1L 5s: 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>2015-05-22 13:12:19 UTC</tt>.<br>
| nLargeSteps = 1
: The original revision id was <tt>551904440</tt>.<br>
| nSmallSteps = 5
: The revision comment was: <tt></tt><br>
| Equalized = 5
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 = Lsssss
<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">There are two notable low-harmonic-entropy scales with this [[MOSScales|MOS]] pattern. The first is [[Tetracot family|tetracot]], in which four generators make a 3/2. The second is a scale in which two generators make a 5/4, which could be referred to by various names. The temperaments "luna", "hemithird", and "hemiwürschmidt" all have 6-note MOSes that are very similar. But perhaps it is best known as [[roulette6]], the six note haplitonic scale for the roulette [[Chromatic pair]].
}}


Other scales include very improper (incomplete) versions of porcupine, negri, etc.
{{MOS intro}}
||||||||||||||~ Generator ||~ Cents ||~ Comments ||
|| 0\1 ||  ||  ||  ||  ||  ||  || 0 ||=  ||
||  ||  ||  || 1\9 ||  ||  ||  || 133.33 ||= L/s = 4 ||
||  ||  ||  ||  ||  ||  ||  || 1200/(5+pi) ||&lt; &lt;span style="display: block; text-align: center;"&gt;
&lt;/span&gt; ||
||  ||  || 1\8 ||  ||  ||  ||  || 150 ||= L/s = 3 ||
||  ||  ||  ||  ||  ||  ||  || 1200/(5+e) ||  ||
||  ||  ||  || 2\15 ||  ||  ||  || 160 ||=  ||
||  ||  ||  ||  || 3\22 ||  ||  || 163.64 ||= Porcupine is around here ||
||  || 1\7 ||  ||  ||  ||  ||  || 171.43 ||= Boundary of propriety
(generators larger than this are proper) ||
||  ||  ||  ||  ||  || 5\34 ||  || 176.47 ||= Tetracot is around here ||
||  ||  ||  ||  || 4\27 ||  ||  || 177.78 ||=  ||
||  ||  ||  || 3\20 ||  ||  ||  || 180 ||=  ||
||  ||  ||  ||  ||  || 8\53 ||  || 181.13 ||=  ||
||  ||  ||  ||  ||  ||  ||  || 1200/(5+phi) ||= Unnamed golden temperament (discussed in [[http://launch.groups.yahoo.com/group/tuning/message/100254|this thread]]) ||
||  ||  ||  ||  || 5\33 ||  ||  || 181.82 ||=  ||
||  ||  || 2\13 ||  ||  ||  ||  || 184.62 ||= Optimum rank range glacial (L/s=3/2) ||
||  ||  ||  || 3\19 ||  ||  ||  || 189.47 ||=  ||
||  ||  ||  ||  || 4\25 ||  ||  || 192 ||=  ||
||  ||  ||  ||  ||  || 5\31 ||  || 193.55 ||=  ||
||  ||  ||  ||  ||  ||  || 6\37 || 194.59 ||= Luna/Hemithird/Roulette is around here: [[roulette6]] ||
|| 1\6 ||  ||  ||  ||  ||  ||  || 200 ||=  ||</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 5s&lt;/title&gt;&lt;/head&gt;&lt;body&gt;There are two notable low-harmonic-entropy scales with this &lt;a class="wiki_link" href="/MOSScales"&gt;MOS&lt;/a&gt; pattern. The first is &lt;a class="wiki_link" href="/Tetracot%20family"&gt;tetracot&lt;/a&gt;, in which four generators make a 3/2. The second is a scale in which two generators make a 5/4, which could be referred to by various names. The temperaments &amp;quot;luna&amp;quot;, &amp;quot;hemithird&amp;quot;, and &amp;quot;hemiwürschmidt&amp;quot; all have 6-note MOSes that are very similar. But perhaps it is best known as &lt;a class="wiki_link" href="/roulette6"&gt;roulette6&lt;/a&gt;, the six note haplitonic scale for the roulette &lt;a class="wiki_link" href="/Chromatic%20pair"&gt;Chromatic pair&lt;/a&gt;.&lt;br /&gt;
&lt;br /&gt;
Other scales include very improper (incomplete) versions of porcupine, negri, etc.&lt;br /&gt;


There are two notable low-harmonic-entropy scales with this [[MOS scale|MOS]] pattern. The first is [[tetracot]], in which four [[generator]]s make a [[3/2]].


