10ed11: Difference between revisions
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Created page with "'''10ED11''' is the equal division of the 11th harmonic into 10 parts of 415.1318 cents each. It is related to the 19-limit temperament which tempers out 57/..." |
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'''10ED11''' is the [[Ed11|equal division of the 11th harmonic]] into 10 parts of 415.1318 [[cent|cents]] each. It is related to the | {{Mathematical interest}} | ||
{{Infobox ET}} | |||
'''10ED11''' is the [[Ed11|equal division of the 11th harmonic]] into 10 parts of 415.1318 [[cent|cents]] each. It is related to the [[Avicennmic temperaments|roman temperament]], which tempers out 65/64, 85/84, 100/99, 105/104, 133/132, and 153/152 in the 2.3.5.7.11.13.19 subgroup, which is supported by [[26edo]] and [[29edo]]. | |||
{| class="wikitable" | {| class="wikitable" | ||
| Line 15: | Line 17: | ||
| | 1 | | | 1 | ||
| | 415.1318 | | | 415.1318 | ||
| | [[19/15]], 33/26 | | | [[19/15]], 33/26, [[14/11]] | ||
| | | | | | ||
|- | |- | ||
| | 2 | | | 2 | ||
| | 830.2636 | | | 830.2636 | ||
| | | | | 21/13, 55/34, [[13/8]] | ||
| | | | | | ||
|- | |- | ||
| Line 30: | Line 32: | ||
| | 4 | | | 4 | ||
| | 1660.5272 | | | 1660.5272 | ||
| | [[13/5]] | | | [[13/5]], [[21/16|21/8]] | ||
| | | | | | ||
|- | |- | ||
| Line 50: | Line 52: | ||
| | 8 | | | 8 | ||
| | 3321.0544 | | | 3321.0544 | ||
| | [[22/13|88/13]], [[17/10|34/5]], | | | [[22/13|88/13]], [[17/10|34/5]], 143/21 | ||
| | | | | | ||
|- | |- | ||
| Line 63: | Line 65: | ||
| | [[11/8|undecimal fourth]] plus three octaves | | | [[11/8|undecimal fourth]] plus three octaves | ||
|} | |} | ||
Latest revision as of 22:14, 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. |
| ← 9ed11 | 10ed11 | 11ed11 → |
(semiconvergent)
10ED11 is the equal division of the 11th harmonic into 10 parts of 415.1318 cents each. It is related to the roman temperament, which tempers out 65/64, 85/84, 100/99, 105/104, 133/132, and 153/152 in the 2.3.5.7.11.13.19 subgroup, which is supported by 26edo and 29edo.
| degree | cents value | corresponding JI intervals |
comments |
|---|---|---|---|
| 0 | 0.0000 | exact 1/1 | |
| 1 | 415.1318 | 19/15, 33/26, 14/11 | |
| 2 | 830.2636 | 21/13, 55/34, 13/8 | |
| 3 | 1245.3954 | 33/16 | |
| 4 | 1660.5272 | 13/5, 21/8 | |
| 5 | 2075.6590 | 33/10, 10/3 | |
| 6 | 2490.7908 | 80/19, 55/13 | |
| 7 | 2905.9226 | 16/3 | |
| 8 | 3321.0544 | 88/13, 34/5, 143/21 | |
| 9 | 3736.1861 | 26/3 | |
| 10 | 4151.3179 | exact 11/1 | undecimal fourth plus three octaves |