Xenharmonic Wiki

14edo: Difference between revisions

← Older editNewer edit →
VisualWikitext
Fredg999 (talk | contribs)
autopatrolled, Interface administrators, Sysops
6,129 edits
→Compositions: 14edo tracks category
Xenllium (talk | contribs)
autopatrolled, emailconfirmed
4,516 edits
No edit summary
Line 18: Line 18:


== Theory ==
== Theory ==
The character of 14edo does not well serve those seeking low-limit JI approaches, with the exception of 5:7:9:11:17:19 (which is quite well approximated, relative to other JI approximations of the low-numbered edos). However, the ratios 7/5, 7/6, 9/7, 10/7, 10/9, 11/7, 11/9, and 11/10 are all recognizably approximated, and if you accept that 14edo offers approximations of these intervals, you end up with a low-complexity, high-damage 11-limit temperament where the commas listed at the bottom of this page are tempered out. This leads to some of the bizarre equivalences described in the second "Approximate Ratios" column in the table below.
The character of 14edo does not well serve those seeking low-limit JI approaches, with the exception of 5:7:9:11:17:19 (which is quite well approximated, relative to other JI approximations of the low-numbered EDOs). However, the ratios 7/5, 7/6, 9/7, 10/7, 10/9, 11/7, 11/9, and 11/10 are all recognizably approximated, and if you accept that 14edo offers approximations of these intervals, you end up with a low-complexity, high-damage 11-limit temperament where the commas listed at the bottom of this page are tempered out. This leads to some of the bizarre equivalences described in the second "Approximate Ratios" column in the table below.


14et has quite a bit of xenharmonic appeal, in a similar way to 17et, on account of having three types of 3rd and three types of 6th, rather than the usual two of 12et. Since 14et also has a recognizable 4th and 5th, this makes it good for those wishing to explore alternative triadic harmonies without adding significantly more notes. It possesses a triad-rich 9-note MOS scale of [[5L 4s]], wherein 7 of 9 notes are tonic to a subminor, supermajor, and/or neutral triad.
14et has quite a bit of xenharmonic appeal, in a similar way to 17et, on account of having three types of 3rd and three types of 6th, rather than the usual two of 12et. Since 14et also has a recognizable 4th and 5th, this makes it good for those wishing to explore alternative triadic harmonies without adding significantly more notes. It possesses a triad-rich 9-note MOS scale of [[5L 4s]], wherein 7 of 9 notes are tonic to a subminor, supermajor, and/or neutral triad.
Line 24: Line 24:
=== Odd harmonics ===
=== Odd harmonics ===
{{Odd harmonics in edo|14}}
{{Odd harmonics in edo|14}}
=== Differences between distributionally-even scales and smaller EDOs ===
{| class="wikitable"
|+
!N
!L-Nedo
!s-Nedo
|-
| 3
| 28.571¢
| -57.143¢
|-
| 4
| 42.857¢
| -42.857¢
|-
| 5
| 17.143¢
| -68.571¢
|-
| 6
| 57.143¢
| -28.571¢
|-
| 8
| 21.429¢
| -64.286¢
|-
| 9
| 38.095¢
| -47.619¢
|-
| 10
| 51.429¢
| -34.286¢
|-
| 11
| 62.338¢
| -23.377¢
|-
| 12
| 71.429¢
| -14.286¢
|-
| 13
| 79.121¢
| -6.593¢
|}


== Intervals ==
== Intervals ==
Line 267: Line 315:


=== Commas ===
=== Commas ===
14et [[tempers out]] the following [[comma]]s. This assumes the [[val]] {{val| 14 22 33 39 48 52 }}.  
14edo [[tempers out]] the following [[comma]]s. This assumes the [[val]] {{val| 14 22 33 39 48 52 }}.  


{| class="commatable wikitable center-all left-3 right-4 left-6"
{| class="commatable wikitable center-all left-3 right-4 left-6"
Retrieved from "https://en.xen.wiki/w/14edo"