22edo tetrachords: Difference between revisions

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<h2>IMPORTED REVISION FROM WIKISPACES</h2>
A chart of all possible [[22edo|22edo]] [[tetrachord|tetrachord]]s (28 altogether):
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
 
: This revision was by author [[User:hstraub|hstraub]] and made on <tt>2012-07-17 06:01:39 UTC</tt>.<br>
{| class="wikitable"
: The original revision id was <tt>353479618</tt>.<br>
|-
: The revision comment was: <tt></tt><br>
| | 1-1-7
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
| | 1-2-6
<h4>Original Wikitext content:</h4>
| | 1-3-5
<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">A chart of all possible [[22edo]] [[tetrachord]]s (28 altogether):
| | 1-4-4
|| 1-1-7 || 1-2-6 || 1-3-5 || 1-4-4 || 1-5-3 || 1-6-2 || 1-7-1 ||
| | 1-5-3
|| 2-1-6 || 2-2-5 || 2-3-4 || 2-4-3 || 2-5-2 || 2-6-1 ||   ||
| | 1-6-2
|| 3-1-5 || 3-2-4 || 3-3-3 || 3-4-2 || 3-5-1 ||   ||   ||
| | 1-7-1
|| 4-1-4 || 4-2-3 || 4-3-2 || 4-4-1 ||   ||   ||   ||
|-
|| 5-1-3 || 5-2-2 || 5-3-1 ||   ||   ||   ||   ||
| | 2-1-6
|| 6-1-2 || 6-2-1 ||   ||   ||   ||   ||   ||
| | 2-2-5
|| 7-1-1 ||   ||   ||   ||   ||   ||   ||
| | 2-3-4
| | 2-4-3
| | 2-5-2
| | 2-6-1
| |  
|-
| | 3-1-5
| | 3-2-4
| | 3-3-3
| | 3-4-2
| | 3-5-1
| |  
| |  
|-
| | 4-1-4
| | 4-2-3
| | 4-3-2
| | 4-4-1
| |  
| |  
| |  
|-
| | 5-1-3
| | 5-2-2
| | 5-3-1
| |  
| |  
| |  
| |  
|-
| | 6-1-2
| | 6-2-1
| |  
| |  
| |  
| |  
| |  
|-
| | 7-1-1
| |  
| |  
| |  
| |  
| |  
| |  
|}


Tetrachord details:
Tetrachord details:
||~ tetrachord notation ||~ steps in cents ||~ interval names ||~ [[22edo Solfege|solfege]] ||~ notes ||
 
