Strictly proper 7-tone 31edo scales: Difference between revisions

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<h2>IMPORTED REVISION FROM WIKISPACES</h2>
This is a list of [[:Category:7-tone scales|7-tone]] scales in [[31edo]] which are strictly proper with regard to the [[Rothenberg propriety]].
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2010-09-05 15:25:39 UTC</tt>.<br>
: The original revision id was <tt>160495655</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">


===Meantone type===
The "type" of a scale is defined by the linear temperament supported by 31edo in which it has the least span. "Breed type" means it is a tie between miracle and hemiwuerschmidt.
|| **{{5535553}}** || Meantone[7]; diatonic scale ||
|| **{{5355553}}** || Melodic minor scale ||
|| **{{5355373}}** || Harmonic minor scale; inverse harmonic major ||
|| **{{5535373}}** || Harmonic major scale; inverse harmonic minor ||
|| **{{5533555}}** || Major locrian scale ||
|| **{{3717355}}** || Diminished diatonic scale ||
|| **{{5535643}}** || Enharmonic major; inverse enharmonic minor ||
|| **{{5346535}}** || Enharmonic minor; inverse enharmonic major ||
|| **{{5535625}}** || Enharmonic mixolydian ||
|| **{{5526535}}** || Inverse enharmonic mixolydian ||
|| **{{5526355}}** || Enharmonic major-minor ||
|| **{{5553625}}** || Inverse enharmonic major-minor ||
|| **{{6435625}}** || Major doubleflat; inverse minor doubleflat ||
|| **{{5346526}}** || Minor doubleflat; inverse major doubleflat ||
|| **{{5553652}}** || Ping ||
|| **{{3555256}}** || Inverse ping ||
|| **{{3726355}}** || Alhijaz; inverse ambika ||
|| **{{6273553}}** || Ambika; inverse alhijaz ||
|| **{{6453652}}** || Kung; inverse ousak ||
|| **{{3546256}}** || Ousak; inverse kung ||


===Miracle type===
== Meantone type ==
|| **{{5436346}}** || Subdom scale; inverse superton ||
|| **{{5643634}}** || Superton scale; inverse subdom ||
|| **{{5436364}}** || Nudia; neutral diatonic ||
|| **{{5463634}}** || Inverse nudia ||
|| **{{3636346}}** || Nurow; Neutral triads in row ||
|| **{{6363643}}** || Inverse nurow ||


===Mohajira type===
{| class="wikitable"
|| **{{4554454}}** || Sikah; Neutral Diatonic Hypolydian ||
|-
|| **{{4444555}}** || Sheimanic ||
! step pattern
|| **{{4554445}}** || Thaiic ||
! name
|| **{{4544455}}** || Inverse thaiic ||
! example(s)
|| **{{4545454}}** || Mohajira; Neutral Dorian ||
|-
| '''<tt>5 5 3 5 5 5 3</tt>'''
| Meantone[7]; diatonic scale
|
|-
| '''<tt>5 3 5 5 5 5 3</tt>'''
| Melodic minor scale
|
|-
| '''<tt>5 3 5 5 3 7 3</tt>'''
| Harmonic minor scale; inverse harmonic major
|
|-
| '''<tt>5 5 3 5 3 7 3</tt>'''
| Harmonic major scale; inverse harmonic minor
|
|-
| '''<tt>5 5 3 3 5 5 5</tt>'''
| Major locrian scale
|
|-
| '''<tt>3 7 1 7 3 5 5</tt>'''
| Diminished diatonic scale
| [http://chrisvaisvil.com/?p=142 Strange Diatonic] by [[Chris Vaisvil]] [http://micro.soonlabel.com/strange-diatonic/strange-diatonic-1.mp3 play]<br>[http://micro.soonlabel.com/gene_ward_smith/Others/Curley/Zach%20Curley%20-%20Omega%20Centauri.mp3 Omega centauri]{{dead link}} by [[Zach Curley]]
|-
| '''<tt>5 5 3 5 6 4 3</tt>'''
| Enharmonic major; inverse enharmonic minor
|
|-
| '''<tt>5 3 4 6 5 3 5</tt>'''
| Enharmonic minor; inverse enharmonic major
|
|-
| '''<tt>5 5 3 5 6 2 5</tt>'''
| Enharmonic mixolydian
|
|-
| '''<tt>5 5 2 6 5 3 5</tt>'''
| Inverse enharmonic mixolydian
|
|-
| '''<tt>5 5 2 6 3 5 5</tt>'''
| Enharmonic major-minor
|
|-
| '''<tt>5 5 5 3 6 2 5</tt>'''
| Inverse enharmonic major-minor
|
|-
| '''<tt>6 4 3 5 6 2 5</tt>'''
| Major doubleflat; inverse minor doubleflat
|
|-
| '''<tt>5 3 4 6 5 2 6</tt>'''
| Minor doubleflat; inverse major doubleflat
|
|-
| '''<tt>5 5 5 3 6 5 2</tt>'''
| Ping
|
|-
| '''<tt>3 5 5 5 2 5 6</tt>'''
| Inverse ping
|
|-
| '''<tt>3 7 2 6 3 5 5</tt>'''
| Alhijaz; inverse ambika
|
|-
| '''<tt>6 2 7 3 5 5 3</tt>'''
| Ambika; inverse alhijaz
|
|-
| '''<tt>6 4 5 3 6 5 2</tt>'''
| Kung; inverse ousak
|
|-
| '''<tt>3 5 4 6 2 5 6</tt>'''
| Ousak; inverse kung
|
|}


