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|31edo]]. The numbers indicate successive intervals, in dieses. Strictly proper scales of seven notes can be found [[Strictly_proper_7-note_31edo_scales|here]].
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 01:04:23 UTC</tt>.<br>
: The original revision id was <tt>267790912</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 ||
| | <tt>'''2 3 3 2 3 2 3 2 3 3 2 3'''</tt>
|| {{**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 ||
| | <tt>'''5 5 3 5 5 5 3'''</tt>
|| {{**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 ||
|-
| | <tt>'''5 3 5 5 3 5 5'''</tt>
| | Thirty-one tone Natural Minor, Intense Diatonic Hypodorian, Aeolian
|-
| | <tt>'''5 3 5 5 5 5 3'''</tt>
| | Thirty-one tone Melodic Minor
|-
| | <tt>'''5 3 5 5 3 7 3'''</tt>
| | Thirty-one tone Harmonic Minor
|-
| | <tt>'''5 5 3 5 3 7 3'''</tt>
| | Thirty-one tone Harmonic Major
|-
| | <tt>'''5 5 3 5 3 5 5'''</tt>
| | Thirty-one tone Major-Minor
|-
| | <tt>'''5 2 6 5 2 5 6'''</tt>
| | "Septimal" Natural Minor
|}


=Euler-Fokker genera=  
=Euler-Fokker genera=


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


|| {{**5 8 5 13**}} || Genus primum ||
{| class="wikitable"
|| {{**10 3 5 5 5 3**}} || Genus secundum ||
|-
|| {{**8 2 8 3 7 3**}} || Genus tertium ||
| | <tt>'''5 8 5 13'''</tt>
|| {{**10 10 10 1**}} || Genus quartum ||
| | Genus primum
|| {{**5 7 6 7 5 1**}} || Genus quintum ||
|-
|| {{**4 6 2 6 4 3 3 3**}} || Genus sextum ||
| | <tt>'''10 3 5 5 5 3'''</tt>
|| {{**4 6 5 6 4 6**}} || Genus septimum ||
| | Genus secundum
|| {{**6 6 6 1 6 6**}} || Genus octavum ||
|-
|| {{**4 6 9 6 4 2**}} || Genus nonum ||
| | <tt>'''8 2 8 3 7 3'''</tt>
|| {{**13 6 6 6**}} || Genus decimum ||
| | Genus tertium
|| {{**5 5 3 5 5 3 2 3**}} || Genus diatonicum ||
|-
|| {{**3 5 2 3 5 3 2 5 3**}} || Genus chromaticum ||
| | <tt>'''10 10 10 1'''</tt>
|| {{**5 5 2 1 5 5 2 3 3**}} || Genus diatonicum cum septimis ||
| | Genus quartum
|| {{**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 ||
| | <tt>'''5 7 6 7 5 1'''</tt>
|| {{**3 2 3 2 3 2 3 3 2 3 2 3**}} || Genus diatonico-chromaticum ||
| | Genus quintum
|| {{**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//) ||
| | <tt>'''4 6 2 6 4 3 3 3'''</tt>
 
