2544edo: Difference between revisions
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2544edo is consistent in the [[15-odd-limit]] and is a satisfactory 2.3.5.7.11.13.23 subgroup (add-23 13-limit) system in addition to that. | 2544edo is consistent in the [[15-odd-limit]] and is a satisfactory 2.3.5.7.11.13.23 subgroup (add-23 13-limit) system in addition to that. | ||
Being a strong higher-limit system with many notable divisors, it tempers out the [[Mercator comma]], as well as the [[landscape comma]], supporting the 7-limit [[aemilic]] | Being a strong higher-limit system with many notable divisors, it tempers out the [[Mercator comma]], as well as the [[landscape comma]], supporting the 7-limit {{nowrap|159 & 954}} temperament known as [[aemilic]]. It also suppors the [[48th-octave temperaments|70/69-48-commatic]] temperament, dividing the octave into 48 parts and using [[70/69]] as a chroma. | ||
=== Prime harmonics === | === Prime harmonics === | ||
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=== Subsets and supersets === | === Subsets and supersets === | ||
Since 2544edo factors as {{Factorization|2544}}, it has subset edos {{EDOs|1, 2, 3, 4, 6, 8, 12, 16, 24, 48, 53, 106, 159, 212, 318, 424, 636, 848, 1272}}. | Since 2544edo factors as {{Factorization|2544}}, it has subset edos {{EDOs|1, 2, 3, 4, 6, 8, 12, 16, 24, 48, 53, 106, 159, 212, 318, 424, 636, 848, 1272}}. | ||
Latest revision as of 13:09, 21 February 2025
| ← 2543edo | 2544edo | 2545edo → |
2544 equal divisions of the octave (abbreviated 2544edo or 2544ed2), also called 2544-tone equal temperament (2544tet) or 2544 equal temperament (2544et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 2544 equal parts of about 0.472 ¢ each. Each step represents a frequency ratio of 21/2544, or the 2544th root of 2.
2544edo is consistent in the 15-odd-limit and is a satisfactory 2.3.5.7.11.13.23 subgroup (add-23 13-limit) system in addition to that.
Being a strong higher-limit system with many notable divisors, it tempers out the Mercator comma, as well as the landscape comma, supporting the 7-limit 159 & 954 temperament known as aemilic. It also suppors the 70/69-48-commatic temperament, dividing the octave into 48 parts and using 70/69 as a chroma.
Prime harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.000 | -0.068 | +0.007 | +0.042 | +0.097 | +0.038 | +0.233 | +0.128 | +0.028 | +0.140 | -0.224 |
| Relative (%) | +0.0 | -14.5 | +1.5 | +8.9 | +20.6 | +8.1 | +49.5 | +27.2 | +5.8 | +29.6 | -47.5 | |
| Steps (reduced) |
2544 (0) |
4032 (1488) |
5907 (819) |
7142 (2054) |
8801 (1169) |
9414 (1782) |
10399 (223) |
10807 (631) |
11508 (1332) |
12359 (2183) |
12603 (2427) | |
Subsets and supersets
Since 2544edo factors as 24 × 3 × 53, it has subset edos 1, 2, 3, 4, 6, 8, 12, 16, 24, 48, 53, 106, 159, 212, 318, 424, 636, 848, 1272.