User:BudjarnLambeth/435zpi: Difference between revisions
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Created page with "'''435zpi''', the 435th zeta peak index, is a compressed-octaves version of 80edo. It can be thought of as 80ed1198.9c or as 14.986cet. 80edo tunes almost all simple harmonics slightly sharp by roughly the same amount (roughly 3 cents), so 435zpi is one possible way of correcting for this. ==Harmonics== ===Odd=== {{Harmonics in cet|14.986|columns=13|intervals=odd|title=Approximation of odd harmonics in 435zpi}} {{Harmonics in cet|14.986|columns=13|start=14|int..." |
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{{Harmonics in cet|14.986|columns=13|start=14|intervals=prime|title=Approximation of prime harmonics in 435zpi}} | {{Harmonics in cet|14.986|columns=13|start=14|intervals=prime|title=Approximation of prime harmonics in 435zpi}} | ||
[[Category:Zeta peak indexes]] | [[Category:Zeta peak indexes]][[Category:80edo]] | ||
Revision as of 05:05, 15 August 2025
435zpi, the 435th zeta peak index, is a compressed-octaves version of 80edo. It can be thought of as 80ed1198.9c or as 14.986cet.
80edo tunes almost all simple harmonics slightly sharp by roughly the same amount (roughly 3 cents), so 435zpi is one possible way of correcting for this.
Harmonics
Odd
| Harmonic | 3 | 5 | 7 | 9 | 11 | 13 | 15 | 17 | 19 | 21 | 23 | 25 | 27 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +1.27 | +1.08 | +3.02 | +2.53 | -0.20 | -4.67 | +2.35 | -4.53 | -2.27 | +4.29 | -3.34 | +2.16 | +3.80 |
| Relative (%) | +8.5 | +7.2 | +20.2 | +16.9 | -1.3 | -31.2 | +15.7 | -30.3 | -15.2 | +28.6 | -22.3 | +14.4 | +25.4 | |
| Step | 127 | 186 | 225 | 254 | 277 | 296 | 313 | 327 | 340 | 352 | 362 | 372 | 381 | |
| Harmonic | 29 | 31 | 33 | 35 | 37 | 39 | 41 | 43 | 45 | 47 | 49 | 51 | 53 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -0.02 | +4.41 | +1.07 | +4.11 | -2.18 | -3.40 | -0.07 | +7.39 | +3.62 | +3.26 | +6.05 | -3.27 | +5.07 |
| Relative (%) | -0.2 | +29.4 | +7.1 | +27.4 | -14.6 | -22.7 | -0.5 | +49.3 | +24.1 | +21.8 | +40.4 | -21.8 | +33.8 | |
| Step | 389 | 397 | 404 | 411 | 417 | 423 | 429 | 435 | 440 | 445 | 450 | 454 | 459 | |
Prime
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | 37 | 41 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -1.12 | +1.27 | +1.08 | +3.02 | -0.20 | -4.67 | -4.53 | -2.27 | -3.34 | -0.02 | +4.41 | -2.18 | -0.07 |
| Relative (%) | -7.5 | +8.5 | +7.2 | +20.2 | -1.3 | -31.2 | -30.3 | -15.2 | -22.3 | -0.2 | +29.4 | -14.6 | -0.5 | |
| Step | 80 | 127 | 186 | 225 | 277 | 296 | 327 | 340 | 362 | 389 | 397 | 417 | 429 | |
| Harmonic | 43 | 47 | 53 | 59 | 61 | 67 | 71 | 73 | 79 | 83 | 89 | 97 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +7.39 | +3.26 | +5.07 | -0.77 | +1.47 | +3.89 | -6.58 | +5.27 | +3.39 | -7.19 | +6.85 | -7.29 |
| Relative (%) | +49.3 | +21.8 | +33.8 | -5.1 | +9.8 | +26.0 | -43.9 | +35.1 | +22.6 | -48.0 | +45.7 | -48.6 | |
| Step | 435 | 445 | 459 | 471 | 475 | 486 | 492 | 496 | 505 | 510 | 519 | 528 | |