19ed5

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Division of the 5th harmonic into 19 equal parts (19ED5) is related to the Bohlen-Pierce scale, but with the 5/1 rather than the 3/1 being just. The step size is about 146.6481 cents, corresponding to 8.1829 EDO. It provides 5, 7, 13, and 15-odd-limit minimax generator for the bohpier temperament.

degree cents value corresponding
JI intervals
comments
0 0.0000 exact 1/1
1 146.6481 49/45
2 293.2962 13/11
3 439.9443 9/7
4 586.5924 7/5
5 733.2405 49/32
6 879.8885 5/3
7 1026.5366 9/5
8 1173.1847 63/32
9 1319.8328 15/7
10 1466.4809 7/3
11 1613.1290 28/11
12 1759.7771 11/4
13 1906.4252 3/1
14 2053.0733 49/15
15 2199.7214 32/9
16 2346.3694 35/9
17 2493.0175 21/5
18 2639.6656 32/7
19 2786.3137 exact 5/1 just major third plus two octaves

See also

  • 13ED3: relative ED3 (Bohlen-Pierce scale)
  • 23ED7: relative ED7