31edo modes: Difference between revisions

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<h2>IMPORTED REVISION FROM WIKISPACES</h2>
Taken originally from Scala, Manuel Op De Coul, this is a user-editable list of modes of [[31edo]]. The numbers indicate successive intervals, in dieses. There is also a dedicated page about [[strictly proper 7-tone 31edo scales]].
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
: This revision was by author [[User:mikesheiman|mikesheiman]] and made on <tt>2011-10-24 00:33:33 UTC</tt>.<br>
: The original revision id was <tt>267786700</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">Taken originally from Scala, Manuel Op De Coul, this is a user-editable list of modes of [[31edo]]. The numbers indicate successive intervals, in dieses. Strictly proper scales of seven notes can be found [[Strictly proper 7-note 31edo scales|here]].


 
== Nothing special ==
=Nothing special=  
Or, to some, the only important thing.
Or, to some, the only important thing.


|| {{**2 3 3 2 3 2 3 2 3 3 2 3**}} || Meantone Chromatic (53/220-comma) ||
{| class="wikitable"
|| {{**5 5 3 5 5 5 3**}} || Thirty-one tone Major, Intense Diatonic Lydian, M.Ionian ||
|-
|| {{**5 3 5 5 3 5 5**}} || Thirty-one tone Natural Minor, Intense Diatonic Hypodorian, Aeolian ||
| {{plaincode|'''2 3 3 2 3 2 3 2 3 3 2 3'''}}
|| {{**5 3 5 5 5 5 3**}} || Thirty-one tone Melodic Minor ||
| Meantone Chromatic (53/220-comma)
|| {{**5 3 5 5 3 7 3**}} || Thirty-one tone Harmonic Minor ||
|-
|| {{**5 5 3 5 3 7 3**}} || Thirty-one tone Harmonic Major ||
| {{plaincode|'''5 5 3 5 5 5 3'''}}
|| {{**5 5 3 5 3 5 5**}} || Thirty-one tone Major-Minor ||
| Thirty-one tone Major, Intense Diatonic Lydian, M.Ionian
|| {{**5 2 6 5 2 5 6**}} || "Septimal" Natural Minor ||
|-
 
| {{plaincode|'''5 3 5 5 3 5 5'''}}
=Euler-Fokker genera=
| Thirty-one tone Natural Minor, Intense Diatonic Hypodorian, Aeolian
 
|-
Boxy shapes from the [3,5,7] lattice.
| {{plaincode|'''5 5 8 5 8'''}}
 
| Thirty-one tone Major Pentatonic
|| {{**5 8 5 13**}} || Genus primum ||
|-
|| {{**10 3 5 5 5 3**}} || Genus secundum ||
| {{plaincode|'''5 3 5 5 5 5 3'''}}
|| {{**8 2 8 3 7 3**}} || Genus tertium ||
| Thirty-one tone Melodic Minor
|| {{**10 10 10 1**}} || Genus quartum ||
|-
|| {{**5 7 6 7 5 1**}} || Genus quintum ||
| {{plaincode|'''5 3 5 5 3 7 3'''}}
|| {{**4 6 2 6 4 3 3 3**}} || Genus sextum ||
| Thirty-one tone Harmonic Minor
|| {{**4 6 5 6 4 6**}} || Genus septimum ||
|-
|| {{**6 6 6 1 6 6**}} || Genus octavum ||
| {{plaincode|'''5 5 3 5 3 7 3'''}}
|| {{**4 6 9 6 4 2**}} || Genus nonum ||
| Thirty-one tone Harmonic Major
|| {{**13 6 6 6**}} || Genus decimum ||
|-
|| {{**5 5 3 5 5 3 2 3**}} || Genus diatonicum ||
| {{plaincode|'''5 5 3 5 3 5 5'''}}
|| {{**3 5 2 3 5 3 2 5 3**}} || Genus chromaticum ||
| Thirty-one tone Major-Minor
|| {{**5 5 2 1 5 5 2 3 3**}} || Genus diatonicum cum septimis ||
|-
|| {{**3 4 3 3 2 1 4 1 4 1 2 3**}} || Genus enharmonicum vocale ||
| {{plaincode|'''8 2 8 2 8 3'''}}
|| {{**2 2 4 2 2 3 3 3 1 3 3 3**}} || Genus enharmonicum instrumentale ||
| Thirty-one tone Augmented
|| {{**3 2 3 2 3 2 3 3 2 3 2 3**}} || Genus diatonico-chromaticum ||
|-
|| {{**5 2 1 2 5 3 2 1 4 1 2 3**}} || Genus bichromaticum ||
| {{plaincode|'''3 5 2 5 3 5 3 5'''}}
|| {{**3 1 2 4 2 4 2 4 2 1 3 3**}} || Genus [3577] (Joel Mandelbaum //Andante cantabile//) ||
| Thirty-one tone Diminished
 
|-
=Greek/tetrachord modes=
| {{plaincode|'''5 2 6 5 2 5 6'''}}
 
| "Septimal" Natural Minor
|| {{**4 4 5 4 4 5 5**}} || Neutral Diatonic Mixolydian ||
|}
|| {{**4 5 4 4 5 5 4**}} || Neutral Diatonic Lydian ||
|| {{**5 4 4 5 5 4 4**}} || Neutral Diatonic Phrygian ||
|| {{**4 4 5 5 4 4 5**}} || Neutral Diatonic Dorian ||
|| {{**4 5 5 4 4 5 4**}} || Neutral Diatonic Hypolydian ||
|| {{**5 5 4 4 5 4 4**}} || Neutral Diatonic Hypophrygian ||
|| {{**5 4 4 5 4 4 5**}} || Neutral Diatonic Hypodorian ||
|| {{**4 5 4 4 5 4 5**}} || Neutral Mixolydian ||
|| {{**5 4 4 5 4 5 4**}} || Neutral Lydian ||
|| {{**4 4 5 4 5 4 5**}} || Neutral Phrygian ||
|| {{**4 5 4 5 4 5 4**}} || Neutral Dorian ||
|| {{**5 4 5 4 5 4 4**}} || Neutral Hypolydian ||
|| {{**4 5 4 5 4 4 5**}} || Neutral Hypophrygian ||
|| {{**5 4 5 4 4 5 4**}} || Neutral Hypodorian ||
|| {{**2 2 9 2 2 9 5**}} || Hemiolic Chromatic Mixolydian ||
|| {{**2 9 2 2 9 5 2**}} || Hemiolic Chromatic Lydian ||
|| {{**9 2 2 9 5 2 2**}} || Hemiolic Chromatic Phrygian ||
|| {{**2 2 9 5 2 2 9**}} || Hemiolic Chromatic Dorian ||
|| {{**2 9 5 2 2 9 2**}} || Hemiolic Chromatic Hypolydian ||
|| {{**9 5 2 2 9 2 2**}} || Hemiolic Chromatic Hypophrygian ||
|| {{**5 2 2 9 2 2 9**}} || Hemiolic Chromatic Hypodorian ||
|| {{**2 3 8 2 3 8 5**}} || Ratio 2:3 Chromatic Mixolydian ||
|| {{**3 8 2 3 8 5 2**}} || Ratio 2:3 Chromatic Lydian ||
|| {{**8 2 3 8 5 2 3**}} || Ratio 2:3 Chromatic Phrygian ||
|| {{**2 3 8 5 2 3 8**}} || Ratio 2:3 Chromatic Dorian ||
|| {{**3 8 5 2 3 8 2**}} || Ratio 2:3 Chromatic Hypolydian ||
|| {{**8 5 2 3 8 2 3**}} || Ratio 2:3 Chromatic Hypophrygian ||
|| {{**5 2 3 8 2 3 8**}} || Ratio 2:3 Chromatic Hypodorian ||
|| {{**3 5 5 3 5 5 5**}} || Intense Diatonic Mixolydian, M.Locrian ||
|| {{**5 3 5 5 5 3 5**}} || Intense Diatonic Phrygian, M.Dorian ||
|| {{**3 5 5 5 3 5 5**}} || Intense Diatonic Dorian, M.Phrygian ||
|| {{**5 5 5 3 5 5 3**}} || Intense Diatonic Hypolydian, M.Lydian ||
|| {{**5 5 3 5 5 3 5**}} || Intense Diatonic Hypophrygian, M.Mixolydian ||
|| {{**2 5 6 2 5 6 5**}} || Soft Diatonic Mixolydian ||
|| {{**5 6 2 5 6 5 2**}} || Soft Diatonic Lydian ||
|| {{**6 2 5 6 5 2 5**}} || Soft Diatonic Phrygian ||
|| {{**2 5 6 5 2 5 6**}} || Soft Diatonic Dorian ||
|| {{**5 6 5 2 5 6 2**}} || Soft Diatonic Hypolydian ||
|| {{**6 5 2 5 6 2 5**}} || Soft Diatonic Hypophrygian ||
|| {{**5 2 5 6 2 5 6**}} || Soft Diatonic Hypodorian ||
|| {{**1 2 10 1 2 10 5**}} || Enharmonic Mixolydian ||
|| {{**2 10 1 2 10 5 1**}} || Enharmonic Lydian ||
|| {{**10 1 2 10 5 1 2**}} || Enharmonic Phrygian ||
|| {{**1 2 10 5 1 2 10**}} || Enharmonic Dorian ||
|| {{**2 10 5 1 2 10 1**}} || Enharmonic Hypolydian ||
|| {{**10 5 1 2 10 1 2**}} || Enharmonic Hypophrygian ||
|| {{**5 1 2 10 1 2 10**}} || Enharmonic Hypodorian ||
 
