10edf
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Prime factorization
2 × 5
Step size
70.1955¢
Octave
17\10edf (1193.32¢)
(semiconvergent)
Twelfth
27\10edf (1895.28¢)
(semiconvergent)
Consistency limit
7
Distinct consistency limit
4
| ← 9edf | 10edf | 11edf → |
(semiconvergent)
(semiconvergent)
Division of the just perfect fifth into 10 equal parts (10EDF) is related to 17 edo, but with the 3/2 rather than the 2/1 being just. The octave is about 6.6765 cents compressed and the step size is about 70.1955 cents. It is consistent to the 7-integer-limit, but not to the 8-integer-limit. In comparison, 17edo is only consistent up to the 4-integer-limit.
Intervals
| degree | Neptunian notation using 8\10edf | Neapolitan notation using 3/10edf | |
|---|---|---|---|
| 0 | C | F | |
| 1 | 70.1955 | ^C, vDb | F^, Gb |
| 2 | 140.391 | C#, Db | F#, Gd |
| 3 | 210.5865 | vD | G |
| 4 | 280.782 | D | G^, Ab |
| 5 | 350.9775 | ^D, vE | G#, Ad |
| 6 | 421.173 | E | A |
| 7 | 491.3685 | ^E, vF | A^, Hb |
| 8 | 561.564 | F | A#, Hd |
| 9 | 631.7595 | ^F, vC | H |
| 10 | 701.955 | C | B |
| 11 | 772.1505 | ^C, vDb | B^, Cb |
| 12 | 842.346 | C#, Db | B#, Cd |
| 13 | 912.5415 | vD | C |
| 14 | 982.737 | D | C^, Db |
| 15 | 1052.9325 | ^D, vE | C#, Dd |
| 16 | 1123.128 | E | D |
| 17 | 1193.3235 | ^E, vF | D^, Eb |
| 18 | 1263.519 | F | D#, Eb |
| 19 | 1333.7145 | ^F, vC | E |
| 20 | 1403.91 | C | F |
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -6.7 | -6.7 | -13.4 | +21.5 | -13.4 | +0.6 | -20.0 | -13.4 | +14.8 | -9.8 | -20.0 |
| Relative (%) | -9.5 | -9.5 | -19.0 | +30.6 | -19.0 | +0.8 | -28.5 | -19.0 | +21.1 | -13.9 | -28.5 | |
| Steps (reduced) |
17 (7) |
27 (7) |
34 (4) |
40 (0) |
44 (4) |
48 (8) |
51 (1) |
54 (4) |
57 (7) |
59 (9) |
61 (1) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -18.2 | -6.1 | +14.8 | -26.7 | +8.7 | -20.0 | +26.8 | +8.2 | -6.1 | -16.5 | -23.2 |
| Relative (%) | -25.9 | -8.7 | +21.1 | -38.0 | +12.4 | -28.5 | +38.1 | +11.6 | -8.7 | -23.4 | -33.1 | |
| Steps (reduced) |
63 (3) |
65 (5) |
67 (7) |
68 (8) |
70 (0) |
71 (1) |
73 (3) |
74 (4) |
75 (5) |
76 (6) |
77 (7) | |