22edo tetrachords

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This revision was by author guest and made on 2009-09-02 01:35:14 UTC.
The original revision id was 86746159.
The revision comment was:

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Original Wikitext content:

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 || [[22edo Solfege|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 || <span style="-webkit-border-horizontal-spacing: 2px; -webkit-border-vertical-spacing: 2px; border-collapse: collapse;"> </span> ||

Tetrachords in families:
||= sML || MsL || sLM || MLs || LsM || LMs || genus || name(s) / notes ||
||||= 1-1-7 ||||= 1-7-1 ||||= 7-1-1 || enharmonic ||   ||
|| 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 ||

Original HTML content:

<html><head><title>22edo tetrachords</title></head><body>Chart of all possible <a class="wiki_link" href="/22edo">22edo</a> tetrachords (28 altogether):<br />


<table class="wiki_table">
    <tr>
        <td>1-1-7<br />
</td>
        <td>1-2-6<br />
</td>
        <td>1-3-5<br />
</td>
        <td>1-4-4<br />
</td>
        <td>1-5-3<br />
</td>
        <td>1-6-2<br />
</td>
        <td>1-7-1<br />
</td>
    </tr>
    <tr>
        <td>2-1-6<br />
</td>
        <td>2-2-5<br />
</td>
        <td>2-3-4<br />
</td>
        <td>2-4-3<br />
</td>
        <td>2-5-2<br />
</td>
        <td>2-6-1<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>3-1-5<br />
</td>
        <td>3-2-4<br />
</td>
        <td>3-3-3<br />
</td>
        <td>3-4-2<br />
</td>
        <td>3-5-1<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>4-1-4<br />
</td>
        <td>4-2-3<br />
</td>
        <td>4-3-2<br />
</td>
        <td>4-4-1<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>5-1-3<br />
</td>
        <td>5-2-2<br />
</td>
        <td>5-3-1<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>6-1-2<br />
</td>
        <td>6-2-1<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>7-1-1<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
    </tr>
</table>

<br />
Tetrachord details:<br />


<table class="wiki_table">
    <tr>
        <td>tetrachord notation<br />
</td>
        <td>steps in cents<br />
</td>
        <td>interval names<br />
</td>
        <td><a class="wiki_link" href="/22edo%20Solfege">solfege</a><br />
</td>
        <td>notes<br />
</td>
    </tr>
    <tr>
        <td>1-1-7<br />
</td>
        <td>55 + 55 + 382<br />
</td>
        <td>P1 d2 m2 P4<br />
</td>
        <td>do di ra fa<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>1-2-6<br />
</td>
        <td>55 + 109 + 327<br />
</td>
        <td>P1 d2 N2 P4<br />
</td>
        <td>do di ru fa<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>1-3-5<br />
</td>
        <td>55 + 164 + 273<br />
</td>
        <td>P1 d2 M2 P4<br />
</td>
        <td>do di re fa<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>1-4-4<br />
</td>
        <td>55 + 218 + 218<br />
</td>
        <td>P1 d2 sm3 P4<br />
</td>
        <td>do di ma fa<br />
</td>
        <td>found in Superpyth Phrygian<br />
</td>
    </tr>
    <tr>
        <td>1-5-3<br />
</td>
        <td>55 + 273 + 164<br />
</td>
        <td>P1 d2 m3 P4<br />
</td>
        <td>do di me fa<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>1-6-2<br />
</td>
        <td>55 + 327 + 109<br />
</td>
        <td>P1 d2 M3 P4<br />
</td>
        <td>do di mi fa<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>1-7-1<br />
</td>
        <td>55 + 382 + 55<br />
</td>
        <td>P1 d2 SM3 P4<br />
</td>
        <td>do di mo fa<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>2-1-6<br />
</td>
        <td>109 + 55 + 327<br />
</td>
        <td>P1 m2 N2 P4<br />
</td>
        <td>do ra ru fa<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>2-2-5<br />
</td>
        <td>109 + 109 + 273<br />
</td>
        <td>P1 m2 M2 P4<br />
</td>
        <td>do ra re fa<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>2-3-4<br />
</td>
        <td>109 + 164 + 218<br />
</td>
        <td>P1 m2 sm3 P4<br />
</td>
        <td>do ra ma fa<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>2-4-3<br />
</td>
        <td>109 + 218 +165<br />
</td>
        <td>P1 m2 m3 P4<br />
</td>
        <td>do ra me fa<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>2-5-2<br />
</td>
        <td>109 + 273 + 109<br />
</td>
        <td>P1 m2 M3 P4<br />
</td>
        <td>do ra mi fa<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>2-6-1<br />
</td>
        <td>109 + 327 + 55<br />
</td>
        <td>P1 m2 SM3 P4<br />
</td>
        <td>do ra mo fa<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>3-1-5<br />
</td>
        <td>164 + 55 + 273<br />
</td>
        <td>P1 N2 M2 P4<br />
</td>
        <td>do ru re fa<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>3-2-4<br />
</td>
        <td>164 + 109 + 218<br />
</td>
        <td>P1 N2 sm3 P4<br />
</td>
        <td>do ru ma fa<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>3-3-3<br />
</td>
        <td>164 + 164 +164<br />
</td>
        <td>P1 N2 m3 P4<br />
</td>
        <td>do ru me fa<br />
</td>
        <td>perfectly even tetrachord, found in Porcupine temperament<br />
</td>
    </tr>
    <tr>
        <td>3-4-2<br />
</td>
        <td>164 + 218 + 109<br />
</td>
        <td>P1 N2 M3 P4<br />
</td>
        <td>do ru mi fa<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>3-5-1<br />
</td>
        <td>164 + 273 + 55<br />
</td>
        <td>P1 N2 SM3 P4<br />
</td>
        <td>do ru mo fa<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>4-1-4<br />
</td>
        <td>218 + 55 + 218<br />
</td>
        <td>P1 M2 sm3 P4<br />
</td>
        <td>do re ma fa<br />
</td>
        <td>found in Superpyth Minor (&amp; Dorian)<br />
</td>
    </tr>
    <tr>
        <td>4-2-3<br />
</td>
        <td>218 + 109 + 164<br />
</td>
        <td>P1 M2 m3 P4<br />
</td>
        <td>do re me fa<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>4-3-2<br />
</td>
        <td>218 + 164 + 109<br />
</td>
        <td>P1 M2 M3 P4<br />
</td>
        <td>do re mi fa<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>4-4-1<br />
</td>
        <td>218 + 218 + 55<br />
</td>
        <td>P1 M2 SM3 P4<br />
</td>
        <td>do re mo fa<br />
</td>
        <td>found in Superpyth Major (&amp; Mixolydian, &amp; Lydian)<br />
</td>
    </tr>
    <tr>
        <td>5-1-3<br />
</td>
        <td>273 + 55 + 164<br />
</td>
        <td>P1 sm3 m3 P4<br />
</td>
        <td>do ma me fa<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>5-2-2<br />
</td>
        <td>273 + 109 + 109<br />
</td>
        <td>P1 sm3 M3 P4<br />
</td>
        <td>do ma mi fa<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>5-3-1<br />
</td>
        <td>273 + 164 + 55<br />
</td>
        <td>P1 sm3 SM3 P4<br />
</td>
        <td>do ma mo fa<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>6-1-2<br />
</td>
        <td>327 + 55 + 109<br />
</td>
        <td>P1 m3 M3 P4<br />
</td>
        <td>do me mi fa<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>6-2-1<br />
</td>
        <td>327 + 109 + 55<br />
</td>
        <td>P1 m3 SM3 P4<br />
</td>
        <td>do me mo fa<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>7-1-1<br />
</td>
        <td>382 + 55 + 55<br />
</td>
        <td>P1 M3 SM3 P4<br />
</td>
        <td>do mi mo fa<br />
</td>
        <td><span style="-webkit-border-horizontal-spacing: 2px; -webkit-border-vertical-spacing: 2px; border-collapse: collapse;"> </span><br />
</td>
    </tr>
</table>