|| 1-1-7 || 55 + 55 + 382 || P1 d2 m2 P4 || do di ra fa ||   ||
{| class="wikitable"
|| 1-2-6 || 55 + 109 + 327 || P1 d2 N2 P4 || do di ru fa ||   ||
|-
|| 1-3-5 || 55 + 164 + 273 || P1 d2 M2 P4 || do di re fa ||   ||
! | tetrachord notation
|| 1-4-4 || 55 + 218 + 218 || P1 d2 sm3 P4 || do di ma fa || found in Superpyth Phrygian ||
! | steps in cents
|| 1-5-3 || 55 + 273 + 164 || P1 d2 m3 P4 || do di me fa ||   ||
! | interval names
|| 1-6-2 || 55 + 327 + 109 || P1 d2 M3 P4 || do di mi fa ||   ||
! | [[22edo_Solfege|solfege]]
|| 1-7-1 || 55 + 382 + 55 || P1 d2 SM3 P4 || do di mo fa ||   ||
! | notes
|| 2-1-6 || 109 + 55 + 327 || P1 m2 N2 P4 || do ra ru fa ||   ||
|-
|| 2-2-5 || 109 + 109 + 273 || P1 m2 M2 P4 || do ra re fa ||   ||
| | 1-1-7
|| 2-3-4 || 109 + 164 + 218 || P1 m2 sm3 P4 || do ra ma fa ||   ||
| | 55 + 55 + 382
|| 2-4-3 || 109 + 218 +165 || P1 m2 m3 P4 || do ra me fa ||   ||
| | P1 d2 m2 P4
|| 2-5-2 || 109 + 273 + 109 || P1 m2 M3 P4 || do ra mi fa ||   ||
| | do di ra fa
|| 2-6-1 || 109 + 327 + 55 || P1 m2 SM3 P4 || do ra mo fa ||   ||
| |  
|| 3-1-5 || 164 + 55 + 273 || P1 N2 M2 P4 || do ru re fa ||   ||
|-
|| 3-2-4 || 164 + 109 + 218 || P1 N2 sm3 P4 || do ru ma fa ||   ||
| | 1-2-6
|| 3-3-3 || 164 + 164 +164 || P1 N2 m3 P4 || do ru me fa || perfectly even tetrachord, found in [[Porcupine]] temperament ||
| | 55 + 109 + 327
|| 3-4-2 || 164 + 218 + 109 || P1 N2 M3 P4 || do ru mi fa ||   ||
| | P1 d2 N2 P4
|| 3-5-1 || 164 + 273 + 55 || P1 N2 SM3 P4 || do ru mo fa ||   ||
| | do di ru fa
|| 4-1-4 || 218 + 55 + 218 || P1 M2 sm3 P4 || do re ma fa || found in Superpyth Minor (&amp; Dorian) ||
| |  
|| 4-2-3 || 218 + 109 + 164 || P1 M2 m3 P4 || do re me fa ||   ||
|-
|| 4-3-2 || 218 + 164 + 109 || P1 M2 M3 P4 || do re mi fa ||   ||
| | 1-3-5
|| 4-4-1 || 218 + 218 + 55 || P1 M2 SM3 P4 || do re mo fa || found in Superpyth Major (&amp; Mixolydian, &amp; Lydian) ||
| | 55 + 164 + 273
|| 5-1-3 || 273 + 55 + 164 || P1 sm3 m3 P4 || do ma me fa ||   ||
| | P1 d2 M2 P4
|| 5-2-2 || 273 + 109 + 109 || P1 sm3 M3 P4 || do ma mi fa ||   ||
| | do di re fa
|| 5-3-1 || 273 + 164 + 55 || P1 sm3 SM3 P4 || do ma mo fa ||   ||
| |  
