19ed11/9: Difference between revisions
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{{Infobox ET}} | {{Infobox ET}} | ||
{{ED intro}} | {{ED intro}} | ||
== Theory == | |||
This tuning tempers out [[81/80]] in the [[5-limit]]; [[49/48]] in the [[7-limit]]; and [[121/120]] in the [[11-limit]]. | |||
=== Harmonics === | |||
{{Harmonics in equal | {{Harmonics in equal | ||
| steps = 19 | | steps = 19 | ||
| num = 11 | | num = 11 | ||
| denom = 9}} | | denom = 9}} | ||
{{Stub}} | {{Stub}} | ||
Latest revision as of 04:16, 9 January 2025
| ← 18ed11/9 | 19ed11/9 | 20ed11/9 → |
(convergent)
19 equal divisions of 11/9 (abbreviated 19ed11/9) is a nonoctave tuning system that divides the interval of 11/9 into 19 equal parts of about 18.3 ¢ each. Each step represents a frequency ratio of (11/9)1/19, or the 19th root of 11/9.
Theory
This tuning tempers out 81/80 in the 5-limit; 49/48 in the 7-limit; and 121/120 in the 11-limit.
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +6.79 | -0.35 | -4.71 | -7.05 | +6.43 | -4.45 | +2.07 | -0.71 | -0.26 | -0.71 | -5.07 |
| Relative (%) | +37.1 | -1.9 | -25.8 | -38.6 | +35.2 | -24.4 | +11.3 | -3.9 | -1.4 | -3.9 | -27.7 | |
| Steps (reduced) |
66 (9) |
104 (9) |
131 (17) |
152 (0) |
170 (18) |
184 (13) |
197 (7) |
208 (18) |
218 (9) |
227 (18) |
235 (7) | |
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