71zpi: Difference between revisions
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'''71zpi''' marks the most prominent zeta peak index in the vicinity of [[20edo]], ranging between 19.5 EDO and 20.5 EDO. It surpasses [[70zpi]] in peak height, integral, and gap. However, while [[70zpi]] is the closest peak to 20 EDO and closely rivals in strength, it does not match the overall superiority of 71zpi. | '''71zpi''' marks the most prominent zeta peak index in the vicinity of [[20edo]], ranging between 19.5 EDO and 20.5 EDO. It surpasses [[70zpi]] in peak height, integral, and gap. However, while [[70zpi]] is the closest peak to 20 EDO and closely rivals in strength, it does not match the overall superiority of 71zpi. | ||
71zpi features a good 3:5:9:11:14:15:16:19:25:26:33 chord, which differs from the harmonic characteristics of [[20edo]].[[File:71zpi.png|thumb]] | 71zpi features a good 3:5:9:11:14:15:16:19:25:26:33 chord, which differs from the harmonic characteristics of [[20edo]].[[File:71zpi.png|thumb]]The nearest zeta peaks to 71zpi that surpass its height are [[65zpi]] and [[75zpi]].{{Harmonics in cet|59.3329806724710|columns=15|title=71zpi}} | ||
{{Harmonics in cet|59.3329806724710|columns=15|title=71zpi}} | |||
{{Harmonics in cet|59.3329806724710|columns=16|start=16|title=71zpi}} | {{Harmonics in cet|59.3329806724710|columns=16|start=16|title=71zpi}} | ||
{{Stub}} | {{Stub}} | ||
Revision as of 22:38, 19 April 2024
71 zeta peak index (abbreviated 71zpi), is the equal-step 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 |
71zpi marks the most prominent zeta peak index in the vicinity of 20edo, ranging between 19.5 EDO and 20.5 EDO. It surpasses 70zpi in peak height, integral, and gap. However, while 70zpi is the closest peak to 20 EDO and closely rivals in strength, it does not match the overall superiority of 71zpi.
71zpi features a good 3:5:9:11:14:15:16:19:25:26:33 chord, which differs from the harmonic characteristics of 20edo.
The nearest zeta peaks to 71zpi that surpass its height are 65zpi and 75zpi.
| 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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