15L 8s: Difference between revisions

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<h2>IMPORTED REVISION FROM WIKISPACES</h2>
{{Infobox MOS}}
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
{{MOS intro}}
: This revision was by author [[User:JosephRuhf|JosephRuhf]] and made on <tt>2015-10-30 11:53:38 UTC</tt>.<br>
: The original revision id was <tt>564485367</tt>.<br>
: The revision comment was: <tt></tt><br>
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
<h4>Original Wikitext content:</h4>
<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;white-space: pre-wrap ! important" class="old-revision-html">This is the MOS where the large steps split 2-2-2-2-2-2-2-1 between the small steps. It is the quarter tone scale of Hemikleimsic temperament, generated by a 'neutral whole tone' no smaller than 3/23edo (156.522 cents).
|| 2/15 ||  ||  ||  ||  || 160 ||
||  ||  ||  ||  || 11/83 || 159.036 ||
||  ||  ||  || 9/68 ||  || 158.8235 ||
||  ||  ||  ||  || 16/121 || 158.678 ||
||  ||  ||  ||  ||  || 158.549 ||
||  ||  || 7/53 ||  ||  || 158.491 ||
||  ||  ||  ||  ||  || 158.36 ||
||  ||  ||  ||  || 19/144 || 158.33 ||
||  ||  ||  ||  ||  || 158.308 ||
||  ||  ||  || 12/91 ||  || 158.242 ||
||  ||  ||  ||  || 17/129 || 158.1395 ||
||  || 5/38 ||  ||  ||  || 157.895 ||
||  ||  ||  ||  || 18/137 || 157.664 ||
||  ||  ||  || 13/99 ||  || 157.576 ||
||  ||  ||  ||  ||  || 157.521 ||
||  ||  ||  ||  || 21/160 || 157.5 ||
||  ||  ||  ||  ||  || 157.465 ||
||  ||  || 8/61 ||  ||  || 157.377 ||
||  ||  ||  ||  || 19/145 || 157.241 ||
||  ||  ||  || 11/84 ||  || 157.143 ||
||  ||  ||  ||  || 14/107 || 157.009 ||
|| 3/23 ||  ||  ||  ||  || 156.522 ||</pre></div>
<h4>Original HTML content:</h4>
<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html">&lt;html&gt;&lt;head&gt;&lt;title&gt;15L 8s&lt;/title&gt;&lt;/head&gt;&lt;body&gt;This is the MOS where the large steps split 2-2-2-2-2-2-2-1 between the small steps. It is the quarter tone scale of Hemikleimsic temperament, generated by a 'neutral whole tone' no smaller than 3/23edo (156.522 cents).&lt;br /&gt;


It is the quarter tone scale of [[Hemikleismic]] temperament, generated by a 'neutral whole tone'.


&lt;table class="wiki_table"&gt;
== Modes ==
    &lt;tr&gt;
{{MOS modes}}
        &lt;td&gt;2/15&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;160&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;11/83&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;159.036&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;9/68&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;158.8235&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;16/121&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;158.678&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;158.549&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;7/53&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;158.491&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;158.36&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;19/144&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;158.33&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;158.308&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;12/91&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;158.242&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;17/129&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;158.1395&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;5/38&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;157.895&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;18/137&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;157.664&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;13/99&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;157.576&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;157.521&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;21/160&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;157.5&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;157.465&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;8/61&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;157.377&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;19/145&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;157.241&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;11/84&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;157.143&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;14/107&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;157.009&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;3/23&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;156.522&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
&lt;/table&gt;


&lt;/body&gt;&lt;/html&gt;</pre></div>
== Intervals ==
{{MOS intervals}}
 
== Scale tree ==
{{MOS tuning spectrum
| 7/2 = [[Hemikleismic]] (includes [[38edo]] and [[53edo]])
}}
 
{{todo|expand}}
[[Category:23-tone scales]]

Latest revision as of 16:55, 28 February 2025

↖ 14L 7s ↑ 15L 7s 16L 7s ↗
← 14L 8s 15L 8s 16L 8s →
↙ 14L 9s ↓ 15L 9s 16L 9s ↘ 
┌╥╥┬╥╥┬╥╥┬╥╥┬╥╥┬╥╥┬╥╥┬╥┬┐
│║║│║║│║║│║║│║║│║║│║║│║││
│││││││││││││││││││││││││
└┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
Scale structure
Step pattern LLsLLsLLsLLsLLsLLsLLsLs
sLsLLsLLsLLsLLsLLsLLsLL
Equave 2/1 (1200.0 ¢)
Period 2/1 (1200.0 ¢)
Generator size
Bright 3\23 to 2\15 (156.5 ¢ to 160.0 ¢)
Dark 13\15 to 20\23 (1040.0 ¢ to 1043.5 ¢)
TAMNAMS information
Related to 7L 1s (pine)
With tunings 3:2 to 2:1 (hyposoft)
Related MOS scales
Parent 8L 7s
Sister 8L 15s
Daughters 23L 15s, 15L 23s
Neutralized 7L 16s
2-Flought 38L 8s, 15L 31s
Equal tunings
Equalized (L:s = 1:1) 3\23 (156.5 ¢)
Supersoft (L:s = 4:3) 11\84 (157.1 ¢)
Soft (L:s = 3:2) 8\61 (157.4 ¢)
Semisoft (L:s = 5:3) 13\99 (157.6 ¢)
Basic (L:s = 2:1) 5\38 (157.9 ¢)
Semihard (L:s = 5:2) 12\91 (158.2 ¢)
Hard (L:s = 3:1) 7\53 (158.5 ¢)
Superhard (L:s = 4:1) 9\68 (158.8 ¢)
Collapsed (L:s = 1:0) 2\15 (160.0 ¢)

