9ed10: Difference between revisions
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Created page with "'''9ED10''' is the equal division of the 10th harmonic into 9 parts of 442.9237 cents each. It is related to the sensis temperament, whi..." Tags: Mobile edit Mobile web edit |
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'''9ED10''' is the [[Ed10|equal division of the 10th harmonic]] into | {{Mathematical interest}} | ||
{{Infobox ET}} | |||
'''9ED10''' is the [[Ed10|equal division of the 10th harmonic]] into nine parts of 442.9237 [[cent|cents]] each. It is related to the [[Sensipent family|sensi temperament]], which tempers out 91/90, 126/125, and 169/168 in the 2.3.5.7.13 subgroup, which is supported by [[19edo]], [[27edo]], [[46edo]], and [[73edo]]. | |||
{| class="wikitable" | {| class="wikitable" | ||
| Line 15: | Line 17: | ||
| | 1 | | | 1 | ||
| | 442.9237 | | | 442.9237 | ||
| | [[9/7]], 84/65 | | | [[9/7]], 84/65, [[13/10]] | ||
| | | | | | ||
|- | |- | ||
| Line 30: | Line 32: | ||
| | 4 | | | 4 | ||
| | 1771.6950 | | | 1771.6950 | ||
| | [[18/13|36/13]], [[25/18|25/9]], 39/14 | | | ([[11/4]]), [[18/13|36/13]], [[25/18|25/9]], 39/14 | ||
| | | | | | ||
|- | |- | ||
| | 5 | | | 5 | ||
| | 2214.6187 | | | 2214.6187 | ||
| | 140/39, [[9/5|18/5]], 65/18 | | | 140/39, [[9/5|18/5]], 65/18, ([[20/11|40/11]]) | ||
| | | | | | ||
|- | |- | ||
| Line 50: | Line 52: | ||
| | 8 | | | 8 | ||
| | 3543.3900 | | | 3543.3900 | ||
| | [[27/14|54/7]], 70/9 | | | 100/13, [[27/14|54/7]], 70/9 | ||
| | | | | | ||
|- | |- | ||
| Line 58: | Line 60: | ||
| | just major third plus three octaves | | | just major third plus three octaves | ||
|} | |} | ||
Latest revision as of 22:18, 10 August 2025
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This page presents a topic of primarily mathematical interest.
While it is derived from sound mathematical principles, its applications in terms of utility for actual music may be limited, highly contrived, or as yet unknown. |
| ← 8ed10 | 9ed10 | 10ed10 → |
(semiconvergent)
9ED10 is the equal division of the 10th harmonic into nine parts of 442.9237 cents each. It is related to the sensi temperament, which tempers out 91/90, 126/125, and 169/168 in the 2.3.5.7.13 subgroup, which is supported by 19edo, 27edo, 46edo, and 73edo.
| degree | cents value | corresponding JI intervals |
comments |
|---|---|---|---|
| 0 | 0.0000 | exact 1/1 | |
| 1 | 442.9237 | 9/7, 84/65, 13/10 | |
| 2 | 885.8475 | 5/3 | |
| 3 | 1328.7712 | 15/7, 28/13, 54/25, 13/6 | |
| 4 | 1771.6950 | (11/4), 36/13, 25/9, 39/14 | |
| 5 | 2214.6187 | 140/39, 18/5, 65/18, (40/11) | |
| 6 | 2657.5425 | 60/13, 65/14, 14/3 | |
| 7 | 3100.4662 | 6/1 | |
| 8 | 3543.3900 | 100/13, 54/7, 70/9 | |
| 9 | 3986.3137 | exact 10/1 | just major third plus three octaves |