1955edo: Difference between revisions
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Created page with "{{EDO intro|1955}} == Theory == {{Harmonics in equal|1955}}" |
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{{Infobox ET}} | |||
{{EDO intro|1955}} | {{EDO intro|1955}} | ||
== Theory == | == Theory == | ||
{{Harmonics in equal|1955}} | {{Harmonics in equal|1955}} | ||
1955edo represents well the 2.9.11.15.17.21 subgroup, 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 {{monzo|80 -8 -13 1}}, and 2.15.17.21 {{monzo|73 -15 4 -7}}}. | |||
The 1955 & 6003 temperament in the 2.15.17.21 subgroup has only 0.000396 cents 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}}}. | |||
=== Miscellany === | |||
1955 factors as 5 x 17 x 23, and has divisors {{EDOs|1, 5, 17, 23, 85, 115, 391}}. | |||
Revision as of 13:15, 4 January 2023
| ← 1954edo | 1955edo | 1956edo → |
Theory
| 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) | |
1955edo represents well the 2.9.11.15.17.21 subgroup, 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 cents per octave of TE error. It is period-23 and has a comma basis {2000033/2000000, 2.5.17.21 [-101 -12 48 -11⟩}.
Miscellany
1955 factors as 5 x 17 x 23, and has divisors 1, 5, 17, 23, 85, 115, 391.