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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]].


{|class="wikitable"
{{ZPI
!colspan="3"|Tuning
| zpi = 34
!colspan="3"|Strength
| steps = 12.0231830072926
!colspan="2"|Closest EDO
| step size = 99.8071807833375
!colspan="2"|Integer limit
| height = 5.193290
|-
| integral = 1.269599
!ZPI
| gap = 15.899282
!Steps per octave
| edo = 12edo
!Step size (cents)
| octave = 1197.68616940005
!Height
| consistent = 10
!Integral
| distinct = 6
!Gap
}}
!EDO
!Octave (cents)
!Consistent
!Distinct
|-
|34zpi
|12.0231830072926
|99.8071807833375
|5.193290
|1.269599
|15.899282
|[[12edo]]
|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="font-size: 105%; white-space: nowrap;" | Intervals in 34zpi
|-
|-
|+ style="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:
* '''<u>Bold Underlined:</u>''' relative error < 8.333 %
* '''<u>Bold Underlined:</u>''' relative error < 8.333 %
* '''Bold:''' relative error < 16.667 %
* '''Bold:''' relative error < 16.667 %
Line 47: Line 30:
! Cents
! Cents
! Ratios
! Ratios
! Ups and Downs Notation
! 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"
Line 387: Line 370:
| +9.610
| +9.610
| +9.629
| +9.629
|- style="background-color: #dddddd;"
|- style="background-color: #cccccc;"
| ''[[13/11]]''
| ''[[13/11]]''
| ''+10.212''
| ''+10.212''
Line 479: Line 462:
| '''+24.618'''
| '''+24.618'''
| '''+24.666'''
| '''+24.666'''
|- style="background-color: #dddddd;"
|- style="background-color: #cccccc;"
| ''[[13/7]]''
| ''[[13/7]]''
| ''+26.177''
| ''+26.177''
Line 491: Line 474:
| +27.923
| +27.923
| +27.977
| +27.977
|- style="background-color: #dddddd;"
|- style="background-color: #cccccc;"
| ''[[14/13]]''
| ''[[14/13]]''
| ''-28.491''
| ''-28.491''
Line 563: Line 546:
| -42.070
| -42.070
| -42.151
| -42.151
|- style="background-color: #dddddd;"
|- style="background-color: #cccccc;"
| ''[[13/5]]''
| ''[[13/5]]''
| ''+42.508''
| ''+42.508''
Line 579: Line 562:
| -44.384
| -44.384
| -44.470
| -44.470
|- style="background-color: #dddddd;"
|- style="background-color: #cccccc;"
| ''[[13/10]]''
| ''[[13/10]]''
| ''+44.822''
| ''+44.822''
Line 599: Line 582:
| +47.525
| +47.525
| +47.617
| +47.617
|- style="background-color: #dddddd;"
|- style="background-color: #cccccc;"
| ''[[11/9]]''
| ''[[11/9]]''
| ''-47.986''
| ''-47.986''
| ''-48.079''
| ''-48.079''
|- style="background-color: #dddddd;"
|- style="background-color: #cccccc;"
| ''[[15/13]]''
| ''[[15/13]]''
| ''-48.127''
| ''-48.127''
Line 611: Line 594:
| +48.516
| +48.516
| +48.610
| +48.610
|- style="background-color: #dddddd;"
|- style="background-color: #cccccc;"
| ''[[12/11]]''
| ''[[12/11]]''
| ''+48.977''
| ''+48.977''
Line 915: Line 898:
| -49.839
| -49.839
| -49.935
| -49.935
|- style="background-color: #dddddd;"
|- style="background-color: #cccccc;"
| ''[[12/11]]''
| ''[[12/11]]''
| ''-50.830''
| ''-50.830''
| ''-50.928''
| ''-50.928''
|- style="background-color: #dddddd;"
|- style="background-color: #cccccc;"
| ''[[15/13]]''
| ''[[15/13]]''
| ''+51.680''
| ''+51.680''
| ''+51.780''
| ''+51.780''
|- style="background-color: #dddddd;"
|- style="background-color: #cccccc;"
| ''[[11/9]]''
| ''[[11/9]]''
| ''+51.821''
| ''+51.821''
| ''+51.921''
| ''+51.921''
|- style="background-color: #dddddd;"
|- style="background-color: #cccccc;"
| ''[[13/10]]''
| ''[[13/10]]''
| ''-54.985''
| ''-54.985''
| ''-55.091''
| ''-55.091''
|- style="background-color: #dddddd;"
|- style="background-color: #cccccc;"
| ''[[13/5]]''
| ''[[13/5]]''
| ''-57.299''
| ''-57.299''
| ''-57.410''
| ''-57.410''
|- style="background-color: #dddddd;"
|- style="background-color: #cccccc;"
| ''[[14/13]]''
| ''[[14/13]]''
| ''+71.316''
| ''+71.316''
| ''+71.454''
| ''+71.454''
|- style="background-color: #dddddd;"
|- style="background-color: #cccccc;"
| ''[[13/7]]''
| ''[[13/7]]''
| ''-73.630''
| ''-73.630''
| ''-73.772''
| ''-73.772''
|- style="background-color: #dddddd;"
|- style="background-color: #cccccc;"
| ''[[13/11]]''
| ''[[13/11]]''
| ''-89.595''
| ''-89.595''
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