| | Genus sextum
=Greek/tetrachord modes=
|-
 
| | <tt>'''4 6 5 6 4 6'''</tt>
|| {{**4 4 5 4 4 5 5**}} || Neutral Diatonic Mixolydian ||
| | Genus septimum
|| {{**4 5 4 4 5 5 4**}} || Neutral Diatonic Lydian ||
|-
|| {{**5 4 4 5 5 4 4**}} || Neutral Diatonic Phrygian ||
| | <tt>'''6 6 6 1 6 6'''</tt>
|| {{**4 4 5 5 4 4 5**}} || Neutral Diatonic Dorian ||
| | Genus octavum
|| {{**4 5 5 4 4 5 4**}} || Neutral Diatonic Hypolydian ||
|-
|| {{**5 5 4 4 5 4 4**}} || Neutral Diatonic Hypophrygian ||
| | <tt>'''4 6 9 6 4 2'''</tt>
|| {{**5 4 4 5 4 4 5**}} || Neutral Diatonic Hypodorian ||
| | Genus nonum
|| {{**4 5 4 4 5 4 5**}} || Neutral Mixolydian ||
|-
|| {{**5 4 4 5 4 5 4**}} || Neutral Lydian ||
| | <tt>'''13 6 6 6'''</tt>
|| {{**4 4 5 4 5 4 5**}} || Neutral Phrygian ||
| | Genus decimum
|| {{**4 5 4 5 4 5 4**}} || Neutral Dorian ||
|-
|| {{**5 4 5 4 5 4 4**}} || Neutral Hypolydian ||
| | <tt>'''5 5 3 5 5 3 2 3'''</tt>
|| {{**4 5 4 5 4 4 5**}} || Neutral Hypophrygian ||
| | Genus diatonicum
|| {{**5 4 5 4 4 5 4**}} || Neutral Hypodorian ||
|-
|| {{**2 2 9 2 2 9 5**}} || Hemiolic Chromatic Mixolydian ||
| | <tt>'''3 5 2 3 5 3 2 5 3'''</tt>
|| {{**2 9 2 2 9 5 2**}} || Hemiolic Chromatic Lydian ||
| | Genus chromaticum
|| {{**9 2 2 9 5 2 2**}} || Hemiolic Chromatic Phrygian ||
|-
|| {{**2 2 9 5 2 2 9**}} || Hemiolic Chromatic Dorian ||
| | <tt>'''5 5 2 1 5 5 2 3 3'''</tt>
|| {{**2 9 5 2 2 9 2**}} || Hemiolic Chromatic Hypolydian ||
| | Genus diatonicum cum septimis
|| {{**9 5 2 2 9 2 2**}} || Hemiolic Chromatic Hypophrygian ||
|-
|| {{**5 2 2 9 2 2 9**}} || Hemiolic Chromatic Hypodorian ||
| | <tt>'''3 4 3 3 2 1 4 1 4 1 2 3'''</tt>
|| {{**2 3 8 2 3 8 5**}} || Ratio 2:3 Chromatic Mixolydian ||
| | Genus enharmonicum vocale
|| {{**3 8 2 3 8 5 2**}} || Ratio 2:3 Chromatic Lydian ||
|-
|| {{**8 2 3 8 5 2 3**}} || Ratio 2:3 Chromatic Phrygian ||
| | <tt>'''2 2 4 2 2 3 3 3 1 3 3 3'''</tt>
|| {{**2 3 8 5 2 3 8**}} || Ratio 2:3 Chromatic Dorian ||
| | Genus enharmonicum instrumentale
|| {{**3 8 5 2 3 8 2**}} || Ratio 2:3 Chromatic Hypolydian ||
|-
|| {{**8 5 2 3 8 2 3**}} || Ratio 2:3 Chromatic Hypophrygian ||
| | <tt>'''3 2 3 2 3 2 3 3 2 3 2 3'''</tt>
|| {{**5 2 3 8 2 3 8**}} || Ratio 2:3 Chromatic Hypodorian ||
| | Genus diatonico-chromaticum
|| {{**3 5 5 3 5 5 5**}} || Intense Diatonic Mixolydian, M.Locrian ||
|-
|| {{**5 3 5 5 5 3 5**}} || Intense Diatonic Phrygian, M.Dorian ||
| | <tt>'''5 2 1 2 5 3 2 1 4 1 2 3'''</tt>
|| {{**3 5 5 5 3 5 5**}} || Intense Diatonic Dorian, M.Phrygian ||
| | Genus bichromaticum
|| {{**5 5 5 3 5 5 3**}} || Intense Diatonic Hypolydian, M.Lydian ||
|-
|| {{**5 5 3 5 5 3 5**}} || Intense Diatonic Hypophrygian, M.Mixolydian ||
| | <tt>'''3 1 2 4 2 4 2 4 2 1 3 3'''</tt>
|| {{**2 5 6 2 5 6 5**}} || Soft Diatonic Mixolydian ||
| | Genus [3577] (Joel Mandelbaum ''Andante cantabile'')
|| {{**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 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) ||
 