=Of particular [[interscalar]] interest=
 
|| {{**6 6 7 6 6**}} || Quasi-equal Pentatonic ||
|| {{**3 3 2 3 3 3 3 3 2 3 3**}} || near [[11edo]] ||
 
=Miscellaneous=
 
|| {{**3 2 2 3 3 2 3 3 2 2 3 3**}} || Fokker 12-tone ||
|| {{**5 3 5 3 5 2 5 3**}} || Modus conjunctus ||
|| {{**3 5 2 5 3 5 3 5**}} || Octatonic ||
|| {{**3 3 4 3 5 3 4 3 3**}} || Hahn symmetric pentachordal ||
|| {{**3 4 3 3 5 3 4 3 3**}} || Hahn pentachordal ||
|| {{**4 4 2 5 3 3 4 3 3**}} || Hahn Nonatonic ||
|| {{**5 3 3 3 3 5 3 3 3**}} || Rothenberg Generalized Diatonic ||
|| {{**(5) 3 1 4 (5) (5)**}}
{{**3 1 (4)**}} || Michael Sheiman's "Dimension" scale (Maqam Rast mixed with Meantone Diatonic...lattice (ratio/chord map) available below
[[image:dimensionscale.jpg width="512" height="197"]] ||
|| {{**(3 2)3 1 4 (3 2)(3 2)**}}
{{**3 1 (1 3)**}} || Michael Sheiman's extended "Dimension ECT" scale (Maqam Rast mixed with Meantone Diatonic and Michael Sheiman's "6-factor" no wolves 12th harmonic scale) ||
 
=MOS and Cradle MOS=
 
|| {{**4 5 4 5 4 5 4**}} || Neutral scale 7-note ||
|| {{**4 1 4 4 1 4 4 4 1 4**}} || Neutral scale 10-note ||
|| {{**4 1 4 4 4 1 4 4 1 4**}} || Breed 10-tone ||
|| {{**4 3 4 3 4 3 4 3 3**}} || Orwell[9] ||
|| {{**5 1 5 1 5 1 5 1 5 1 1**}} || de Vries 11-tone ||
|| {{**3 1 3 1 3 1 3 1 3 1 3 1 3 1 3**}} || Pseudo-Porcupine 15-note ||
|| {{**1 7 1 2 1 7 1 2 1 7 1**}} || Nested Bees ||
|| {{**4 2 4 2 4 2 4 3 3 3**}} || Lumma Decatonic ||
|| {{**2 5 2 2 5 2 2 2 5 2 2**}} || Secor/Barton no-fives ||</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;31edo modes&lt;/title&gt;&lt;/head&gt;&lt;body&gt;Taken originally from Scala, Manuel Op De Coul, this is a user-editable list of modes of &lt;a class="wiki_link" href="/31edo"&gt;31edo&lt;/a&gt;. The numbers indicate successive intervals, in dieses. Strictly proper scales of seven notes can be found &lt;a class="wiki_link" href="/Strictly%20proper%207-note%2031edo%20scales"&gt;here&lt;/a&gt;.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc0"&gt;&lt;a name="Nothing special"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;Nothing special&lt;/h1&gt;
Or, to some, the only important thing.&lt;br /&gt;
&lt;br /&gt;
 
 
&lt;table class="wiki_table"&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt;&lt;strong&gt;2 3 3 2 3 2 3 2 3 3 2 3&lt;/strong&gt;&lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Meantone Chromatic (53/220-comma)&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt;&lt;strong&gt;5 5 3 5 5 5 3&lt;/strong&gt;&lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Thirty-one tone Major, Intense Diatonic Lydian, M.Ionian&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt;&lt;strong&gt;5 3 5 5 3 5 5&lt;/strong&gt;&lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Thirty-one tone Natural Minor, Intense Diatonic Hypodorian, Aeolian&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt;&lt;strong&gt;5 3 5 5 5 5 3&lt;/strong&gt;&lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Thirty-one tone Melodic Minor&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt;&lt;strong&gt;5 3 5 5 3 7 3&lt;/strong&gt;&lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Thirty-one tone Harmonic Minor&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt;&lt;strong&gt;5 5 3 5 3 7 3&lt;/strong&gt;&lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Thirty-one tone Harmonic Major&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt;&lt;strong&gt;5 5 3 5 3 5 5&lt;/strong&gt;&lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Thirty-one tone Major-Minor&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt;&lt;strong&gt;5 2 6 5 2 5 6&lt;/strong&gt;&lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&amp;quot;Septimal&amp;quot; Natural Minor&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
&lt;/table&gt;


&lt;br /&gt;
== MOS ==
&lt;!-- ws:start:WikiTextHeadingRule:2:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc1"&gt;&lt;a name="Euler-Fokker genera"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;Euler-Fokker genera&lt;/h1&gt;
{| class="wikitable"
&lt;br /&gt;
|-
Boxy shapes from the [3,5,7] lattice.&lt;br /&gt;
| {{plaincode|'''4 5 4 5 4 5 4'''}}
&lt;br /&gt;
| Neutral[7]
|-
| {{plaincode|'''4 1 4 4 4 1 4 4 1 4'''}}
| Breed 10-tone / Neutral[10]
|-
| {{plaincode|'''7 7 7 7 3'''}}
| Orwell[5]
|-
| {{plaincode|'''4 3 4 3 4 3 4 3 3'''}}
| Orwell[9]
|-
| {{plaincode|'''3 1 3 3 1 3 3 1 3 3 1 3 3'''}}
| Orwell[13]
|-
| {{plaincode|'''9 9 2 9 2'''}}
| Squares[5]
|-
| {{plaincode|'''2 7 2 7 2 2 7 2'''}}
| Squares[8]
|-
| {{plaincode|'''2 5 2 2 2 5 2 2 2 5 2'''}}
| Secor/Barton no-fives / Squares[11]
|-
| {{plaincode|'''5 5 5 5 5 6'''}}
| Whole Tone / Tutone[6]
|-
| {{plaincode|'''4 1 4 1 4 1 4 1 4 1 4 1 1'''}}
| Tutone[13]
|-
| {{plaincode|'''6 6 6 6 1 6'''}}
| Mothra[6]
|-
| {{plaincode|'''5 1 5 1 5 1 5 1 5 1 1'''}}
| de Vries 11-tone / Mothra[11]
|-
| {{plaincode|'''3 4 3 3 3 3 3 3 3 3'''}}
| Miracle[10]
|-
| {{plaincode|'''1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1'''}}
| Blackjack / Miracle[21]
|-
| {{plaincode|'''3 4 4 4 4 4 4 4'''}}
| Greeley[8]
|-
| {{plaincode|'''3 1 3 1 3 1 3 1 3 1 3 1 3 1 3'''}}
| Pseudo-Porcupine 15-note / Nusecond[15]
|-
| {{plaincode|'''2 2 2 2 2 2 2 2 2 2 1 2 2 2 2 2'''}}
| Semi-Equalized Armodue / Valentine[16]
|-
| {{plaincode|'''5 7 5 7 7'''}}
| A-Team[5]
|-
| {{plaincode|'''5 5 2 5 5 2 5 2'''}}
| Oneirotonic / A-Team[8]
|-
| {{plaincode|'''3 2 3 2 2 3 2 2 3 2 3 2 2'''}}
| A-Team[13]
|-
| {{plaincode|'''11 3 11 3 3'''}}
| Joan[5]
|-
| {{plaincode|'''8 3 3 8 3 3 3'''}}
| Hypermavila / Joan[7]
|-
| {{plaincode|'''5 3 3 3 3 5 3 3 3'''}}
| Rothenberg Generalized Diatonic / Joan[9]
|-
| {{plaincode|'''3 2 3 3 3 3 2 3 3 3 3'''}}
| Joan[11]
|-
| {{plaincode|'''8 1 1 8 1 1 8 1 1 1'''}}
| Würschmidt[10]
|-
| {{plaincode|'''1 1 6 1 1 6 1 1 6 1 6'''}}
| Myna[11]
|-
| {{plaincode|'''1 1 12 1 1 1 1 12 1'''}}
| Tritonic[9]
|}