&lt;table class="wiki_table"&gt;
The second is a scale in which two generators make a 5/4, which could be referred to by various names. The temperaments "[[luna]]", "[[hemithird]]", and "[[hemiwürschmidt]]" all have [[hexatonic|6-note]] MOSes that are very similar. But perhaps it is best known as [[roulette6]], the six note haplitonic scale for the roulette [[Chromatic pair]].
    &lt;tr&gt;
        &lt;th colspan="7"&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;0&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\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 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;&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/(5+pi)&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: left;"&gt;&lt;span style="display: block; text-align: center;"&gt;&lt;br /&gt;
&lt;/span&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\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 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;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1200/(5+e)&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;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 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\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 style="text-align: center;"&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;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 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;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;5\34&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;176.47&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;Tetracot 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;4\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;177.78&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\20&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;180&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;8\53&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;181.13&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;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1200/(5+phi)&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;Unnamed golden temperament (discussed in &lt;a class="wiki_link_ext" href="http://launch.groups.yahoo.com/group/tuning/message/100254" rel="nofollow"&gt;this thread&lt;/a&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\33&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;181.82&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\13&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;184.62&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;Optimum rank range glacial (L/s=3/2)&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\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;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;189.47&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\25&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;192&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;5\31&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;193.55&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;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;6\37&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;194.59&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;Luna/Hemithird/Roulette is around here: &lt;a class="wiki_link" href="/roulette6"&gt;roulette6&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&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 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>
This scale can be seen as the equal-tempered whole-tone scale ([[6edo]]), but with one "whole tone" that is larger than the others.
 
Other scales include very improper (incomplete) versions of [[porcupine]], [[negri]], etc.
 
== Scale properties ==
{{TAMNAMS use}}
 
=== Intervals ===
{{MOS intervals}}
 
=== Generator chain ===
{{MOS genchain}}
 
=== Modes ===
{{MOS mode degrees}}
 
== Scales ==
=== Scale list ===
* [[Roulette6]]
* [[Tutone6]]
* [[Deutone6]]
* [[Leantone6]]
* [[Glacial6]]
 
=== Scale tree ===
{{MOS tuning spectrum
| 6/5 = [[Luna]]/[[hemithirds]]/[[hemiwürschmidt]]<br />[[Didacus]]/[[roulette]]<br />[[Isra]]/[[tutone]]/[[leantone]]
| 5/4 = Isra/leantone
| 9/7 = Isra/deutone
| 4/3 = [[Spell]]
| 3/2 = [[Glacial]]
| 13/8 = Wilson Golden 2 (1018.6773{{c}})
| 9/5 = [[Tetracot]]
| 7/3 = [[Porcupine]] (incomplete)
| 12/5 = Porcupine/[[porcupinefish]]
| 13/5 = Wilson Golden 1 (1042.4790{{c}})
| 11/4 = [[Nusecond]]
| 7/2 = [[Progression]] (incomplete)
| 9/2 = [[Negri]] (incomplete)
| 5/1 = [[Miracle]] (incomplete)
| 6/1 = [[Passion]] (incomplete) ↓, [[ripple]] (incomplete) ↓
}}
 
[[Category:6-tone scales]]

