814edo: Difference between revisions
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The '''814 equal division''' divides the octave into 814 equal parts of 1.474 | The '''814 equal division''' divides the [[octave]] into 814 [[equal]] parts of 1.474 [[cent]]s each. It is uniquely [[consistent]] to the [[17-odd-limit]] and is a strong 17-limit system. It tempers out [[32805/32768]] in the 5-limit and [[2401/2400]] in the 7-limit, so that it [[support]]s and gives a good tuning for [[sesquiquartififths]]. In the 11-limit it tempers out [[9801/9800]], in the 13-limit [[4225/4224]] and [[6656/6655]], and in the 17-limit [[1701/1700]], [[2058/2057]], [[2601/2600]], [[4914/4913]] and [[5832/5831]]. The 171&643 temperament gives an extension of sesquiquartififths to the 17-limit for which 814edo provides the [[optimal patent val]]. | ||
=== Prime harmonics === | |||
{{Harmonics in equal|814|columns=11}} | |||
=== Miscellany === | |||
Since 814 = 2 × 11 × 37, 814edo has subset edos {{EDOs| 2, 11, 22, 37, 74, and 407 }}. | |||
[[Category:Equal divisions of the octave|###]] <!-- 3-digit number --> | [[Category:Equal divisions of the octave|###]] <!-- 3-digit number --> | ||
[[Category:Sesquiquartififths]] | [[Category:Sesquiquartififths]] | ||
Revision as of 14:32, 27 November 2022
| ← 813edo | 814edo | 815edo → |
The 814 equal division divides the octave into 814 equal parts of 1.474 cents each. It is uniquely consistent to the 17-odd-limit and is a strong 17-limit system. It tempers out 32805/32768 in the 5-limit and 2401/2400 in the 7-limit, so that it supports and gives a good tuning for sesquiquartififths. In the 11-limit it tempers out 9801/9800, in the 13-limit 4225/4224 and 6656/6655, and in the 17-limit 1701/1700, 2058/2057, 2601/2600, 4914/4913 and 5832/5831. The 171&643 temperament gives an extension of sesquiquartififths to the 17-limit for which 814edo provides the optimal patent val.
Prime harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.000 | -0.235 | -0.073 | -0.276 | +0.033 | -0.233 | -0.287 | +0.276 | -0.265 | -0.585 | +0.419 |
| Relative (%) | +0.0 | -15.9 | -4.9 | -18.7 | +2.3 | -15.8 | -19.5 | +18.7 | -17.9 | -39.7 | +28.4 | |
| Steps (reduced) |
814 (0) |
1290 (476) |
1890 (262) |
2285 (657) |
2816 (374) |
3012 (570) |
3327 (71) |
3458 (202) |
3682 (426) |
3954 (698) |
4033 (777) | |
Miscellany
Since 814 = 2 × 11 × 37, 814edo has subset edos 2, 11, 22, 37, 74, and 407.