15L 8s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 15 large steps and 8 small steps, repeating every octave. 15L 8s is a grandchild scale of 7L 1s, expanding it by 15 tones. Generators that produce this scale range from 156.5 ¢ to 160 ¢, or from 1040 ¢ to 1043.5 ¢.

It is the quarter tone scale of Hemikleismic temperament, generated by a 'neutral whole tone'.

Modes

Modes of 15L 8s
UDP Cyclic
order		 Step
pattern
22|0 1 LLsLLsLLsLLsLLsLLsLLsLs
21|1 4 LLsLLsLLsLLsLLsLLsLsLLs
20|2 7 LLsLLsLLsLLsLLsLsLLsLLs
19|3 10 LLsLLsLLsLLsLsLLsLLsLLs
18|4 13 LLsLLsLLsLsLLsLLsLLsLLs
17|5 16 LLsLLsLsLLsLLsLLsLLsLLs
16|6 19 LLsLsLLsLLsLLsLLsLLsLLs
15|7 22 LsLLsLLsLLsLLsLLsLLsLLs
14|8 2 LsLLsLLsLLsLLsLLsLLsLsL
13|9 5 LsLLsLLsLLsLLsLLsLsLLsL
12|10 8 LsLLsLLsLLsLLsLsLLsLLsL
11|11 11 LsLLsLLsLLsLsLLsLLsLLsL
10|12 14 LsLLsLLsLsLLsLLsLLsLLsL
9|13 17 LsLLsLsLLsLLsLLsLLsLLsL
8|14 20 LsLsLLsLLsLLsLLsLLsLLsL
7|15 23 sLLsLLsLLsLLsLLsLLsLLsL
6|16 3 sLLsLLsLLsLLsLLsLLsLsLL
5|17 6 sLLsLLsLLsLLsLLsLsLLsLL
4|18 9 sLLsLLsLLsLLsLsLLsLLsLL
3|19 12 sLLsLLsLLsLsLLsLLsLLsLL
2|20 15 sLLsLLsLsLLsLLsLLsLLsLL
1|21 18 sLLsLsLLsLLsLLsLLsLLsLL
0|22 21 sLsLLsLLsLLsLLsLLsLLsLL

