1L 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>
| Periods = 1
: This revision was by author [[User:JosephRuhf|JosephRuhf]] and made on <tt>2015-05-23 15:24:59 UTC</tt>.<br>
| nLargeSteps = 1
: The original revision id was <tt>551971800</tt>.<br>
| nSmallSteps = 8
: The revision comment was: <tt></tt><br>
| Equalized = 8
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
| Collapsed = 1
<h4>Original Wikitext content:</h4>
| Pattern = Lssssssss
<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 a generator of up to 1/9edo (133 1/3 cents), represents temperaments like Miracle (2&lt;L&lt;3 s=1) and Negri (3&lt;L&lt;4 s=2). Of all the temperaments it represents, the harmonic entropy minimum is the one where the scale is generated by an interval near 3/28edo (L near 4 s=3).
}}
|| 0/1 ||  ||  ||  ||  || 0 ||=   ||=  ||
||  ||  ||  ||  || 1/13 || 92 4/13 ||=  ||=  ||
||  ||  ||  || 1/12 ||  || 100 ||=  ||= L/s = 4 ||
||  ||  ||  ||  || 2/23 || 104.347826 ||=  ||=   ||
||  ||  ||  ||  ||  || 1200/(8+pi)) ||  ||  ||
||  ||  || 1/11 ||  ||  || 109 1/11 ||= Miracle generators from here... ||= L/s = 3 ||
||  ||  ||  ||  ||  || 1200/(8+e) ||  ||  ||
||  ||  ||  ||  || 3/32 || 112.5 ||=  ||=  ||
||  ||  ||  || 2/21 ||  || 114 2/7 ||=   ||=  ||
||  ||  ||  ||  || 3/31 || 116.129032 ||=  ||=  ||
||  || 1/10 ||  ||  ||  || 120 ||= ...to here;
Negri generators from here... ||= Boundary of propriety:
generators larger than this are proper ||
||  ||  ||  ||  || 4/39 || 123 1/13 ||=  ||=  ||
||  ||  ||  || 3/29 ||  || 124.137931 ||=  ||=  ||
||  ||  ||  ||  || 5/48 || 125 ||=  ||=  ||
||  ||  || 2/19 ||  ||  || 126.315789 ||= ...to here ||=  ||
||  ||  ||  ||  || 5/47 || 127.659574 ||=  ||=  ||
||  ||  ||  || 3/28 ||  || 128 4/7 ||=  ||=  ||
||  ||  ||  ||  || 4/37 || 129 27/37 ||=  ||=  ||
|| 1/9 ||  ||  ||  ||  || 133 1/3 ||=  ||=   ||</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;1L 8s&lt;/title&gt;&lt;/head&gt;&lt;body&gt;This MOS, with a generator of up to 1/9edo (133 1/3 cents), represents temperaments like Miracle (2&amp;lt;L&amp;lt;3 s=1) and Negri (3&amp;lt;L&amp;lt;4 s=2). Of all the temperaments it represents, the harmonic entropy minimum is the one where the scale is generated by an interval near 3/28edo (L near 4 s=3).&lt;br /&gt;


{{MOS intro}}


&lt;table class="wiki_table"&gt;
This MOS represents temperaments like [[Miracle]] and [[Negri]]. Of all the temperaments it represents, the [[harmonic entropy]] minimum is the one where the scale is generated by an interval near [[28edo|3\28]] (around [[14/13]]).
    &lt;tr&gt;
        &lt;td&gt;0/1&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;0&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&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;1/13&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;92 4/13&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&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;1/12&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;100&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;L/s = 4&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;2/23&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;104.347826&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&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;1200/(8+pi))&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;/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;1/11&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;109 1/11&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;Miracle generators from here...&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;L/s = 3&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;1200/(8+e)&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;/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;3/32&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;112.5&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&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;2/21&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;114 2/7&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&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;3/31&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;116.129032&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1/10&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;120&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;...to here;&lt;br /&gt;
Negri generators from here...&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;Boundary of propriety:&lt;br /&gt;
generators larger than this are proper&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;4/39&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;123 1/13&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&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;3/29&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;124.137931&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&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;5/48&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;125&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&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;2/19&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;126.315789&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;...to here&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&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;5/47&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;127.659574&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&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;3/28&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;128 4/7&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&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;4/37&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;129 27/37&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;1/9&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;133 1/3&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
&lt;/table&gt;


