6L 7s: Difference between revisions

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<h2>IMPORTED REVISION FROM WIKISPACES</h2>
{{Infobox MOS}}
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
{{MOS intro}}
: This revision was by author [[User:JosephRuhf|JosephRuhf]] and made on <tt>2015-02-12 12:57:56 UTC</tt>.<br>
: The original revision id was <tt>540779172</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">This MOS is the chromatic scale of a family of temperaments which are index 2 subtemperaments of various meantone temperaments. It is a great early step into un-syntonic temperaments by virtue of this property, though admittedly Neutral thirds/Mohajira is greater in this respect if you don't mind essentially giving up major and minor seconds/sevenths and thirds/sixths (syntonic temperaments are index 2 subtemperaments of them) because it at least has an albitonic sized MOS which feels like a division of the octave, which cannot be said for the temperaments which this scale belongs to (Happy and Grumpy scales have a very strong period dysphoric feeling due to the common practice use of the equally divided chromatic scale, and Grumpy scales have it stronger because their small step is the the odd step out).
||||||~ Generator ||~ cents ||~ 3g ||~ 5g ||
|| 2/13 ||  ||  || 184 8/13 || 553 11/13 || 923 1/13 ||
|| 9/58 ||  ||  || 186 6/29 || 558 18/29 || 931 1/29 ||
||  || 16/103 ||  || 186 42/103 || 559 23/103 || 932 7/103 ||
|| 7/45 ||  ||  || 186 2/3 || 560 || 933 1/3 ||
||  || 19/122 ||  || 186 54/61 || 560 20/61 || 934 26/61 ||
||  || 12/77 ||  || 187 1/77 || 561 3/77 || 935 5/77 ||
||  || 17/109 ||  || 187 17/109 || 561 51/109 || 935 85/109 ||
||  || 22/141 ||  || 187 11/47 || 561 33/47 || 936 8/47 ||
|| 5/32 ||  ||  || 187.5 || 562.5 || 937.5 ||
||  || 23/147 ||  || 187 37/49 || 563 13/49 || 938 38/49 ||
||  || 18/115 ||  || 187 19/23 || 563 11/23 || 939 3/23 ||
||  || 13/83 ||  || 188 6/83 || 564 18/83 || 940 30/83 ||
||  || 8/51 ||  || 188 4/17 || 564 12/17 || 941 3/17 ||
||  || 11/70 ||  || 188 4/7 || 565 5/7 || 942 6/7 ||
||  || 14/89 ||  || 188 68/89 || 566 26/89 || 943 73/89 ||
||  || 17/108 ||  || 188 8/9 || 566 2/3 || 944 4/9 ||
||  || 20/127 ||  || 188 124/127 || 566 118/127 || 944 112/127 ||
||  || 23/146 ||  || 189 3/73 || 567 9/73 || 945 15/73 ||
||  || 26/165 ||  || 189 1/11 || 567 3/11 || 945 5/11 ||
||  || 29/184 ||  || 189 3/23 || 567 9/23 || 945 15/23 ||
||  || 32/203 ||  || 189 33/203 || 567 99/203 || 945 165/203 ||
||  || 35/222 ||  || 189 7/37 || 567 21/37 || 945 35/37 ||
||  || 38/241 ||  || 189 51/241 || 567 153/241 || 946 9/241 ||
|| 3/19 ||  ||  || 189 9/19 || 568 8/19 || 947 7/19 ||
||  || 31/196 ||  || 189 39/49 || 568 19/49 || 948 48/49 ||
||  || 28/177 ||  || 189 49/59 || 568 29/59 || 949 9/59 ||
