1230edo: Difference between revisions
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1230edo is [[consistent]] to the [[5-odd-limit]], but [[harmonic]] [[3/1|3]] is about halfway between its steps. As every other step of [[2460edo]], it is excellent in approximating harmonics [[5/1|5]], [[7/1|7]], [[9/1|9]], [[11/1|11]], [[19/1|19]], and [[23/1|23]], making it suitable for a 2.9.5.7.11.19.23 [[subgroup]] interpretation, on which it is identical to 2460edo. | |||
=== Odd harmonics === | === Odd harmonics === | ||
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=== Miscellaneous properties === | === Miscellaneous properties === | ||
1230edo | 1230edo could be called a "highly Kartvelian edo" because it supports the largest number of scales dividing its patent val 4/3 and 3/2 into even parts relative to its size. See [[Kartvelian scales]]. | ||
[[ | === Subsets and supersets === | ||
Since 1230 factors into {{factorization|1230}}, 1230edo has subset edos {{EDOs| 2, 3, 5, 6, 10, 15, 30, 41, 82, 123, 205, 246, 410, and 615 }}. A step of 1230edo is exactly 2 [[mina]]s (2\2460). | |||
Latest revision as of 17:12, 20 February 2025
| ← 1229edo | 1230edo | 1231edo → |
1230 equal divisions of the octave (abbreviated 1230edo or 1230ed2), also called 1230-tone equal temperament (1230tet) or 1230 equal temperament (1230et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 1230 equal parts of about 0.976 ¢ each. Each step represents a frequency ratio of 21/1230, or the 1230th root of 2.
1230edo is consistent to the 5-odd-limit, but harmonic 3 is about halfway between its steps. As every other step of 2460edo, it is excellent in approximating harmonics 5, 7, 9, 11, 19, and 23, making it suitable for a 2.9.5.7.11.19.23 subgroup interpretation, on which it is identical to 2460edo.
Odd harmonics
| Harmonic | 3 | 5 | 7 | 9 | 11 | 13 | 15 | 17 | 19 | 21 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.484 | +0.028 | -0.045 | -0.008 | -0.098 | +0.448 | -0.464 | +0.410 | +0.048 | +0.439 | +0.018 |
| Relative (%) | +49.6 | +2.8 | -4.7 | -0.8 | -10.1 | +45.9 | -47.5 | +42.1 | +4.9 | +45.0 | +1.9 | |
| Steps (reduced) |
1950 (720) |
2856 (396) |
3453 (993) |
3899 (209) |
4255 (565) |
4552 (862) |
4805 (1115) |
5028 (108) |
5225 (305) |
5403 (483) |
5564 (644) | |
Miscellaneous properties
1230edo could be called a "highly Kartvelian edo" because it supports the largest number of scales dividing its patent val 4/3 and 3/2 into even parts relative to its size. See Kartvelian scales.
Subsets and supersets
Since 1230 factors into 2 × 3 × 5 × 41, 1230edo has subset edos 2, 3, 5, 6, 10, 15, 30, 41, 82, 123, 205, 246, 410, and 615. A step of 1230edo is exactly 2 minas (2\2460).