User:BudjarnLambeth/435zpi: Difference between revisions
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'''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. | '''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 | 80edo tunes almost all simple harmonics slightly sharp by roughly the same amount, so 435zpi is one possible way of correcting for this. | ||
==Harmonics== | ==Harmonics== | ||
Revision as of 05:10, 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, 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 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 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 |
| 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 | |
| Step | 389 | 397 | 404 | 411 | 417 | 423 | 429 | 435 | 440 | 445 | 450 | 454 | |
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 | |