10L 7s: Difference between revisions

From Xenharmonic Wiki
Jump to navigation Jump to search
← Older edit
VisualWikitext
Wikispaces>JosephRuhf
**Imported revision 530093828 - Original comment: **
m Removed outright wrong info
Tags: Mobile edit Mobile web edit
 
(12 intermediate revisions by 7 users not shown)
Line 1: Line 1:
<h2>IMPORTED REVISION FROM WIKISPACES</h2>
{{Infobox MOS
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
| Name =
: This revision was by author [[User:JosephRuhf|JosephRuhf]] and made on <tt>2014-11-08 09:33:52 UTC</tt>.<br>
| Periods = 1
: The original revision id was <tt>530093828</tt>.<br>
| nLargeSteps = 10
: The revision comment was: <tt></tt><br>
| nSmallSteps = 7
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
| Equalized = 5
<h4>Original Wikitext content:</h4>
| Collapsed = 3
<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 MOS, with intervals of 2L-L-2L-L-2L-L-L between its small steps, is like the neutral thirds version of Schismic temperament. It has a generator between 5/17edo (352 16/17) and 3/10edo (360 cents), making it an improper MOS of Beatles temperament (generator = c. 19/64 ~ 356.25 cents).
| Pattern = LLsLsLLsLsLLsLsLs
|| 3/10 ||  ||  ||  ||  || 360 ||
}}
||  ||  ||  ||  || 17/57 || 357 17/19 ||
{{MOS intro}} The range of the bright generator makes it an [[improper]] MOS of [[Beatles]] temperament (generator = c. 19\64 ~ 356.25{{cent}}).
||  ||  ||  || 14/47 ||  || 357 21/47 ||
||  ||  ||  ||  || 25/84 || 357 1/7 ||
||  ||  || 11/37 ||  ||  || 356 28/37 ||
||  ||  ||  ||  || 30/101 || 356 44/101 ||
||  ||  ||  || 19/64 ||  || 356.25 ||
||  ||  ||  ||  || 27/91 || 356 4/91 ||
||  || 8/27 ||  ||  ||  || 355 5/9 ||
||  ||  ||  ||  || 29/98 || 355 5/49 ||
||  ||  ||  || 21/71 ||  || 354 66/71 ||
||  ||  ||  ||  || 34/115 || 354 18/23 ||
||  ||  || 13/44 ||  ||  || 354 6/11 ||
||  ||  ||  ||  || 31/105 || 354 2/7 ||
||  ||  ||  || 18/61 ||  || 354 6/61 ||
||  ||  ||  ||  || 23/78 || 353 11/13 ||
|| 5/17 ||  ||  ||  ||  || 352 16/17 ||</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;10L 7s&lt;/title&gt;&lt;/head&gt;&lt;body&gt;This MOS, with intervals of 2L-L-2L-L-2L-L-L between its small steps, is like the neutral thirds version of Schismic temperament. It has a generator between 5/17edo (352 16/17) and 3/10edo (360 cents), making it an improper MOS of Beatles temperament (generator = c. 19/64 ~ 356.25 cents).&lt;br /&gt;


== Modes ==
{{MOS modes}}


&lt;table class="wiki_table"&gt;
== Intervals ==
    &lt;tr&gt;
{{MOS intervals}}
        &lt;td&gt;3/10&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;360&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;17/57&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;357 17/19&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;14/47&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;357 21/47&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;25/84&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;357 1/7&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;11/37&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;356 28/37&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;30/101&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;356 44/101&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;19/64&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;356.25&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;27/91&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;356 4/91&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;8/27&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;355 5/9&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;29/98&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;355 5/49&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;21/71&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;354 66/71&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;34/115&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;354 18/23&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;13/44&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;354 6/11&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;31/105&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;354 2/7&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;18/61&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;354 6/61&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;23/78&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;353 11/13&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;5/17&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;352 16/17&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
&lt;/table&gt;


