# 9900edo

← 9899edo | 9900edo | 9901edo → |

^{2}× 3^{2}× 5^{2}× 11**9900 equal divisions of the octave** (abbreviated **9900edo**), or **9900-tone equal temperament** (**9900tet**), **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 of 9900edo represents a frequency ratio of 2^{1/9900}, or the 9900th root of 2.

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 | -13 | -9 | +19 | -37 | -35 | +12 | -48 | -26 | -1 | +46 | |

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.

As an interval size measure, one step of 9900edo is known as the **purdal**.