=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;
&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;
&lt;br /&gt;
Boxy shapes from the [3,5,7] lattice.&lt;br /&gt;
&lt;br /&gt;
 
 
&lt;table class="wiki_table"&gt;
    &lt;tr&gt;
        &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;
        &lt;td&gt;Genus primum&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &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;
        &lt;td&gt;Genus secundum&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &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;
        &lt;td&gt;Genus tertium&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &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;
        &lt;td&gt;Genus quartum&lt;br /&gt;
&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;
&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;
&lt;br /&gt;
 


&lt;table class="wiki_table"&gt;
=Greek/tetrachord modes=
    &lt;tr&gt;
        &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;
| | <tt>'''4 4 5 4 4 5 5'''</tt>
| | Neutral Diatonic Mixolydian
|-
| | <tt>'''4 5 4 4 5 5 4'''</tt>
| | Neutral Diatonic Lydian
|-
| | <tt>'''5 4 4 5 5 4 4'''</tt>
| | Neutral Diatonic Phrygian
|-
| | <tt>'''4 4 5 5 4 4 5'''</tt>
| | Neutral Diatonic Dorian
|-
| | <tt>'''4 5 5 4 4 5 4'''</tt>
| | Neutral Diatonic Hypolydian
|-
| | <tt>'''5 5 4 4 5 4 4'''</tt>
| | Neutral Diatonic Hypophrygian
|-
| | <tt>'''5 4 4 5 4 4 5'''</tt>
| | Neutral Diatonic Hypodorian
|-
| | <tt>'''4 5 4 4 5 4 5'''</tt>
| | Neutral Mixolydian
|-
| | <tt>'''5 4 4 5 4 5 4'''</tt>
| | Neutral Lydian
|-
| | <tt>'''4 4 5 4 5 4 5'''</tt>
| | Neutral Phrygian
|-
| | <tt>'''4 5 4 5 4 5 4'''</tt>
| | Neutral Dorian
|-
| | <tt>'''5 4 5 4 5 4 4'''</tt>
| | Neutral Hypolydian
|-
| | <tt>'''4 5 4 5 4 4 5'''</tt>
| | Neutral Hypophrygian
|-
| | <tt>'''5 4 5 4 4 5 4'''</tt>
| | Neutral Hypodorian
|-
| | <tt>'''2 2 9 2 2 9 5'''</tt>
| | Hemiolic Chromatic Mixolydian
|-
| | <tt>'''2 9 2 2 9 5 2'''</tt>
| | Hemiolic Chromatic Lydian
|-
| | <tt>'''9 2 2 9 5 2 2'''</tt>
