User:Recentlymaterialized/1099826edo
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Prime factorization
2 × 7 × 13 × 6043
Step size
0.00109108¢
Fifth
643357\1099826 (701.955¢) (→49489\84602)
Semitones (A1:m2)
104195:82693 (113.7¢ : 90.22¢)
Consistency limit
55
Distinct consistency limit
at least 43
| This page presents a novelty topic. It features ideas which are less likely to find practical applications in xenharmonic music. It may contain numbers that are impractically large, exceedingly complex, or chosen arbitrarily. Novelty topics are often developed by a single person or a small group. As such, this page may also feature idiosyncratic terms, notations, or conceptual frameworks. |
| ← 1099825edo | 1099826edo | 1099827edo → |
1099826 equal divisions of the octave (abbreviated 1099826edo or 1099826ed2), also called 1099826-tone equal temperament (1099826tet) or 1099826 equal temperament (1099826et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 1099826 equal parts of about 0.00109 ¢ each. Each step represents a frequency ratio of 21/1099826, or the 1099826th root of 2.
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | |
|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.0000000 | +0.0000357 | +0.0001212 | +0.0000715 | +0.0001752 | +0.0002035 | +0.0001016 | -0.0001368 |
| Relative (%) | +0.0 | +3.3 | +11.1 | +6.5 | +16.1 | +18.7 | +9.3 | -12.5 | |
| Steps (reduced) |
1099826 (0) |
1743183 (643357) |
2553717 (354065) |
3087602 (887950) |
3804773 (505295) |
4069840 (770362) |
4495498 (96194) |
4671981 (272677) | |
| Harmonic | 23 | 29 | 31 | 37 | 41 | 43 | 47 | 53 | |
|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -0.0000566 | +0.0002117 | +0.0000968 | -0.0002807 | +0.0000098 | -0.0000656 | -0.0002601 | +0.0001725 |
| Relative (%) | -5.2 | +19.4 | +8.9 | -25.7 | +0.9 | -6.0 | -23.8 | +15.8 | |
| Steps (reduced) |
4975131 (575827) |
5342934 (943630) |
5448754 (1049450) |
5729492 (230362) |
5892375 (393245) |
5967947 (468817) |
6109081 (609951) |
6299716 (800586) | |
| Harmonic | 59 | 61 | 67 | 71 | 73 | 79 | 83 | 89 | |
|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.0002461 | -0.0001342 | +0.0004255 | +0.0002450 | +0.0000160 | +0.0000380 | -0.0001283 | +0.0000039 |
| Relative (%) | +22.6 | -12.3 | +39.0 | +22.5 | +1.5 | +3.5 | -11.8 | +0.4 | |
| Steps (reduced) |
6469884 (970754) |
6522779 (1023649) |
6671643 (72687) |
6763652 (164696) |
6807730 (208774) |
6933062 (334106) |
7011434 (412478) |
7122180 (523224) | |
| Harmonic | 97 | 101 | 103 | 107 | 109 | 113 | 127 | 131 | |
|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.0002820 | -0.0001115 | -0.0001405 | +0.0003603 | -0.0001017 | -0.0001610 | -0.0001356 | -0.0005304 |
| Relative (%) | +25.8 | -10.2 | -12.9 | +33.0 | -9.3 | -14.8 | -12.4 | -48.6 | |
| Steps (reduced) |
7258756 (659800) |
7322874 (723918) |
7353987 (755031) |
7414441 (815485) |
7443825 (844869) |
7501010 (902054) |
7686337 (1087381) |
7735541 (36759) | |