11ed5: Difference between revisions
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'''11ED5''' is the [[Ed5|equal division of the 5th harmonic]] into 11 parts of 252.3012 [[cent|cents]] each. It is | {{Infobox ET}} | ||
'''11ED5''' is the [[Ed5|equal division of the 5th harmonic]] into 11 parts of 252.3012 [[cent|cents]] each. It is related to the [[Meantone family|godzilla temperament]], which tempers out 49/48, 81/80, and 91/90 in the 2.3.5.7.13 subgroup. | |||
== Intervals == | |||
{| class="wikitable" | {| class="wikitable" | ||
|- | |- | ||
| Line 15: | Line 17: | ||
| | 1 | | | 1 | ||
| | 253.3012 | | | 253.3012 | ||
| | [[8/7]], [[7/6]] | | | [[8/7]], [[15/13]], [[7/6]] | ||
| | | | | | ||
|- | |- | ||
| Line 35: | Line 37: | ||
| | 5 | | | 5 | ||
| | 1266.5062 | | | 1266.5062 | ||
| | [[25/24|25/12]], [[21/20|21/10]] | | | [[27/26|27/13]], [[25/24|25/12]], [[21/20|21/10]] | ||
| | | | | | ||
|- | |- | ||
| Line 50: | Line 52: | ||
| | 8 | | | 8 | ||
| | 2026.4100 | | | 2026.4100 | ||
| | [[16/5]], | | | [[16/5]], [[13/4]] | ||
| | | | | | ||
|- | |- | ||
| Line 60: | Line 62: | ||
| | 10 | | | 10 | ||
| | 2533.0125 | | | 2533.0125 | ||
| | [[15/14|30/7]], [[35/32|35/8]] | | | [[15/14|30/7]], [[13/3]], [[35/32|35/8]] | ||
| | | | | | ||
|- | |- | ||
| Line 69: | Line 71: | ||
|} | |} | ||
== Harmonics == | |||
{{Harmonics in equal | |||
| steps = 11 | |||
| num = 5 | |||
| denom = 1 | |||
}} | |||
{{Harmonics in equal | |||
| steps = 11 | |||
| num = 5 | |||
| denom = 1 | |||
| start = 12 | |||
| collapsed = 1 | |||
}} | |||
Latest revision as of 19:20, 1 August 2025
| ← 10ed5 | 11ed5 | 12ed5 → |
11ED5 is the equal division of the 5th harmonic into 11 parts of 252.3012 cents each. It is related to the godzilla temperament, which tempers out 49/48, 81/80, and 91/90 in the 2.3.5.7.13 subgroup.
Intervals
| degree | cents value | corresponding JI intervals |
comments |
|---|---|---|---|
| 0 | 0.0000 | exact 1/1 | |
| 1 | 253.3012 | 8/7, 15/13, 7/6 | |
| 2 | 506.6025 | 4/3 | |
| 3 | 759.9037 | 14/9 | |
| 4 | 1013.2050 | 9/5 | |
| 5 | 1266.5062 | 27/13, 25/12, 21/10 | |
| 6 | 1519.8075 | 12/5 | |
| 7 | 1773.1087 | 14/5 | |
| 8 | 2026.4100 | 16/5, 13/4 | |
| 9 | 2279.7112 | 15/4 | |
| 10 | 2533.0125 | 30/7, 13/3, 35/8 | |
| 11 | 2786.3137 | exact 5/1 | just major third plus two octaves |
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +67 | +124 | -120 | +0 | -62 | -76 | -54 | -4 | +67 | -98 | +4 |
| Relative (%) | +26.3 | +49.1 | -47.5 | +0.0 | -24.6 | -30.0 | -21.2 | -1.7 | +26.3 | -38.9 | +1.6 | |
| Steps (reduced) |
5 (5) |
8 (8) |
9 (9) |
11 (0) |
12 (1) |
13 (2) |
14 (3) |
15 (4) |
16 (5) |
16 (5) |
17 (6) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +119 | -9 | +124 | +13 | -92 | +62 | -31 | -120 | +49 | -32 | -109 |
| Relative (%) | +46.9 | -3.7 | +49.1 | +5.0 | -36.4 | +24.5 | -12.4 | -47.5 | +19.2 | -12.6 | -43.0 | |
| Steps (reduced) |
18 (7) |
18 (7) |
19 (8) |
19 (8) |
19 (8) |
20 (9) |
20 (9) |
20 (9) |
21 (10) |
21 (10) |
21 (10) | |