== MODMOS ==
{| class="wikitable"
|-
| {{plaincode|'''3 4 3 4 4 3 4 3 3'''}}
| Graham Orwell
|-
| {{plaincode|'''5 4 4 5 5 4 4'''}}
| Maqam Rast
|-
| {{plaincode|'''4 4 5 5 3 5 5'''}}
| Maqam Bayati
|-
| {{plaincode|'''5 5 3 5 4 5 4'''}}
| Turkish Major
|-
| {{plaincode|'''4 5 5 4 4 4 5'''}}
| Thaiic
|-
| {{plaincode|'''4 4 4 4 5 5 5'''}}
| Sheimanic
|-
| {{plaincode|'''5 5 4 4 5 5 3'''}}
| Screamapillar
|-
| {{plaincode|'''5 3 5 5 5 4 4'''}}
| Altered Dorian
|-
| {{plaincode|'''3 5 5 5 5 4 4'''}}
| Altered Neapolitan Major
|-
| {{plaincode|'''7 2 7 2 7 2 2 2'''}}
| Onydim
|-
| {{plaincode|'''5 5 2 2 2 2 5 2 2 2 2'''}}
| Squares Major
|-
| {{plaincode|'''5 5 4 6 5 6'''}}
| Harmonic Whole Tone
|-
| {{plaincode|'''5 5 5 2 5 2 5 2'''}}
| Dylydian / Archeodim
|-
| {{plaincode|'''5 2 5 2 5 2 8 2'''}}
| Harmonic Mnarian
|-
| {{plaincode|'''3 4 3 2 3 3 3 4 3 3'''}}
| Miracle Major
|-
| {{plaincode|'''3 4 3 4 4 5 4 4'''}}
| Greeley Major
|-
| {{plaincode|'''7 6 5 7 6'''}}
| Subminor Pentatonic
|-
| {{plaincode|'''5 6 7 6 7'''}}
| Supermajor Pentatonic
|-
| {{plaincode|'''1 6 1 1 1 6 1 1 6 1 6'''}}
| Submyna
|}


&lt;table class="wiki_table"&gt;
== Cradle MOS ==
    &lt;tr&gt;
{| class="wikitable"
        &lt;td&gt;&lt;tt&gt;&lt;strong&gt;5 8 5 13&lt;/strong&gt;&lt;/tt&gt;&lt;br /&gt;
|-
&lt;/td&gt;
| {{plaincode|'''1 7 1 2 1 7 1 2 1 7 1'''}}
        &lt;td&gt;Genus primum&lt;br /&gt;
| Nested Bees
&lt;/td&gt;
|-
    &lt;/tr&gt;
| {{plaincode|'''3 1 6 1 3 3 1 6 1 3 3'''}}
    &lt;tr&gt;
| Arc Aurelius
        &lt;td&gt;&lt;tt&gt;&lt;strong&gt;10 3 5 5 5 3&lt;/strong&gt;&lt;/tt&gt;&lt;br /&gt;
|-
&lt;/td&gt;
| {{plaincode|'''5 4 5 4 2 5 4 2'''}}
        &lt;td&gt;Genus secundum&lt;br /&gt;
| Xenosquare
&lt;/td&gt;
|-
    &lt;/tr&gt;
| {{plaincode|'''5 4 5 3 5 4 5'''}}
    &lt;tr&gt;
| Scorp
        &lt;td&gt;&lt;tt&gt;&lt;strong&gt;8 2 8 3 7 3&lt;/strong&gt;&lt;/tt&gt;&lt;br /&gt;
|-
&lt;/td&gt;
| {{plaincode|'''5 6 2 5 5 6 2'''}}
        &lt;td&gt;Genus tertium&lt;br /&gt;
| Harrison Major
&lt;/td&gt;
|-
    &lt;/tr&gt;
| {{plaincode|'''4 2 4 2 4 2 4 3 3 3'''}}
    &lt;tr&gt;
| Lumma Decatonic
        &lt;td&gt;&lt;tt&gt;&lt;strong&gt;10 10 10 1&lt;/strong&gt;&lt;/tt&gt;&lt;br /&gt;
|-
&lt;/td&gt;
| {{plaincode|'''8 2 8 2 8 2 1'''}}
        &lt;td&gt;Genus quartum&lt;br /&gt;
| AugmentedPlus
&lt;/td&gt;
|}
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt;&lt;strong&gt;5 7 6 7 5 1&lt;/strong&gt;&lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Genus quintum&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt;&lt;strong&gt;4 6 2 6 4 3 3 3&lt;/strong&gt;&lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Genus sextum&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt;&lt;strong&gt;4 6 5 6 4 6&lt;/strong&gt;&lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Genus septimum&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt;&lt;strong&gt;6 6 6 1 6 6&lt;/strong&gt;&lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Genus octavum&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt;&lt;strong&gt;4 6 9 6 4 2&lt;/strong&gt;&lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Genus nonum&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt;&lt;strong&gt;13 6 6 6&lt;/strong&gt;&lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Genus decimum&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt;&lt;strong&gt;5 5 3 5 5 3 2 3&lt;/strong&gt;&lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Genus diatonicum&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt;&lt;strong&gt;3 5 2 3 5 3 2 5 3&lt;/strong&gt;&lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Genus chromaticum&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt;&lt;strong&gt;5 5 2 1 5 5 2 3 3&lt;/strong&gt;&lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Genus diatonicum cum septimis&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt;&lt;strong&gt;3 4 3 3 2 1 4 1 4 1 2 3&lt;/strong&gt;&lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Genus enharmonicum vocale&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt;&lt;strong&gt;2 2 4 2 2 3 3 3 1 3 3 3&lt;/strong&gt;&lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Genus enharmonicum instrumentale&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt;&lt;strong&gt;3 2 3 2 3 2 3 3 2 3 2 3&lt;/strong&gt;&lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Genus diatonico-chromaticum&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt;&lt;strong&gt;5 2 1 2 5 3 2 1 4 1 2 3&lt;/strong&gt;&lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Genus bichromaticum&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt;&lt;strong&gt;3 1 2 4 2 4 2 4 2 1 3 3&lt;/strong&gt;&lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Genus [3577] (Joel Mandelbaum &lt;em&gt;Andante cantabile&lt;/em&gt;)&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
&lt;/table&gt;


&lt;br /&gt;
== Hexany ==
&lt;!-- ws:start:WikiTextHeadingRule:4:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc2"&gt;&lt;a name="Greek/tetrachord modes"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:4 --&gt;Greek/tetrachord modes&lt;/h1&gt;
{| class="wikitable"
&lt;br /&gt;
|-
| {{plaincode|'''5 5 8 5 5 3'''}}
| 1-3-5-9
|-
| {{plaincode|'''5 6 7 6 5 2'''}}
| 1-3-7-9
|-
| {{plaincode|'''3 7 6 2 6 7'''}}
| 1-3-5-7
|-
| {{plaincode|'''9 4 1 4 9 4'''}}
| 1-3-9-11
|-
| {{plaincode|'''4 4 6 4 4 9'''}}
| 1-3-5-11
|-
| {{plaincode|'''4 7 7 7 4 2'''}}
| 1-3-7-11
|-
| {{plaincode|'''8 4 6 4 8 1'''}}
| 1-3-5-13
|}