Intervals

Intervals of 15L 8s
Intervals Steps
subtended 		Range in cents
Generic Specific Abbrev.
0-mosstep Perfect 0-mosstep P0ms 0 0.0 ¢
1-mosstep Minor 1-mosstep m1ms s 0.0 ¢ to 52.2 ¢
Major 1-mosstep M1ms L 52.2 ¢ to 80.0 ¢
2-mosstep Minor 2-mosstep m2ms L + s 80.0 ¢ to 104.3 ¢
Major 2-mosstep M2ms 2L 104.3 ¢ to 160.0 ¢
3-mosstep Diminished 3-mosstep d3ms L + 2s 80.0 ¢ to 156.5 ¢
Perfect 3-mosstep P3ms 2L + s 156.5 ¢ to 160.0 ¢
4-mosstep Minor 4-mosstep m4ms 2L + 2s 160.0 ¢ to 208.7 ¢
Major 4-mosstep M4ms 3L + s 208.7 ¢ to 240.0 ¢
5-mosstep Minor 5-mosstep m5ms 3L + 2s 240.0 ¢ to 260.9 ¢
Major 5-mosstep M5ms 4L + s 260.9 ¢ to 320.0 ¢
6-mosstep Minor 6-mosstep m6ms 3L + 3s 240.0 ¢ to 313.0 ¢
Major 6-mosstep M6ms 4L + 2s 313.0 ¢ to 320.0 ¢
7-mosstep Minor 7-mosstep m7ms 4L + 3s 320.0 ¢ to 365.2 ¢
Major 7-mosstep M7ms 5L + 2s 365.2 ¢ to 400.0 ¢
8-mosstep Minor 8-mosstep m8ms 5L + 3s 400.0 ¢ to 417.4 ¢
Major 8-mosstep M8ms 6L + 2s 417.4 ¢ to 480.0 ¢
9-mosstep Minor 9-mosstep m9ms 5L + 4s 400.0 ¢ to 469.6 ¢
Major 9-mosstep M9ms 6L + 3s 469.6 ¢ to 480.0 ¢
10-mosstep Minor 10-mosstep m10ms 6L + 4s 480.0 ¢ to 521.7 ¢
Major 10-mosstep M10ms 7L + 3s 521.7 ¢ to 560.0 ¢
11-mosstep Minor 11-mosstep m11ms 7L + 4s 560.0 ¢ to 573.9 ¢
Major 11-mosstep M11ms 8L + 3s 573.9 ¢ to 640.0 ¢
12-mosstep Minor 12-mosstep m12ms 7L + 5s 560.0 ¢ to 626.1 ¢
Major 12-mosstep M12ms 8L + 4s 626.1 ¢ to 640.0 ¢
13-mosstep Minor 13-mosstep m13ms 8L + 5s 640.0 ¢ to 678.3 ¢
Major 13-mosstep M13ms 9L + 4s 678.3 ¢ to 720.0 ¢
14-mosstep Minor 14-mosstep m14ms 9L + 5s 720.0 ¢ to 730.4 ¢
Major 14-mosstep M14ms 10L + 4s 730.4 ¢ to 800.0 ¢
15-mosstep Minor 15-mosstep m15ms 9L + 6s 720.0 ¢ to 782.6 ¢
Major 15-mosstep M15ms 10L + 5s 782.6 ¢ to 800.0 ¢
16-mosstep Minor 16-mosstep m16ms 10L + 6s 800.0 ¢ to 834.8 ¢
Major 16-mosstep M16ms 11L + 5s 834.8 ¢ to 880.0 ¢
17-mosstep Minor 17-mosstep m17ms 11L + 6s 880.0 ¢ to 887.0 ¢
Major 17-mosstep M17ms 12L + 5s 887.0 ¢ to 960.0 ¢
18-mosstep Minor 18-mosstep m18ms 11L + 7s 880.0 ¢ to 939.1 ¢
Major 18-mosstep M18ms 12L + 6s 939.1 ¢ to 960.0 ¢
19-mosstep Minor 19-mosstep m19ms 12L + 7s 960.0 ¢ to 991.3 ¢
Major 19-mosstep M19ms 13L + 6s 991.3 ¢ to 1040.0 ¢
20-mosstep Perfect 20-mosstep P20ms 13L + 7s 1040.0 ¢ to 1043.5 ¢
Augmented 20-mosstep A20ms 14L + 6s 1043.5 ¢ to 1120.0 ¢
21-mosstep Minor 21-mosstep m21ms 13L + 8s 1040.0 ¢ to 1095.7 ¢
Major 21-mosstep M21ms 14L + 7s 1095.7 ¢ to 1120.0 ¢
22-mosstep Minor 22-mosstep m22ms 14L + 8s 1120.0 ¢ to 1147.8 ¢
Major 22-mosstep M22ms 15L + 7s 1147.8 ¢ to 1200.0 ¢
23-mosstep Perfect 23-mosstep P23ms 15L + 8s 1200.0 ¢

Scale tree

Scale tree and tuning spectrum of 15L 8s
Generator(edo) Cents Step ratio Comments
Bright Dark L:s Hardness
3\23 156.522 1043.478 1:1 1.000 Equalized 15L 8s
17\130 156.923 1043.077 6:5 1.200
14\107 157.009 1042.991 5:4 1.250
25\191 157.068 1042.932 9:7 1.286
11\84 157.143 1042.857 4:3 1.333 Supersoft 15L 8s
30\229 157.205 1042.795 11:8 1.375
19\145 157.241 1042.759 7:5 1.400
27\206 157.282 1042.718 10:7 1.429
8\61 157.377 1042.623 3:2 1.500 Soft 15L 8s
29\221 157.466 1042.534 11:7 1.571
21\160 157.500 1042.500 8:5 1.600
34\259 157.529 1042.471 13:8 1.625
13\99 157.576 1042.424 5:3 1.667 Semisoft 15L 8s
31\236 157.627 1042.373 12:7 1.714
18\137 157.664 1042.336 7:4 1.750
23\175 157.714 1042.286 9:5 1.800
5\38 157.895 1042.105 2:1 2.000 Basic 15L 8s
Scales with tunings softer than this are proper
22\167 158.084 1041.916 9:4 2.250
17\129 158.140 1041.860 7:3 2.333
29\220 158.182 1041.818 12:5 2.400
12\91 158.242 1041.758 5:2 2.500 Semihard 15L 8s
31\235 158.298 1041.702 13:5 2.600
19\144 158.333 1041.667 8:3 2.667
26\197 158.376 1041.624 11:4 2.750
7\53 158.491 1041.509 3:1 3.000 Hard 15L 8s
23\174 158.621 1041.379 10:3 3.333
16\121 158.678 1041.322 7:2 3.500 Hemikleismic (includes 38edo and 53edo)
25\189 158.730 1041.270 11:3 3.667
9\68 158.824 1041.176 4:1 4.000 Superhard 15L 8s
20\151 158.940 1041.060 9:2 4.500
11\83 159.036 1040.964 5:1 5.000
13\98 159.184 1040.816 6:1 6.000
2\15 160.000 1040.000 1:0 → ∞ Collapsed 15L 8s
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