13edt

From Xenharmonic Wiki
Jump to: navigation, search

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.

13edt.png

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 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

See also