== Harmonic Series ==
{| class="wikitable"
|-
| {{plaincode|'''8 7 6 5 5'''}}
| Mode 5
|-
| {{plaincode|'''7 6 5 5 4 4'''}}
| Mode 6
|-
| {{plaincode|'''6 5 5 4 4 4 3'''}}
| Mode 7
|-
| {{plaincode|'''5 5 4 4 4 3 3 3'''}}
| Mode 8
|-
| {{plaincode|'''4 4 4 3 3 3 3 2 3 2'''}}
| Mode 10
|-
| {{plaincode|'''4 3 3 3 3 2 3 2 2 2 2 2'''}}
| Mode 12
|-
| {{plaincode|'''3 3 3 2 3 2 2 2 2 2 2 2 1 2'''}}
| Mode 14
|-
| {{plaincode|'''3 2 3 2 2 2 2 2 2 2 1 2 2 1 2 1'''}}
| Mode 16
|-
| {{plaincode|'''4 4 5 5 6 7'''}}
| Mode 6-over
|-
| {{plaincode|'''2 3 3 3 3 4 4 4 5'''}}
| Mode 9-over
|-
| {{plaincode|'''1 2 2 1 2 2 2 2 2 2 2 3 2 3 3'''}}
| Mode 15-over
|}


&lt;table class="wiki_table"&gt;
== Euler–Fokker genera ==
    &lt;tr&gt;
Boxy shapes from the {{nowrap|[3, 5, 7]}} lattice.
        &lt;td&gt;&lt;tt&gt;&lt;strong&gt;4 4 5 4 4 5 5&lt;/strong&gt;&lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Neutral Diatonic Mixolydian&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt;&lt;strong&gt;4 5 4 4 5 5 4&lt;/strong&gt;&lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Neutral Diatonic Lydian&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt;&lt;strong&gt;5 4 4 5 5 4 4&lt;/strong&gt;&lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Neutral Diatonic Phrygian&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt;&lt;strong&gt;4 4 5 5 4 4 5&lt;/strong&gt;&lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Neutral Diatonic Dorian&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt;&lt;strong&gt;4 5 5 4 4 5 4&lt;/strong&gt;&lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Neutral Diatonic Hypolydian&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt;&lt;strong&gt;5 5 4 4 5 4 4&lt;/strong&gt;&lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Neutral Diatonic Hypophrygian&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt;&lt;strong&gt;5 4 4 5 4 4 5&lt;/strong&gt;&lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Neutral Diatonic Hypodorian&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt;&lt;strong&gt;4 5 4 4 5 4 5&lt;/strong&gt;&lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Neutral Mixolydian&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt;&lt;strong&gt;5 4 4 5 4 5 4&lt;/strong&gt;&lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Neutral Lydian&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt;&lt;strong&gt;4 4 5 4 5 4 5&lt;/strong&gt;&lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Neutral Phrygian&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt;&lt;strong&gt;4 5 4 5 4 5 4&lt;/strong&gt;&lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Neutral Dorian&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt;&lt;strong&gt;5 4 5 4 5 4 4&lt;/strong&gt;&lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Neutral Hypolydian&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt;&lt;strong&gt;4 5 4 5 4 4 5&lt;/strong&gt;&lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Neutral Hypophrygian&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt;&lt;strong&gt;5 4 5 4 4 5 4&lt;/strong&gt;&lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Neutral Hypodorian&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt;&lt;strong&gt;2 2 9 2 2 9 5&lt;/strong&gt;&lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Hemiolic Chromatic Mixolydian&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt;&lt;strong&gt;2 9 2 2 9 5 2&lt;/strong&gt;&lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Hemiolic Chromatic Lydian&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt;&lt;strong&gt;9 2 2 9 5 2 2&lt;/strong&gt;&lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Hemiolic Chromatic Phrygian&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt;&lt;strong&gt;2 2 9 5 2 2 9&lt;/strong&gt;&lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Hemiolic Chromatic Dorian&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt;&lt;strong&gt;2 9 5 2 2 9 2&lt;/strong&gt;&lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Hemiolic Chromatic Hypolydian&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt;&lt;strong&gt;9 5 2 2 9 2 2&lt;/strong&gt;&lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Hemiolic Chromatic Hypophrygian&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt;&lt;strong&gt;5 2 2 9 2 2 9&lt;/strong&gt;&lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Hemiolic Chromatic Hypodorian&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt;&lt;strong&gt;2 3 8 2 3 8 5&lt;/strong&gt;&lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Ratio 2:3 Chromatic Mixolydian&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt;&lt;strong&gt;3 8 2 3 8 5 2&lt;/strong&gt;&lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Ratio 2:3 Chromatic Lydian&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt;&lt;strong&gt;8 2 3 8 5 2 3&lt;/strong&gt;&lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Ratio 2:3 Chromatic Phrygian&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt;&lt;strong&gt;2 3 8 5 2 3 8&lt;/strong&gt;&lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Ratio 2:3 Chromatic Dorian&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt;&lt;strong&gt;3 8 5 2 3 8 2&lt;/strong&gt;&lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Ratio 2:3 Chromatic Hypolydian&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt;&lt;strong&gt;8 5 2 3 8 2 3&lt;/strong&gt;&lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Ratio 2:3 Chromatic Hypophrygian&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt;&lt;strong&gt;5 2 3 8 2 3 8&lt;/strong&gt;&lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Ratio 2:3 Chromatic Hypodorian&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt;&lt;strong&gt;3 5 5 3 5 5 5&lt;/strong&gt;&lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Intense Diatonic Mixolydian, M.Locrian&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt;&lt;strong&gt;5 3 5 5 5 3 5&lt;/strong&gt;&lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Intense Diatonic Phrygian, M.Dorian&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt;&lt;strong&gt;3 5 5 5 3 5 5&lt;/strong&gt;&lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Intense Diatonic Dorian, M.Phrygian&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt;&lt;strong&gt;5 5 5 3 5 5 3&lt;/strong&gt;&lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Intense Diatonic Hypolydian, M.Lydian&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt;&lt;strong&gt;5 5 3 5 5 3 5&lt;/strong&gt;&lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Intense Diatonic Hypophrygian, M.Mixolydian&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt;&lt;strong&gt;2 5 6 2 5 6 5&lt;/strong&gt;&lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Soft Diatonic Mixolydian&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt;&lt;strong&gt;5 6 2 5 6 5 2&lt;/strong&gt;&lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Soft Diatonic Lydian&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt;&lt;strong&gt;6 2 5 6 5 2 5&lt;/strong&gt;&lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Soft Diatonic Phrygian&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt;&lt;strong&gt;2 5 6 5 2 5 6&lt;/strong&gt;&lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Soft Diatonic Dorian&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt;&lt;strong&gt;5 6 5 2 5 6 2&lt;/strong&gt;&lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Soft Diatonic Hypolydian&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt;&lt;strong&gt;6 5 2 5 6 2 5&lt;/strong&gt;&lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Soft Diatonic Hypophrygian&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt;&lt;strong&gt;5 2 5 6 2 5 6&lt;/strong&gt;&lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Soft Diatonic Hypodorian&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt;&lt;strong&gt;1 2 10 1 2 10 5&lt;/strong&gt;&lt;/tt&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;tt&gt;&lt;strong&gt;2 10 1 2 10 5 1&lt;/strong&gt;&lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Enharmonic Lydian&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt;&lt;strong&gt;10 1 2 10 5 1 2&lt;/strong&gt;&lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Enharmonic Phrygian&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt;&lt;strong&gt;1 2 10 5 1 2 10&lt;/strong&gt;&lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Enharmonic Dorian&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt;&lt;strong&gt;2 10 5 1 2 10 1&lt;/strong&gt;&lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Enharmonic Hypolydian&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt;&lt;strong&gt;10 5 1 2 10 1 2&lt;/strong&gt;&lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Enharmonic Hypophrygian&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt;&lt;strong&gt;5 1 2 10 1 2 10&lt;/strong&gt;&lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Enharmonic Hypodorian&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
&lt;/table&gt;