||  || 25/158 ||  || 189 69/79 || 568 49/79 || 949 19/49 ||
||  || 22/139 ||  || 189 129/130 || 569 109/139 || 949 89/139 ||
||  || 19/120 ||  || 190 || 570 || 950 ||
||  || 16/101 ||  || 190 10/101 || 570 30/101 || 950 50/101 ||
||  || 13/82 ||  || 190 10/41 || 570 30/41 || 951 9/41 ||
||  || 10/63 ||  || 190 10/21 || 571 3/7 || 952 8/21 ||
||  ||  || 17/107 || 190 70/107 || 571 103/107 || 953 29/107 ||
||  || 7/44 ||  || 190 10/11 || 572 8/11 || 954 6/11 ||
||  ||  || 18/113 || 191 17/113 || 573 51/113 || 955 85/113 ||
||  || 11/69 ||  || 191 7/23 || 573 21/23 || 956 12/23 ||
||  || 15/94 ||  || 191 23/47 || 574 22/47 || 957 21/47 ||
||  || 19/119 ||  || 191 71/119 || 574 94/119 || 957 117/119 ||
||  || 23/144 ||  || 191 2/3 || 575 || 958 1/3 ||
||  || 27/169 ||  || 191 121/169 || 575 25/169 || 958 98/169 ||
||  || 31/194 ||  || 191 73/97 || 575 25/97 || 959 49/97 ||
||  ||  ||  || 191.946658 || 575.839975 || 959.733291 ||
|| 4/25 ||  ||  || 192 || 576 || 960 ||
||  ||  ||  || 192.053125 || 576.159376 || 960.2656265 ||
||  || 21/131 ||  || 192 48/131 || 577 13/131 || 961 109/131 ||
||  || 17/106 ||  || 192 24/53 || 577 19/53 || 962 19/53 ||
||  || 13/81 ||  || 192 16/27 || 577 7/9 || 962 26/27 ||
||  ||  || 22/137 || 192 96/137 || 578 14/137 || 963 69/137 ||
||  || 9/56 ||  || 192 6/7 || 578 3/7 || 964 1/7 ||
||  || 14/87 ||  || 193 3/29 || 579 9/29 || 965 15/29 ||
||  || 19/118 ||  || 193 13/59 || 579 39/59 || 966 6/59 ||
|| 5/31 ||  ||  || 193 17/31 || 580 20/31 || 967 23/31 ||
||  || 26/161 ||  || 193 127/161 || 581 59/161 || 968 152/161 ||
||  || 21/130 ||  || 193 11/13 || 581 7/13 || 969 3/13 ||
||  || 16/99 ||  || 193 31/33 || 581 9/11 || 969 23/33 ||
||  || 11/68 ||  || 194 2/17 || 582 6/17 || 970 10/17 ||
||  || 17/105 ||  || 194 2/7 || 582 6/7 || 971 3/7 ||
|| 6/37 ||  ||  || 194 22/37 || 583 29/37 || 972 36/37 ||
|| 1/6 ||  ||  || 200 || 600 || 1000 ||</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;6L 7s&lt;/title&gt;&lt;/head&gt;&lt;body&gt;This MOS is the chromatic scale of a family of temperaments which are index 2 subtemperaments of various meantone temperaments. It is a great early step into un-syntonic temperaments by virtue of this property, though admittedly Neutral thirds/Mohajira is greater in this respect if you don't mind essentially giving up major and minor seconds/sevenths and thirds/sixths (syntonic temperaments are index 2 subtemperaments of them) because it at least has an albitonic sized MOS which feels like a division of the octave, which cannot be said for the temperaments which this scale belongs to (Happy and Grumpy scales have a very strong period dysphoric feeling due to the common practice use of the equally divided chromatic scale, and Grumpy scales have it stronger because their small step is the the odd step out).&lt;br /&gt;