|| 6-1-2 || 327 + 55 + 109 || P1 m3 M3 P4 || do me mi fa ||   ||
|-
|| 6-2-1 || 327 + 109 + 55 || P1 m3 SM3 P4 || do me mo fa ||   ||
| | 1-4-4
|| 7-1-1 || 382 + 55 + 55 || P1 M3 SM3 P4 || do mi mo fa ||   ||
| | 55 + 218 + 218
| | P1 d2 sm3 P4
| | do di ma fa
| | found in Superpyth Phrygian
|-
| | 1-5-3
| | 55 + 273 + 164
| | P1 d2 m3 P4
| | do di me fa
| |  
|-
| | 1-6-2
| | 55 + 327 + 109
| | P1 d2 M3 P4
| | do di mi fa
| |  
|-
| | 1-7-1
| | 55 + 382 + 55
| | P1 d2 SM3 P4
| | do di mo fa
| |  
|-
| | 2-1-6
| | 109 + 55 + 327
| | P1 m2 N2 P4
| | do ra ru fa
| |  
|-
| | 2-2-5
| | 109 + 109 + 273
| | P1 m2 M2 P4
| | do ra re fa
| |  
|-
| | 2-3-4
| | 109 + 164 + 218
| | P1 m2 sm3 P4
| | do ra ma fa
| |  
|-
| | 2-4-3
| | 109 + 218 +165
| | P1 m2 m3 P4
| | do ra me fa
| |  
|-
| | 2-5-2
| | 109 + 273 + 109
| | P1 m2 M3 P4
| | do ra mi fa
| |  
|-
| | 2-6-1
| | 109 + 327 + 55
| | P1 m2 SM3 P4
| | do ra mo fa
| |  
|-
| | 3-1-5
| | 164 + 55 + 273
| | P1 N2 M2 P4
| | do ru re fa
| |  
|-
| | 3-2-4
| | 164 + 109 + 218
| | P1 N2 sm3 P4
| | do ru ma fa
| |  
|-
| | 3-3-3
| | 164 + 164 +164
| | P1 N2 m3 P4
| | do ru me fa
| | perfectly even tetrachord, found in [[Porcupine|Porcupine]] temperament
|-
| | 3-4-2
| | 164 + 218 + 109
| | P1 N2 M3 P4
| | do ru mi fa
| |  
|-
| | 3-5-1
| | 164 + 273 + 55
| | P1 N2 SM3 P4
| | do ru mo fa
| |  
|-
| | 4-1-4
| | 218 + 55 + 218
| | P1 M2 sm3 P4
| | do re ma fa
| | found in Superpyth Minor (&amp; Dorian)
|-
| | 4-2-3
| | 218 + 109 + 164
| | P1 M2 m3 P4
| | do re me fa
| |  
|-
| | 4-3-2
| | 218 + 164 + 109
| | P1 M2 M3 P4
| | do re mi fa
| |  
|-
| | 4-4-1
| | 218 + 218 + 55
| | P1 M2 SM3 P4
| | do re mo fa
| | found in Superpyth Major (&amp; Mixolydian, &amp; Lydian)
|-
| | 5-1-3
| | 273 + 55 + 164
| | P1 sm3 m3 P4
| | do ma me fa
| |  
|-
| | 5-2-2
| | 273 + 109 + 109
| | P1 sm3 M3 P4
| | do ma mi fa
| |  
|-
| | 5-3-1
| | 273 + 164 + 55
| | P1 sm3 SM3 P4
| | do ma mo fa
| |  
|-
| | 6-1-2
| | 327 + 55 + 109
| | P1 m3 M3 P4
| | do me mi fa
| |  
|-
| | 6-2-1
| | 327 + 109 + 55
| | P1 m3 SM3 P4
| | do me mo fa
| |  
|-
| | 7-1-1
| | 382 + 55 + 55
| | P1 M3 SM3 P4
| | do mi mo fa
| |  
|}


