Xenharmonic Wiki

27edo: Difference between revisions

← Older editNewer edit →
VisualWikitext
→Music: cleanup
→JI approximation: adopt new template, make the old table collapsed
Line 353: Line 353:
=== 15-odd-limit interval mappings ===
=== 15-odd-limit interval mappings ===
The following table shows how [[15-odd-limit intervals]] are represented in 27edo. Prime harmonics are in '''bold'''; inconsistent intervals are in ''italic''.
The following table shows how [[15-odd-limit intervals]] are represented in 27edo. Prime harmonics are in '''bold'''; inconsistent intervals are in ''italic''.
{| class="wikitable center-all"
{| class="wikitable center-all mw-collapsible mw-collapsed"
|+ Direct mapping (even if inconsistent)
|+style=white-space:nowrap| 15-odd-limit intervals by direct approximation (even if inconsistent)
|-
|-
! Interval, complement
! Interval, complement
! Error (abs, ¢)
! Error (abs, ¢)
! Error (rel, %)
|-
|-
| [[7/6]], [[12/7]]
| [[7/6]], [[12/7]]
| 0.204
| 0.204
| 0.5
|-
|-
| ''[[15/11]], [[22/15]]''
| ''[[15/11]], [[22/15]]''
| ''3.617''
| ''3.617''
| ''8.1''
|-
|-
| '''[[16/13]], [[13/8]]'''
| '''[[13/8]], [[16/13]]'''
| '''3.917'''
| '''3.917'''
| '''8.8'''
|-
|-
| [[6/5]], [[5/3]]
| [[5/3]], [[6/5]]
| 4.530
| 4.530
| 10.2
|-
|-
| [[10/9]], [[9/5]]
| [[9/5]], [[10/9]]
| 4.626
| 4.626
| 10.4
|-
|-
| [[7/5]], [[10/7]]
| [[7/5]], [[10/7]]
| 4.734
| 4.734
| 10.7
|-
|-
| [[14/13]], [[13/7]]
| [[13/7]], [[14/13]]
| 5.035
| 5.035
| 11.3
|-
|-
| [[13/12]], [[24/13]]
| [[13/12]], [[24/13]]
| 5.239
| 5.239
| 11.8
|-
|-
| ''[[11/9]], [[18/11]]''
| ''[[11/9]], [[18/11]]''
| ''8.148''
| ''8.148''
| ''18.3''
|-
|-
| '''[[8/7]], [[7/4]]'''
| '''[[7/4]], [[8/7]]'''
| '''8.952'''
| '''8.952'''
| '''20.1'''
|-
|-
| '''[[4/3]], [[3/2]]'''
| '''[[3/2]], [[4/3]]'''
| '''9.156'''
| '''9.156'''
| '''20.6'''
|-
|-
| [[9/7]], [[14/9]]
| [[9/7]], [[14/9]]
| 9.360
| 9.360
| 21.1
|-
|-
| [[13/10]], [[20/13]]
| [[13/10]], [[20/13]]
| 9.770
| 9.770
| 22.0
|-
|-
| ''[[11/10]], [[20/11]]''
| ''[[11/10]], [[20/11]]''
| ''12.774''
| ''12.774''
| ''28.7''
|-
|-
| '''[[5/4]], [[8/5]]'''
| '''[[5/4]], [[8/5]]'''
| '''13.686'''
| '''13.686'''
| '''30.8'''
|-
|-
| [[15/14]], [[28/15]]
| [[15/14]], [[28/15]]
| 13.891
| 13.891
| 31.3
|-
|-
| [[18/13]], [[13/9]]
| [[13/9]], [[18/13]]
| 14.395
| 14.395
| 32.4
|-
|-
| ''[[12/11]], [[11/6]]''
| ''[[11/6]], [[12/11]]''
| ''17.304''
| ''17.304''
| ''38.9''
|-
|-
| ''[[14/11]], [[11/7]]''
| ''[[11/7]], [[14/11]]''
| ''17.508''
| ''17.508''
| ''39.4''
|-
|-
| '''[[11/8]], [[16/11]]'''
| '''[[11/8]], [[16/11]]'''
| '''17.985'''
| '''17.985'''
| '''40.5'''
|-
|-
| [[9/8]], [[16/9]]
| [[9/8]], [[16/9]]
| 18.312
| 18.312
| 41.2
|-
|-
| [[15/13]], [[26/15]]
| [[15/13]], [[26/15]]
| 18.926
| 18.926
| 42.6
|-
|-
| ''[[16/15]], [[15/8]]''
| ''[[15/8]], [[16/15]]''
| ''21.602''
| ''21.602''
| ''48.6''
|-
|-
| [[13/11]], [[22/13]]
| [[13/11]], [[22/13]]
| 21.901
| 21.901
| 49.3
|}
|}
 
{{15-odd-limit|27}}
{| class="wikitable center-all"
|+ Patent val mapping
|-
! Interval, complement
! Error (abs, ¢)
|-
| [[7/6]], [[12/7]]
| 0.204
|-
| '''[[16/13]], [[13/8]]'''
| '''3.917'''
|-
| [[6/5]], [[5/3]]
| 4.530
|-
| [[10/9]], [[9/5]]
| 4.626
|-
| [[7/5]], [[10/7]]
| 4.734
|-
| [[14/13]], [[13/7]]
| 5.035
|-
| [[13/12]], [[24/13]]
| 5.239
|-
| '''[[8/7]], [[7/4]]'''
| '''8.952'''
|-
| '''[[4/3]], [[3/2]]'''
| '''9.156'''
|-
| [[9/7]], [[14/9]]
| 9.360
|-
| [[13/10]], [[20/13]]
| 9.770
|-
| '''[[5/4]], [[8/5]]'''
| '''13.686'''
|-
| [[15/14]], [[28/15]]
| 13.891
|-
| [[18/13]], [[13/9]]
| 14.395
|-
| '''[[11/8]], [[16/11]]'''
| '''17.985'''
|-
| [[9/8]], [[16/9]]
| 18.312
|-
| [[15/13]], [[26/15]]
| 18.926
|-
| [[13/11]], [[22/13]]
| 21.901
|-
| ''[[16/15]], [[15/8]]''
| ''22.842''
|-
| ''[[14/11]], [[11/7]]''
| ''26.936''
|-
| ''[[12/11]], [[11/6]]''
| ''27.141''
|-
| ''[[11/10]], [[20/11]]''
| ''31.671''
|-
| ''[[11/9]], [[18/11]]''
| ''36.297''
|-
| ''[[15/11]], [[22/15]]''
| ''40.827''
|}


== Regular temperament properties ==
== Regular temperament properties ==
Retrieved from "https://en.xen.wiki/w/27edo"