13edt: Difference between revisions
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| Line 11: | Line 11: | ||
! | Steps | ! | Steps | ||
! | Cents | ! | Cents | ||
!Hekts | |||
! | BP nonatonic degree | ! | BP nonatonic degree | ||
! | Corresponding JI intervals | ! | Corresponding JI intervals | ||
| Line 18: | Line 19: | ||
| | 1 | | | 1 | ||
| | 146.3 | | | 146.3 | ||
|100 | |||
| | A1/m2 | | | A1/m2 | ||
| | 27/25~49/45 | | | 27/25~49/45 | ||
| Line 25: | Line 27: | ||
| | 2 | | | 2 | ||
| | 292.6 | | | 292.6 | ||
|200 | |||
| | M2/d3 | | | M2/d3 | ||
| | 25/21 | | | 25/21 | ||
| Line 32: | Line 35: | ||
| | 3 | | | 3 | ||
| | 438.9 | | | 438.9 | ||
|300 | |||
| | A2/P3/d4 | | | A2/P3/d4 | ||
| | 9/7 | | | 9/7 | ||
| Line 39: | Line 43: | ||
| | 4 | | | 4 | ||
| | 585.2 | | | 585.2 | ||
|400 | |||
| | A3/m4/d5 | | | A3/m4/d5 | ||
| | 7/5 | | | 7/5 | ||
| Line 46: | Line 51: | ||
| | 5 | | | 5 | ||
| | 731.5 | | | 731.5 | ||
|500 | |||
| | M4/m5 | | | M4/m5 | ||
| | 75/49 | | | 75/49 | ||
| Line 53: | Line 59: | ||
| | 6 | | | 6 | ||
| | 877.8 | | | 877.8 | ||
|600 | |||
| | A4/M5 | | | A4/M5 | ||
| | 5/3 | | | 5/3 | ||
| Line 60: | Line 67: | ||
| | 7 | | | 7 | ||
| | 1024.1 | | | 1024.1 | ||
|700 | |||
| | A5/m6/d7 | | | A5/m6/d7 | ||
| | 9/5 | | | 9/5 | ||
| Line 67: | Line 75: | ||
| | 8 | | | 8 | ||
| | 1170.4 | | | 1170.4 | ||
|800 | |||
| | M6/m7 | | | M6/m7 | ||
| | 49/25 | | | 49/25 | ||
| Line 74: | Line 83: | ||
| | 9 | | | 9 | ||
| | 1316.7 | | | 1316.7 | ||
|900 | |||
| | A6/M7/d8 | | | A6/M7/d8 | ||
| | 15/7 | | | 15/7 | ||
| Line 80: | Line 90: | ||
|- | |- | ||
| | 10 | | | 10 | ||
| | 1463 | | | 1463 | ||
|1000 | |||
| | P8/d9 | | | P8/d9 | ||
| | 7/3 | | | 7/3 | ||
| Line 88: | Line 99: | ||
| | 11 | | | 11 | ||
| | 1609.3 | | | 1609.3 | ||
|1100 | |||
| | A8/m9 | | | A8/m9 | ||
| | 63/25 | | | 63/25 | ||
| Line 95: | Line 107: | ||
| | 12 | | | 12 | ||
| | 1755.7 | | | 1755.7 | ||
|1200 | |||
| | M9/d10 | | | M9/d10 | ||
| | 25/9~135/49 | | | 25/9~135/49 | ||
| Line 102: | Line 115: | ||
| | 13 | | | 13 | ||
| | 1902.0 | | | 1902.0 | ||
|1300 | |||
| | A9/P10 | | | A9/P10 | ||
| | 3/1 | | | 3/1 | ||
Revision as of 17:21, 13 April 2019
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 | 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 |