===Hemiwuerschmidt type===
== Valentine ==
|| **{{5555515}}** || Hemiwuerschmidt/Hemithirds[7] ||
|| **{{5544652}}** || Hemaj; inverse hemin ||
|| **{{4455256}}** || Hemin; inverse hemaj ||
|| **{{4525546}}** || Gypsi; 11/9-10/7-7/4 chord on tonic ||
|| **{{4552546}}** || Inverse gypsi; 11/9-10/7-7/4 chord on tonic ||
|| **{{5555542}}** || Leadhole ||
|| **{{5555524}}** || Inverse leadhole ||


===Mothra type===
{| class="wikitable"
|| **{{}}** || ||
|-
|| **{{}}** || ||
! schema
|| **{{}}** || ||
! name
|| **{{}}** || ||
|-
|| **{{}}** || ||
| '''<tt>6 4 4 6 2 7 2</tt>'''
|| **{{}}** || ||
| Silver
|| **{{}}** ||  ||
|-
|| **{{}}** ||  ||</pre></div>
| '''<tt>6 4 4 4 4 7 2</tt>'''
<h4>Original HTML content:</h4>
| Harmonia
<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;Strictly proper 7-note 31edo scales&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;br /&gt;
|-
&lt;br /&gt;
| '''<tt>4 4 4 6 2 7 4</tt>'''
&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc0"&gt;&lt;a name="x--Meantone type"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;Meantone type&lt;/h3&gt;
| Inverse harmonia
|-
| '''<tt>6 4 4 4 5 6 2</tt>'''
| Pendragon
|-
| '''<tt>4 6 2 6 5 4 4</tt>'''
| Inverse pendragon
|-
| '''<tt>6 2 6 4 4 6 3</tt>'''
| Hipop
|-
| '''<tt>4 6 2 6 3 6 4</tt>'''
| Inverse Hipop
|-
| '''<tt>4 6 2 6 4 4 5</tt>'''
| Malakon
|-
| '''<tt>4 6 2 6 4 5 4</tt>'''
| Inverse malakon
|-
| '''<tt>4 4 6 4 5 2 6</tt>'''
| Bagpipe
|-
| '''<tt>4 6 4 4 6 2 5</tt>'''
| Inverse bagpipe
|-
| '''<tt>6 4 4 4 6 2 5</tt>'''
| Pitu
|-
| '''<tt>6 4 4 4 6 5 2</tt>'''
| Inverse pitu
|-
| '''<tt>6 4 4 4 4 4 5</tt>'''
| Porch
|-
| '''<tt>4 4 4 6 5 4 4</tt>'''
| Inverse porch
|}


