1L 4s: 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:keenanpepper|keenanpepper]] and made on <tt>2011-04-23 01:33:20 UTC</tt>.<br>
| nLargeSteps = 1
: The original revision id was <tt>222374370</tt>.<br>
| nSmallSteps = 4
: The revision comment was: <tt></tt><br>
| Equalized = 4
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 = Lssss
<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">The only notable low-harmonic-entropy scale for this [[MOSScales|MOS]] pattern is [[gamelismic clan|slendric or gamelismic]], in which the generator is 8/7 and three of them make a 3/2. Other scales include very [[Rothenberg propriety|improper]] (incomplete) versions of [[porcupine family|porcupine]], [[marvel temperaments|negri]], etc.
| Name = pedal
}}


||||||||||||||||~ Generator ||~ Cents ||~ Comments ||
{{MOS intro}}
|| 0\1 ||  ||  ||  ||  ||  ||  ||  ||  ||  ||
||  ||  ||  ||  ||  || 1\10 ||  ||  || 120 ||  ||
||  ||  ||  ||  ||  ||  || 2\19 ||  || 126.32 || Negri is around here ||
||  ||  ||  ||  || 1\9 ||  ||  ||  || 133.33 ||  ||
||  ||  ||  || 1\8 ||  ||  ||  ||  || 150 ||  ||
||  ||  ||  ||  || 2\15 ||  ||  ||  || 160 ||  ||
||  ||  ||  ||  ||  || 3\22 ||  ||  || 163.64 || Porcupine is around here ||
||  ||  || 1\7 ||  ||  ||  ||  ||  || 171.43 ||  ||
||  || 1\6 ||  ||  ||  ||  ||  ||  || 200 || Boundary of propriety ||
||  ||  || 2\11 ||  ||  ||  ||  ||  || 218.18 ||  ||
||  ||  ||  || 3\16 ||  ||  ||  ||  || 225 ||  ||
||  ||  ||  ||  || 4\21 ||  ||  ||  || 228.57 ||  ||
||  ||  ||  ||  ||  || 5\26 ||  ||  || 230.77 ||  ||
||  ||  ||  ||  ||  ||  || 6\31 ||  || 232.26 ||  ||
||  ||  ||  ||  ||  ||  ||  || 7\36 || 233.33 || Slendric is around here ||
|| 1\5 ||  ||  ||  ||  ||  ||  ||  || 240 ||  ||
</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 4s&lt;/title&gt;&lt;/head&gt;&lt;body&gt;The only notable low-harmonic-entropy scale for this &lt;a class="wiki_link" href="/MOSScales"&gt;MOS&lt;/a&gt; pattern is &lt;a class="wiki_link" href="/gamelismic%20clan"&gt;slendric or gamelismic&lt;/a&gt;, in which the generator is 8/7 and three of them make a 3/2. Other scales include very &lt;a class="wiki_link" href="/Rothenberg%20propriety"&gt;improper&lt;/a&gt; (incomplete) versions of &lt;a class="wiki_link" href="/porcupine%20family"&gt;porcupine&lt;/a&gt;, &lt;a class="wiki_link" href="/marvel%20temperaments"&gt;negri&lt;/a&gt;, etc.&lt;br /&gt;
&lt;br /&gt;


The only notable low-[[harmonic entropy|harmonic-entropy]] scale for this [[MOS]] pattern is [[Gamelismic clan|slendric or gamelismic]], in which the [[generator]] is [[8/7]] and three of them make a [[3/2]]. Other scales include very [[improper]] (incomplete) versions of [[Porcupine family|porcupine]], [[Marvel temperaments #Negri|negri]], etc.


&lt;table class="wiki_table"&gt;
== Modes ==
    &lt;tr&gt;
{{MOS modes}}
        &lt;th colspan="8"&gt;Generator&lt;br /&gt;
&lt;/th&gt;
        &lt;th&gt;Cents&lt;br /&gt;
&lt;/th&gt;
        &lt;th&gt;Comments&lt;br /&gt;
&lt;/th&gt;
    &lt;/tr&gt;
    &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;&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;/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;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;120&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;&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;126.32&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Negri is around here&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\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;133.33&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;1\8&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;150&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;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;160&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;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;3\22&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;163.64&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Porcupine is around here&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\7&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;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;171.43&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;1\6&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;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;200&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Boundary of propriety&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\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;&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;218.18&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;3\16&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;225&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;4\21&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;228.57&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;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;5\26&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;230.77&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;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;6\31&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;232.26&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;&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;7\36&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;233.33&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Slendric is around here&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;1\5&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;&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;240&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
&lt;/table&gt;


