2100edo: Difference between revisions
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+prime error table; +subsets and supersets |
not sure how there's 7 limit in 1/4cm but ok |
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{{EDO intro|2100}} | {{EDO intro|2100}} | ||
The [[patent val]] [[Tempering out|tempers out]] [[32805/32768]] in the 5-limit and [[2401/2400]] in the 7-limit, and thereby provides an excellent tuning for 5-limit [[schismatic|schismatic aka helmholtz]] temperament, and the 7-limit [[sesquiquartififths]] temperament. As with any equal division of this size, it [[support]]s a number of possible meantone tunings, but | The [[patent val]] [[Tempering out|tempers out]] [[32805/32768]] in the 5-limit and [[2401/2400]] in the 7-limit, and thereby provides an excellent tuning for 5-limit [[schismatic|schismatic aka helmholtz]] temperament, and the 7-limit [[sesquiquartififths]] temperament. As with any equal division of this size, it [[support]]s a number of possible meantone tunings, but the 1219\2100 fifth is notable for being an extremely close approximation to [[quarter-comma meantone]]. | ||
=== Odd harmonics === | === Odd harmonics === | ||
Revision as of 22:38, 13 February 2024
| ← 2099edo | 2100edo | 2101edo → |
The patent val tempers out 32805/32768 in the 5-limit and 2401/2400 in the 7-limit, and thereby provides an excellent tuning for 5-limit schismatic aka helmholtz temperament, and the 7-limit sesquiquartififths temperament. As with any equal division of this size, it supports a number of possible meantone tunings, but the 1219\2100 fifth is notable for being an extremely close approximation to quarter-comma meantone.
Odd harmonics
| Harmonic | 3 | 5 | 7 | 9 | 11 | 13 | 15 | 17 | 19 | 21 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -0.241 | -0.028 | -0.254 | +0.090 | +0.111 | +0.044 | -0.269 | +0.187 | +0.201 | +0.076 | -0.274 |
| Relative (%) | -42.1 | -4.9 | -44.5 | +15.7 | +19.4 | +7.7 | -47.0 | +32.8 | +35.2 | +13.3 | -48.0 | |
| Steps (reduced) |
3328 (1228) |
4876 (676) |
5895 (1695) |
6657 (357) |
7265 (965) |
7771 (1471) |
8204 (1904) |
8584 (184) |
8921 (521) |
9224 (824) |
9499 (1099) | |
Subsets and supersets
Since 2100 factors into 22 × 3 × 52 × 7, 2100edo has subset edos 2, 3, 4, 5, 6, 7, 10, 12, 14, 15, 20, 21, 25, 28, 30, 35, 42, 50, 60, 70, 75, 84, 100, 105, 140, 150, 175, 210, 300, 350, 420, 525, 700, and 1050.