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5L 7s: Difference between revisions

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<h2>IMPORTED REVISION FROM WIKISPACES</h2>
{{interwiki
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
| de =
: This revision was by author [[User:keenanpepper|keenanpepper]] and made on <tt>2011-05-12 21:29:31 UTC</tt>.<br>
| en = 5L 7s
: The original revision id was <tt>228068766</tt>.<br>
| es =
: The revision comment was: <tt></tt><br>
| ja = 5L 7s
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>
{{Infobox MOS}}
<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 is the MOS pattern of the Pythagorean/[[Schismatic family|schismatic/Helmholtz/Garibaldi]] chromatic scale, and also the [[Archytas clan|superpyth]] chromatic scale. In contrast to the [[7L 5s|meantone chromatic scale]], in which "diatonic" semitones are larger than "chromatic" semitones, here the reverse is true: diatonic semitones are smaller than chromatic semitones, so the [[5L 2s|diatonic scale]] subset is actually [[Rothenberg propriety|improper]].
{{MOS intro|Other Names=p-chromatic}}


The two distinct harmonic entropy minima with this MOS pattern are, on the one hand, scales very close to Pythagorean such that 64/63 is not tempered out, such as the schismatic temperaments known as "Helmholtz" and "Garibaldi", and on the other hand, the much simpler scale known as "superpyth" in which 64/63 is tempered out.
5L 7s represents the chromatic scales of [[Pythagorean tuning|Pythagorean]]/[[schismic]] and [[superpyth]], the former being [[Rothenberg propriety|proper]] but the latter improper until expanded by 5 more notes, producing Superpyth[17]. Such scales are characterized by having a small step ([[diatonic semitone]]) that is smaller than the [[chroma]] ([[chromatic semitone]]), the reverse of [[7L 5s]]. The two distinct harmonic entropy minima for this scale correspond to schismic and superpyth.


The Pythagorean/schismatic version is proper, but the superpyth version is improper (it doesn't become proper until you add 5 more notes to form the superpyth "enharmonic" scale, superpyth[17]).
== Scale properties ==
{{TAMNAMS use}}


||||||||||~ Generator ||~ in cents ||~ Comments ||
=== Intervals ===
||= 5\12 ||=  ||=  ||=  ||=  ||= 500.000 ||=  ||
{{MOS intervals}}
||=  ||=  ||=  ||=  ||= 22\53 ||= 498.113 ||= Pythagorean/Helmholtz/Garibaldi
is around here ||
||=  ||=  ||=  ||= 17\41 ||=  ||= 497.591 ||=  ||
||=  ||=  ||=  ||=  ||= 29\70 ||= 497.143 ||=  ||
||=  ||=  ||= 12\29 ||=  ||=  ||= 496.552 ||=  ||
||=  ||=  ||=  ||=  ||= 31\75 ||= 496.000 ||=  ||
||=  ||=  ||=  ||= 19\46 ||=  ||= 495.652 ||=  ||
||=  ||=  ||=  ||=  ||= 26\63 ||= 495.238 ||=  ||
||=  ||= 7\17 ||=  ||=  ||=  ||= 494.118 ||= Boundary of propriety (generators
larger than this are proper) ||
||=  ||=  ||=  ||=  ||= 23\56 ||= 492.857 ||=  ||
||=  ||=  ||=  ||= 16\39 ||=  ||= 492.308 ||=  ||
||=  ||=  ||=  ||=  ||= 25\61 ||= 491.803 ||=  ||
||=  ||=  ||= 9\22 ||=  ||=  ||= 490.909 ||= Superpyth is in this region ||
||=  ||=  ||=  ||=  ||= 20\49 ||= 489.796 ||=  ||
||=  ||=  ||=  ||= 11\27 ||=  ||= 488.889 ||=  ||
||=  ||=  ||=  ||=  ||= 13\32 ||= 487.500 ||=  ||
||= 2\5 ||=  ||=  ||=  ||=  ||= 480.000 ||=  ||</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;5L 7s&lt;/title&gt;&lt;/head&gt;&lt;body&gt;This is the MOS pattern of the Pythagorean/&lt;a class="wiki_link" href="/Schismatic%20family"&gt;schismatic/Helmholtz/Garibaldi&lt;/a&gt; chromatic scale, and also the &lt;a class="wiki_link" href="/Archytas%20clan"&gt;superpyth&lt;/a&gt; chromatic scale. In contrast to the &lt;a class="wiki_link" href="/7L%205s"&gt;meantone chromatic scale&lt;/a&gt;, in which &amp;quot;diatonic&amp;quot; semitones are larger than &amp;quot;chromatic&amp;quot; semitones, here the reverse is true: diatonic semitones are smaller than chromatic semitones, so the &lt;a class="wiki_link" href="/5L%202s"&gt;diatonic scale&lt;/a&gt; subset is actually &lt;a class="wiki_link" href="/Rothenberg%20propriety"&gt;improper&lt;/a&gt;.&lt;br /&gt;
&lt;br /&gt;
The two distinct harmonic entropy minima with this MOS pattern are, on the one hand, scales very close to Pythagorean such that 64/63 is not tempered out, such as the schismatic temperaments known as &amp;quot;Helmholtz&amp;quot; and &amp;quot;Garibaldi&amp;quot;, and on the other hand, the much simpler scale known as &amp;quot;superpyth&amp;quot; in which 64/63 is tempered out.&lt;br /&gt;
&lt;br /&gt;
The Pythagorean/schismatic version is proper, but the superpyth version is improper (it doesn't become proper until you add 5 more notes to form the superpyth &amp;quot;enharmonic&amp;quot; scale, superpyth[17]).&lt;br /&gt;
&lt;br /&gt;