Latest revision as of 18:49, 3 March 2025

↑ 1L 4s 2L 4s ↗
1L 5s 2L 5s →
↓ 1L 6s 2L 6s ↘
Scale structure
Step pattern Lsssss
sssssL
Equave 2/1 (1200.0 ¢)
Period 2/1 (1200.0 ¢)
Generator size
Bright 5\6 to 1\1 (1000.0 ¢ to 1200.0 ¢)
Dark 0\1 to 1\6 (0.0 ¢ to 200.0 ¢)
TAMNAMS information
Name antimachinoid
Prefix amech-
Abbrev. amk
Related MOS scales
Parent 1L 4s
Sister 5L 1s
Daughters 6L 1s, 1L 6s
Neutralized 2L 4s
2-Flought 7L 5s, 1L 11s
Equal tunings
Equalized (L:s = 1:1) 5\6 (1000.0 ¢)
Supersoft (L:s = 4:3) 16\19 (1010.5 ¢)
Soft (L:s = 3:2) 11\13 (1015.4 ¢)
Semisoft (L:s = 5:3) 17\20 (1020.0 ¢)
Basic (L:s = 2:1) 6\7 (1028.6 ¢)
Semihard (L:s = 5:2) 13\15 (1040.0 ¢)
Hard (L:s = 3:1) 7\8 (1050.0 ¢)
Superhard (L:s = 4:1) 8\9 (1066.7 ¢)
Collapsed (L:s = 1:0) 1\1 (1200.0 ¢)
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1L 5s, named antimachinoid in TAMNAMS, is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 1 large step and 5 small steps, repeating every octave. Generators that produce this scale range from 1000 ¢ to 1200 ¢, or from 0 ¢ to 200 ¢.

There are two notable low-harmonic-entropy scales with this MOS pattern. The first is tetracot, in which four generators make a 3/2.

The second is a scale in which two generators make a 5/4, which could be referred to by various names. The temperaments "luna", "hemithird", and "hemiwürschmidt" all have 6-note MOSes that are very similar. But perhaps it is best known as roulette6, the six note haplitonic scale for the roulette Chromatic pair.

This scale can be seen as the equal-tempered whole-tone scale (6edo), but with one "whole tone" that is larger than the others.

Other scales include very improper (incomplete) versions of porcupine, negri, etc.

Scale properties

This article uses TAMNAMS conventions for the names of this scale's intervals and scale degrees. The use of 1-indexed ordinal names is reserved for interval regions.

Intervals

Intervals of 1L 5s
Intervals Steps
subtended 		Range in cents
Generic Specific Abbrev.
0-amechstep Perfect 0-amechstep P0amks 0 0.0 ¢
1-amechstep Perfect 1-amechstep P1amks s 0.0 ¢ to 200.0 ¢
Augmented 1-amechstep A1amks L 200.0 ¢ to 1200.0 ¢
2-amechstep Minor 2-amechstep m2amks 2s 0.0 ¢ to 400.0 ¢
Major 2-amechstep M2amks L + s 400.0 ¢ to 1200.0 ¢
3-amechstep Minor 3-amechstep m3amks 3s 0.0 ¢ to 600.0 ¢
Major 3-amechstep M3amks L + 2s 600.0 ¢ to 1200.0 ¢
4-amechstep Minor 4-amechstep m4amks 4s 0.0 ¢ to 800.0 ¢
Major 4-amechstep M4amks L + 3s 800.0 ¢ to 1200.0 ¢
5-amechstep Diminished 5-amechstep d5amks 5s 0.0 ¢ to 1000.0 ¢
Perfect 5-amechstep P5amks L + 4s 1000.0 ¢ to 1200.0 ¢
6-amechstep Perfect 6-amechstep P6amks L + 5s 1200.0 ¢