== Miracle type ==


&lt;table class="wiki_table"&gt;
{| class="wikitable"
    &lt;tr&gt;
|-
        &lt;td&gt;&lt;strong&gt;&lt;tt&gt;5535553&lt;/tt&gt;&lt;/strong&gt;&lt;br /&gt;
! schema
&lt;/td&gt;
! name
        &lt;td&gt;Meantone[7]; diatonic scale&lt;br /&gt;
|-
&lt;/td&gt;
| '''<tt>5 4 3 6 3 4 6</tt>'''
    &lt;/tr&gt;
| Subdom scale; inverse superton
    &lt;tr&gt;
|-
        &lt;td&gt;&lt;strong&gt;&lt;tt&gt;5355553&lt;/tt&gt;&lt;/strong&gt;&lt;br /&gt;
| '''<tt>5 6 4 3 6 3 4</tt>'''
&lt;/td&gt;
| Superton scale; inverse subdom
        &lt;td&gt;Melodic minor scale&lt;br /&gt;
|-
&lt;/td&gt;
| '''<tt>5 4 3 6 3 6 4</tt>'''
    &lt;/tr&gt;
| Nudia; neutral diatonic
    &lt;tr&gt;
|-
        &lt;td&gt;&lt;strong&gt;&lt;tt&gt;5355373&lt;/tt&gt;&lt;/strong&gt;&lt;br /&gt;
| '''<tt>5 4 6 3 6 3 4</tt>'''
&lt;/td&gt;
| Inverse nudia
        &lt;td&gt;Harmonic minor scale; inverse harmonic major&lt;br /&gt;
|-
&lt;/td&gt;
| '''<tt>3 6 3 6 3 4 6</tt>'''
    &lt;/tr&gt;
| Nurow; Neutral triads in row
    &lt;tr&gt;
|-
        &lt;td&gt;&lt;strong&gt;&lt;tt&gt;5535373&lt;/tt&gt;&lt;/strong&gt;&lt;br /&gt;
| '''<tt>6 3 6 3 6 4 3</tt>'''
&lt;/td&gt;
| Inverse nurow
        &lt;td&gt;Harmonic major scale; inverse harmonic minor&lt;br /&gt;
|}
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;strong&gt;&lt;tt&gt;5533555&lt;/tt&gt;&lt;/strong&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Major locrian scale&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;strong&gt;&lt;tt&gt;3717355&lt;/tt&gt;&lt;/strong&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Diminished diatonic scale&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;strong&gt;&lt;tt&gt;5535643&lt;/tt&gt;&lt;/strong&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Enharmonic major; inverse enharmonic minor&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;strong&gt;&lt;tt&gt;5346535&lt;/tt&gt;&lt;/strong&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Enharmonic minor; inverse enharmonic major&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;strong&gt;&lt;tt&gt;5535625&lt;/tt&gt;&lt;/strong&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Enharmonic mixolydian&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;strong&gt;&lt;tt&gt;5526535&lt;/tt&gt;&lt;/strong&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Inverse enharmonic mixolydian&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;strong&gt;&lt;tt&gt;5526355&lt;/tt&gt;&lt;/strong&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Enharmonic major-minor&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;strong&gt;&lt;tt&gt;5553625&lt;/tt&gt;&lt;/strong&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Inverse enharmonic major-minor&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;strong&gt;&lt;tt&gt;6435625&lt;/tt&gt;&lt;/strong&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Major doubleflat; inverse minor doubleflat&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;strong&gt;&lt;tt&gt;5346526&lt;/tt&gt;&lt;/strong&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Minor doubleflat; inverse major doubleflat&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;strong&gt;&lt;tt&gt;5553652&lt;/tt&gt;&lt;/strong&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Ping&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;strong&gt;&lt;tt&gt;3555256&lt;/tt&gt;&lt;/strong&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Inverse ping&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;strong&gt;&lt;tt&gt;3726355&lt;/tt&gt;&lt;/strong&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Alhijaz; inverse ambika&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;strong&gt;&lt;tt&gt;6273553&lt;/tt&gt;&lt;/strong&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Ambika; inverse alhijaz&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;strong&gt;&lt;tt&gt;6453652&lt;/tt&gt;&lt;/strong&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Kung; inverse ousak&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;strong&gt;&lt;tt&gt;3546256&lt;/tt&gt;&lt;/strong&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Ousak; inverse kung&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
&lt;/table&gt;


&lt;br /&gt;
== Mohajira type ==
&lt;!-- ws:start:WikiTextHeadingRule:2:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc1"&gt;&lt;a name="x--Miracle type"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;Miracle type&lt;/h3&gt;


{| class="wikitable"
|-
! schema
! name
|-
| '''<tt>4 5 5 4 4 5 4</tt>'''
| Sikah; Rast; Neutral Diatonic Hypolydian
|-
| '''<tt>4 4 4 4 5 5 5</tt>'''
| Sheimanic
|-
| '''<tt>4 5 5 4 4 4 5</tt>'''
| Thaiic
|-
| '''<tt>4 5 4 4 4 5 5</tt>'''
| Inverse thaiic
|-
| '''<tt>4 5 4 5 4 5 4</tt>'''
| Mohajira; Neutral Dorian
|}


