13edt: Difference between revisions
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==JI approximation== | == JI approximation == | ||
[[File:13ed3-17-001.svg|alt=alt : Your browser has no SVG support.]] | [[File:13ed3-17-001.svg|alt=alt : Your browser has no SVG support.]] | ||
== Regular temperament properties == | |||
{{Main| Bohlen-Pierce #Regular temperament properties }} | |||
== See also == | |||
==See also== | |||
*[[Catalog of 3.5.7 subgroup rank two temperaments]] | *[[Catalog of 3.5.7 subgroup rank two temperaments]] | ||
[[Category:3/1]] | [[Category:3/1]] | ||
[[Category: | [[Category:Edt]] | ||
[[Category: | [[Category:Tritave]] | ||
[[category: | [[category:Macrotonal]] | ||
[[category: | [[category:Nonoctave]] | ||
Revision as of 06:40, 16 July 2021
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.
Theory
| Prime interval | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | |
|---|---|---|---|---|---|---|---|---|---|
| Error | absolute (¢) | -29.6 | 0.0 | -6.5 | -3.8 | -54.8 | -51.4 | +69.4 | +23.1 |
| relative (%) | -20 | 0 | -4 | -3 | -37 | -35 | +47 | +16 | |
| Patent val | 8 | 13 | 19 | 23 | 28 | 30 | 34 | 35 | |
| Fifthspan | -1 | 0 | -4 | +2 | +3 | +6 | -1 | -6 | |
Intervals
| Steps | Cents | Hekts | BP nonatonic degree | Corresponding JI intervals | Comments | Generator for... |
|---|---|---|---|---|---|---|
| 1 | 146.3 | 100 | A1/m2 | 27/25~49/45 | ||
| 2 | 292.6 | 200 | M2/d3 | 25/21 | Sirius | |
| 3 | 438.9 | 300 | A2/P3/d4 | 9/7 | Linear BP | |
| 4 | 585.2 | 400 | A3/m4/d5 | 7/5 | Canopus | |
| 5 | 731.5 | 500 | M4/m5 | 75/49 | False 3/2 | false Father |
| 6 | 877.8 | 600 | A4/M5 | 5/3 | Arcturus | |
| 7 | 1024.1 | 700 | A5/m6/d7 | 9/5 | Arcturus | |
| 8 | 1170.4 | 800 | M6/m7 | 49/25 | False 2/1 | false Father |
| 9 | 1316.7 | 900 | A6/M7/d8 | 15/7 | Canopus | |
| 10 | 1463.0 | 1000 | P8/d9 | 7/3 | Linear BP | |
| 11 | 1609.3 | 1100 | A8/m9 | 63/25 | Sirius | |
| 12 | 1755.7 | 1200 | M9/d10 | 25/9~135/49 | ||
| 13 | 1902.0 | 1300 | A9/P10 | 3/1 | Tritave |
JI approximation