&lt;/body&gt;&lt;/html&gt;</pre></div>
== Modes ==
{{MOS modes}}
 
=== Degrees ===
{{MOS mode degrees}}
 
== Intervals ==
{{MOS intervals}}
 
== Scale tree ==
Generator ranges:
* Chroma-positive generator: 1066.6667 cents (8\9) to 1200 cents (1\1)
* Chroma-negative generator: 0 cents (0\1) to 133.3333 cents (1\9)
 
{| class="wikitable center-all"
! colspan="6" | Small step <br><span style="font-size:0.85em">(chroma-negative generator)</span>
! Cents
! L
! s
! L/s
! Comments
|-
| 1\9 || || || || || || 133.333 || 1 || 1 || 1.000 ||
|-
| || || || || || 5\46 || 130.435 || 6 || 5 || 1.200 ||
|-
| || || || || 4\37 || || 129.730 || 5 || 4 || 1.250 ||
|-
| || || || || || 7\65 || 129.231 || 9 || 7 || 1.286 ||
|-
| || || || 3\28 || || || 128.571 || 4 || 3 || 1.333 ||
|-
| || || || || || 8\75 || 128.000 || 11 || 8 || 1.375 ||
|-
| || || || || 5\47 || || 127.660 || 7 || 5 || 1.400 ||
|-
| || || || || || 7\66 || 127.273 || 10 || 7 || 1.429 ||
|-
| || || 2\19 || || || || 126.316 || 3 || 2 || 1.500 || [[Negri]]
|-
| || || || || || 7\67 || 125.373 || 11 || 7 || 1.571 ||
|-
| || || || || 5\48 || || 125.000 || 8 || 5 || 1.600 ||
|-
| || || || || || 8\77 || 124.675 || 13 || 8 || 1.625 || Golden negri (124.7656¢)
|-
| || || || 3\29 || || || 124.138 || 5 || 3 || 1.667 ||
|-
| || || || || || 7\68 || 123.529 || 12 || 7 || 1.714 ||
|-
| || || || || 4\39 || || 123.077 || 7 || 4 || 1.750 ||
|-
| || || || || || 5\49 || 122.449 || 9 || 5 || 1.800 ||
|-
| || 1\10 || || || || || 120.000 || 2 || 1 || 2.000 || Basic 1L 8s <br>(small steps larger than this are proper)
|-
| || || || || || 4\41 || 117.073 || 9 || 4 || 2.250 || [[Miracle]]
|-
| || || || || 3\31 || || 116.129 || 7 || 3 || 2.333 || Miracle/[[revelation]]
|-
| || || || || || 5\52 || 115.385 || 12 || 5 || 2.400 ||
|-
| || || || 2\21 || || || 114.286 || 5 || 2 || 2.500 ||
|-
| || || || || || 5\53 || 113.208 || 13 || 5 || 2.600 || Golden [[misneb]] (113.0153¢)
|-
| || || || || 3\32 || || 112.500 || 8 || 3 || 2.667 ||
|-
| || || || || || 4\43 || 111.628 || 11 || 4 || 2.750 ||
|-
| || || 1\11 || || || || 109.091 || 3 || 1 || 3.000 ||
|-
| || || || || || 3\34 || 105.882 || 10 || 3 || 3.333 ||
|-
| || || || || 2\23 || || 104.348 || 7 || 2 || 3.500 ||
|-
| || || || || || 3\35 || 102.857 || 11 || 3 || 3.667 ||
|-
| || || || 1\12 || || || 100.000 || 4 || 1 || 4.000 || [[Ripple]]
|-
| || || || || || 2\25 || 96.000 || 9 || 2 || 4.500 || [[Passion]]
|-
| || || || || 1\13 || || 92.308 || 5 || 1 || 5.000 ||
|-
| || || || || || 1\14 || 85.714 || 6 || 1 || 6.000 ||
|-
| 0\1 || || || || || || 0.000 || 1 || 0 || → inf ||
|}
 