&lt;br /&gt;
{| class="wikitable"
&lt;!-- ws:start:WikiTextHeadingRule:6:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc3"&gt;&lt;a name="Of particular interscalar interest"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:6 --&gt;Of particular &lt;a class="wiki_link" href="/interscalar"&gt;interscalar&lt;/a&gt; interest&lt;/h1&gt;
|-
&lt;br /&gt;
| {{plaincode|'''5 8 5 13'''}}
| Genus primum
|-
| {{plaincode|'''10 3 5 5 5 3'''}}
| Genus secundum
|-
| {{plaincode|'''8 2 8 3 7 3'''}}
| Genus tertium
|-
| {{plaincode|'''10 10 10 1'''}}
| Genus quartum
|-
| {{plaincode|'''5 7 6 7 5 1'''}}
| Genus quintum
|-
| {{plaincode|'''4 6 2 6 4 3 3 3'''}}
| Genus sextum
|-
| {{plaincode|'''4 6 5 6 4 6'''}}
| Genus septimum
|-
| {{plaincode|'''6 6 6 1 6 6'''}}
| Genus octavum
|-
| {{plaincode|'''4 6 9 6 4 2'''}}
| Genus nonum
|-
| {{plaincode|'''13 6 6 6'''}}
| Genus decimum
|-
| {{plaincode|'''5 5 3 5 5 3 2 3'''}}
| Genus diatonicum
|-
| {{plaincode|'''3 5 2 3 5 3 2 5 3'''}}
| Genus chromaticum
|-
| {{plaincode|'''5 5 2 1 5 5 2 3 3'''}}
| Genus diatonicum cum septimis
|-
| {{plaincode|'''3 4 3 3 2 1 4 1 4 1 2 3'''}}
| Genus enharmonicum vocale
|-
| {{plaincode|'''2 2 4 2 2 3 3 3 1 3 3 3'''}}
| Genus enharmonicum instrumentale
|-
| {{plaincode|'''3 2 3 2 3 2 3 3 2 3 2 3'''}}
| Genus diatonico-chromaticum
|-
| {{plaincode|'''5 2 1 2 5 3 2 1 4 1 2 3'''}}
| Genus bichromaticum
|-
| {{plaincode|'''3 1 2 4 2 4 2 4 2 1 3 3'''}}
| Genus [3577] (Joel Mandelbaum ''Andante cantabile'')
|}


== Strictly proper modes ==
''See [[Strictly proper 7-tone 31edo scales]]''


&lt;table class="wiki_table"&gt;
== Greek/tetrachord modes ==
    &lt;tr&gt;
{| class="wikitable"
        &lt;td&gt;&lt;tt&gt;&lt;strong&gt;6 6 7 6 6&lt;/strong&gt;&lt;/tt&gt;&lt;br /&gt;
|-
&lt;/td&gt;
| {{plaincode|'''4 4 5 4 4 5 5'''}}
        &lt;td&gt;Quasi-equal Pentatonic&lt;br /&gt;
| Neutral Diatonic Mixolydian
&lt;/td&gt;
|-
    &lt;/tr&gt;
| {{plaincode|'''4 5 4 4 5 5 4'''}}
    &lt;tr&gt;
| Neutral Diatonic Lydian
        &lt;td&gt;&lt;tt&gt;&lt;strong&gt;3 3 2 3 3 3 3 3 2 3 3&lt;/strong&gt;&lt;/tt&gt;&lt;br /&gt;
|-
&lt;/td&gt;
| {{plaincode|'''5 4 4 5 5 4 4'''}}
        &lt;td&gt;near &lt;a class="wiki_link" href="/11edo"&gt;11edo&lt;/a&gt;&lt;br /&gt;
| Neutral Diatonic Phrygian
&lt;/td&gt;
|-
    &lt;/tr&gt;
| {{plaincode|'''4 4 5 5 4 4 5'''}}
&lt;/table&gt;
| Neutral Diatonic Dorian
|-
| {{plaincode|'''4 5 5 4 4 5 4'''}}
| Neutral Diatonic Hypolydian
|-
| {{plaincode|'''5 5 4 4 5 4 4'''}}
| Neutral Diatonic Hypophrygian
|-
| {{plaincode|'''5 4 4 5 4 4 5'''}}
| Neutral Diatonic Hypodorian
|-
| {{plaincode|'''4 5 4 4 5 4 5'''}}
| Neutral Mixolydian
|-
| {{plaincode|'''5 4 4 5 4 5 4'''}}
| Neutral Lydian
|-
| {{plaincode|'''4 4 5 4 5 4 5'''}}
| Neutral Phrygian
|-
| {{plaincode|'''4 5 4 5 4 5 4'''}}
| Neutral Dorian
|-
| {{plaincode|'''5 4 5 4 5 4 4'''}}
| Neutral Hypolydian
|-
| {{plaincode|'''4 5 4 5 4 4 5'''}}
| Neutral Hypophrygian
|-
| {{plaincode|'''5 4 5 4 4 5 4'''}}
| Neutral Hypodorian
|-
| {{plaincode|'''2 2 9 2 2 9 5'''}}
| Hemiolic Chromatic Mixolydian
|-
| {{plaincode|'''2 9 2 2 9 5 2'''}}
| Hemiolic Chromatic Lydian
|-
| {{plaincode|'''9 2 2 9 5 2 2'''}}
| Hemiolic Chromatic Phrygian
|-
| {{plaincode|'''2 2 9 5 2 2 9'''}}
| Hemiolic Chromatic Dorian
|-
| {{plaincode|'''2 9 5 2 2 9 2'''}}
| Hemiolic Chromatic Hypolydian
|-
| {{plaincode|'''9 5 2 2 9 2 2'''}}
| Hemiolic Chromatic Hypophrygian
|-
| {{plaincode|'''5 2 2 9 2 2 9'''}}
| Hemiolic Chromatic Hypodorian
|-
| {{plaincode|'''2 3 8 2 3 8 5'''}}
| Ratio 2:3 Chromatic Mixolydian
|-
| {{plaincode|'''3 8 2 3 8 5 2'''}}
| Ratio 2:3 Chromatic Lydian
|-
| {{plaincode|'''8 2 3 8 5 2 3'''}}
| Ratio 2:3 Chromatic Phrygian
|-
| {{plaincode|'''2 3 8 5 2 3 8'''}}
| Ratio 2:3 Chromatic Dorian
|-
| {{plaincode|'''3 8 5 2 3 8 2'''}}
| Ratio 2:3 Chromatic Hypolydian
|-
| {{plaincode|'''8 5 2 3 8 2 3'''}}
| Ratio 2:3 Chromatic Hypophrygian
|-
| {{plaincode|'''5 2 3 8 2 3 8'''}}
| Ratio 2:3 Chromatic Hypodorian
|-
| {{plaincode|'''3 5 5 3 5 5 5'''}}
| Intense Diatonic Mixolydian, M.Locrian
|-
| {{plaincode|'''5 3 5 5 5 3 5'''}}
| Intense Diatonic Phrygian, M.Dorian
|-
| {{plaincode|'''3 5 5 5 3 5 5'''}}
| Intense Diatonic Dorian, M.Phrygian
|-
| {{plaincode|'''5 5 5 3 5 5 3'''}}
| Intense Diatonic Hypolydian, M.Lydian
|-
| {{plaincode|'''5 5 3 5 5 3 5'''}}
| Intense Diatonic Hypophrygian, M.Mixolydian
|-
| {{plaincode|'''2 5 6 2 5 6 5'''}}
| Soft Diatonic Mixolydian
|-
| {{plaincode|'''5 6 2 5 6 5 2'''}}
| Soft Diatonic Lydian
|-
| {{plaincode|'''6 2 5 6 5 2 5'''}}
| Soft Diatonic Phrygian
|-
| {{plaincode|'''2 5 6 5 2 5 6'''}}
| Soft Diatonic Dorian
|-
| {{plaincode|'''5 6 5 2 5 6 2'''}}
| Soft Diatonic Hypolydian
|-
| {{plaincode|'''6 5 2 5 6 2 5'''}}
| Soft Diatonic Hypophrygian
|-
| {{plaincode|'''5 2 5 6 2 5 6'''}}
| Soft Diatonic Hypodorian
|-
| {{plaincode|'''1 2 10 1 2 10 5'''}}
| Enharmonic Mixolydian
|-
| {{plaincode|'''2 10 1 2 10 5 1'''}}
| Enharmonic Lydian
|-
| {{plaincode|'''10 1 2 10 5 1 2'''}}
| Enharmonic Phrygian
|-
| {{plaincode|'''1 2 10 5 1 2 10'''}}
| Enharmonic Dorian
|-
| {{plaincode|'''2 10 5 1 2 10 1'''}}
| Enharmonic Hypolydian
|-
| {{plaincode|'''10 5 1 2 10 1 2'''}}
| Enharmonic Hypophrygian
|-
| {{plaincode|'''5 1 2 10 1 2 10'''}}
| Enharmonic Hypodorian
|}