&lt;table class="wiki_table"&gt;
== Hemiwuerschmidt type ==
    &lt;tr&gt;
        &lt;td&gt;&lt;strong&gt;&lt;tt&gt;5436346&lt;/tt&gt;&lt;/strong&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Subdom scale; inverse superton&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;strong&gt;&lt;tt&gt;5643634&lt;/tt&gt;&lt;/strong&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Superton scale; inverse subdom&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;strong&gt;&lt;tt&gt;5436364&lt;/tt&gt;&lt;/strong&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Nudia; neutral diatonic&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;strong&gt;&lt;tt&gt;5463634&lt;/tt&gt;&lt;/strong&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Inverse nudia&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;strong&gt;&lt;tt&gt;3636346&lt;/tt&gt;&lt;/strong&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Nurow; Neutral triads in row&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;strong&gt;&lt;tt&gt;6363643&lt;/tt&gt;&lt;/strong&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Inverse nurow&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
&lt;/table&gt;


&lt;br /&gt;
{| class="wikitable"
&lt;!-- ws:start:WikiTextHeadingRule:4:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc2"&gt;&lt;a name="x--Mohajira type"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:4 --&gt;Mohajira type&lt;/h3&gt;
|-
! schema
! name
|-
| '''<tt>5 5 5 5 5 1 5</tt>'''
| Hemiwuerschmidt/Hemithirds[7]
|-
| '''<tt>5 5 4 4 6 5 2</tt>'''
| Hemaj; inverse hemin
|-
| '''<tt>4 4 5 5 2 5 6</tt>'''
| Hemin; inverse hemaj
|-
| '''<tt>4 5 2 5 5 4 6</tt>'''
| Gypsi; 11/9-10/7-7/4 chord on tonic
|-
| '''<tt>4 5 5 2 5 4 6</tt>'''
| Inverse gypsi; 11/9-10/7-7/4 chord on tonic
|-
| '''<tt>5 5 5 5 5 4 2</tt>'''
| Leadhole
|-
| '''<tt>5 5 5 5 5 2 4</tt>'''
| Inverse leadhole
|}


== Mothra type ==


&lt;table class="wiki_table"&gt;
{| class="wikitable"
    &lt;tr&gt;
|-
        &lt;td&gt;&lt;strong&gt;&lt;tt&gt;4554454&lt;/tt&gt;&lt;/strong&gt;&lt;br /&gt;
! schema
&lt;/td&gt;
! name
        &lt;td&gt;Sikah; Neutral Diatonic Hypolydian&lt;br /&gt;
|-
&lt;/td&gt;
| '''<tt>5 5 5 3 6 4 3</tt>'''
    &lt;/tr&gt;
| Lydic
    &lt;tr&gt;
|-
        &lt;td&gt;&lt;strong&gt;&lt;tt&gt;4444555&lt;/tt&gt;&lt;/strong&gt;&lt;br /&gt;
| '''<tt>5 5 5 3 4 6 3</tt>'''
&lt;/td&gt;
| Inverse lydic
        &lt;td&gt;Sheimanic&lt;br /&gt;
|-
&lt;/td&gt;
| '''<tt>5 5 3 5 4 6 3</tt>'''
    &lt;/tr&gt;
| Ionic
    &lt;tr&gt;
|-
        &lt;td&gt;&lt;strong&gt;&lt;tt&gt;4554445&lt;/tt&gt;&lt;/strong&gt;&lt;br /&gt;
| '''<tt>5 3 6 4 5 3 5</tt>'''
&lt;/td&gt;
| Aeolic; inverse ionic
        &lt;td&gt;Thaiic&lt;br /&gt;
|-
&lt;/td&gt;
| '''<tt>4 6 4 4 4 6 3</tt>'''
    &lt;/tr&gt;
| Quahog
    &lt;tr&gt;
|-
        &lt;td&gt;&lt;strong&gt;&lt;tt&gt;4544455&lt;/tt&gt;&lt;/strong&gt;&lt;br /&gt;
| '''<tt>6 4 4 4 6 4 3</tt>'''
&lt;/td&gt;
| Inverse quahog
        &lt;td&gt;Inverse thaiic&lt;br /&gt;
|-
&lt;/td&gt;
| '''<tt>6 4 5 3 6 4 3</tt>'''
    &lt;/tr&gt;
| Higasi
    &lt;tr&gt;
|-
        &lt;td&gt;&lt;strong&gt;&lt;tt&gt;4545454&lt;/tt&gt;&lt;/strong&gt;&lt;br /&gt;
| '''<tt>4 6 3 5 4 6 3</tt>'''
&lt;/td&gt;
| Inverse higasi
        &lt;td&gt;Mohajira; Neutral Dorian&lt;br /&gt;
|}
&lt;/td&gt;
    &lt;/tr&gt;
&lt;/table&gt;


