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"
{| class="wikitable"
|+
|+
Hemififths
!#\181
!#\181
!Cents
!Cents
Line 14: Line 15:
|53
|53
|351.381
|351.381
|11/9
|11/9, 16/13
|-
|-
|84
|84
|556.906
|556.906
|'''11/8'''
|11/8, 18/13
|-
|-
|106
|106
|702.762
|702.762
|'''3/2'''
|3/2
|-
|-
|137
|137
Line 32: Line 33:
|11/6
|11/6
|-
|-
|181
|'''181'''
|1200.000
|'''1200.000'''
|2/1
|'''2/1'''
|}
|}


== Stretched Hemififths ==
== Stretched Hemififths ==


This mode can be improved in 181edo by stretching some small "s" with 1 step of 181edo: 31 22 31 23 31 22 23
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, more JI ratios are approximated
With this stretched mode, various simple [[Just intonation|Just Intonation]] ratios are approximated thoughout the octaves.


{| class="wikitable"
{| class="wikitable"
|+
|+
Stretched Hemififths (octave-reduced )
!#\181
!#\181
!Cents
!Cents
Line 52: Line 53:
|31
|31
|205.525
|205.525
|
|9/8
|-
|-
|53
|53
|351.381
|351.381
|
|11/9, 16/13
|-
|-
|84
|84
|556.906
|556.906
|
|11/8, 18/13
|-
|-
|107
|107
|709.392
|709.392
|
|3/2
|-
|-
|138
|138
|914.917
|914.917
|
|22/13
|-
|-
|160
|160
|1060.773
|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
|
|
|-
|-
|183
|140
|1213.260
|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'''
|
|
|}
|}
<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 ==
* [[93edo and stretched hemififths]]
[[Category:181edo]]
[[Category:Hemififths]]

Latest revision as of 20:31, 10 March 2023

Normal Hemififths

181edo supports normal Hemififths (MOS 3L 4s) with the mode 31 22 31 22 31 22 22

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 ratios are approximated thoughout the octaves.

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 
! 181edo_stretched-hemififths.scl
!
181edo stretched hemififths
7
!
205.524862
351.381215
556.906077
709.392265
914.917127
1060.773481
1213.259669

See Also

Retrieved from "https://en.xen.wiki/index.php?title=181edo_and_stretched_hemififths&oldid=105260"