&lt;/body&gt;&lt;/html&gt;</pre></div>
== Scale tree ==
{{MOS tuning spectrum}}

Latest revision as of 03:32, 18 June 2025

↖ 9L 6s ↑ 10L 6s 11L 6s ↗
← 9L 7s 10L 7s 11L 7s →
↙ 9L 8s ↓ 10L 8s 11L 8s ↘ 
┌╥╥┬╥┬╥╥┬╥┬╥╥┬╥┬╥┬┐
│║║│║│║║│║│║║│║│║││
│││││││││││││││││││
└┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
Scale structure
Step pattern LLsLsLLsLsLLsLsLs
sLsLsLLsLsLLsLsLL
Equave 2/1 (1200.0 ¢)
Period 2/1 (1200.0 ¢)
Generator size
Bright 5\17 to 3\10 (352.9 ¢ to 360.0 ¢)
Dark 7\10 to 12\17 (840.0 ¢ to 847.1 ¢)
TAMNAMS information
Related to 7L 3s (dicoid)
With tunings 1:1 to 2:1 (soft-of-basic)
Related MOS scales
Parent 7L 3s
Sister 7L 10s
Daughters 17L 10s, 10L 17s
Neutralized 3L 14s
2-Flought 27L 7s, 10L 24s
Equal tunings
Equalized (L:s = 1:1) 5\17 (352.9 ¢)
Supersoft (L:s = 4:3) 18\61 (354.1 ¢)
Soft (L:s = 3:2) 13\44 (354.5 ¢)
Semisoft (L:s = 5:3) 21\71 (354.9 ¢)
Basic (L:s = 2:1) 8\27 (355.6 ¢)
Semihard (L:s = 5:2) 19\64 (356.2 ¢)
Hard (L:s = 3:1) 11\37 (356.8 ¢)
Superhard (L:s = 4:1) 14\47 (357.4 ¢)
Collapsed (L:s = 1:0) 3\10 (360.0 ¢)

10L 7s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 10 large steps and 7 small steps, repeating every octave. 10L 7s is a child scale of 7L 3s, expanding it by 7 tones. Generators that produce this scale range from 352.9 ¢ to 360 ¢, or from 840 ¢ to 847.1 ¢. The range of the bright generator makes it an improper MOS of Beatles temperament (generator = c. 19\64 ~ 356.25 ¢).

Modes

Modes of 10L 7s
UDP Cyclic
order		 Step
pattern
16|0 1 LLsLsLLsLsLLsLsLs
15|1 6 LLsLsLLsLsLsLLsLs
14|2 11 LLsLsLsLLsLsLLsLs
13|3 16 LsLLsLsLLsLsLLsLs
12|4 4 LsLLsLsLLsLsLsLLs
11|5 9 LsLLsLsLsLLsLsLLs
10|6 14 LsLsLLsLsLLsLsLLs
9|7 2 LsLsLLsLsLLsLsLsL
8|8 7 LsLsLLsLsLsLLsLsL
7|9 12 LsLsLsLLsLsLLsLsL
6|10 17 sLLsLsLLsLsLLsLsL
5|11 5 sLLsLsLLsLsLsLLsL
4|12 10 sLLsLsLsLLsLsLLsL
3|13 15 sLsLLsLsLLsLsLLsL
2|14 3 sLsLLsLsLLsLsLsLL
1|15 8 sLsLLsLsLsLLsLsLL
0|16 13 sLsLsLLsLsLLsLsLL

