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:Andrew_Heathwaite|Andrew_Heathwaite]] and made on <tt>2009-04-30 01:47:46 UTC</tt>.<br>
: The original revision id was <tt>70556337</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">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 ||  ||  ||  ||  ||  ||  ||


Tetrachords with interval names. Primary tetrachords in bold - tetrachords containing exactly one second and one third (16 altogether):
{| class="wikitable"
|| tetrachord notation || interval names ||
|-
|| 1-1-7 || P1 d2 m2 P4 ||
| | 1-1-7
|| 1-2-6 || P1 d2 N2 P4 ||
| | 1-2-6
|| 1-3-5 || P1 d2 M2 P4 ||
| | 1-3-5
|| **1-4-4** || **P1 d2 sm3 P4** ||
| | 1-4-4
|| **1-5-3** || **P1 d2 m3 P4** ||
| | 1-5-3
|| **1-6-2** || **P1 d2 M3 P4** ||
| | 1-6-2
|| **1-7-1** || **P1 d2 SM3 P4** ||
| | 1-7-1
|| 2-1-6 || P1 m2 N2 P4 ||
|-
|| 2-2-5 || P1 m2 M2 P4 ||
| | 2-1-6
|| **2-3-4** || **P1 m2 sm3 P4** ||
| | 2-2-5
|| **2-4-3** || **P1 m2 m3 P4** ||
| | 2-3-4
|| **2-5-2** || **P1 m2 M3 P4** ||
| | 2-4-3
|| **2-6-1** || **P1 m2 SM3 P4** ||
| | 2-5-2
|| 3-1-5 || P1 N2 M2 P4 ||
| | 2-6-1
|| **3-2-4** || **P1 N2 sm3 P4** ||
| |  
|| **3-3-3** || **P1 N2 m3 P4** ||
|-
|| **3-4-2** || **P1 N2 M3 P4** ||
| | 3-1-5
|| **3-5-1** || **P1 N2 SM3 P4** ||
| | 3-2-4
|| **4-1-4** || **P1 M2 sm3 P4** ||
| | 3-3-3
|| **4-2-3** || **P1 M2 m3 P4** ||
| | 3-4-2
|| **4-3-2** || **P1 M2 M3 P4** ||
| | 3-5-1
|| **4-4-1** || **P1 M2 SM3 P4** ||
| |  
|| 5-1-3 || P1 sm3 m3 P4 ||
| |  
|| 5-2-2 || P1 sm3 M3 P4 ||
|-
|| 5-3-1 || P1 sm3 SM3 P4 ||
| | 4-1-4
|| 6-1-2 || P1 m3 M3 P4 ||
| | 4-2-3
|| 6-2-1 || P1 m3 SM3 P4 ||
| | 4-3-2
|| 7-1-1 || P1 M3 SM3 P4 ||</pre></div>
| | 4-4-1
<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;Chart of all possible &lt;a class="wiki_link" href="/22edo"&gt;22edo&lt;/a&gt; tetrachords (28 altogether):&lt;br /&gt;
| |  
| |
|-
| | 5-1-3
| | 5-2-2
| | 5-3-1
| |
| |
| |  
| |  
|-
| | 6-1-2
| | 6-2-1
| |  
| |  
| |
| |
| |
|-
| | 7-1-1
| |  
| |  
| |
| |
| |
| |
|}


Tetrachord details:


&lt;table class="wiki_table"&gt;
{| class="wikitable"
    &lt;tr&gt;
|-
        &lt;td&gt;1-1-7&lt;br /&gt;
! | tetrachord notation
&lt;/td&gt;
! | steps in cents
        &lt;td&gt;1-2-6&lt;br /&gt;
! | interval names
&lt;/td&gt;
! | [[22edo_Solfege|solfege]]
        &lt;td&gt;1-3-5&lt;br /&gt;
! | notes
&lt;/td&gt;
|-
        &lt;td&gt;1-4-4&lt;br /&gt;
| | 1-1-7
&lt;/td&gt;
| | 55 + 55 + 382
        &lt;td&gt;1-5-3&lt;br /&gt;
| | P1 d2 m2 P4
&lt;/td&gt;
| | do di ra fa
        &lt;td&gt;1-6-2&lt;br /&gt;
| |
&lt;/td&gt;
|-
        &lt;td&gt;1-7-1&lt;br /&gt;
| | 1-2-6
&lt;/td&gt;
| | 55 + 109 + 327
    &lt;/tr&gt;
| | P1 d2 N2 P4
    &lt;tr&gt;
| | do di ru fa
        &lt;td&gt;2-1-6&lt;br /&gt;
| |
&lt;/td&gt;
|-
        &lt;td&gt;2-2-5&lt;br /&gt;
| | 1-3-5
&lt;/td&gt;
| | 55 + 164 + 273
        &lt;td&gt;2-3-4&lt;br /&gt;
| | P1 d2 M2 P4
&lt;/td&gt;
| | do di re fa
        &lt;td&gt;2-4-3&lt;br /&gt;
| |
&lt;/td&gt;
|-
        &lt;td&gt;2-5-2&lt;br /&gt;
| | 1-4-4
&lt;/td&gt;
| | 55 + 218 + 218
        &lt;td&gt;2-6-1&lt;br /&gt;
| | P1 d2 sm3 P4
&lt;/td&gt;
| | do di ma fa
        &lt;td&gt;&lt;br /&gt;
| | found in Superpyth Phrygian
&lt;/td&gt;
|-
    &lt;/tr&gt;
| | 1-5-3
    &lt;tr&gt;
| | 55 + 273 + 164
        &lt;td&gt;3-1-5&lt;br /&gt;
| | P1 d2 m3 P4
&lt;/td&gt;
| | do di me fa
        &lt;td&gt;3-2-4&lt;br /&gt;
| |
&lt;/td&gt;
|-
        &lt;td&gt;3-3-3&lt;br /&gt;
| | 1-6-2
&lt;/td&gt;
| | 55 + 327 + 109
        &lt;td&gt;3-4-2&lt;br /&gt;
| | P1 d2 M3 P4
&lt;/td&gt;
| | do di mi fa
        &lt;td&gt;3-5-1&lt;br /&gt;
| |
&lt;/td&gt;
|-
        &lt;td&gt;&lt;br /&gt;
| | 1-7-1
&lt;/td&gt;
| | 55 + 382 + 55
        &lt;td&gt;&lt;br /&gt;
| | P1 d2 SM3 P4
&lt;/td&gt;
| | do di mo fa
    &lt;/tr&gt;
| |
    &lt;tr&gt;
|-
        &lt;td&gt;4-1-4&lt;br /&gt;
| | 2-1-6
&lt;/td&gt;
| | 109 + 55 + 327
        &lt;td&gt;4-2-3&lt;br /&gt;
| | P1 m2 N2 P4
&lt;/td&gt;
| | do ra ru fa
        &lt;td&gt;4-3-2&lt;br /&gt;
| |
&lt;/td&gt;
|-
        &lt;td&gt;4-4-1&lt;br /&gt;
| | 2-2-5
&lt;/td&gt;
| | 109 + 109 + 273
        &lt;td&gt;&lt;br /&gt;
| | P1 m2 M2 P4
&lt;/td&gt;
| | do ra re fa
        &lt;td&gt;&lt;br /&gt;
| |
&lt;/td&gt;
|-
        &lt;td&gt;&lt;br /&gt;
| | 2-3-4
&lt;/td&gt;
| | 109 + 164 + 218
    &lt;/tr&gt;
| | P1 m2 sm3 P4
    &lt;tr&gt;
| | do ra ma fa
        &lt;td&gt;5-1-3&lt;br /&gt;
| |
&lt;/td&gt;
|-
        &lt;td&gt;5-2-2&lt;br /&gt;
| | 2-4-3
&lt;/td&gt;
| | 109 + 218 +165
        &lt;td&gt;5-3-1&lt;br /&gt;
| | P1 m2 m3 P4
&lt;/td&gt;
| | do ra me fa
        &lt;td&gt;&lt;br /&gt;
| |
&lt;/td&gt;
|-
        &lt;td&gt;&lt;br /&gt;
| | 2-5-2
&lt;/td&gt;
| | 109 + 273 + 109
        &lt;td&gt;&lt;br /&gt;
| | P1 m2 M3 P4
&lt;/td&gt;
| | do ra mi fa
        &lt;td&gt;&lt;br /&gt;
| |
&lt;/td&gt;
|-
    &lt;/tr&gt;
| | 2-6-1
    &lt;tr&gt;
| | 109 + 327 + 55
        &lt;td&gt;6-1-2&lt;br /&gt;
| | P1 m2 SM3 P4
&lt;/td&gt;
| | do ra mo fa
        &lt;td&gt;6-2-1&lt;br /&gt;
| |
&lt;/td&gt;
|-
        &lt;td&gt;&lt;br /&gt;
| | 3-1-5
&lt;/td&gt;
| | 164 + 55 + 273
        &lt;td&gt;&lt;br /&gt;
| | P1 N2 M2 P4
&lt;/td&gt;
| | do ru re fa
        &lt;td&gt;&lt;br /&gt;
| |
&lt;/td&gt;
|-
        &lt;td&gt;&lt;br /&gt;
| | 3-2-4
&lt;/td&gt;
| | 164 + 109 + 218
        &lt;td&gt;&lt;br /&gt;
| | P1 N2 sm3 P4
&lt;/td&gt;
| | do ru ma fa
    &lt;/tr&gt;
| |
    &lt;tr&gt;
|-
        &lt;td&gt;7-1-1&lt;br /&gt;
| | 3-3-3
&lt;/td&gt;
| | 164 + 164 +164
        &lt;td&gt;&lt;br /&gt;
| | P1 N2 m3 P4
&lt;/td&gt;
| | do ru me fa
        &lt;td&gt;&lt;br /&gt;
| | perfectly even tetrachord, found in [[Porcupine|Porcupine]] temperament
&lt;/td&gt;
|-
        &lt;td&gt;&lt;br /&gt;
| | 3-4-2
&lt;/td&gt;
| | 164 + 218 + 109
        &lt;td&gt;&lt;br /&gt;
| | P1 N2 M3 P4
&lt;/td&gt;
| | do ru mi fa
        &lt;td&gt;&lt;br /&gt;
| |
&lt;/td&gt;
|-
        &lt;td&gt;&lt;br /&gt;
| | 3-5-1
&lt;/td&gt;
| | 164 + 273 + 55
    &lt;/tr&gt;
| | P1 N2 SM3 P4
&lt;/table&gt;
| | 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
| |
|}


