71zpi: Difference between revisions
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!ZPI | !ZPI | ||
!Steps per octave | !Steps per octave | ||
! | !Step size (cents) | ||
!Height | !Height | ||
!Integral | !Integral | ||
!Gap | !Gap | ||
!EDO | !EDO | ||
!Octave | !Octave (cents) | ||
!Consistent | !Consistent | ||
!Distinct | !Distinct | ||
Revision as of 21:55, 19 April 2024
71 zeta peak index (abbreviated 71zpi), is the tuning system obtained from the 71st peak of the Riemann zeta function.
| Tuning | Strength | Closest EDO | Integer limit | ||||||
|---|---|---|---|---|---|---|---|---|---|
| ZPI | Steps per octave | Step size (cents) | Height | Integral | Gap | EDO | Octave (cents) | Consistent | Distinct |
| 71zpi | 20.2248393119540 | 59.3329806724710 | 3.531097 | 0.613581 | 12.986080 | 20edo | 1186.65961344942 | 6 | 6 |
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -13.3 | -3.3 | -26.7 | +2.3 | -16.6 | +13.2 | +19.3 | -6.6 | -11.0 | +2.0 | +29.4 | +9.4 | -0.2 | -1.0 | +6.0 |
| Relative (%) | -22.5 | -5.6 | -45.0 | +3.9 | -28.0 | +22.2 | +32.5 | -11.1 | -18.5 | +3.4 | +49.5 | +15.9 | -0.3 | -1.6 | +10.1 | |
| Step | 20 | 32 | 40 | 47 | 52 | 57 | 61 | 64 | 67 | 70 | 73 | 75 | 77 | 79 | 81 | |
| Harmonic | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 | 25 | 26 | 27 | 28 | 29 | 30 | 31 | 32 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +19.7 | -19.9 | +5.1 | -24.3 | +9.9 | -11.3 | -29.0 | +16.0 | +4.7 | -3.9 | -9.9 | -13.5 | -14.9 | -14.3 | -11.7 | -7.4 |
| Relative (%) | +33.2 | -33.6 | +8.6 | -41.0 | +16.6 | -19.1 | -48.8 | +27.0 | +7.9 | -6.6 | -16.7 | -22.8 | -25.2 | -24.1 | -19.8 | -12.4 | |
| Step | 83 | 84 | 86 | 87 | 89 | 90 | 91 | 93 | 94 | 95 | 96 | 97 | 98 | 99 | 100 | 101 | |
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