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181edo and stretched hemififths: Difference between revisions

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== Normal Hemififths ==
== Normal Hemififths ==


181edo supports normal Hemififths (MOS 3L 4s) with the mode 31 22 31 22 31 22 22
[[181edo]] supports normal [[Hemififths]] ([[3L 4s|MOS 3L 4s]]) with the mode 31 22 31 22 31 22 22
{| class="wikitable"
|+
Hemififths
!#\181
!Cents
!Approximated Ratios
|-
|31
|205.525
|9/8
|-
|53
|351.381
|11/9, 16/13
|-
|84
|556.906
|11/8, 18/13
|-
|106
|702.762
|3/2
|-
|137
|908.287
|22/13
|-
|159
|1054.144
|11/6
|-
|'''181'''
|'''1200.000'''
|'''2/1'''
|}


== Stretched Hemififths ==
This mode can be improved in 181edo by adding 1 more step on the fifth, and 1 more step on the octave: 31 22 31 23 31 22 23
With this stretched mode, various simple [[Just intonation|Just Intonation]] ratios are approximated thoughout the octaves.
{| class="wikitable"
|+
Stretched Hemififths (octave-reduced )
!#\181
!Cents
!Approximated Ratios
|-
|31
|205.525
|9/8
|-
|53
|351.381
|11/9, 16/13
|-
|84
|556.906
|11/8, 18/13
|-
|107
|709.392
|3/2
|-
|138
|914.917
|22/13
|-
|160
|1060.773
|24/13
|-
|'''2'''
|'''13.260'''
|'''2/1'''
|-
|33
|218.785
|9/8, 8/7
|-
|55
|364.641
|16/13
|-
|86
|570.166
|18/13
|-
|109
|722.652
|
|-
|140
|928.177
|12/7
|-
|162
|1074.033
|13/7
|-
|'''4'''
|'''26.519'''
|
|-
|35
|232.044
|8/7
|-
|57
|377.901
|5/4
|-
|88
|583.425
|7/5
|-
|111
|735.912
|20/13
|-
|142
|941.436
|12/7
|-
|164
|1087.293
|15/8
|-
|'''6'''
|'''39.779'''
|
|-
|37
|245.304
|15/13
|-
|59
|391.160
|5/4
|-
|90
|596.685
|7/5
|-
|113
|749.171
|20/13
|-
|144
|954.696
|26/15
|-
|166
|1100.552
|15/8
|-
|'''8'''
|'''53.039'''
|
|}


== Stretched Hemififths ==
<pre>
! 181edo_stretched-hemififths.scl
!
181edo stretched hemififths
7
!
205.524862
351.381215
556.906077
709.392265
914.917127
1060.773481
1213.259669
</pre>
 
== See Also ==


This mode can be improved in 181edo by stretching some small "s" with 1 step of 181edo: 31 22 31 23 31 22 23
* [[93edo and stretched hemififths]]


With this stretched mode, more JI ratios are approximated
[[Category:181edo]]
[[Category:Hemififths]]
Retrieved from "https://en.xen.wiki/w/181edo_and_stretched_hemififths"