{{todo|expand}}
[[Category:9-tone scales]]

Latest revision as of 08:31, 15 December 2024

↑ 1L 7s 2L 7s ↗
1L 8s 2L 8s →
↓ 1L 9s 2L 9s ↘ 
┌╥┬┬┬┬┬┬┬┬┐
│║│││││││││
│││││││││││
└┴┴┴┴┴┴┴┴┴┘
Scale structure
Step pattern Lssssssss
ssssssssL
Equave 2/1 (1200.0 ¢)
Period 2/1 (1200.0 ¢)
Generator size
Bright 8\9 to 1\1 (1066.7 ¢ to 1200.0 ¢)
Dark 0\1 to 1\9 (0.0 ¢ to 133.3 ¢)
TAMNAMS information
Name antisubneutralic
Prefix ablu-
Abbrev. ablu
Related MOS scales
Parent 1L 7s
Sister 8L 1s
Daughters 9L 1s, 1L 9s
Neutralized 2L 7s
2-Flought 10L 8s, 1L 17s
Equal tunings
Equalized (L:s = 1:1) 8\9 (1066.7 ¢)
Supersoft (L:s = 4:3) 25\28 (1071.4 ¢)
Soft (L:s = 3:2) 17\19 (1073.7 ¢)
Semisoft (L:s = 5:3) 26\29 (1075.9 ¢)
Basic (L:s = 2:1) 9\10 (1080.0 ¢)
Semihard (L:s = 5:2) 19\21 (1085.7 ¢)
Hard (L:s = 3:1) 10\11 (1090.9 ¢)
Superhard (L:s = 4:1) 11\12 (1100.0 ¢)
Collapsed (L:s = 1:0) 1\1 (1200.0 ¢)

1L 8s, named antisubneutralic in TAMNAMS, is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 1 large step and 8 small steps, repeating every octave. Generators that produce this scale range from 1066.7 ¢ to 1200 ¢, or from 0 ¢ to 133.3 ¢.

This MOS represents temperaments like Miracle and Negri. Of all the temperaments it represents, the harmonic entropy minimum is the one where the scale is generated by an interval near 3\28 (around 14/13).

Modes

Modes of 1L 8s
UDP Cyclic
order		 Step
pattern
8|0 1 Lssssssss
7|1 9 sLsssssss
6|2 8 ssLssssss
5|3 7 sssLsssss
4|4 6 ssssLssss
3|5 5 sssssLsss
2|6 4 ssssssLss
1|7 3 sssssssLs
0|8 2 ssssssssL

Degrees

Scale degrees of the modes of 1L 8s
UDP Cyclic
order 		Step
pattern 		Scale degree (abludegree)
0 1 2 3 4 5 6 7 8 9
8|0 1 Lssssssss Perf. Aug. Maj. Maj. Maj. Maj. Maj. Maj. Perf. Perf.
7|1 9 sLsssssss Perf. Perf. Maj. Maj. Maj. Maj. Maj. Maj. Perf. Perf.
6|2 8 ssLssssss Perf. Perf. Min. Maj. Maj. Maj. Maj. Maj. Perf. Perf.
5|3 7 sssLsssss Perf. Perf. Min. Min. Maj. Maj. Maj. Maj. Perf. Perf.
4|4 6 ssssLssss Perf. Perf. Min. Min. Min. Maj. Maj. Maj. Perf. Perf.
3|5 5 sssssLsss Perf. Perf. Min. Min. Min. Min. Maj. Maj. Perf. Perf.
2|6 4 ssssssLss Perf. Perf. Min. Min. Min. Min. Min. Maj. Perf. Perf.
1|7 3 sssssssLs Perf. Perf. Min. Min. Min. Min. Min. Min. Perf. Perf.
0|8 2 ssssssssL Perf. Perf. Min. Min. Min. Min. Min. Min. Dim. Perf.