<br />
Tetrachords in families:<br />


<table class="wiki_table">
    <tr>
        <td style="text-align: center;">sML<br />
</td>
        <td>MsL<br />
</td>
        <td>sLM<br />
</td>
        <td>MLs<br />
</td>
        <td>LsM<br />
</td>
        <td>LMs<br />
</td>
        <td>genus<br />
</td>
        <td>name(s) / notes<br />
</td>
    </tr>
    <tr>
        <td colspan="2" style="text-align: center;">1-1-7<br />
</td>
        <td colspan="2" style="text-align: center;">1-7-1<br />
</td>
        <td colspan="2" style="text-align: center;">7-1-1<br />
</td>
        <td>enharmonic<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>1-2-6<br />
</td>
        <td>2-1-6<br />
</td>
        <td>1-6-2<br />
</td>
        <td>2-6-1<br />
</td>
        <td>6-1-2<br />
</td>
        <td>6-2-1<br />
</td>
        <td>chromatic<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>1-3-5<br />
</td>
        <td>3-1-5<br />
</td>
        <td>1-5-3<br />
</td>
        <td>3-5-1<br />
</td>
        <td>5-1-3<br />
</td>
        <td>5-3-1<br />
</td>
        <td>chromatic<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td colspan="2" style="text-align: center;">2-2-5<br />
</td>
        <td colspan="2" style="text-align: center;">2-5-2<br />
</td>
        <td colspan="2" style="text-align: center;">5-2-2<br />
</td>
        <td>chromatic<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>2-3-4<br />
</td>
        <td>3-2-4<br />
</td>
        <td>2-4-3<br />
</td>
        <td>3-4-2<br />
</td>
        <td>4-2-3<br />
</td>
        <td>4-3-2<br />
</td>
        <td>diatonic<br />
</td>
        <td>similar in function to JI tetrachord 16/15 • 9/8 • 10/9, but altered<br />
</td>
    </tr>
    <tr>
        <td colspan="2" style="text-align: center;">1-1-4<br />
</td>
        <td colspan="2" style="text-align: center;">1-4-1<br />
</td>
        <td colspan="2" style="text-align: center;">4-1-1<br />
</td>
        <td>diatonic<br />
</td>
        <td>SuperPyth<br />
</td>
    </tr>
    <tr>
        <td colspan="6" style="text-align: center;">3-3-3<br />
</td>
        <td>diatonic<br />
</td>
        <td>Porcupine<br />
</td>
    </tr>
</table>

</body></html>
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