This MOS is the chromatic scale of a family of temperaments which are index-2 subtemperaments (that is, taking every other step of the generator chain) of various [[meantone]] temperaments: that is, those that are generated by a ''mean tone'', that being specifically a whole tone of tunings with a fifth in between that of [[26edo]] and [[12edo]], and roughly speaking between [[10/9]] and [[9/8]].


&lt;table class="wiki_table"&gt;
The most notable temperaments generating this scale are [[didacus]] in the [[2.5.7 subgroup]] and [[Hemimean clan|its extensions]], with its generator identified with ~[[28/25]], whose optimum makes a [[superhard]] tuning, similarly to the situation with [[5L&nbsp;6s]] and [[slendric]].
    &lt;tr&gt;
        &lt;th colspan="3"&gt;Generator&lt;br /&gt;
&lt;/th&gt;
        &lt;th&gt;cents&lt;br /&gt;
&lt;/th&gt;
        &lt;th&gt;3g&lt;br /&gt;
&lt;/th&gt;
        &lt;th&gt;5g&lt;br /&gt;
&lt;/th&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;2/13&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;184 8/13&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;553 11/13&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;923 1/13&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;9/58&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;186 6/29&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;558 18/29&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;931 1/29&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;16/103&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;186 42/103&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;559 23/103&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;932 7/103&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;7/45&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;186 2/3&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;560&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;933 1/3&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;19/122&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;186 54/61&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;560 20/61&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;934 26/61&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;12/77&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;187 1/77&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;561 3/77&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;935 5/77&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;17/109&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;187 17/109&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;561 51/109&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;935 85/109&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;22/141&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;187 11/47&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;561 33/47&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;936 8/47&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;5/32&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;187.5&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;562.5&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;937.5&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;23/147&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;187 37/49&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;563 13/49&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;938 38/49&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;18/115&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;187 19/23&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;563 11/23&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;939 3/23&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;13/83&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;188 6/83&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;564 18/83&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;940 30/83&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;8/51&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;188 4/17&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;564 12/17&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;941 3/17&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;11/70&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;188 4/7&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;565 5/7&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;942 6/7&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;14/89&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;188 68/89&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;566 26/89&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;943 73/89&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;17/108&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;188 8/9&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;566 2/3&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;944 4/9&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;20/127&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;188 124/127&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;566 118/127&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;944 112/127&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;23/146&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;189 3/73&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;567 9/73&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;945 15/73&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;26/165&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;189 1/11&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;567 3/11&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;945 5/11&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;29/184&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;189 3/23&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;567 9/23&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;945 15/23&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;32/203&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;189 33/203&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;567 99/203&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;945 165/203&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;35/222&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;189 7/37&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;567 21/37&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;945 35/37&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;38/241&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;189 51/241&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;567 153/241&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;946 9/241&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;3/19&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;189 9/19&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;568 8/19&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;947 7/19&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;31/196&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;189 39/49&lt;br /&gt;
&lt;/td&gt;
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        &lt;td&gt;571 103/107&lt;br /&gt;
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        &lt;td&gt;190 10/11&lt;br /&gt;
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        &lt;td&gt;572 8/11&lt;br /&gt;
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        &lt;td&gt;573 51/113&lt;br /&gt;
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        &lt;td&gt;11/69&lt;br /&gt;
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        &lt;td&gt;15/94&lt;br /&gt;
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        &lt;td&gt;191 73/97&lt;br /&gt;
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        &lt;td&gt;193 17/31&lt;br /&gt;
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        &lt;td&gt;26/161&lt;br /&gt;
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        &lt;td&gt;582 6/17&lt;br /&gt;
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        &lt;td&gt;200&lt;br /&gt;
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&lt;/table&gt;


&lt;/body&gt;&lt;/html&gt;</pre></div>
== Scale properties ==
{{TAMNAMS use}}
 
=== Intervals ===
{{MOS intervals}}
 
=== Generator chain ===
{{MOS genchain}}
 
=== Modes ===
{{MOS mode degrees}}
 
== Scale tree ==
{{MOS tuning spectrum
| 11/3 = [[Hemithirds]]/[[luna]]
| 4/1 = [[Didacus]]/[[hemiwürschmidt]]
| 5/1 = [[Roulette]]/[[mediantone]]
}}
 
[[Category:Abstract MOS patterns]]