Tetrachords in families:
Tetrachords in families:
||~ sML ||~ MsL ||~ sLM ||~ MLs ||~ LsM ||~ LMs ||~ genus ||~ name(s) / notes ||
||||= 1-1-7 ||||= 1-7-1 ||||= 7-1-1 || enharmonic || close to Didymos's Enharmonic, 32/31 • 31/30 • 5/4. ||
|| 1-2-6 || 2-1-6 || 1-6-2 || 2-6-1 || 6-1-2 || 6-2-1 || chromatic ||  ||
|| 1-3-5 || 3-1-5 || 1-5-3 || 3-5-1 || 5-1-3 || 5-3-1 || chromatic ||  ||
||||= 2-2-5 ||||= 2-5-2 ||||= 5-2-2 || chromatic ||  ||
|| 2-3-4 || 3-2-4 || 2-4-3 || 3-4-2 || 4-2-3 || 4-3-2 || diatonic || similar in function to JI tetrachord 16/15 • 9/8 • 10/9, but altered ||
||||= 1-1-4 ||||= 1-4-1 ||||= 4-1-1 || diatonic || SuperPyth ||
||||||||||||= 3-3-3 || diatonic || Porcupine ||
See also: [[17edo tetrachords]], [[Tricesimoprimal Tetrachordal Tesseract]].</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;22edo tetrachords&lt;/title&gt;&lt;/head&gt;&lt;body&gt;A chart of all possible &lt;a class="wiki_link" href="/22edo"&gt;22edo&lt;/a&gt; &lt;a class="wiki_link" href="/tetrachord"&gt;tetrachord&lt;/a&gt;s (28 altogether):&lt;br /&gt;
&lt;table class="wiki_table"&gt;
    &lt;tr&gt;
        &lt;td&gt;1-1-7&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1-2-6&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1-3-5&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1-4-4&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1-5-3&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1-6-2&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1-7-1&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;2-1-6&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;2-2-5&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;2-3-4&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;2-4-3&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;2-5-2&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;2-6-1&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;3-1-5&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;3-2-4&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;3-3-3&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;3-4-2&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;3-5-1&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;4-1-4&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;4-2-3&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;4-3-2&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;4-4-1&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;5-1-3&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;5-2-2&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;5-3-1&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;6-1-2&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;6-2-1&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;7-1-1&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
&lt;/table&gt;
&lt;br /&gt;
Tetrachord details:&lt;br /&gt;
&lt;table class="wiki_table"&gt;
    &lt;tr&gt;
        &lt;th&gt;tetrachord notation&lt;br /&gt;
&lt;/th&gt;
        &lt;th&gt;steps in cents&lt;br /&gt;
&lt;/th&gt;
        &lt;th&gt;interval names&lt;br /&gt;
&lt;/th&gt;
        &lt;th&gt;&lt;a class="wiki_link" href="/22edo%20Solfege"&gt;solfege&lt;/a&gt;&lt;br /&gt;
&lt;/th&gt;
        &lt;th&gt;notes&lt;br /&gt;
&lt;/th&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;1-1-7&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;55 + 55 + 382&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;P1 d2 m2 P4&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;do di ra fa&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;1-2-6&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;55 + 109 + 327&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;P1 d2 N2 P4&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;do di ru fa&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;1-3-5&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;55 + 164 + 273&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;P1 d2 M2 P4&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;do di re fa&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;1-4-4&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;55 + 218 + 218&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;P1 d2 sm3 P4&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;do di ma fa&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;found in Superpyth Phrygian&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;1-5-3&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;55 + 273 + 164&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;P1 d2 m3 P4&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;do di me fa&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;1-6-2&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;55 + 327 + 109&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;P1 d2 M3 P4&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;do di mi fa&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;1-7-1&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;55 + 382 + 55&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;P1 d2 SM3 P4&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;do di mo fa&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;2-1-6&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;109 + 55 + 327&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;P1 m2 N2 P4&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;do ra ru fa&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;2-2-5&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;109 + 109 + 273&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;P1 