&lt;br /&gt;
== Of particular [[interscalar]] interest ==
&lt;!-- ws:start:WikiTextHeadingRule:8:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc4"&gt;&lt;a name="Miscellaneous"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:8 --&gt;Miscellaneous&lt;/h1&gt;
{| class="wikitable"
&lt;br /&gt;
|-
| {{plaincode|'''6 6 7 6 6'''}}
| [[Quasi-equal]] Pentatonic
|-
| {{plaincode|'''3 3 2 3 3 3 3 3 2 3 3'''}}
| near [[11edo|11edo]]
|}


== Dimension scales ==
{| class="wikitable"
|-
| {{plaincode|'''(5) 3 1 4 (5) (5)'''}} <br> {{plaincode|'''3 1 4'''}}
| Michael Sheiman's "Dimension" scale (Maqam Rast mixed with Meantone Diatonic...lattice (ratio/chord map) available below <br> [[File:dimensionscale.jpg|alt=dimensionscale.jpg|512x197px|dimensionscale.jpg]]
|-
| {{plaincode|'''(3 2)3 1 4 (3 2)(3 2)'''}} <br> {{plaincode|'''3 1 4'''}}
| Michael Sheiman's extended 12 tone "Dimension ECT" scale (Maqam Rast mixed with Meantone Diatonic and Michael Sheiman's "6-factor" no wolves 12th harmonic scale)
|}


&lt;table class="wiki_table"&gt;
== Miscellaneous ==
    &lt;tr&gt;
{| class="wikitable"
        &lt;td&gt;&lt;tt&gt;&lt;strong&gt;3 2 2 3 3 2 3 3 2 2 3 3&lt;/strong&gt;&lt;/tt&gt;&lt;br /&gt;
|-
&lt;/td&gt;
| {{plaincode|'''4 1 4 1 3 4 1 4 1 4 1 3'''}}
        &lt;td&gt;Fokker 12-tone&lt;br /&gt;
| Iceface
&lt;/td&gt;
|-
    &lt;/tr&gt;
| {{plaincode|'''1 4 2 3 3 1 4 2 3 2 3 3'''}}
    &lt;tr&gt;
| Centaurus
        &lt;td&gt;&lt;tt&gt;&lt;strong&gt;5 3 5 3 5 2 5 3&lt;/strong&gt;&lt;/tt&gt;&lt;br /&gt;
|-
&lt;/td&gt;
| {{plaincode|'''3 2 2 3 3 2 3 3 2 2 3 3'''}}
        &lt;td&gt;Modus conjunctus&lt;br /&gt;
| Fokker 12-tone
&lt;/td&gt;
|-
    &lt;/tr&gt;
| {{plaincode|'''5 3 5 3 5 2 5 3'''}}
    &lt;tr&gt;
| Modus conjunctus
        &lt;td&gt;&lt;tt&gt;&lt;strong&gt;3 5 2 5 3 5 3 5&lt;/strong&gt;&lt;/tt&gt;&lt;br /&gt;
|-
&lt;/td&gt;
| {{plaincode|'''2 5 3 5 3 5 2 6'''}}
        &lt;td&gt;Octatonic&lt;br /&gt;
| Subminor Diminished
&lt;/td&gt;
|-
    &lt;/tr&gt;
| {{plaincode|'''2 5 3 5 5 5 6'''}}
    &lt;tr&gt;
| Subminor Altered
        &lt;td&gt;&lt;tt&gt;&lt;strong&gt;3 3 4 3 5 3 4 3 3&lt;/strong&gt;&lt;/tt&gt;&lt;br /&gt;
|-
&lt;/td&gt;
| {{plaincode|'''2 8 3 5 2 5 6'''}}
        &lt;td&gt;Hahn symmetric pentachordal&lt;br /&gt;
| Phrygian Harmonic
&lt;/td&gt;
|-
    &lt;/tr&gt;
| {{plaincode|'''5 5 3 5 5 2 3 3'''}}
    &lt;tr&gt;
| Bebop Harmonic
        &lt;td&gt;&lt;tt&gt;&lt;strong&gt;3 4 3 3 5 3 4 3 3&lt;/strong&gt;&lt;/tt&gt;&lt;br /&gt;
|-
&lt;/td&gt;
| {{plaincode|'''5 7 1 5 7 5 1'''}}
        &lt;td&gt;Hahn pentachordal&lt;br /&gt;
| Tropical Major
&lt;/td&gt;
|-
    &lt;/tr&gt;
| {{plaincode|'''3 3 4 3 5 3 4 3 3'''}}
    &lt;tr&gt;
| Hahn symmetric pentachordal
        &lt;td&gt;&lt;tt&gt;&lt;strong&gt;4 4 2 5 3 3 4 3 3&lt;/strong&gt;&lt;/tt&gt;&lt;br /&gt;
|-
&lt;/td&gt;
| {{plaincode|'''3 4 3 3 5 3 4 3 3'''}}
        &lt;td&gt;Hahn Nonatonic&lt;br /&gt;
| Hahn pentachordal
&lt;/td&gt;
|-
    &lt;/tr&gt;
| {{plaincode|'''4 4 2 5 3 3 4 3 3'''}}
    &lt;tr&gt;
| Hahn Nonatonic
        &lt;td&gt;&lt;tt&gt;&lt;strong&gt;5 3 3 3 3 5 3 3 3&lt;/strong&gt;&lt;/tt&gt;&lt;br /&gt;
|-
&lt;/td&gt;
| {{plaincode|'''8 5 2 3 6 2 5'''}}
        &lt;td&gt;Rothenberg Generalized Diatonic&lt;br /&gt;
| Hyperblue Dorian (this is the original/default tuning)
&lt;/td&gt;
|-
    &lt;/tr&gt;
| {{plaincode|'''8 5 2 3 2 9 2'''}}
    &lt;tr&gt;
| Hyperblue harmonic (this is the original/default tuning)
        &lt;td&gt;&lt;tt&gt;&lt;strong&gt;(5) 3 1 4 (5) (5)&lt;/strong&gt;&lt;/tt&gt;&lt;br /&gt;
|-
&lt;tt&gt;&lt;strong&gt;3 1 (4)&lt;/strong&gt;&lt;/tt&gt;&lt;br /&gt;
| {{plaincode|'''5 5 4 8 3 6'''}}
&lt;/td&gt;
| Harmonic Prometheus
        &lt;td&gt;Michael Sheiman's &amp;quot;Dimension&amp;quot; scale (Maqam Rast mixed with Meantone Diatonic...lattice (ratio/chord map) available below&lt;br /&gt;
|-
&lt;!-- ws:start:WikiTextLocalImageRule:582:&amp;lt;img src=&amp;quot;/file/view/dimensionscale.jpg/260089260/512x197/dimensionscale.jpg&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; style=&amp;quot;height: 197px; width: 512px;&amp;quot; /&amp;gt; --&gt;&lt;img src="/file/view/dimensionscale.jpg/260089260/512x197/dimensionscale.jpg" alt="dimensionscale.jpg" title="dimensionscale.jpg" style="height: 197px; width: 512px;" /&gt;&lt;!-- ws:end:WikiTextLocalImageRule:582 --&gt;&lt;br /&gt;
| {{plaincode|'''3 2 3 2 2 2 2 2 2 3 2 3 3'''}}
&lt;/td&gt;
| Major Miniscale (Mode 16 x Mode 15-over)
    &lt;/tr&gt;
|-
    &lt;tr&gt;
| {{plaincode|'''7 3 4 4 7 6'''}}
        &lt;td&gt;&lt;tt&gt;&lt;strong&gt;(3 2)3 1 4 (3 2)(3 2)&lt;/strong&gt;&lt;/tt&gt;&lt;br /&gt;
| Graham Hexatonic
&lt;tt&gt;&lt;strong&gt;3 1 (1 3)&lt;/strong&gt;&lt;/tt&gt;&lt;br /&gt;
|-
&lt;/td&gt;
| {{plaincode|'''5 7 3 3 4 4 5'''}}
        &lt;td&gt;Michael Sheiman's extended &amp;quot;Dimension ECT&amp;quot; scale (Maqam Rast mixed with Meantone Diatonic and Michael Sheiman's &amp;quot;6-factor&amp;quot; no wolves 12th harmonic scale)&lt;br /&gt;
| [[Maeve Gutierrez#Scale recommendations|Superlydian b7 d6]]
&lt;/td&gt;
|-
    &lt;/tr&gt;
| {{plaincode|'''3 7 8 8 5'''}}
&lt;/table&gt;
| [[Magnetosphere scale|Magnetosphere]]
|-
| {{plaincode|'''5 4 1 3 5 2 3 6 2'''}}
| [[Oclock]]
|}


