1955edo: Difference between revisions
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{{Infobox ET}} | |||
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1955edo is in[[consistent]] to the [[5-odd-limit]] and [[harmonic]]s [[3/1|3]], [[5/1|5]], and [[7/1|7]] are all about halfway between its steps. As such, it commends itself to a 2.9.15.21.11.17 [[subgroup]] interpretation, with a [[comma basis]] {43923/43904, 163863/163840, 334125/334084, 1285956/1285625, 1434818/1434375}. | |||
1955edo | In particular, 1955edo is an excellent 2.15.17.21 subgroup tuning with harmonics are represented to within 3% error, with the comma basis {2000033/2000000, 2.15.17.21 {{monzo| 80 -8 -13 1 }}, and 2.15.17.21 {{monzo| 73 -15 4 -7 }}}. The {{nowrap|1955 & 6003}} temperament in the 2.15.17.21 subgroup has only 0.000396{{c}} per octave of TE error. It is period-23 and has a comma basis {2000033/2000000, 2.5.17.21 {{monzo| -101 -12 48 -11 }}}. | ||
=== Odd harmonics === | |||
{{Harmonics in equal|1955}} | |||
1955 factors | === Subsets and supersets === | ||
Since 1955 factors into {{factorization|1955}}, 1955edo has subset edos {{EDOs| 5, 17, 23, 85, 115, 391 }}. | |||
Latest revision as of 23:16, 20 February 2025
| ← 1954edo | 1955edo | 1956edo → |
1955 equal divisions of the octave (abbreviated 1955edo or 1955ed2), also called 1955-tone equal temperament (1955tet) or 1955 equal temperament (1955et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 1955 equal parts of about 0.614 ¢ each. Each step represents a frequency ratio of 21/1955, or the 1955th root of 2.
1955edo is inconsistent to the 5-odd-limit and harmonics 3, 5, and 7 are all about halfway between its steps. As such, it commends itself to a 2.9.15.21.11.17 subgroup interpretation, with a comma basis {43923/43904, 163863/163840, 334125/334084, 1285956/1285625, 1434818/1434375}.
In particular, 1955edo is an excellent 2.15.17.21 subgroup tuning with harmonics are represented to within 3% error, with the comma basis {2000033/2000000, 2.15.17.21 [80 -8 -13 1⟩, and 2.15.17.21 [73 -15 4 -7⟩}. The 1955 & 6003 temperament in the 2.15.17.21 subgroup has only 0.000396 ¢ per octave of TE error. It is period-23 and has a comma basis {2000033/2000000, 2.5.17.21 [-101 -12 48 -11⟩}.
Odd harmonics
| Harmonic | 3 | 5 | 7 | 9 | 11 | 13 | 15 | 17 | 19 | 21 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.244 | -0.227 | -0.233 | -0.125 | -0.116 | -0.221 | +0.018 | +0.006 | +0.185 | +0.012 | +0.268 |
| Relative (%) | +39.8 | -36.9 | -37.9 | -20.3 | -18.9 | -36.0 | +2.9 | +1.0 | +30.2 | +1.9 | +43.6 | |
| Steps (reduced) |
3099 (1144) |
4539 (629) |
5488 (1578) |
6197 (332) |
6763 (898) |
7234 (1369) |
7638 (1773) |
7991 (171) |
8305 (485) |
8587 (767) |
8844 (1024) | |
Subsets and supersets
Since 1955 factors into 5 × 17 × 23, 1955edo has subset edos 5, 17, 23, 85, 115, 391.