Latest revision as of 14:01, 5 May 2025

↖ 5L 6s ↑ 6L 6s 7L 6s ↗
← 5L 7s 6L 7s 7L 7s →
↙ 5L 8s ↓ 6L 8s 7L 8s ↘
Scale structure
Step pattern LsLsLsLsLsLss
ssLsLsLsLsLsL
Equave 2/1 (1200.0 ¢)
Period 2/1 (1200.0 ¢)
Generator size
Bright 2\13 to 1\6 (184.6 ¢ to 200.0 ¢)
Dark 5\6 to 11\13 (1000.0 ¢ to 1015.4 ¢)
TAMNAMS information
Related to 6L 1s (archaeotonic)
With tunings 2:1 to 1:0 (hard-of-basic)
Related MOS scales
Parent 6L 1s
Sister 7L 6s
Daughters 13L 6s, 6L 13s
Neutralized 12L 1s
2-Flought 19L 7s, 6L 20s
Equal tunings
Equalized (L:s = 1:1) 2\13 (184.6 ¢)
Supersoft (L:s = 4:3) 7\45 (186.7 ¢)
Soft (L:s = 3:2) 5\32 (187.5 ¢)
Semisoft (L:s = 5:3) 8\51 (188.2 ¢)
Basic (L:s = 2:1) 3\19 (189.5 ¢)
Semihard (L:s = 5:2) 7\44 (190.9 ¢)
Hard (L:s = 3:1) 4\25 (192.0 ¢)
Superhard (L:s = 4:1) 5\31 (193.5 ¢)
Collapsed (L:s = 1:0) 1\6 (200.0 ¢)
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6L 7s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 6 large steps and 7 small steps, repeating every octave. 6L 7s is a child scale of 6L 1s, expanding it by 6 tones. Generators that produce this scale range from 184.6 ¢ to 200 ¢, or from 1000 ¢ to 1015.4 ¢.

This MOS is the chromatic scale of a family of temperaments which are index-2 subtemperaments (that is, taking every other step of the generator chain) of various meantone temperaments: that is, those that are generated by a mean tone, that being specifically a whole tone of tunings with a fifth in between that of 26edo and 12edo, and roughly speaking between 10/9 and 9/8.

The most notable temperaments generating this scale are didacus in the 2.5.7 subgroup and its extensions, with its generator identified with ~28/25, whose optimum makes a superhard tuning, similarly to the situation with 5L 6s and slendric.

Scale properties

This article uses TAMNAMS conventions for the names of this scale's intervals and scale degrees. The use of 1-indexed ordinal names is reserved for interval regions.