&lt;br /&gt;
== Nonoctave ==
&lt;!-- ws:start:WikiTextHeadingRule:10:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc5"&gt;&lt;a name="MOS and Cradle MOS"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:10 --&gt;MOS and Cradle MOS&lt;/h1&gt;
{| class="wikitable"
&lt;br /&gt;
|-
| {{plaincode|'''4 2 4 2 4 2 4 2 4 2'''}}
| Blackwood
|-
| {{plaincode|'''4 4 6 4 4 4 6'''}}
| Mavila
|-
| {{plaincode|'''8 2 8 2 8 2'''}}
| Suboctave Augmented
|-
| {{plaincode|'''2 6 2 6 2 6 2 6'''}}
| Superoctave Diminished
|-
| {{plaincode|'''4 4 3 7 3 5 3 (7)'''}}
| Saba
|-
| {{plaincode|'''5 5 5 3 5 5 5'''}}
| Superlydian
|-
| {{plaincode|''See main article''}}
| The [[Erose-McClain double mode]]s
|}


== 9-tone ==
{{main|9-tone 31edo scales}}


&lt;table class="wiki_table"&gt;
{{Navbox scale gallery}}
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt;&lt;strong&gt;4 5 4 5 4 5 4&lt;/strong&gt;&lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Neutral scale 7-note&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt;&lt;strong&gt;4 1 4 4 1 4 4 4 1 4&lt;/strong&gt;&lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Neutral scale 10-note&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt;&lt;strong&gt;4 1 4 4 4 1 4 4 1 4&lt;/strong&gt;&lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Breed 10-tone&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt;&lt;strong&gt;4 3 4 3 4 3 4 3 3&lt;/strong&gt;&lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Orwell[9]&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt;&lt;strong&gt;5 1 5 1 5 1 5 1 5 1 1&lt;/strong&gt;&lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;de Vries 11-tone&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt;&lt;strong&gt;3 1 3 1 3 1 3 1 3 1 3 1 3 1 3&lt;/strong&gt;&lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Pseudo-Porcupine 15-note&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt;&lt;strong&gt;1 7 1 2 1 7 1 2 1 7 1&lt;/strong&gt;&lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Nested Bees&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt;&lt;strong&gt;4 2 4 2 4 2 4 3 3 3&lt;/strong&gt;&lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Lumma Decatonic&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt;&lt;strong&gt;2 5 2 2 5 2 2 2 5 2 2&lt;/strong&gt;&lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Secor/Barton no-fives&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
&lt;/table&gt;


&lt;/body&gt;&lt;/html&gt;</pre></div>
[[Category:31edo]]
[[Category:Modes]]
[[Category:Lists of scales]]

Latest revision as of 01:17, 17 December 2025

Taken originally from Scala, Manuel Op De Coul, this is a user-editable list of modes of 31edo. The numbers indicate successive intervals, in dieses. There is also a dedicated page about strictly proper 7-tone 31edo scales.

Nothing special

Or, to some, the only important thing.

2 3 3 2 3 2 3 2 3 3 2 3 Meantone Chromatic (53/220-comma)
5 5 3 5 5 5 3 Thirty-one tone Major, Intense Diatonic Lydian, M.Ionian
5 3 5 5 3 5 5 Thirty-one tone Natural Minor, Intense Diatonic Hypodorian, Aeolian
5 5 8 5 8 Thirty-one tone Major Pentatonic
5 3 5 5 5 5 3 Thirty-one tone Melodic Minor
5 3 5 5 3 7 3 Thirty-one tone Harmonic Minor
5 5 3 5 3 7 3 Thirty-one tone Harmonic Major
5 5 3 5 3 5 5 Thirty-one tone Major-Minor
8 2 8 2 8 3 Thirty-one tone Augmented
3 5 2 5 3 5 3 5 Thirty-one tone Diminished
5 2 6 5 2 5 6 "Septimal" Natural Minor

MOS

4 5 4 5 4 5 4 Neutral[7]
4 1 4 4 4 1 4 4 1 4 Breed 10-tone / Neutral[10]
7 7 7 7 3 Orwell[5]
4 3 4 3 4 3 4 3 3 Orwell[9]
3 1 3 3 1 3 3 1 3 3 1 3 3 Orwell[13]
9 9 2 9 2 Squares[5]
2 7 2 7 2 2 7 2 Squares[8]
2 5 2 2 2 5 2 2 2 5 2 Secor/Barton no-fives / Squares[11]
5 5 5 5 5 6 Whole Tone / Tutone[6]
4 1 4 1 4 1 4 1 4 1 4 1 1 Tutone[13]
6 6 6 6 1 6 Mothra[6]
5 1 5 1 5 1 5 1 5 1 1 de Vries 11-tone / Mothra[11]
3 4 3 3 3 3 3 3 3 3 Miracle[10]
1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 Blackjack / Miracle[21]
3 4 4 4 4 4 4 4 Greeley[8]
3 1 3 1 3 1 3 1 3 1 3 1 3 1 3 Pseudo-Porcupine 15-note / Nusecond[15]
2 2 2 2 2 2 2 2 2 2 1 2 2 2 2 2 Semi-Equalized Armodue / Valentine[16]
5 7 5 7 7 A-Team[5]
5 5 2 5 5 2 5 2 Oneirotonic / A-Team[8]
3 2 3 2 2 3 2 2 3 2 3 2 2 A-Team[13]
11 3 11 3 3 Joan[5]
8 3 3 8 3 3 3 Hypermavila / Joan[7]
5 3 3 3 3 5 3 3 3 Rothenberg Generalized Diatonic / Joan[9]
3 2 3 3 3 3 2 3 3 3 3 Joan[11]
8 1 1 8 1 1 8 1 1 1 Würschmidt[10]
1 1 6 1 1 6 1 1 6 1 6 Myna[11]
1 1 12 1 1 1 1 12 1 Tritonic[9]

MODMOS

3 4 3 4 4 3 4 3 3 Graham Orwell
5 4 4 5 5 4 4 Maqam Rast
4 4 5 5 3 5 5 Maqam Bayati
5 5 3 5 4 5 4 Turkish Major
4 5 5 4 4 4 5 Thaiic
4 4 4 4 5 5 5 Sheimanic
5 5 4 4 5 5 3 Screamapillar
5 3 5 5 5 4 4 Altered Dorian
3 5 5 5 5 4 4 Altered Neapolitan Major
7 2 7 2 7 2 2 2 Onydim
5 5 2 2 2 2 5 2 2 2 2 Squares Major
5 5 4 6 5 6 Harmonic Whole Tone
5 5 5 2 5 2 5 2 Dylydian / Archeodim
5 2 5 2 5 2 8 2 Harmonic Mnarian
3 4 3 2 3 3 3 4 3 3 Miracle Major
3 4 3 4 4 5 4 4 Greeley Major
7 6 5 7 6 Subminor Pentatonic
5 6 7 6 7 Supermajor Pentatonic
1 6 1 1 1 6 1 1 6 1 6 Submyna

Cradle MOS

1 7 1 2 1 7 1 2 1 7 1 Nested Bees
3 1 6 1 3 3 1 6 1 3 3 Arc Aurelius
5 4 5 4 2 5 4 2 Xenosquare
5 4 5 3 5 4 5 Scorp
5 6 2 5 5 6 2 Harrison Major
4 2 4 2 4 2 4 3 3 3 Lumma Decatonic
8 2 8 2 8 2 1 AugmentedPlus

Hexany

5 5 8 5 5 3 1-3-5-9
5 6 7 6 5 2 1-3-7-9
3 7 6 2 6 7 1-3-5-7
9 4 1 4 9 4 1-3-9-11
4 4 6 4 4 9 1-3-5-11
4 7 7 7 4 2 1-3-7-11
8 4 6 4 8 1 1-3-5-13

Harmonic Series

8 7 6 5 5 Mode 5
7 6 5 5 4 4 Mode 6
6 5 5 4 4 4 3 Mode 7
5 5 4 4 4 3 3 3 Mode 8
4 4 4 3 3 3 3 2 3 2 Mode 10
4 3 3 3 3 2 3 2 2 2 2 2 Mode 12
3 3 3 2 3 2 2 2 2 2 2 2 1 2 Mode 14
3 2 3 2 2 2 2 2 2 2 1 2 2 1 2 1 Mode 16
4 4 5 5 6 7 Mode 6-over
2 3 3 3 3 4 4 4 5 Mode 9-over
1 2 2 1 2 2 2 2 2 2 2 3 2 3 3 Mode 15-over

Euler–Fokker genera

Boxy shapes from the [3, 5, 7] lattice.