&lt;br /&gt;
== Orwell type ==
&lt;!-- ws:start:WikiTextHeadingRule:6:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc3"&gt;&lt;a name="x--Hemiwuerschmidt type"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:6 --&gt;Hemiwuerschmidt type&lt;/h3&gt;


{| class="wikitable"
|-
! schema
! name
|-
| '''<tt>5 3 6 4 4 6 3</tt>'''
| Orminor
|-
| '''<tt>4 6 4 4 6 4 3</tt>'''
| Ormed
|-
| '''<tt>4 6 4 4 3 6 4</tt>'''
| Augton
|-
| '''<tt>4 6 4 4 6 3 4</tt>'''
| Inverse augton
|}


&lt;table class="wiki_table"&gt;
== Breed type ==
    &lt;tr&gt;
        &lt;td&gt;&lt;strong&gt;&lt;tt&gt;5555515&lt;/tt&gt;&lt;/strong&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Hemiwuerschmidt/Hemithirds[7]&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;strong&gt;&lt;tt&gt;5544652&lt;/tt&gt;&lt;/strong&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Hemaj; inverse hemin&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;strong&gt;&lt;tt&gt;4455256&lt;/tt&gt;&lt;/strong&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Hemin; inverse hemaj&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;strong&gt;&lt;tt&gt;4525546&lt;/tt&gt;&lt;/strong&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Gypsi; 11/9-10/7-7/4 chord on tonic&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;strong&gt;&lt;tt&gt;4552546&lt;/tt&gt;&lt;/strong&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Inverse gypsi; 11/9-10/7-7/4 chord on tonic&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;strong&gt;&lt;tt&gt;5555542&lt;/tt&gt;&lt;/strong&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Leadhole&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;strong&gt;&lt;tt&gt;5555524&lt;/tt&gt;&lt;/strong&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Inverse leadhole&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
&lt;/table&gt;


&lt;br /&gt;
{| class="wikitable"
&lt;!-- ws:start:WikiTextHeadingRule:8:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc4"&gt;&lt;a name="x--Mothra type"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:8 --&gt;Mothra type&lt;/h3&gt;
|-
! schema
! name
|-
| '''<tt>3 4 5 6 2 6 5</tt>'''
| Hemisub
|-
| '''<tt>4 3 5 6 2 6 5</tt>'''
| Inverse hemisub
|-
| '''<tt>6 3 5 4 5 3 5</tt>'''
| Heminewt
|-
| '''<tt>4 5 3 6 5 3 5</tt>'''
| Inverse heminewt
|}


== See also ==
* [[31edo modes]]
* [[Strictly proper 19edo scales]]


&lt;table class="wiki_table"&gt;
[[Category:Lists of scales]]
    &lt;tr&gt;
[[Category:7-tone scales| ]]
        &lt;td&gt;&lt;strong&gt;&lt;/strong&gt;&lt;br /&gt;
[[Category:31edo]]
&lt;/td&gt;
[[Category:Listen]]
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;strong&gt;&lt;/strong&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;strong&gt;&lt;/strong&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;strong&gt;&lt;/strong&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;strong&gt;&lt;/strong&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;strong&gt;&lt;/strong&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;strong&gt;&lt;/strong&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;strong&gt;&lt;/strong&gt;&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>

Latest revision as of 20:19, 23 March 2025

This is a list of 7-tone scales in 31edo which are strictly proper with regard to the Rothenberg propriety.

The "type" of a scale is defined by the linear temperament supported by 31edo in which it has the least span. "Breed type" means it is a tie between miracle and hemiwuerschmidt.

