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13edt divides the tritave (3/1) into 13 equal parts of 146.304 cents each, corresponding to 8.202[[edo]]. It is the equal-tempered version of the well-known '''[[Bohlen-Pierce]]''' scale. In the 7-limit, it tempers out 245/243 and 3125/3087, the same commas as [[Sensamagic_clan#Bohpier|bohpier temperament]]. It is less impressive in higher p-limits, but makes for excellent no-twos 7-limit harmony. For higher limits, the multiples of 13 ([[26edt]], [[39edt]] and [[52edt]]) come to the fore. | |||
Below is a plot of the [[The_Riemann_Zeta_Function_and_Tuning#Removing primes|no-twos Z-function]], in terms of which 13edt is the fourth no-twos zeta peak edt. | Below is a plot of the [[The_Riemann_Zeta_Function_and_Tuning#Removing primes|no-twos Z-function]], in terms of which 13edt is the fourth no-twos zeta peak edt. | ||
| Line 28: | Line 28: | ||
| | 25/21 | | | 25/21 | ||
| | | | | | ||
| | [[ | | | [[Sirius]] | ||
|- | |- | ||
| | 3 | | | 3 | ||
| Line 42: | Line 42: | ||
| | 7/5 | | | 7/5 | ||
| | | | | | ||
| | [[ | | | [[Canopus]] | ||
|- | |- | ||
| | 5 | | | 5 | ||
| Line 56: | Line 56: | ||
| | 5/3 | | | 5/3 | ||
| | | | | | ||
| | [[ | | | [[Arcturus]] | ||
|- | |- | ||
| | 7 | | | 7 | ||
| Line 109: | Line 109: | ||
==See also== | ==See also== | ||
*[[Catalog of 3.5.7 subgroup rank two temperaments]] | |||
[[Category:3/1]] | |||
[[Category:edt]] | [[Category:edt]] | ||
[[Category:tritave]] | [[Category:tritave]] | ||
[[category:macrotonal]] | [[category:macrotonal]] | ||
[[category:nonoctave]] | |||
Revision as of 17:25, 10 December 2018
13edt divides the tritave (3/1) into 13 equal parts of 146.304 cents each, corresponding to 8.202edo. It is the equal-tempered version of the well-known Bohlen-Pierce scale. In the 7-limit, it tempers out 245/243 and 3125/3087, the same commas as bohpier temperament. It is less impressive in higher p-limits, but makes for excellent no-twos 7-limit harmony. For higher limits, the multiples of 13 (26edt, 39edt and 52edt) come to the fore.
Below is a plot of the no-twos Z-function, in terms of which 13edt is the fourth no-twos zeta peak edt.
Intervals
| Steps | Cents | BP nonatonic degree | Corresponding JI intervals | Comments | Generator for... |
|---|---|---|---|---|---|
| 1 | 146.3 | A1/m2 | 27/25~49/45 | ||
| 2 | 292.6 | M2/d3 | 25/21 | Sirius | |
| 3 | 438.9 | A2/P3/d4 | 9/7 | Linear BP | |
| 4 | 585.2 | A3/m4/d5 | 7/5 | Canopus | |
| 5 | 731.5 | M4/m5 | 75/49 | False 3/2 | false Father |
| 6 | 877.8 | A4/M5 | 5/3 | Arcturus | |
| 7 | 1024.1 | A5/m6/d7 | 9/5 | Arcturus | |
| 8 | 1170.4 | M6/m7 | 49/25 | False 2/1 | false Father |
| 9 | 1316.7 | A6/M7/d8 | 15/7 | Canopus | |
| 10 | 1463.0 | P8/d9 | 7/3 | Linear BP | |
| 11 | 1609.3 | A8/m9 | 63/25 | Sirius | |
| 12 | 1755.7 | M9/d10 | 25/9~135/49 | ||
| 13 | 1902.0 | A9/P10 | 3/1 | Tritave |