Intervals

Intervals of 1L 8s
Intervals Steps
subtended 		Range in cents
Generic Specific Abbrev.
0-ablustep Perfect 0-ablustep P0ablus 0 0.0 ¢
1-ablustep Perfect 1-ablustep P1ablus s 0.0 ¢ to 133.3 ¢
Augmented 1-ablustep A1ablus L 133.3 ¢ to 1200.0 ¢
2-ablustep Minor 2-ablustep m2ablus 2s 0.0 ¢ to 266.7 ¢
Major 2-ablustep M2ablus L + s 266.7 ¢ to 1200.0 ¢
3-ablustep Minor 3-ablustep m3ablus 3s 0.0 ¢ to 400.0 ¢
Major 3-ablustep M3ablus L + 2s 400.0 ¢ to 1200.0 ¢
4-ablustep Minor 4-ablustep m4ablus 4s 0.0 ¢ to 533.3 ¢
Major 4-ablustep M4ablus L + 3s 533.3 ¢ to 1200.0 ¢
5-ablustep Minor 5-ablustep m5ablus 5s 0.0 ¢ to 666.7 ¢
Major 5-ablustep M5ablus L + 4s 666.7 ¢ to 1200.0 ¢
6-ablustep Minor 6-ablustep m6ablus 6s 0.0 ¢ to 800.0 ¢
Major 6-ablustep M6ablus L + 5s 800.0 ¢ to 1200.0 ¢
7-ablustep Minor 7-ablustep m7ablus 7s 0.0 ¢ to 933.3 ¢
Major 7-ablustep M7ablus L + 6s 933.3 ¢ to 1200.0 ¢
8-ablustep Diminished 8-ablustep d8ablus 8s 0.0 ¢ to 1066.7 ¢
Perfect 8-ablustep P8ablus L + 7s 1066.7 ¢ to 1200.0 ¢
9-ablustep Perfect 9-ablustep P9ablus L + 8s 1200.0 ¢

Scale tree

Generator ranges:

  • Chroma-positive generator: 1066.6667 cents (8\9) to 1200 cents (1\1)
  • Chroma-negative generator: 0 cents (0\1) to 133.3333 cents (1\9)
Small step
(chroma-negative generator) 		Cents L s L/s Comments
1\9 133.333 1 1 1.000
5\46 130.435 6 5 1.200
4\37 129.730 5 4 1.250
7\65 129.231 9 7 1.286
3\28 128.571 4 3 1.333
8\75 128.000 11 8 1.375
5\47 127.660 7 5 1.400
7\66 127.273 10 7 1.429
2\19 126.316 3 2 1.500 Negri
7\67 125.373 11 7 1.571
5\48 125.000 8 5 1.600
8\77 124.675 13 8 1.625 Golden negri (124.7656¢)
3\29 124.138 5 3 1.667
7\68 123.529 12 7 1.714
4\39 123.077 7 4 1.750
5\49 122.449 9 5 1.800
1\10 120.000 2 1 2.000 Basic 1L 8s
(small steps larger than this are proper)
4\41 117.073 9 4 2.250 Miracle
3\31 116.129 7 3 2.333 Miracle/revelation
5\52 115.385 12 5 2.400
2\21 114.286 5 2 2.500
5\53 113.208 13 5 2.600 Golden misneb (113.0153¢)
3\32 112.500 8 3 2.667
4\43 111.628 11 4 2.750
1\11 109.091 3 1 3.000
3\34 105.882 10 3 3.333
2\23 104.348 7 2 3.500
3\35 102.857 11 3 3.667
1\12 100.000 4 1 4.000 Ripple
2\25 96.000 9 2 4.500 Passion
1\13 92.308 5 1 5.000
1\14 85.714 6 1 6.000
0\1 0.000 1 0 → inf
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