Intervals

Intervals of 6L 7s
Intervals Steps
subtended 		Range in cents
Generic Specific Abbrev.
0-mosstep Perfect 0-mosstep P0ms 0 0.0 ¢
1-mosstep Minor 1-mosstep m1ms s 0.0 ¢ to 92.3 ¢
Major 1-mosstep M1ms L 92.3 ¢ to 200.0 ¢
2-mosstep Diminished 2-mosstep d2ms 2s 0.0 ¢ to 184.6 ¢
Perfect 2-mosstep P2ms L + s 184.6 ¢ to 200.0 ¢
3-mosstep Minor 3-mosstep m3ms L + 2s 200.0 ¢ to 276.9 ¢
Major 3-mosstep M3ms 2L + s 276.9 ¢ to 400.0 ¢
4-mosstep Minor 4-mosstep m4ms L + 3s 200.0 ¢ to 369.2 ¢
Major 4-mosstep M4ms 2L + 2s 369.2 ¢ to 400.0 ¢
5-mosstep Minor 5-mosstep m5ms 2L + 3s 400.0 ¢ to 461.5 ¢
Major 5-mosstep M5ms 3L + 2s 461.5 ¢ to 600.0 ¢
6-mosstep Minor 6-mosstep m6ms 2L + 4s 400.0 ¢ to 553.8 ¢
Major 6-mosstep M6ms 3L + 3s 553.8 ¢ to 600.0 ¢
7-mosstep Minor 7-mosstep m7ms 3L + 4s 600.0 ¢ to 646.2 ¢
Major 7-mosstep M7ms 4L + 3s 646.2 ¢ to 800.0 ¢
8-mosstep Minor 8-mosstep m8ms 3L + 5s 600.0 ¢ to 738.5 ¢
Major 8-mosstep M8ms 4L + 4s 738.5 ¢ to 800.0 ¢
9-mosstep Minor 9-mosstep m9ms 4L + 5s 800.0 ¢ to 830.8 ¢
Major 9-mosstep M9ms 5L + 4s 830.8 ¢ to 1000.0 ¢
10-mosstep Minor 10-mosstep m10ms 4L + 6s 800.0 ¢ to 923.1 ¢
Major 10-mosstep M10ms 5L + 5s 923.1 ¢ to 1000.0 ¢
11-mosstep Perfect 11-mosstep P11ms 5L + 6s 1000.0 ¢ to 1015.4 ¢
Augmented 11-mosstep A11ms 6L + 5s 1015.4 ¢ to 1200.0 ¢
12-mosstep Minor 12-mosstep m12ms 5L + 7s 1000.0 ¢ to 1107.7 ¢
Major 12-mosstep M12ms 6L + 6s 1107.7 ¢ to 1200.0 ¢
13-mosstep Perfect 13-mosstep P13ms 6L + 7s 1200.0 ¢

Generator chain

Generator chain of 6L 7s
Bright gens Scale degree Abbrev.
18 Augmented 10-mosdegree A10md
17 Augmented 8-mosdegree A8md
16 Augmented 6-mosdegree A6md
15 Augmented 4-mosdegree A4md
14 Augmented 2-mosdegree A2md
13 Augmented 0-mosdegree A0md
12 Augmented 11-mosdegree A11md
11 Major 9-mosdegree M9md
10 Major 7-mosdegree M7md
9 Major 5-mosdegree M5md
8 Major 3-mosdegree M3md
7 Major 1-mosdegree M1md
6 Major 12-mosdegree M12md
5 Major 10-mosdegree M10md
4 Major 8-mosdegree M8md
3 Major 6-mosdegree M6md
2 Major 4-mosdegree M4md
1 Perfect 2-mosdegree P2md
0 Perfect 0-mosdegree
Perfect 13-mosdegree		 P0md
P13md
−1 Perfect 11-mosdegree P11md
−2 Minor 9-mosdegree m9md
−3 Minor 7-mosdegree m7md
−4 Minor 5-mosdegree m5md
−5 Minor 3-mosdegree m3md
−6 Minor 1-mosdegree m1md
−7 Minor 12-mosdegree m12md
−8 Minor 10-mosdegree m10md
−9 Minor 8-mosdegree m8md
−10 Minor 6-mosdegree m6md
−11 Minor 4-mosdegree m4md
−12 Diminished 2-mosdegree d2md
−13 Diminished 13-mosdegree d13md
−14 Diminished 11-mosdegree d11md
−15 Diminished 9-mosdegree d9md
−16 Diminished 7-mosdegree d7md
−17 Diminished 5-mosdegree d5md
−18 Diminished 3-mosdegree d3md

