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12L 5s: 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|Other Names=p-enharmonic}}
: This revision was by author [[User:JosephRuhf|JosephRuhf]] and made on <tt>2012-11-04 23:47:04 UTC</tt>.<br>
Temperaments supported by this scale include those under the [[Pythagorean tuning|Pythagorean]] and [[Schismatic family|schismic]] families, characterized by a diesis (the difference between a large step and two small steps) that is smaller than the [[chroma]].
: The original revision id was <tt>379201672</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 separates its small steps by intervals of 3L-2L-2L-3L-2L. Its major third of -4 generators approximates an interval between 19/16 and 32/25, thus its generator is a perfect fourth between 7/17edo (494 7/17) and 5/12edo (500 cents).
|| 7/17 ||  ||  ||  ||  || 494 7/17 ||
||  ||  ||  ||  || 33/80 || 495 ||
||  ||  ||  || 26/63 ||  || 495 5/21 ||
||  ||  ||  ||  || 45/109 || 495 45/109 ||
||  ||  || 19/46 ||  ||  || 495 15/23 ||
||  ||  ||  ||  || 50/121 || 495 105/121 ||
||  ||  ||  || 31/75 ||  || 496 ||
||  ||  ||  ||  || 43/104 || 496 2/13 ||
||  || 12/29 ||  ||  ||  || 496 16/29 ||
||  ||  ||  ||  || 41/99 || 496 32/33 ||
||  ||  ||  || 29/70 ||  || 497 1/7 ||
||  ||  ||  ||  || 46/111 || 497 11/37 ||
||  ||  || 17/41 ||  ||  || 497 23/41 ||
||  ||  ||  ||  || 39/94 || 497 41/47 ||
||  ||  ||  || 22/53 ||  || 498 6/53 ||
||  ||  ||  ||  || 27/65 || 498 6/13 ||
|| 5/12 ||  ||  ||  ||  || 500 ||</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;12L 5s&lt;/title&gt;&lt;/head&gt;&lt;body&gt;This MOS separates its small steps by intervals of 3L-2L-2L-3L-2L. Its major third of -4 generators approximates an interval between 19/16 and 32/25, thus its generator is a perfect fourth between 7/17edo (494 7/17) and 5/12edo (500 cents).&lt;br /&gt;


The [[leapday]]/[[leapweek]] version is proper, but the Pythagorean/schismic version is improper (it does not become proper until you add 12 more notes to form the schismic 29-note scale).


&lt;table class="wiki_table"&gt;
== Scale properties ==
    &lt;tr&gt;
{{TAMNAMS use}}
        &lt;td&gt;7/17&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;494 7/17&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&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;33/80&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;495&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&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;26/63&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;495 5/21&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&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;45/109&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;495 45/109&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;19/46&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;495 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;&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;50/121&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;495 105/121&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&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;31/75&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;496&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&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;43/104&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;496 2/13&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;12/29&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;496 16/29&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&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;41/99&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;496 32/33&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&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;29/70&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;497 1/7&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&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;46/111&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;497 11/37&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;17/41&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;497 23/41&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&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;39/94&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;497 41/47&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&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;22/53&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;498 6/53&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&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;27/65&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;498 6/13&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;5/12&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;500&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
&lt;/table&gt;


&lt;/body&gt;&lt;/html&gt;</pre></div>
=== Intervals ===
{{MOS intervals}}
 
=== Generator chain ===
{{MOS genchain}}
 
=== Modes ===
{{MOS mode degrees}}
 
=== Proposed tuning-specific names ===
[[Declan Paul Boushy]] has proposed names for these modes corresponding to step ratios [[Subaru scale|3:1]] and [[Tanegashima scale|4:1]].
{{todo|add etymology|add Template:MOS modes and annotate each row using Boushy’s names}}
 
== Scales ==
* [[Edson17]] – 29edo tuning
* [[Subaru scale]] – 41edo tuning
* [[Cotoneum17]] – 217edo tuning
* [[Garibaldi17]] – 94edo tuning
* [[Pythagorean17]] – Pythagorean tuning
* [[Tanegashima scale]] – 53edo tuning
* [[Nestoria17]] – 171edo tuning
 
== Scale tree ==
{{MOS tuning spectrum
| 4/3 = [[Leapfrog]]
| 7/5 = [[Leapweek]]
| 3/2 = [[Leapday]]
| 11/7 = [[Polypyth]]
| 13/8 = Golden neogothic (495.904{{c}})
| 7/3 = [[Undecental]]
| 12/5 = Argent tuning (497.056{{c}})
| 13/5 = Unnamed golden tuning (497.254{{c}})
| 11/4 = [[Kwai]]
| 3/1 = [[Garibaldi]] / [[andromeda]]
| 7/2 = Garibaldi / [[cassandra]]
| 4/1 = Garibaldi / [[helenus]], Pythagorean tuning (498.045{{c}})
| 9/2 = [[Pontiac]]
| 5/1 = [[Photia]]
| 6/1 = ↓&nbsp;[[Grackle]], ↓↓&nbsp;[[gracecordial]]
}}
 
[[Category:17-tone scales]]
[[Category:Mega chromatic scales]]
Retrieved from "https://en.xen.wiki/w/12L_5s"