&lt;/body&gt;&lt;/html&gt;</pre></div>
=== Degrees ===
{{MOS mode degrees}}
 
== Intervals ==
{{MOS intervals}}
 
== Scale tree ==
Generator ranges:
* Chroma-positive generator: 960 cents (4\5) to 1200 cents (1\1)
* Chroma-negative generator: 0 cents (0\1) to 240 cents (1\5)
 
{| 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\5 || || || || || || 240.000 || 1 || 1 || 1.000 ||
|-
| || || || || || 5\26 || 230.769 || 6 || 5 || 1.200 ||
|-
| || || || || 4\21 || || 228.571 || 5 || 4 || 1.250 || [[Laconic]]/[[gorgo]]
|-
| || || || || || 7\37 || 227.027 || 9 || 7 || 1.286 || [[Semaja]]
|-
| || || || 3\16 || || || 225.000 || 4 || 3 || 1.333 ||
|-
| || || || || || 8\43 || 223.256 || 11 || 8 || 1.375 ||
|-
| || || || || 5\27 || || 222.222 || 7 || 5 || 1.400 ||
|-
| || || || || || 7\38 || 221.053 || 10 || 7 || 1.429 ||
|-
| || || 2\11 || || || || 218.182 || 3 || 2 || 1.500 ||
|-
| || || || || || 7\39 || 215.385 || 11 || 7 || 1.571 ||
|-
| || || || || 5\28 || || 214.286 || 8 || 5 || 1.600 ||
|-
| || || || || || 8\45 || 213.333 || 13 || 8 || 1.625 || Golden [[machine]] (213.5979¢)
|-
| || || || 3\17 || || || 211.765 || 5 || 3 || 1.667 ||
|-
| || || || || || 7\40 || 210.000 || 12 || 7 || 1.714 ||
|-
| || || || || 4\23 || || 208.696 || 7 || 4 || 1.750 ||
|-
| || || || || || 5\29 || 206.897 || 9 || 5 || 1.800 ||
|-
| || 1\6 || || || || || 200.000 || 2 || 1 || 2.000 || Basic 1L 4s <br>(small steps larger than this are proper)
|-
| || || || || || 4\25 || 192.000 || 9 || 4 || 2.250 || [[Luna]]/[[hemithirds]], [[Isra]]/[[leantone]]
|-
| || || || || 3\19 || || 189.474 || 7 || 3 || 2.333 || [[Spell]]
|-
| || || || || || 5\32 || 187.500 || 12 || 5 || 2.400 ||
|-
| || || || 2\13 || || || 184.615 || 5 || 2 || 2.500 ||
|-
| || || || || || 5\33 || 181.818 || 13 || 5 || 2.600 || Wilson Golden 2 (181.3227¢)
|-
| || || || || 3\20 || || 180.000 || 8 || 3 || 2.667 ||
|-
| || || || || || 4\27 || 177.778 || 11 || 4 || 2.750 ||
|-
| || || 1\7 || || || || 171.429 || 3 || 1 || 3.000 ||
|-
| || || || || || 3\22 || 163.636 || 10 || 3 || 3.333 || [[Porcupine]]
|-
| || || || || 2\15 || || 160.000 || 7 || 2 || 3.500 ||
|-
| || || || || || 3\23 || 156.522 || 11 || 3 || 3.667 ||
|-
| || || || 1\8 || || || 150.000 || 4 || 1 || 4.000 ||
|-
| || || || || || 2\17 || 141.176 || 9 || 2 || 4.500 || [[Bleu]]/[[jerome]]
|-
| || || || || 1\9 || || 133.333 || 5 || 1 || 5.000 ||
|-
| || || || || || 1\10 || 120.000 || 6 || 1 || 6.000 || [[Negri]]
|-
| 0\1 || || || || || || 0.000 || 1 || 0 || → inf ||
|}
 
[[Category:5-tone scales]]

Latest revision as of 08:25, 15 December 2024

↑ 1L 3s 2L 3s ↗
1L 4s 2L 4s →
↓ 1L 5s 2L 5s ↘ 
┌╥┬┬┬┬┐
│║│││││
│││││││
└┴┴┴┴┴┘
Scale structure
Step pattern Lssss
ssssL
Equave 2/1 (1200.0 ¢)
Period 2/1 (1200.0 ¢)
Generator size
Bright 4\5 to 1\1 (960.0 ¢ to 1200.0 ¢)
Dark 0\1 to 1\5 (0.0 ¢ to 240.0 ¢)
Related MOS scales
Parent 1L 3s
Sister 4L 1s
Daughters 5L 1s, 1L 5s
Neutralized 2L 3s
2-Flought 6L 4s, 1L 9s
Equal tunings
Equalized (L:s = 1:1) 4\5 (960.0 ¢)
Supersoft (L:s = 4:3) 13\16 (975.0 ¢)
Soft (L:s = 3:2) 9\11 (981.8 ¢)
Semisoft (L:s = 5:3) 14\17 (988.2 ¢)
Basic (L:s = 2:1) 5\6 (1000.0 ¢)
Semihard (L:s = 5:2) 11\13 (1015.4 ¢)
Hard (L:s = 3:1) 6\7 (1028.6 ¢)
Superhard (L:s = 4:1) 7\8 (1050.0 ¢)
Collapsed (L:s = 1:0) 1\1 (1200.0 ¢)

1L 4s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 1 large step and 4 small steps, repeating every octave. Generators that produce this scale range from 960 ¢ to 1200 ¢, or from 0 ¢ to 240 ¢.