| | Hemiolic Chromatic Phrygian
|-
| | <tt>'''2 2 9 5 2 2 9'''</tt>
| | Hemiolic Chromatic Dorian
|-
| | <tt>'''2 9 5 2 2 9 2'''</tt>
| | Hemiolic Chromatic Hypolydian
|-
| | <tt>'''9 5 2 2 9 2 2'''</tt>
| | Hemiolic Chromatic Hypophrygian
|-
| | <tt>'''5 2 2 9 2 2 9'''</tt>
| | Hemiolic Chromatic Hypodorian
|-
| | <tt>'''2 3 8 2 3 8 5'''</tt>
| | Ratio 2:3 Chromatic Mixolydian
|-
| | <tt>'''3 8 2 3 8 5 2'''</tt>
| | Ratio 2:3 Chromatic Lydian
|-
| | <tt>'''8 2 3 8 5 2 3'''</tt>
| | Ratio 2:3 Chromatic Phrygian
|-
| | <tt>'''2 3 8 5 2 3 8'''</tt>
| | Ratio 2:3 Chromatic Dorian
|-
| | <tt>'''3 8 5 2 3 8 2'''</tt>
| | Ratio 2:3 Chromatic Hypolydian
|-
| | <tt>'''8 5 2 3 8 2 3'''</tt>
| | Ratio 2:3 Chromatic Hypophrygian
|-
| | <tt>'''5 2 3 8 2 3 8'''</tt>
| | Ratio 2:3 Chromatic Hypodorian
|-
| | <tt>'''3 5 5 3 5 5 5'''</tt>
| | Intense Diatonic Mixolydian, M.Locrian
|-
| | <tt>'''5 3 5 5 5 3 5'''</tt>
| | Intense Diatonic Phrygian, M.Dorian
|-
| | <tt>'''3 5 5 5 3 5 5'''</tt>
| | Intense Diatonic Dorian, M.Phrygian
|-
| | <tt>'''5 5 5 3 5 5 3'''</tt>
| | Intense Diatonic Hypolydian, M.Lydian
|-
| | <tt>'''5 5 3 5 5 3 5'''</tt>
| | Intense Diatonic Hypophrygian, M.Mixolydian
|-
| | <tt>'''2 5 6 2 5 6 5'''</tt>
| | Soft Diatonic Mixolydian
|-
| | <tt>'''5 6 2 5 6 5 2'''</tt>
| | Soft Diatonic Lydian
|-
| | <tt>'''6 2 5 6 5 2 5'''</tt>
| | Soft Diatonic Phrygian
|-
| | <tt>'''2 5 6 5 2 5 6'''</tt>
| | Soft Diatonic Dorian
|-
| | <tt>'''5 6 5 2 5 6 2'''</tt>
| | Soft Diatonic Hypolydian
|-
| | <tt>'''6 5 2 5 6 2 5'''</tt>
| | Soft Diatonic Hypophrygian
|-
| | <tt>'''5 2 5 6 2 5 6'''</tt>
| | Soft Diatonic Hypodorian
|-
| | <tt>'''1 2 10 1 2 10 5'''</tt>
| | Enharmonic Mixolydian
|-
| | <tt>'''2 10 1 2 10 5 1'''</tt>
| | Enharmonic Lydian
|-
| | <tt>'''10 1 2 10 5 1 2'''</tt>
| | Enharmonic Phrygian
|-
| | <tt>'''1 2 10 5 1 2 10'''</tt>
| | Enharmonic Dorian
|-
| | <tt>'''2 10 5 1 2 10 1'''</tt>
| | Enharmonic Hypolydian
|-
| | <tt>'''10 5 1 2 10 1 2'''</tt>
| | Enharmonic Hypophrygian
|-
| | <tt>'''5 1 2 10 1 2 10'''</tt>
| | Enharmonic Hypodorian
|}