m2 M2 P4&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;do ra re fa&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;2-3-4&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;109 + 164 + 218&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;P1 m2 sm3 P4&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;do ra ma fa&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;2-4-3&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;109 + 218 +165&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;P1 m2 m3 P4&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;do ra me fa&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;2-5-2&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;109 + 273 + 109&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;P1 m2 M3 P4&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;do ra mi fa&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;2-6-1&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;109 + 327 + 55&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;P1 m2 SM3 P4&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;do ra mo fa&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;3-1-5&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;164 + 55 + 273&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;P1 N2 M2 P4&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;do ru re fa&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;3-2-4&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;164 + 109 + 218&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;P1 N2 sm3 P4&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;do ru ma fa&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;3-3-3&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;164 + 164 +164&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;P1 N2 m3 P4&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;do ru me fa&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;perfectly even tetrachord, found in &lt;a class="wiki_link" href="/Porcupine"&gt;Porcupine&lt;/a&gt; temperament&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;3-4-2&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;164 + 218 + 109&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;P1 N2 M3 P4&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;do ru mi fa&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;3-5-1&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;164 + 273 + 55&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;P1 N2 SM3 P4&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;do ru mo fa&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;4-1-4&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;218 + 55 + 218&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;P1 M2 sm3 P4&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;do re ma fa&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;found in Superpyth Minor (&amp;amp; Dorian)&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;4-2-3&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;218 + 109 + 164&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;P1 M2 m3 P4&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;do re me fa&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;4-3-2&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;218 + 164 + 109&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;P1 M2 M3 P4&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;do re mi fa&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;4-4-1&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;218 + 218 + 55&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;P1 M2 SM3 P4&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;do re mo fa&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;found in Superpyth Major (&amp;amp; Mixolydian, &amp;amp; Lydian)&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;5-1-3&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;273 + 55 + 164&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;P1 sm3 m3 P4&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;do ma me fa&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;5-2-2&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;273 + 109 + 109&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;P1 sm3 M3 P4&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;do ma mi fa&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;5-3-1&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;273 + 164 + 55&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;P1 sm3 SM3 P4&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;do ma mo fa&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;6-1-2&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;327 + 55 + 109&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;P1 m3 M3 P4&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;do me mi fa&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;6-2-1&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;327 + 109 + 55&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;P1 m3 SM3 P4&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;do me mo fa&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;7-1-1&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;382 + 55 + 55&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;P1 M3 SM3 P4&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;do mi mo fa&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
&lt;/table&gt;
&lt;br /&gt;
Tetrachords in families:&lt;br /&gt;


