19ed11: Difference between revisions
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Created page with "'''19ED11''' is the equal division of the 11th harmonic into 19 parts of 218.4904 cents each. It is similar to every second step of 11edo. {| class="wik..." Tags: Mobile edit Mobile web edit |
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{{Infobox ET}} | |||
{{ED intro}} It is similar to every second step of [[11edo]]. | |||
== Intervals == | |||
{| class="wikitable" | {| class="wikitable" | ||
|- | |- | ||
| Line 25: | Line 27: | ||
| | 3 | | | 3 | ||
| | 655.4713 | | | 655.4713 | ||
| | | | | 187/128, [[19/13]] | ||
| | | | | | ||
|- | |- | ||
| | 4 | | | 4 | ||
| | 873.9617 | | | 873.9617 | ||
| | | | | 48/29, 53/32, 58/35 | ||
| | | | | | ||
|- | |- | ||
| | 5 | | | 5 | ||
| | 1092.4521 | | | 1092.4521 | ||
| | ([[15/8]]), ([[32/17]]) | | | ([[15/8]]), 216/115, ([[32/17]]) | ||
| | | | | | ||
|- | |- | ||
| Line 50: | Line 52: | ||
| | 8 | | | 8 | ||
| | 1747.9233 | | | 1747.9233 | ||
| | | | | ([[11/4]]) | ||
| | | | | | ||
|- | |- | ||
| Line 60: | Line 62: | ||
| | 10 | | | 10 | ||
| | 2184.9042 | | | 2184.9042 | ||
| | [[30/17|60/17]], 99/28 | | | [[30/17|60/17]], 272/77, 99/28 | ||
| | | | | | ||
|- | |- | ||
| Line 90: | Line 92: | ||
| | 16 | | | 16 | ||
| | 3495.8467 | | | 3495.8467 | ||
| | [[32/17|128/17]] | | | 143/19, [[32/17|128/17]] | ||
| | | | | | ||
|- | |- | ||
| | 17 | | | 17 | ||
| | 3714.3371 | | | 3714.3371 | ||
| | | | | 1000/117 | ||
| | | | | | ||
|- | |- | ||
| Line 109: | Line 111: | ||
|} | |} | ||
== Harmonics == | |||
{{Harmonics in equal | |||
| steps = 19 | |||
| num = 11 | |||
| denom = 1 | |||
}} | |||
{{Harmonics in equal | |||
| steps = 19 | |||
| num = 11 | |||
| denom = 1 | |||
| start = 12 | |||
| collapsed = 1 | |||
}} | |||
Latest revision as of 19:20, 1 August 2025
| ← 18ed11 | 19ed11 | 20ed11 → |
19 equal divisions of the 11th harmonic (abbreviated 19ed11) is a nonoctave tuning system that divides the interval of 11/1 into 19 equal parts of about 218 ¢ each. Each step represents a frequency ratio of 111/19, or the 19th root of 11. It is similar to every second step of 11edo.
Intervals
| degree | cents value | corresponding JI intervals |
comments |
|---|---|---|---|
| 0 | 0.0000 | exact 1/1 | |
| 1 | 218.4904 | (17/15) | |
| 2 | 436.9808 | (9/7) | |
| 3 | 655.4713 | 187/128, 19/13 | |
| 4 | 873.9617 | 48/29, 53/32, 58/35 | |
| 5 | 1092.4521 | (15/8), 216/115, (32/17) | |
| 6 | 1310.9425 | 32/15 | |
| 7 | 1529.4329 | 121/50, 46/19 | |
| 8 | 1747.9233 | (11/4) | |
| 9 | 1966.4138 | 28/9, 187/60 | |
| 10 | 2184.9042 | 60/17, 272/77, 99/28 | |
| 11 | 2403.3946 | (4/1) | |
| 12 | 2621.8850 | 209/46, 50/11 | |
| 13 | 2840.3754 | 165/32 | |
| 14 | 3058.8659 | ||
| 15 | 3277.3563 | ||
| 16 | 3495.8467 | 143/19, 128/17 | |
| 17 | 3714.3371 | 1000/117 | |
| 18 | 3932.8275 | ||
| 19 | 4151.3179 | exact 11/1 | undecimal fourth plus three octaves |
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -107.5 | +64.5 | +3.4 | +54.1 | -43.1 | -91.5 | -104.2 | -89.6 | -53.5 | +0.0 | +67.9 |
| Relative (%) | -49.2 | +29.5 | +1.6 | +24.7 | -19.7 | -41.9 | -47.7 | -41.0 | -24.5 | +0.0 | +31.1 | |
| Steps (reduced) |
5 (5) |
9 (9) |
11 (11) |
13 (13) |
14 (14) |
15 (15) |
16 (16) |
17 (17) |
18 (18) |
19 (0) |
20 (1) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -70.7 | +19.5 | -100.0 | +6.8 | -98.2 | +21.4 | -72.2 | +57.5 | -27.0 | -107.5 | +34.0 |
| Relative (%) | -32.4 | +8.9 | -45.8 | +3.1 | -44.9 | +9.8 | -33.1 | +26.3 | -12.4 | -49.2 | +15.6 | |
| Steps (reduced) |
20 (1) |
21 (2) |
21 (2) |
22 (3) |
22 (3) |
23 (4) |
23 (4) |
24 (5) |
24 (5) |
24 (5) |
25 (6) | |