5 8 5 13 Genus primum
10 3 5 5 5 3 Genus secundum
8 2 8 3 7 3 Genus tertium
10 10 10 1 Genus quartum
5 7 6 7 5 1 Genus quintum
4 6 2 6 4 3 3 3 Genus sextum
4 6 5 6 4 6 Genus septimum
6 6 6 1 6 6 Genus octavum
4 6 9 6 4 2 Genus nonum
13 6 6 6 Genus decimum
5 5 3 5 5 3 2 3 Genus diatonicum
3 5 2 3 5 3 2 5 3 Genus chromaticum
5 5 2 1 5 5 2 3 3 Genus diatonicum cum septimis
3 4 3 3 2 1 4 1 4 1 2 3 Genus enharmonicum vocale
2 2 4 2 2 3 3 3 1 3 3 3 Genus enharmonicum instrumentale
3 2 3 2 3 2 3 3 2 3 2 3 Genus diatonico-chromaticum
5 2 1 2 5 3 2 1 4 1 2 3 Genus bichromaticum
3 1 2 4 2 4 2 4 2 1 3 3 Genus [3577] (Joel Mandelbaum Andante cantabile)

Strictly proper modes

See Strictly proper 7-tone 31edo scales

Greek/tetrachord modes

4 4 5 4 4 5 5 Neutral Diatonic Mixolydian
4 5 4 4 5 5 4 Neutral Diatonic Lydian
5 4 4 5 5 4 4 Neutral Diatonic Phrygian
4 4 5 5 4 4 5 Neutral Diatonic Dorian
4 5 5 4 4 5 4 Neutral Diatonic Hypolydian
5 5 4 4 5 4 4 Neutral Diatonic Hypophrygian
5 4 4 5 4 4 5 Neutral Diatonic Hypodorian
4 5 4 4 5 4 5 Neutral Mixolydian
5 4 4 5 4 5 4 Neutral Lydian
4 4 5 4 5 4 5 Neutral Phrygian
4 5 4 5 4 5 4 Neutral Dorian
5 4 5 4 5 4 4 Neutral Hypolydian
4 5 4 5 4 4 5 Neutral Hypophrygian
5 4 5 4 4 5 4 Neutral Hypodorian
2 2 9 2 2 9 5 Hemiolic Chromatic Mixolydian
2 9 2 2 9 5 2 Hemiolic Chromatic Lydian
9 2 2 9 5 2 2 Hemiolic Chromatic Phrygian
2 2 9 5 2 2 9 Hemiolic Chromatic Dorian
2 9 5 2 2 9 2 Hemiolic Chromatic Hypolydian
9 5 2 2 9 2 2 Hemiolic Chromatic Hypophrygian
5 2 2 9 2 2 9 Hemiolic Chromatic Hypodorian
2 3 8 2 3 8 5 Ratio 2:3 Chromatic Mixolydian
3 8 2 3 8 5 2 Ratio 2:3 Chromatic Lydian
8 2 3 8 5 2 3 Ratio 2:3 Chromatic Phrygian
2 3 8 5 2 3 8 Ratio 2:3 Chromatic Dorian
3 8 5 2 3 8 2 Ratio 2:3 Chromatic Hypolydian
8 5 2 3 8 2 3 Ratio 2:3 Chromatic Hypophrygian
5 2 3 8 2 3 8 Ratio 2:3 Chromatic Hypodorian
3 5 5 3 5 5 5 Intense Diatonic Mixolydian, M.Locrian
5 3 5 5 5 3 5 Intense Diatonic Phrygian, M.Dorian
3 5 5 5 3 5 5 Intense Diatonic Dorian, M.Phrygian
5 5 5 3 5 5 3 Intense Diatonic Hypolydian, M.Lydian
5 5 3 5 5 3 5 Intense Diatonic Hypophrygian, M.Mixolydian
2 5 6 2 5 6 5 Soft Diatonic Mixolydian
5 6 2 5 6 5 2 Soft Diatonic Lydian
6 2 5 6 5 2 5 Soft Diatonic Phrygian
2 5 6 5 2 5 6 Soft Diatonic Dorian
5 6 5 2 5 6 2 Soft Diatonic Hypolydian
6 5 2 5 6 2 5 Soft Diatonic Hypophrygian
5 2 5 6 2 5 6 Soft Diatonic Hypodorian
1 2 10 1 2 10 5 Enharmonic Mixolydian
2 10 1 2 10 5 1 Enharmonic Lydian
10 1 2 10 5 1 2 Enharmonic Phrygian
1 2 10 5 1 2 10 Enharmonic Dorian
2 10 5 1 2 10 1 Enharmonic Hypolydian
10 5 1 2 10 1 2 Enharmonic Hypophrygian
5 1 2 10 1 2 10 Enharmonic Hypodorian

Of particular interscalar interest

6 6 7 6 6 Quasi-equal Pentatonic
3 3 2 3 3 3 3 3 2 3 3 near 11edo

Dimension scales

(5) 3 1 4 (5) (5)
3 1 4 		Michael Sheiman's "Dimension" scale (Maqam Rast mixed with Meantone Diatonic...lattice (ratio/chord map) available below
dimensionscale.jpg
(3 2)3 1 4 (3 2)(3 2)
3 1 4 		Michael Sheiman's extended 12 tone "Dimension ECT" scale (Maqam Rast mixed with Meantone Diatonic and Michael Sheiman's "6-factor" no wolves 12th harmonic scale)

Miscellaneous

4 1 4 1 3 4 1 4 1 4 1 3 Iceface
1 4 2 3 3 1 4 2 3 2 3 3 Centaurus
3 2 2 3 3 2 3 3 2 2 3 3 Fokker 12-tone
5 3 5 3 5 2 5 3 Modus conjunctus
2 5 3 5 3 5 2 6 Subminor Diminished
2 5 3 5 5 5 6 Subminor Altered
2 8 3 5 2 5 6 Phrygian Harmonic
5 5 3 5 5 2 3 3 Bebop Harmonic
5 7 1 5 7 5 1 Tropical Major
3 3 4 3 5 3 4 3 3 Hahn symmetric pentachordal
3 4 3 3 5 3 4 3 3 Hahn pentachordal
4 4 2 5 3 3 4 3 3 Hahn Nonatonic
8 5 2 3 6 2 5 Hyperblue Dorian (this is the original/default tuning)
8 5 2 3 2 9 2 Hyperblue harmonic (this is the original/default tuning)
5 5 4 8 3 6 Harmonic Prometheus
3 2 3 2 2 2 2 2 2 3 2 3 3 Major Miniscale (Mode 16 x Mode 15-over)
7 3 4 4 7 6 Graham Hexatonic
5 7 3 3 4 4 5 Superlydian b7 d6
3 7 8 8 5 Magnetosphere
5 4 1 3 5 2 3 6 2 Oclock

Nonoctave

4 2 4 2 4 2 4 2 4 2 Blackwood
4 4 6 4 4 4 6 Mavila
8 2 8 2 8 2 Suboctave Augmented
2 6 2 6 2 6 2 6 Superoctave Diminished
4 4 3 7 3 5 3 (7) Saba
5 5 5 3 5 5 5 Superlydian
See main article The Erose-McClain double modes

9-tone

Main article: 9-tone 31edo scales


View • Talk • EditScale galleries
JI scales 12-tone JI • Combination product set • Constant structure • Harry Partch-related • Maximal harmony epimorphic • MOS transversal • Non-octave JI • Wakalix • Z-polygon transversal • Other JI
Full list: Category:Just intonation scales
Tempered scales 11-tone MOS • 12-tone tempered • Chromatic pair • Clipper • Double mode • Essentially tempered • Fantasy detemper • Marvel woo • Meantone • Min ambiguity • MOS cradle • Negri-9 • Neutral third • Non-octave tempered • Scalesmith systematic • Ternary • Other tempered
Full list: Category:Tempered scales
Scales in EDOs in 10edo • 11 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 • 26 • 27 • 28 • 29 • 30 • 31 • 33 • 34 • 35 • 36 • 37 • 38 • 40 • 41 • 42 • 43 • 46 • 49 • 53 • 72 • 80
All other scale gallery pages are included in Category:Lists of scales
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