=Of particular [[interscalar|interscalar]] interest=


&lt;table class="wiki_table"&gt;
{| class="wikitable"
    &lt;tr&gt;
|-
        &lt;td&gt;&lt;tt&gt;&lt;strong&gt;6 6 7 6 6&lt;/strong&gt;&lt;/tt&gt;&lt;br /&gt;
| | <tt>'''6 6 7 6 6'''</tt>
&lt;/td&gt;
| | Quasi-equal Pentatonic
        &lt;td&gt;Quasi-equal Pentatonic&lt;br /&gt;
|-
&lt;/td&gt;
| | <tt>'''3 3 2 3 3 3 3 3 2 3 3'''</tt>
    &lt;/tr&gt;
| | near [[11edo|11edo]]
    &lt;tr&gt;
|}
        &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;
        &lt;td&gt;near &lt;a class="wiki_link" href="/11edo"&gt;11edo&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
&lt;/table&gt;


&lt;br /&gt;
=Miscellaneous=
&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;
&lt;br /&gt;


{| class="wikitable"
|-
| | <tt>'''3 2 2 3 3 2 3 3 2 2 3 3'''</tt>
| | Fokker 12-tone
|-
| | <tt>'''5 3 5 3 5 2 5 3'''</tt>
| | Modus conjunctus
|-
| | <tt>'''3 5 2 5 3 5 3 5'''</tt>
| | Octatonic
|-
| | <tt>'''3 3 4 3 5 3 4 3 3'''</tt>
| | Hahn symmetric pentachordal
|-
| | <tt>'''3 4 3 3 5 3 4 3 3'''</tt>
| | Hahn pentachordal
|-
| | <tt>'''4 4 2 5 3 3 4 3 3'''</tt>
| | Hahn Nonatonic
|-
| | <tt>'''5 3 3 3 3 5 3 3 3'''</tt>
| | Rothenberg Generalized Diatonic
|-
| | <tt>'''(5) 3 1 4 (5) (5)'''</tt>


&lt;table class="wiki_table"&gt;
<tt>'''3 1 4'''</tt>
    &lt;tr&gt;
| | Michael Sheiman's "Dimension" scale (Maqam Rast mixed with Meantone Diatonic...lattice (ratio/chord map) available below
        &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;
        &lt;td&gt;Fokker 12-tone&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &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;
        &lt;td&gt;Modus conjunctus&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &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;
        &lt;td&gt;Octatonic&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &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;
        &lt;td&gt;Hahn symmetric pentachordal&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 5 3 4 3 3&lt;/strong&gt;&lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Hahn pentachordal&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &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;
        &lt;td&gt;Hahn Nonatonic&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &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;
        &lt;td&gt;Rothenberg Generalized Diatonic&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &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;
&lt;/td&gt;
        &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;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &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;
&lt;tt&gt;&lt;strong&gt;3 1 4&lt;/strong&gt;&lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Michael Sheiman's extended 12 tone &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;
&lt;/td&gt;
    &lt;/tr&gt;
&lt;/table&gt;


&lt;br /&gt;
[[File:dimensionscale.jpg|alt=dimensionscale.jpg|512x197px|dimensionscale.jpg]]
&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;
|-
&lt;br /&gt;
| | <tt>'''(3 2)3 1 4 (3 2)(3 2)'''</tt>


<tt>'''3 1 4'''</tt>
| | 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;
=MOS and Cradle MOS=
    &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>
{| class="wikitable"
|-
| | <tt>'''4 5 4 5 4 5 4'''</tt>
| | Neutral scale 7-note
|-
| | <tt>'''4 1 4 4 1 4 4 4 1 4'''</tt>
| | Neutral scale 10-note
|-
| | <tt>'''4 1 4 4 4 1 4 4 1 4'''</tt>
| | Breed 10-tone
|-
| | <tt>'''4 3 4 3 4 3 4 3 3'''</tt>
| | Orwell[9]
|-
| | <tt>'''5 1 5 1 5 1 5 1 5 1 1'''</tt>
| | de Vries 11-tone
|-
| | <tt>'''3 1 3 1 3 1 3 1 3 1 3 1 3 1 3'''</tt>
| | Pseudo-Porcupine 15-note
|-
| | <tt>'''1 7 1 2 1 7 1 2 1 7 1'''</tt>
| | Nested Bees
|-
| | <tt>'''4 2 4 2 4 2 4 3 3 3'''</tt>
| | Lumma Decatonic
|-
| | <tt>'''2 5 2 2 5 2 2 2 5 2 2'''</tt>
| | Secor/Barton no-fives
|}
[[Category:31edo]]
[[Category:modes]]

Revision as of 00:00, 17 July 2018

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 here.

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 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
5 2 6 5 2 5 6 "Septimal" Natural Minor

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)

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

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

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)

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
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