&lt;table class="wiki_table"&gt;
{| class="wikitable"
    &lt;tr&gt;
|-
        &lt;th&gt;sML&lt;br /&gt;
! | sML
&lt;/th&gt;
! | MsL
        &lt;th&gt;MsL&lt;br /&gt;
! | sLM
&lt;/th&gt;
! | MLs
        &lt;th&gt;sLM&lt;br /&gt;
! | LsM
&lt;/th&gt;
! | LMs
        &lt;th&gt;MLs&lt;br /&gt;
! | genus
&lt;/th&gt;
! | name(s) / notes
        &lt;th&gt;LsM&lt;br /&gt;
|-
&lt;/th&gt;
| colspan="2" style="text-align:center;" | 1-1-7
        &lt;th&gt;LMs&lt;br /&gt;
| colspan="2" style="text-align:center;" | 1-7-1
&lt;/th&gt;
| colspan="2" style="text-align:center;" | 7-1-1
        &lt;th&gt;genus&lt;br /&gt;
| | enharmonic
&lt;/th&gt;
| | close to Didymos's Enharmonic, 32/31 • 31/30 • 5/4.
        &lt;th&gt;name(s) / notes&lt;br /&gt;
|-
&lt;/th&gt;
| | 1-2-6
    &lt;/tr&gt;
| | 2-1-6
    &lt;tr&gt;
| | 1-6-2
        &lt;td colspan="2" style="text-align: center;"&gt;1-1-7&lt;br /&gt;
| | 2-6-1
&lt;/td&gt;
| | 6-1-2
        &lt;td colspan="2" style="text-align: center;"&gt;1-7-1&lt;br /&gt;
| | 6-2-1
&lt;/td&gt;
| | chromatic
        &lt;td colspan="2" style="text-align: center;"&gt;7-1-1&lt;br /&gt;
| |
&lt;/td&gt;
|-
        &lt;td&gt;enharmonic&lt;br /&gt;
| | 1-3-5
&lt;/td&gt;
| | 3-1-5
        &lt;td&gt;close to Didymos's Enharmonic, 32/31 • 31/30 • 5/4.&lt;br /&gt;
| | 1-5-3
&lt;/td&gt;
| | 3-5-1
    &lt;/tr&gt;
| | 5-1-3
    &lt;tr&gt;
| | 5-3-1
        &lt;td&gt;1-2-6&lt;br /&gt;
| | chromatic
&lt;/td&gt;
| |
        &lt;td&gt;2-1-6&lt;br /&gt;
|-
&lt;/td&gt;
| colspan="2" style="text-align:center;" | 2-2-5
        &lt;td&gt;1-6-2&lt;br /&gt;
| colspan="2" style="text-align:center;" | 2-5-2
&lt;/td&gt;
| colspan="2" style="text-align:center;" | 5-2-2
        &lt;td&gt;2-6-1&lt;br /&gt;
| | chromatic
&lt;/td&gt;
| |
        &lt;td&gt;6-1-2&lt;br /&gt;
|-
&lt;/td&gt;
| | 2-3-4
        &lt;td&gt;6-2-1&lt;br /&gt;
| | 3-2-4
&lt;/td&gt;
| | 2-4-3
        &lt;td&gt;chromatic&lt;br /&gt;
| | 3-4-2
&lt;/td&gt;
| | 4-2-3
        &lt;td&gt;&lt;br /&gt;
| | 4-3-2
&lt;/td&gt;
| | diatonic
    &lt;/tr&gt;
| | similar in function to JI tetrachord 16/15 • 9/8 • 10/9, but altered
    &lt;tr&gt;
|-
        &lt;td&gt;1-3-5&lt;br /&gt;
| colspan="2" style="text-align:center;" | 1-1-4
&lt;/td&gt;
| colspan="2" style="text-align:center;" | 1-4-1
        &lt;td&gt;3-1-5&lt;br /&gt;
| colspan="2" style="text-align:center;" | 4-1-1
&lt;/td&gt;
| | diatonic
        &lt;td&gt;1-5-3&lt;br /&gt;
| | SuperPyth
&lt;/td&gt;
|-
        &lt;td&gt;3-5-1&lt;br /&gt;
| colspan="6" style="text-align:center;" | 3-3-3
&lt;/td&gt;
| | diatonic
        &lt;td&gt;5-1-3&lt;br /&gt;
| | Porcupine
&lt;/td&gt;
|}
        &lt;td&gt;5-3-1&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;chromatic&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td colspan="2" style="text-align: center;"&gt;2-2-5&lt;br /&gt;
&lt;/td&gt;
        &lt;td colspan="2" style="text-align: center;"&gt;2-5-2&lt;br /&gt;
&lt;/td&gt;
        &lt;td colspan="2" style="text-align: center;"&gt;5-2-2&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;chromatic&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;2-3-4&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;3-2-4&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;2-4-3&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;3-4-2&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;4-2-3&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;4-3-2&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;diatonic&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;similar in function to JI tetrachord 16/15 • 9/8 • 10/9, but altered&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td colspan="2" style="text-align: center;"&gt;1-1-4&lt;br /&gt;
&lt;/td&gt;
        &lt;td colspan="2" style="text-align: center;"&gt;1-4-1&lt;br /&gt;
&lt;/td&gt;
        &lt;td colspan="2" style="text-align: center;"&gt;4-1-1&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;diatonic&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;SuperPyth&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td colspan="6" style="text-align: center;"&gt;3-3-3&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;diatonic&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Porcupine&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
&lt;/table&gt;


