User:BudjarnLambeth/435zpi: Difference between revisions
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==Prime harmonics== | ==Prime harmonics== | ||
{{Harmonics in cet|14.986|columns= | {{Harmonics in cet|14.986|columns=7|intervals=prime|title=Approximation of prime harmonics in 435zpi}} | ||
{{Harmonics in cet|14.986|columns= | {{Harmonics in cet|14.986|columns=7|start=8|intervals=prime|title=Approximation of prime harmonics in 435zpi}} | ||
[[Category:Zeta peak indexes]][[Category:80edo]] | [[Category:Zeta peak indexes]][[Category:80edo]] | ||
Revision as of 05:16, 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.
Prime harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | |
|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -1.12 | +1.27 | +1.08 | +3.02 | -0.20 | -4.67 | -4.53 |
| Relative (%) | -7.5 | +8.5 | +7.2 | +20.2 | -1.3 | -31.2 | -30.3 | |
| Step | 80 | 127 | 186 | 225 | 277 | 296 | 327 | |
| Harmonic | 19 | 23 | 29 | 31 | 37 | 41 | 43 | |
|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -2.27 | -3.34 | -0.02 | +4.41 | -2.18 | -0.07 | +7.39 |
| Relative (%) | -15.2 | -22.3 | -0.2 | +29.4 | -14.6 | -0.5 | +49.3 | |
| Step | 340 | 362 | 389 | 397 | 417 | 429 | 435 | |