Meantone type

step pattern name example(s)
5 5 3 5 5 5 3 Meantone[7]; diatonic scale
5 3 5 5 5 5 3 Melodic minor scale
5 3 5 5 3 7 3 Harmonic minor scale; inverse harmonic major
5 5 3 5 3 7 3 Harmonic major scale; inverse harmonic minor
5 5 3 3 5 5 5 Major locrian scale
3 7 1 7 3 5 5 Diminished diatonic scale Strange Diatonic by Chris Vaisvil play
Omega centauri[dead link] by Zach Curley
5 5 3 5 6 4 3 Enharmonic major; inverse enharmonic minor
5 3 4 6 5 3 5 Enharmonic minor; inverse enharmonic major
5 5 3 5 6 2 5 Enharmonic mixolydian
5 5 2 6 5 3 5 Inverse enharmonic mixolydian
5 5 2 6 3 5 5 Enharmonic major-minor
5 5 5 3 6 2 5 Inverse enharmonic major-minor
6 4 3 5 6 2 5 Major doubleflat; inverse minor doubleflat
5 3 4 6 5 2 6 Minor doubleflat; inverse major doubleflat
5 5 5 3 6 5 2 Ping
3 5 5 5 2 5 6 Inverse ping
3 7 2 6 3 5 5 Alhijaz; inverse ambika
6 2 7 3 5 5 3 Ambika; inverse alhijaz
6 4 5 3 6 5 2 Kung; inverse ousak
3 5 4 6 2 5 6 Ousak; inverse kung

Valentine

schema name
6 4 4 6 2 7 2 Silver
6 4 4 4 4 7 2 Harmonia
4 4 4 6 2 7 4 Inverse harmonia
6 4 4 4 5 6 2 Pendragon
4 6 2 6 5 4 4 Inverse pendragon
6 2 6 4 4 6 3 Hipop
4 6 2 6 3 6 4 Inverse Hipop
4 6 2 6 4 4 5 Malakon
4 6 2 6 4 5 4 Inverse malakon
4 4 6 4 5 2 6 Bagpipe
4 6 4 4 6 2 5 Inverse bagpipe
6 4 4 4 6 2 5 Pitu
6 4 4 4 6 5 2 Inverse pitu
6 4 4 4 4 4 5 Porch
4 4 4 6 5 4 4 Inverse porch

Miracle type

schema name
5 4 3 6 3 4 6 Subdom scale; inverse superton
5 6 4 3 6 3 4 Superton scale; inverse subdom
5 4 3 6 3 6 4 Nudia; neutral diatonic
5 4 6 3 6 3 4 Inverse nudia
3 6 3 6 3 4 6 Nurow; Neutral triads in row
6 3 6 3 6 4 3 Inverse nurow

Mohajira type

schema name
4 5 5 4 4 5 4 Sikah; Rast; Neutral Diatonic Hypolydian
4 4 4 4 5 5 5 Sheimanic
4 5 5 4 4 4 5 Thaiic
4 5 4 4 4 5 5 Inverse thaiic
4 5 4 5 4 5 4 Mohajira; Neutral Dorian

Hemiwuerschmidt type

schema name
5 5 5 5 5 1 5 Hemiwuerschmidt/Hemithirds[7]
5 5 4 4 6 5 2 Hemaj; inverse hemin
4 4 5 5 2 5 6 Hemin; inverse hemaj
4 5 2 5 5 4 6 Gypsi; 11/9-10/7-7/4 chord on tonic
4 5 5 2 5 4 6 Inverse gypsi; 11/9-10/7-7/4 chord on tonic
5 5 5 5 5 4 2 Leadhole
5 5 5 5 5 2 4 Inverse leadhole

Mothra type

schema name
5 5 5 3 6 4 3 Lydic
5 5 5 3 4 6 3 Inverse lydic
5 5 3 5 4 6 3 Ionic
5 3 6 4 5 3 5 Aeolic; inverse ionic
4 6 4 4 4 6 3 Quahog
6 4 4 4 6 4 3 Inverse quahog
6 4 5 3 6 4 3 Higasi
4 6 3 5 4 6 3 Inverse higasi

Orwell type

schema name
5 3 6 4 4 6 3 Orminor
4 6 4 4 6 4 3 Ormed
4 6 4 4 3 6 4 Augton
4 6 4 4 6 3 4 Inverse augton

Breed type

schema name
3 4 5 6 2 6 5 Hemisub
4 3 5 6 2 6 5 Inverse hemisub
6 3 5 4 5 3 5 Heminewt
4 5 3 6 5 3 5 Inverse heminewt

See also

Retrieved from "https://en.xen.wiki/index.php?title=Strictly_proper_7-tone_31edo_scales&oldid=187968"