9900edo: Difference between revisions
Created page with "{{Infobox ET}} {{EDO intro|9900}} 9900edo is consistent in the 9-odd-limit and it is otherwise a good 2.3.5.7.17.29 subgroup system. In the 7-limit, it is a septiruthenia..." |
Merge from Purdal page, reorganize sections |
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{{Infobox ET}} | {{Infobox ET}} | ||
{{ | {{ED intro}} | ||
9900edo's step size is sometimes called a '''purdal''', a term proposed by [[Osmiorisbendi]], when used as an interval size unit. | |||
== Theory == | |||
9900edo is consistent in the 9-odd-limit and it is otherwise a good 2.3.5.7.17.29 subgroup system. | 9900edo is consistent in the 9-odd-limit and it is otherwise a good 2.3.5.7.17.29 subgroup system. | ||
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=== Prime harmonics === | === Prime harmonics === | ||
{{harmonics in equal|9900}} | {{harmonics in equal|9900}} | ||
=== Subsets and supersets === | === Subsets and supersets === | ||
9900edo has subset edos {{EDOs|1, 2, 3, 4, 5, 6, 9, 10, 11, 12, 15, 18, 20, 22, 25, 30, 33, 36, 44, 45, 50, 55, 60, 66, 75, 90, 99, 100, 110, 132, 150, 165, 180, 198, 220, 225, 275, 300, 330, 396, 450, 495, 550, 660, 825, 900, 990, 1100, 1650, 1980, 2475, 3300, 4950}}. Its abundancy index is around 2.42. | 9900edo has subset edos {{EDOs|1, 2, 3, 4, 5, 6, 9, 10, 11, 12, 15, 18, 20, 22, 25, 30, 33, 36, 44, 45, 50, 55, 60, 66, 75, 90, 99, 100, 110, 132, 150, 165, 180, 198, 220, 225, 275, 300, 330, 396, 450, 495, 550, 660, 825, 900, 990, 1100, 1650, 1980, 2475, 3300, 4950}}. Its abundancy index is around 2.42. | ||
[[Category:Purdal]] | [[Category:Purdal]] | ||
Latest revision as of 21:38, 27 July 2026
| ← 9899edo | 9900edo | 9901edo → |
9900 equal divisions of the octave (abbreviated 9900edo or 9900ed2), also called 9900-tone equal temperament (9900tet) or 9900 equal temperament (9900et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 9900 equal parts of about 0.121 ¢ each. Each step represents a frequency ratio of 21/9900, or the 9900th root of 2.
9900edo's step size is sometimes called a purdal, a term proposed by Osmiorisbendi, when used as an interval size unit.
Theory
9900edo is consistent in the 9-odd-limit and it is otherwise a good 2.3.5.7.17.29 subgroup system.
In the 7-limit, it is a septiruthenian system, setting 64/63 to 1\44, so that the septimal comma is 225 purdals. It is a member of the optimal ET sequence for the ruthenium temperament with an additional prescribed mapping for 5 in the 13-limit.
Prime harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.0000 | -0.0156 | -0.0107 | +0.0226 | -0.0452 | -0.0428 | +0.0143 | -0.0585 | -0.0319 | -0.0014 | +0.0553 |
| Relative (%) | +0.0 | -12.9 | -8.8 | +18.6 | -37.3 | -35.3 | +11.8 | -48.2 | -26.3 | -1.2 | +45.7 | |
| Steps (reduced) |
9900 (0) |
15691 (5791) |
22987 (3187) |
27793 (7993) |
34248 (4548) |
36634 (6934) |
40466 (866) |
42054 (2454) |
44783 (5183) |
48094 (8494) |
49047 (9447) | |
Subsets and supersets
9900edo has subset edos 1, 2, 3, 4, 5, 6, 9, 10, 11, 12, 15, 18, 20, 22, 25, 30, 33, 36, 44, 45, 50, 55, 60, 66, 75, 90, 99, 100, 110, 132, 150, 165, 180, 198, 220, 225, 275, 300, 330, 396, 450, 495, 550, 660, 825, 900, 990, 1100, 1650, 1980, 2475, 3300, 4950. Its abundancy index is around 2.42.