=== Generator chain ===
{{MOS genchain}}


&lt;table class="wiki_table"&gt;
=== Modes ===
    &lt;tr&gt;
{{MOS mode degrees}}
        &lt;th colspan="5"&gt;Generator&lt;br /&gt;
&lt;/th&gt;
        &lt;th&gt;in cents&lt;br /&gt;
&lt;/th&gt;
        &lt;th&gt;Comments&lt;br /&gt;
&lt;/th&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;5\12&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;500.000&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;22\53&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;498.113&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;Pythagorean/Helmholtz/Garibaldi&lt;br /&gt;
is around here&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;17\41&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;497.591&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;29\70&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;497.143&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;12\29&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;496.552&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;31\75&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;496.000&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;19\46&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;495.652&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;26\63&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;495.238&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;7\17&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;494.118&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;Boundary of propriety (generators&lt;br /&gt;
larger than this are proper)&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;23\56&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;492.857&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;16\39&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;492.308&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;25\61&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;491.803&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;9\22&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;490.909&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;Superpyth is in this region&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;20\49&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;489.796&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;11\27&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;488.889&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;13\32&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;487.500&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;2\5&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;480.000&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
&lt;/table&gt;


&lt;/body&gt;&lt;/html&gt;</pre></div>
=== Proposed names ===
The modes are named by [[Eliora]] after Chinese zodiac animals. 5L 7s is the opposite mos to [[7L 5s]], named after a Western concept, Gregorian months, therefore this mos scale has Eastern nomenclature. Furthermore, 12edo (equalized tuning of this MOS) was independently discovered in China.
 
{{MOS modes
| Mode Names=
Rat $
Ox $
Tiger $
Rabbit $
Dragon $
Snake $
Horse $
Goat $
Monkey $
Rooster $
Dog $
Pig $
}}
 
== Scales ==
* [[Pythagorean12]] – Pythagorean tuning
* [[Garibaldi12]] – 94edo tuning
* [[Cotoneum12]] – 217edo tuning
* [[Edson12]] – 29edo tuning
* [[Pepperoni12]] – 271edo tuning
* [[Supra12]] – 56edo tuning
* [[Archy12]] – 49edo tuning
* [[12-22a]] – 22edo tuning
 
== Scale tree ==
{{MOS tuning spectrum
| 6/5 = [[Photia]], ↑&nbsp;[[grackle]]
| 5/4 = [[Helmholtz (temperament)|Helmholtz]], [[Pythagorean tuning]] (701.955{{c}})
| 9/7 = [[Garibaldi]] / [[cassandra]]
| 4/3 = Garibaldi / [[andromeda]]
| 11/8 = [[Kwai]]
| 10/7 = [[Undecental]], argent tuning (702.944{{c}})
| 3/2 = [[Edson]]
| 13/8 = [[Polypyth]], golden neogothic (704.096{{c}})
| 5/3 = [[Leapday]]
| 12/7 = [[Leapweek]]
| 9/5 = [[Leapmonth]]
| 7/3 = [[Supra]]
| 13/5 = Golden supra (708.054{{c}})
| 8/3 = [[Quasisuper]] / [[quasisupra]]
| 3/1 = [[Suprapyth]]
| 7/2 = [[Superpyth]]
| 6/1 = ↓&nbsp;[[Oceanfront]] / [[ultrapyth]]
}}
 
[[Category:12-tone scales]]
[[Category:P-chromatic| ]]<!-- main article -->
[[Category:Chromatic scales]]
Retrieved from "https://en.xen.wiki/w/5L_7s"