{Harmonics in equal | ||
Latest revision as of 13:43, 6 March 2026
| ← 5ed9/7 | 6ed9/7 | 7ed9/7 → |
6 equal divisions of 9/7 (abbreviated 6ed9/7) is a nonoctave tuning system that divides the interval of 9/7 into 6 equal parts of about 72.5 ¢ each. Each step represents a frequency ratio of (9/7)1/6, or the 6th root of 9/7.
Theory
This tuning tempers out 21/20 in the 7-limit, 55/54 in the 11-limit, 27/26, 55/52, and 16/13 in the 13-limit, 17/16 and 17/13 in the 17-limit, and 38/33 in the 19-limit.
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +32.7 | -16.6 | -7.0 | -30.8 | +16.1 | -33.2 | +25.7 | -33.2 | +2.0 | -18.0 | -23.6 | -17.2 | -0.4 | +25.1 | -14.1 | +26.0 | -0.4 | -21.5 | +34.7 | +22.7 |
| Relative (%) | +45.1 | -22.9 | -9.7 | -42.4 | +22.3 | -45.8 | +35.4 | -45.8 | +2.7 | -24.8 | -32.6 | -23.7 | -0.6 | +34.7 | -19.4 | +35.9 | -0.6 | -29.7 | +47.8 | +31.4 | |
| Steps (reduced) |
17 (5) |
26 (2) |
33 (3) |
38 (2) |
43 (1) |
46 (4) |
50 (2) |
52 (4) |
55 (1) |
57 (3) |
59 (5) |
61 (1) |
63 (3) |
65 (5) |
66 (0) |
68 (2) |
69 (3) |
70 (4) |
72 (0) |
73 (1) | |