The only notable low-harmonic-entropy scale for this MOS pattern is slendric or gamelismic, in which the generator is 8/7 and three of them make a 3/2. Other scales include very improper (incomplete) versions of porcupine, negri, etc.

Modes

Modes of 1L 4s
UDP Cyclic
order		 Step
pattern
4|0 1 Lssss
3|1 5 sLsss
2|2 4 ssLss
1|3 3 sssLs
0|4 2 ssssL

Degrees

Scale degrees of the modes of 1L 4s
UDP Cyclic
order 		Step
pattern 		Scale degree (mosdegree)
0 1 2 3 4 5
4|0 1 Lssss Perf. Aug. Maj. Maj. Perf. Perf.
3|1 5 sLsss Perf. Perf. Maj. Maj. Perf. Perf.
2|2 4 ssLss Perf. Perf. Min. Maj. Perf. Perf.
1|3 3 sssLs Perf. Perf. Min. Min. Perf. Perf.
0|4 2 ssssL Perf. Perf. Min. Min. Dim. Perf.

Intervals

Intervals of 1L 4s
Intervals Steps
subtended 		Range in cents
Generic Specific Abbrev.
0-mosstep Perfect 0-mosstep P0ms 0 0.0 ¢
1-mosstep Perfect 1-mosstep P1ms s 0.0 ¢ to 240.0 ¢
Augmented 1-mosstep A1ms L 240.0 ¢ to 1200.0 ¢
2-mosstep Minor 2-mosstep m2ms 2s 0.0 ¢ to 480.0 ¢
Major 2-mosstep M2ms L + s 480.0 ¢ to 1200.0 ¢
3-mosstep Minor 3-mosstep m3ms 3s 0.0 ¢ to 720.0 ¢
Major 3-mosstep M3ms L + 2s 720.0 ¢ to 1200.0 ¢
4-mosstep Diminished 4-mosstep d4ms 4s 0.0 ¢ to 960.0 ¢
Perfect 4-mosstep P4ms L + 3s 960.0 ¢ to 1200.0 ¢
5-mosstep Perfect 5-mosstep P5ms L + 4s 1200.0 ¢

Scale tree

Generator ranges:

  • Chroma-positive generator: 960 cents (4\5) to 1200 cents (1\1)
  • Chroma-negative generator: 0 cents (0\1) to 240 cents (1\5)
Small step
(chroma-negative generator) 		Cents L s L/s Comments
1\5 240.000 1 1 1.000
5\26 230.769 6 5 1.200
4\21 228.571 5 4 1.250 Laconic/gorgo
7\37 227.027 9 7 1.286 Semaja
3\16 225.000 4 3 1.333
8\43 223.256 11 8 1.375
5\27 222.222 7 5 1.400
7\38 221.053 10 7 1.429
2\11 218.182 3 2 1.500
7\39 215.385 11 7 1.571
5\28 214.286 8 5 1.600
8\45 213.333 13 8 1.625 Golden machine (213.5979¢)
3\17 211.765 5 3 1.667
7\40 210.000 12 7 1.714
4\23 208.696 7 4 1.750
5\29 206.897 9 5 1.800
1\6 200.000 2 1 2.000 Basic 1L 4s
(small steps larger than this are proper)
4\25 192.000 9 4 2.250 Luna/hemithirds, Isra/leantone
3\19 189.474 7 3 2.333 Spell
5\32 187.500 12 5 2.400
2\13 184.615 5 2 2.500
5\33 181.818 13 5 2.600 Wilson Golden 2 (181.3227¢)
3\20 180.000 8 3 2.667
4\27 177.778 11 4 2.750
1\7 171.429 3 1 3.000
3\22 163.636 10 3 3.333 Porcupine
2\15 160.000 7 2 3.500
3\23 156.522 11 3 3.667
1\8 150.000 4 1 4.000
2\17 141.176 9 2 4.500 Bleu/jerome
1\9 133.333 5 1 5.000
1\10 120.000 6 1 6.000 Negri
0\1 0.000 1 0 → inf
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