Modes

Scale degrees of the modes of 6L 7s
UDP Cyclic
order 		Step
pattern 		Scale degree (mosdegree)
0 1 2 3 4 5 6 7 8 9 10 11 12 13
12|0 1 LsLsLsLsLsLss Perf. Maj. Perf. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Aug. Maj. Perf.
11|1 3 LsLsLsLsLssLs Perf. Maj. Perf. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Perf. Maj. Perf.
10|2 5 LsLsLsLssLsLs Perf. Maj. Perf. Maj. Maj. Maj. Maj. Maj. Maj. Min. Maj. Perf. Maj. Perf.
9|3 7 LsLsLssLsLsLs Perf. Maj. Perf. Maj. Maj. Maj. Maj. Min. Maj. Min. Maj. Perf. Maj. Perf.
8|4 9 LsLssLsLsLsLs Perf. Maj. Perf. Maj. Maj. Min. Maj. Min. Maj. Min. Maj. Perf. Maj. Perf.
7|5 11 LssLsLsLsLsLs Perf. Maj. Perf. Min. Maj. Min. Maj. Min. Maj. Min. Maj. Perf. Maj. Perf.
6|6 13 sLsLsLsLsLsLs Perf. Min. Perf. Min. Maj. Min. Maj. Min. Maj. Min. Maj. Perf. Maj. Perf.
5|7 2 sLsLsLsLsLssL Perf. Min. Perf. Min. Maj. Min. Maj. Min. Maj. Min. Maj. Perf. Min. Perf.
4|8 4 sLsLsLsLssLsL Perf. Min. Perf. Min. Maj. Min. Maj. Min. Maj. Min. Min. Perf. Min. Perf.
3|9 6 sLsLsLssLsLsL Perf. Min. Perf. Min. Maj. Min. Maj. Min. Min. Min. Min. Perf. Min. Perf.
2|10 8 sLsLssLsLsLsL Perf. Min. Perf. Min. Maj. Min. Min. Min. Min. Min. Min. Perf. Min. Perf.
1|11 10 sLssLsLsLsLsL Perf. Min. Perf. Min. Min. Min. Min. Min. Min. Min. Min. Perf. Min. Perf.
0|12 12 ssLsLsLsLsLsL Perf. Min. Dim. Min. Min. Min. Min. Min. Min. Min. Min. Perf. Min. Perf.

Scale tree

Scale tree and tuning spectrum of 6L 7s
Generator(edo) Cents Step ratio Comments
Bright Dark L:s Hardness
2\13 184.615 1015.385 1:1 1.000 Equalized 6L 7s
11\71 185.915 1014.085 6:5 1.200
9\58 186.207 1013.793 5:4 1.250
16\103 186.408 1013.592 9:7 1.286
7\45 186.667 1013.333 4:3 1.333 Supersoft 6L 7s
19\122 186.885 1013.115 11:8 1.375
12\77 187.013 1012.987 7:5 1.400
17\109 187.156 1012.844 10:7 1.429
5\32 187.500 1012.500 3:2 1.500 Soft 6L 7s
18\115 187.826 1012.174 11:7 1.571
13\83 187.952 1012.048 8:5 1.600
21\134 188.060 1011.940 13:8 1.625
8\51 188.235 1011.765 5:3 1.667 Semisoft 6L 7s
19\121 188.430 1011.570 12:7 1.714
11\70 188.571 1011.429 7:4 1.750
14\89 188.764 1011.236 9:5 1.800
3\19 189.474 1010.526 2:1 2.000 Basic 6L 7s
Scales with tunings softer than this are proper
13\82 190.244 1009.756 9:4 2.250
10\63 190.476 1009.524 7:3 2.333
17\107 190.654 1009.346 12:5 2.400
7\44 190.909 1009.091 5:2 2.500 Semihard 6L 7s
18\113 191.150 1008.850 13:5 2.600
11\69 191.304 1008.696 8:3 2.667
15\94 191.489 1008.511 11:4 2.750
4\25 192.000 1008.000 3:1 3.000 Hard 6L 7s
13\81 192.593 1007.407 10:3 3.333
9\56 192.857 1007.143 7:2 3.500
14\87 193.103 1006.897 11:3 3.667 Hemithirds/luna
5\31 193.548 1006.452 4:1 4.000 Superhard 6L 7s
Didacus/hemiwürschmidt
11\68 194.118 1005.882 9:2 4.500
6\37 194.595 1005.405 5:1 5.000 Roulette/mediantone
7\43 195.349 1004.651 6:1 6.000
1\6 200.000 1000.000 1:0 → ∞ Collapsed 6L 7s
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