Generator chain

Generator chain of 1L 5s
Bright gens Scale degree Abbrev.
6 Augmented 0-amechdegree A0amkd
5 Augmented 1-amechdegree A1amkd
4 Major 2-amechdegree M2amkd
3 Major 3-amechdegree M3amkd
2 Major 4-amechdegree M4amkd
1 Perfect 5-amechdegree P5amkd
0 Perfect 0-amechdegree
Perfect 6-amechdegree		 P0amkd
P6amkd
−1 Perfect 1-amechdegree P1amkd
−2 Minor 2-amechdegree m2amkd
−3 Minor 3-amechdegree m3amkd
−4 Minor 4-amechdegree m4amkd
−5 Diminished 5-amechdegree d5amkd
−6 Diminished 6-amechdegree d6amkd

Modes

Scale degrees of the modes of 1L 5s
UDP Cyclic
order 		Step
pattern 		Scale degree (amechdegree)
0 1 2 3 4 5 6
5|0 1 Lsssss Perf. Aug. Maj. Maj. Maj. Perf. Perf.
4|1 6 sLssss Perf. Perf. Maj. Maj. Maj. Perf. Perf.
3|2 5 ssLsss Perf. Perf. Min. Maj. Maj. Perf. Perf.
2|3 4 sssLss Perf. Perf. Min. Min. Maj. Perf. Perf.
1|4 3 ssssLs Perf. Perf. Min. Min. Min. Perf. Perf.
0|5 2 sssssL Perf. Perf. Min. Min. Min. Dim. Perf.

Scales

Scale list

Scale tree

Scale tree and tuning spectrum of 1L 5s
Generator(edo) Cents Step ratio Comments
Bright Dark L:s Hardness
5\6 1000.000 200.000 1:1 1.000 Equalized 1L 5s
26\31 1006.452 193.548 6:5 1.200 Luna/hemithirds/hemiwürschmidt
Didacus/roulette
Isra/tutone/leantone
21\25 1008.000 192.000 5:4 1.250 Isra/leantone
37\44 1009.091 190.909 9:7 1.286 Isra/deutone
16\19 1010.526 189.474 4:3 1.333 Supersoft 1L 5s
Spell
43\51 1011.765 188.235 11:8 1.375
27\32 1012.500 187.500 7:5 1.400
38\45 1013.333 186.667 10:7 1.429
11\13 1015.385 184.615 3:2 1.500 Soft 1L 5s
Glacial
39\46 1017.391 182.609 11:7 1.571
28\33 1018.182 181.818 8:5 1.600
45\53 1018.868 181.132 13:8 1.625 Wilson Golden 2 (1018.6773 ¢)
17\20 1020.000 180.000 5:3 1.667 Semisoft 1L 5s
40\47 1021.277 178.723 12:7 1.714
23\27 1022.222 177.778 7:4 1.750
29\34 1023.529 176.471 9:5 1.800 Tetracot
6\7 1028.571 171.429 2:1 2.000 Basic 1L 5s
Scales with tunings softer than this are proper
25\29 1034.483 165.517 9:4 2.250
19\22 1036.364 163.636 7:3 2.333 Porcupine (incomplete)
32\37 1037.838 162.162 12:5 2.400 Porcupine/porcupinefish
13\15 1040.000 160.000 5:2 2.500 Semihard 1L 5s
33\38 1042.105 157.895 13:5 2.600 Wilson Golden 1 (1042.4790 ¢)
20\23 1043.478 156.522 8:3 2.667
27\31 1045.161 154.839 11:4 2.750 Nusecond
7\8 1050.000 150.000 3:1 3.000 Hard 1L 5s
22\25 1056.000 144.000 10:3 3.333
15\17 1058.824 141.176 7:2 3.500 Progression (incomplete)
23\26 1061.538 138.462 11:3 3.667
8\9 1066.667 133.333 4:1 4.000 Superhard 1L 5s
17\19 1073.684 126.316 9:2 4.500 Negri (incomplete)
9\10 1080.000 120.000 5:1 5.000 Miracle (incomplete)
10\11 1090.909 109.091 6:1 6.000 Passion (incomplete) ↓, ripple (incomplete) ↓
1\1 1200.000 0.000 1:0 → ∞ Collapsed 1L 5s
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