1547edo: Difference between revisions
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Created page with "{{EDO intro|1547}} ==Theory== {{harmonics in equal|1547}} 1547edo is excellent in the 7-limit. In the 5-limit, it supports gross. In the 17-limit, it supports 91th-octa..." |
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In the 5-limit, it supports [[gross]]. | In the 5-limit, it supports [[gross]]. | ||
In the 7-limit, it supports [[semidimi]] and [[brahmagupta]]. | |||
In the 17-limit, it supports 91th-octave temperament protactinium. | In the 17-limit, it supports 91th-octave temperament protactinium. | ||
1547's divisors are 1, 7, 13, 17, 91, 119, 221. | |||
==Regular temperament properties== | ==Regular temperament properties== | ||
===Rank-2 temperaments by generator=== | ===Rank-2 temperaments by generator=== | ||
| Line 16: | Line 20: | ||
! Associated<br>ratio | ! Associated<br>ratio | ||
! Temperaments | ! Temperaments | ||
|- | |||
|1 | |||
|118\1547 | |||
|91.532 | |||
|[9 -32 18> | |||
|[[Gross]] | |||
|- | |||
|1 | |||
|579\1547 | |||
|449.127 | |||
|35/27 | |||
|[[Semidimi]] | |||
|- | |||
|7 | |||
|670\1547 | |||
(7\1547) | |||
|519.715 | |||
(5.429) | |||
|27/20 | |||
(325/324) | |||
|[[Brahmagupta]] | |||
|- | |- | ||
| 91 | | 91 | ||
Revision as of 19:30, 15 September 2022
Theory
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.000 | +0.049 | -0.018 | +0.017 | +0.201 | +0.326 | -0.237 | +0.354 | +0.039 | -0.230 | -0.110 |
| Relative (%) | +0.0 | +6.3 | -2.3 | +2.2 | +25.9 | +42.0 | -30.5 | +45.6 | +5.0 | -29.7 | -14.2 | |
| Steps (reduced) |
1547 (0) |
2452 (905) |
3592 (498) |
4343 (1249) |
5352 (711) |
5725 (1084) |
6323 (135) |
6572 (384) |
6998 (810) |
7515 (1327) |
7664 (1476) | |
1547edo is excellent in the 7-limit.
In the 5-limit, it supports gross.
In the 7-limit, it supports semidimi and brahmagupta.
In the 17-limit, it supports 91th-octave temperament protactinium.
1547's divisors are 1, 7, 13, 17, 91, 119, 221.
Regular temperament properties
Rank-2 temperaments by generator
| Periods per octave |
Generator (reduced) |
Cents (reduced) |
Associated ratio |
Temperaments |
|---|---|---|---|---|
| 1 | 118\1547 | 91.532 | [9 -32 18> | Gross |
| 1 | 579\1547 | 449.127 | 35/27 | Semidimi |
| 7 | 670\1547
(7\1547) |
519.715
(5.429) |
27/20
(325/324) |
Brahmagupta |
| 91 | 905\1547 (4\1547) |
702.003 (3.103) |
3/2 (?) |
Protactinium |