Intervals

Intervals of 10L 7s
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 70.6 ¢
Major 1-mosstep M1ms L 70.6 ¢ to 120.0 ¢
2-mosstep Minor 2-mosstep m2ms L + s 120.0 ¢ to 141.2 ¢
Major 2-mosstep M2ms 2L 141.2 ¢ to 240.0 ¢
3-mosstep Minor 3-mosstep m3ms L + 2s 120.0 ¢ to 211.8 ¢
Major 3-mosstep M3ms 2L + s 211.8 ¢ to 240.0 ¢
4-mosstep Minor 4-mosstep m4ms 2L + 2s 240.0 ¢ to 282.4 ¢
Major 4-mosstep M4ms 3L + s 282.4 ¢ to 360.0 ¢
5-mosstep Diminished 5-mosstep d5ms 2L + 3s 240.0 ¢ to 352.9 ¢
Perfect 5-mosstep P5ms 3L + 2s 352.9 ¢ to 360.0 ¢
6-mosstep Minor 6-mosstep m6ms 3L + 3s 360.0 ¢ to 423.5 ¢
Major 6-mosstep M6ms 4L + 2s 423.5 ¢ to 480.0 ¢
7-mosstep Minor 7-mosstep m7ms 4L + 3s 480.0 ¢ to 494.1 ¢
Major 7-mosstep M7ms 5L + 2s 494.1 ¢ to 600.0 ¢
8-mosstep Minor 8-mosstep m8ms 4L + 4s 480.0 ¢ to 564.7 ¢
Major 8-mosstep M8ms 5L + 3s 564.7 ¢ to 600.0 ¢
9-mosstep Minor 9-mosstep m9ms 5L + 4s 600.0 ¢ to 635.3 ¢
Major 9-mosstep M9ms 6L + 3s 635.3 ¢ to 720.0 ¢
10-mosstep Minor 10-mosstep m10ms 5L + 5s 600.0 ¢ to 705.9 ¢
Major 10-mosstep M10ms 6L + 4s 705.9 ¢ to 720.0 ¢
11-mosstep Minor 11-mosstep m11ms 6L + 5s 720.0 ¢ to 776.5 ¢
Major 11-mosstep M11ms 7L + 4s 776.5 ¢ to 840.0 ¢
12-mosstep Perfect 12-mosstep P12ms 7L + 5s 840.0 ¢ to 847.1 ¢
Augmented 12-mosstep A12ms 8L + 4s 847.1 ¢ to 960.0 ¢
13-mosstep Minor 13-mosstep m13ms 7L + 6s 840.0 ¢ to 917.6 ¢
Major 13-mosstep M13ms 8L + 5s 917.6 ¢ to 960.0 ¢
14-mosstep Minor 14-mosstep m14ms 8L + 6s 960.0 ¢ to 988.2 ¢
Major 14-mosstep M14ms 9L + 5s 988.2 ¢ to 1080.0 ¢
15-mosstep Minor 15-mosstep m15ms 8L + 7s 960.0 ¢ to 1058.8 ¢
Major 15-mosstep M15ms 9L + 6s 1058.8 ¢ to 1080.0 ¢
16-mosstep Minor 16-mosstep m16ms 9L + 7s 1080.0 ¢ to 1129.4 ¢
Major 16-mosstep M16ms 10L + 6s 1129.4 ¢ to 1200.0 ¢
17-mosstep Perfect 17-mosstep P17ms 10L + 7s 1200.0 ¢

Scale tree

Scale tree and tuning spectrum of 10L 7s
Generator(edo) Cents Step ratio Comments
Bright Dark L:s Hardness
5\17 352.941 847.059 1:1 1.000 Equalized 10L 7s
28\95 353.684 846.316 6:5 1.200
23\78 353.846 846.154 5:4 1.250
41\139 353.957 846.043 9:7 1.286
18\61 354.098 845.902 4:3 1.333 Supersoft 10L 7s
49\166 354.217 845.783 11:8 1.375
31\105 354.286 845.714 7:5 1.400
44\149 354.362 845.638 10:7 1.429
13\44 354.545 845.455 3:2 1.500 Soft 10L 7s
47\159 354.717 845.283 11:7 1.571
34\115 354.783 845.217 8:5 1.600
55\186 354.839 845.161 13:8 1.625
21\71 354.930 845.070 5:3 1.667 Semisoft 10L 7s
50\169 355.030 844.970 12:7 1.714
29\98 355.102 844.898 7:4 1.750
37\125 355.200 844.800 9:5 1.800
8\27 355.556 844.444 2:1 2.000 Basic 10L 7s
Scales with tunings softer than this are proper
35\118 355.932 844.068 9:4 2.250
27\91 356.044 843.956 7:3 2.333
46\155 356.129 843.871 12:5 2.400
19\64 356.250 843.750 5:2 2.500 Semihard 10L 7s
49\165 356.364 843.636 13:5 2.600
30\101 356.436 843.564 8:3 2.667
41\138 356.522 843.478 11:4 2.750
11\37 356.757 843.243 3:1 3.000 Hard 10L 7s
36\121 357.025 842.975 10:3 3.333
25\84 357.143 842.857 7:2 3.500
39\131 357.252 842.748 11:3 3.667
14\47 357.447 842.553 4:1 4.000 Superhard 10L 7s
31\104 357.692 842.308 9:2 4.500
17\57 357.895 842.105 5:1 5.000
20\67 358.209 841.791 6:1 6.000
3\10 360.000 840.000 1:0 → ∞ Collapsed 10L 7s
Retrieved from "https://en.xen.wiki/index.php?title=10L_7s&oldid=199892"