34zpi: Difference between revisions
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'''34 zeta peak index''' (abbreviated '''34zpi'''), is the [[Equal-step tuning|equal-step]] [[tuning system]] obtained from the 34th [[Zeta peak index|peak]] of the [[The Riemann zeta function and tuning|Riemann zeta function]]. | '''34 zeta peak index''' (abbreviated '''34zpi'''), is the [[Equal-step tuning|equal-step]] [[tuning system]] obtained from the 34th [[Zeta peak index|peak]] of the [[The Riemann zeta function and tuning|Riemann zeta function]]. | ||
{ | {{ZPI | ||
| zpi = 34 | |||
| steps = 12.0231830072926 | |||
| step size = 99.8071807833375 | |||
| height = 5.193290 | |||
| integral = 1.269599 | |||
| gap = 15.899282 | |||
| edo = 12edo | |||
| octave = 1197.68616940005 | |||
| consistent = 10 | |||
| distinct = 6 | |||
}} | |||
|99.8071807833375 | |||
|5.193290 | |||
|1.269599 | |||
|15.899282 | |||
| | |||
|1197.68616940005 | |||
|10 | |||
|6 | |||
== Intervals == | == Intervals == | ||
{| class="wikitable center-1 right-2 left-3 center-4" | {| class="wikitable center-1 right-2 left-3 center-4" | ||
|+ style="white-space:nowrap" | Intervals in 34zpi | |+ style="font-size: 105%; white-space: nowrap;" | Intervals in 34zpi | ||
|- | |- | ||
| colspan="3" style="text-align:left;" | JI ratios are comprised of 16-integer-limit ratios,<br>and are stylized as follows to indicate their accuracy: | | colspan="3" style="text-align:left;" | JI ratios are comprised of 16-integer-limit ratios,<br>and are stylized as follows to indicate their accuracy: | ||
| Line 42: | Line 25: | ||
* <small><small>Small Small:</small></small> relative error < 41.667 % | * <small><small>Small Small:</small></small> relative error < 41.667 % | ||
* <small><small><small>Small Small Small:</small></small></small> relative error < 50 % | * <small><small><small>Small Small Small:</small></small></small> relative error < 50 % | ||
| style="text-align:right;" | <center>'''⟨12 19]'''</center | | style="text-align:right;" | <center>'''⟨12 19]'''</center><br>[[9/8|Whole tone]] = 2 steps<br>[[256/243|Limma]] = 1 step<br>[[2187/2048|Apotome]] = 1 step | ||
|- | |- | ||
! Degree | ! Degree | ||
! Cents | ! Cents | ||
! Ratios | ! Ratios | ||
! Ups and | ! Ups and downs notation | ||
|- | |- | ||
| 0 | | 0 | ||
| Line 299: | Line 282: | ||
=== Interval mappings === | === Interval mappings === | ||
The following tables show how 16-integer-limit intervals are represented in 34zpi. Prime harmonics are in '''bold'''; inconsistent intervals are in ''italics''. | The following tables show how 16-integer-limit intervals are represented in 34zpi. Prime harmonics are in '''bold'''; inconsistent intervals are in ''italics''. | ||
{| class="wikitable center-1 right-2 right-3 mw-collapsible mw-collapsed" | {| class="wikitable center-1 right-2 right-3 mw-collapsible mw-collapsed" | ||