814edo: Difference between revisions
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The '''814 equal division''' divides the octave into 814 equal parts of 1.474 cents each.It is uniquely [[consistent|consistent]] to the 17-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 [[Schismatic_family#Sesquiquartififths|sesquiquartififths temperament]]. In the 11-limit it tempers out 9801/9800, in the 13-limit 4224/4224 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|optimal patent val]]. | The '''814 equal division''' divides the octave into 814 equal parts of 1.474 cents each.It is uniquely [[consistent|consistent]] to the 17-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 [[Schismatic_family#Sesquiquartififths|sesquiquartififths temperament]]. In the 11-limit it tempers out 9801/9800, in the 13-limit 4224/4224 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|optimal patent val]]. | ||
[[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 22:03, 4 October 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-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 temperament. In the 11-limit it tempers out 9801/9800, in the 13-limit 4224/4224 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.