&lt;br /&gt;
See also: [[17edo_tetrachords|17edo tetrachords]], [[Tricesimoprimal_Tetrachordal_Tesseract|Tricesimoprimal Tetrachordal Tesseract]].
&lt;br /&gt;
[[Category:22edo]]
See also: &lt;a class="wiki_link" href="/17edo%20tetrachords"&gt;17edo tetrachords&lt;/a&gt;, &lt;a class="wiki_link" href="/Tricesimoprimal%20Tetrachordal%20Tesseract"&gt;Tricesimoprimal Tetrachordal Tesseract&lt;/a&gt;.&lt;/body&gt;&lt;/html&gt;</pre></div>
[[Category:chords]]
[[Category:edo]]
[[Category:tetrachord]]

Revision as of 00:00, 17 July 2018

A chart of all possible 22edo tetrachords (28 altogether):

1-1-7 1-2-6 1-3-5 1-4-4 1-5-3 1-6-2 1-7-1
2-1-6 2-2-5 2-3-4 2-4-3 2-5-2 2-6-1
3-1-5 3-2-4 3-3-3 3-4-2 3-5-1
4-1-4 4-2-3 4-3-2 4-4-1
5-1-3 5-2-2 5-3-1
6-1-2 6-2-1
7-1-1

Tetrachord details:

tetrachord notation steps in cents interval names solfege notes
1-1-7 55 + 55 + 382 P1 d2 m2 P4 do di ra fa
1-2-6 55 + 109 + 327 P1 d2 N2 P4 do di ru fa
1-3-5 55 + 164 + 273 P1 d2 M2 P4 do di re fa
1-4-4 55 + 218 + 218 P1 d2 sm3 P4 do di ma fa found in Superpyth Phrygian
1-5-3 55 + 273 + 164 P1 d2 m3 P4 do di me fa
1-6-2 55 + 327 + 109 P1 d2 M3 P4 do di mi fa
1-7-1 55 + 382 + 55 P1 d2 SM3 P4 do di mo fa
2-1-6 109 + 55 + 327 P1 m2 N2 P4 do ra ru fa
2-2-5 109 + 109 + 273 P1 m2 M2 P4 do ra re fa
2-3-4 109 + 164 + 218 P1 m2 sm3 P4 do ra ma fa
2-4-3 109 + 218 +165 P1 m2 m3 P4 do ra me fa
2-5-2 109 + 273 + 109 P1 m2 M3 P4 do ra mi fa
2-6-1 109 + 327 + 55 P1 m2 SM3 P4 do ra mo fa
3-1-5 164 + 55 + 273 P1 N2 M2 P4 do ru re fa
3-2-4 164 + 109 + 218 P1 N2 sm3 P4 do ru ma fa
3-3-3 164 + 164 +164 P1 N2 m3 P4 do ru me fa perfectly even tetrachord, found in Porcupine temperament
3-4-2 164 + 218 + 109 P1 N2 M3 P4 do ru mi fa
3-5-1 164 + 273 + 55 P1 N2 SM3 P4 do ru mo fa
4-1-4 218 + 55 + 218 P1 M2 sm3 P4 do re ma fa found in Superpyth Minor (& Dorian)
4-2-3 218 + 109 + 164 P1 M2 m3 P4 do re me fa
4-3-2 218 + 164 + 109 P1 M2 M3 P4 do re mi fa
4-4-1 218 + 218 + 55 P1 M2 SM3 P4 do re mo fa found in Superpyth Major (& Mixolydian, & Lydian)
5-1-3 273 + 55 + 164 P1 sm3 m3 P4 do ma me fa
5-2-2 273 + 109 + 109 P1 sm3 M3 P4 do ma mi fa
5-3-1 273 + 164 + 55 P1 sm3 SM3 P4 do ma mo fa
6-1-2 327 + 55 + 109 P1 m3 M3 P4 do me mi fa
6-2-1 327 + 109 + 55 P1 m3 SM3 P4 do me mo fa
7-1-1 382 + 55 + 55 P1 M3 SM3 P4 do mi mo fa

Tetrachords in families:

sML MsL sLM MLs LsM LMs genus name(s) / notes
1-1-7 1-7-1 7-1-1 enharmonic close to Didymos's Enharmonic, 32/31 • 31/30 • 5/4.
1-2-6 2-1-6 1-6-2 2-6-1 6-1-2 6-2-1 chromatic
1-3-5 3-1-5 1-5-3 3-5-1 5-1-3 5-3-1 chromatic
2-2-5 2-5-2 5-2-2 chromatic
2-3-4 3-2-4 2-4-3 3-4-2 4-2-3 4-3-2 diatonic similar in function to JI tetrachord 16/15 • 9/8 • 10/9, but altered
1-1-4 1-4-1 4-1-1 diatonic SuperPyth
3-3-3 diatonic Porcupine

See also: 17edo tetrachords, Tricesimoprimal Tetrachordal Tesseract.

Retrieved from "https://en.xen.wiki/index.php?title=22edo_tetrachords&oldid=462"