&lt;br /&gt;
Tetrachords in families:
Tetrachords with interval names. Primary tetrachords in bold - tetrachords containing exactly one second and one third (16 altogether):&lt;br /&gt;


{| class="wikitable"
|-
! | sML
! | MsL
! | sLM
! | MLs
! | LsM
! | LMs
! | genus
! | name(s) / notes
|-
| colspan="2" style="text-align:center;" | 1-1-7
| colspan="2" style="text-align:center;" | 1-7-1
| colspan="2" style="text-align:center;" | 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
| |
|-
| colspan="2" style="text-align:center;" | 2-2-5
| colspan="2" style="text-align:center;" | 2-5-2
| colspan="2" style="text-align:center;" | 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
|-
| colspan="2" style="text-align:center;" | 1-1-4
| colspan="2" style="text-align:center;" | 1-4-1
| colspan="2" style="text-align:center;" | 4-1-1
| | diatonic
| | SuperPyth
|-
| colspan="6" style="text-align:center;" | 3-3-3
| | diatonic
| | Porcupine
|}


&lt;table class="wiki_table"&gt;
See also: [[17edo_tetrachords|17edo tetrachords]], [[Tricesimoprimal_Tetrachordal_Tesseract|Tricesimoprimal Tetrachordal Tesseract]].
    &lt;tr&gt;
[[Category:22edo]]
        &lt;td&gt;tetrachord notation&lt;br /&gt;
[[Category:Tetrachords]]
&lt;/td&gt;
        &lt;td&gt;interval names&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;1-1-7&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;P1 d2 m2 P4&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;P1 d2 N2 P4&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;P1 d2 M2 P4&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;strong&gt;1-4-4&lt;/strong&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;strong&gt;P1 d2 sm3 P4&lt;/strong&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;strong&gt;1-5-3&lt;/strong&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;strong&gt;P1 d2 m3 P4&lt;/strong&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;strong&gt;1-6-2&lt;/strong&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;strong&gt;P1 d2 M3 P4&lt;/strong&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;strong&gt;1-7-1&lt;/strong&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;strong&gt;P1 d2 SM3 P4&lt;/strong&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;P1 m2 N2 P4&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;P1 m2 M2 P4&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;strong&gt;2-3-4&lt;/strong&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;strong&gt;P1 m2 sm3 P4&lt;/strong&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;strong&gt;2-4-3&lt;/strong&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;strong&gt;P1 m2 m3 P4&lt;/strong&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;strong&gt;2-5-2&lt;/strong&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;strong&gt;P1 m2 M3 P4&lt;/strong&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;strong&gt;2-6-1&lt;/strong&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;strong&gt;P1 m2 SM3 P4&lt;/strong&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;P1 N2 M2 P4&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;strong&gt;3-2-4&lt;/strong&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;strong&gt;P1 N2 sm3 P4&lt;/strong&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;strong&gt;3-3-3&lt;/strong&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;strong&gt;P1 N2 m3 P4&lt;/strong&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;strong&gt;3-4-2&lt;/strong&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;strong&gt;P1 N2 M3 P4&lt;/strong&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;strong&gt;3-5-1&lt;/strong&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;strong&gt;P1 N2 SM3 P4&lt;/strong&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;strong&gt;4-1-4&lt;/strong&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;strong&gt;P1 M2 sm3 P4&lt;/strong&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;strong&gt;4-2-3&lt;/strong&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;strong&gt;P1 M2 m3 P4&lt;/strong&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;strong&gt;4-3-2&lt;/strong&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;strong&gt;P1 M2 M3 P4&lt;/strong&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;strong&gt;4-4-1&lt;/strong&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;strong&gt;P1 M2 SM3 P4&lt;/strong&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;P1 sm3 m3 P4&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;P1 sm3 M3 P4&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;P1 sm3 SM3 P4&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;P1 m3 M3 P4&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;P1 m3 SM3 P4&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;P1 M3 SM3 P4&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
&lt;/table&gt;
 
&lt;/body&gt;&lt;/html&gt;</pre></div>

Latest revision as of 17:12, 8 June 2022

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.

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