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7L 1s: 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:genewardsmith|genewardsmith]] and made on <tt>2011-03-11 00:11:19 UTC</tt>.<br>
== Name ==
: The original revision id was <tt>209503350</tt>.<br>
{{TAMNAMS name}}
: 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">The range between 2\15 and 5\37, including 3\22, is the [[Porcupine family|porcupine]] range of grumpy. Between 4\31 and 2\15, including 3\23, is the [[Chromatic pairs|greeley]] range.


Form: L L L L L L L s = Major Scale
== Scale properties ==
L s L L L L L L = Minor Scale


Equal Temperaments:
=== Intervals ===
2 2 2 2 2 2 2 1
{{MOS intervals}}
2 1 2 2 2 2 2 2: __[[15edo]]__


3 3 3 3 3 3 3 1
=== Generator chain ===
3 1 3 3 3 3 3 3: **__[[22edo]]__**
{{MOS genchain}}


4 4 4 4 4 4 4 1
=== Modes ===
4 1 4 4 4 4 4 4: __[[29edo]]__
{{MOS mode degrees}}


4 4 4 4 4 4 4 2
=== Proposed names ===
4 2 4 4 4 4 4 4: __[[30edo]]__
Mode names are from [[Porcupine Temperament Modal Harmony|Porcupine temperament modal harmony]]. Descriptive mode names are based on using {{dash|1, 4, 7}}, i.e. 3+3 triads as a basis for harmony.
{{MOS modes
| Mode names =
octopus $
mantis $
dolphin $
crab $
tuna $
salmon $
starfish $
whale $
| Table Headers=Name Origin
| Table Entries=
Bright quartal $
Dark quartal $
Bright major $
Middle major $
Dark major $
Bright minor $
Middle minor $
Dark minor $
}}


5 5 5 5 5 5 5 2
== Theory ==
5 2 5 5 5 5 5 5: __**[[37edo]]**__
=== Low harmonic entropy scales ===
There are three notable [[harmonic entropy]] minima with this [[mos]] pattern.


6 6 6 6 6 6 6 2
* The lowest accuracy one is [[porcupine]], in which two generators make a [[6/5]] and three make a [[4/3]]. The range of porcupine tunings is about 2\15 to 3\22.
6 2 6 6 6 6 6 6: __[[44edo]]__
* Less well-known and more accurate is [[greeley]], in which two generators are still 6/5 but three fall quite short of a 4/3, but the scale happens to closely approximate a lot of higher-complexity intervals like [[10/7]], [[11/7]], etc.
* Thirdly and finally, [[tempering out]] [[4000/3993|S10/S11]] so that ([[4/3]])/([[11/10]])<sup>3</sup> is tempered out results in an unusually high accuracy and efficient rank-2 temperament in the 2.3.11/5 subgroup for which interpretation as a rank-3 temperament in 2.3.5.11 (the no-7's [[11-limit]]) is natural, making [[10/9]] and [[12/11]] [[square superparticular|equidistant from 11/10]] and offering many fruitful tempering opportunities. Note therefore that [[porkypine]] can be seen as a trivial tuning of [[4000/3993|pine]] tempering out {{nowrap|[[100/99]] {{=}} S10}} and {{nowrap|[[121/120]] {{=}} S11}}.


6 6 6 6 6 6 6 3
== Scale tree ==
6 3 6 6 6 6 6 6: __[[45edo]]__
{{MOS tuning spectrum
| 5/2 = General range of porcupine
| 2/1 = Optimum rank range for porcupine
| 13/8 = Golden porcupine/hemikleismic
| 10/7 = General range of greeley
}}


7 7 7 7 7 7 7 3
[[Category:8-tone scales]]
7 3 7 7 7 7 7 7: __[[52edo]]__</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;7L 1s&lt;/title&gt;&lt;/head&gt;&lt;body&gt;The range between 2\15 and 5\37, including 3\22, is the &lt;a class="wiki_link" href="/Porcupine%20family"&gt;porcupine&lt;/a&gt; range of grumpy. Between 4\31 and 2\15, including 3\23, is the &lt;a class="wiki_link" href="/Chromatic%20pairs"&gt;greeley&lt;/a&gt; range.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Form: L L L L L L L s = Major Scale&lt;br /&gt;
L s L L L L L L = Minor Scale&lt;br /&gt;
&lt;br /&gt;
Equal Temperaments:&lt;br /&gt;
2 2 2 2 2 2 2 1&lt;br /&gt;
2 1 2 2 2 2 2 2: &lt;u&gt;&lt;a class="wiki_link" href="/15edo"&gt;15edo&lt;/a&gt;&lt;/u&gt;&lt;br /&gt;
&lt;br /&gt;
3 3 3 3 3 3 3 1&lt;br /&gt;
3 1 3 3 3 3 3 3: &lt;strong&gt;&lt;u&gt;&lt;a class="wiki_link" href="/22edo"&gt;22edo&lt;/a&gt;&lt;/u&gt;&lt;/strong&gt;&lt;br /&gt;
&lt;br /&gt;
4 4 4 4 4 4 4 1&lt;br /&gt;
4 1 4 4 4 4 4 4: &lt;u&gt;&lt;a class="wiki_link" href="/29edo"&gt;29edo&lt;/a&gt;&lt;/u&gt;&lt;br /&gt;
&lt;br /&gt;
4 4 4 4 4 4 4 2&lt;br /&gt;
4 2 4 4 4 4 4 4: &lt;u&gt;&lt;a class="wiki_link" href="/30edo"&gt;30edo&lt;/a&gt;&lt;/u&gt;&lt;br /&gt;
&lt;br /&gt;
5 5 5 5 5 5 5 2&lt;br /&gt;
5 2 5 5 5 5 5 5: &lt;u&gt;&lt;strong&gt;&lt;a class="wiki_link" href="/37edo"&gt;37edo&lt;/a&gt;&lt;/strong&gt;&lt;/u&gt;&lt;br /&gt;
&lt;br /&gt;
6 6 6 6 6 6 6 2&lt;br /&gt;
6 2 6 6 6 6 6 6: &lt;u&gt;&lt;a class="wiki_link" href="/44edo"&gt;44edo&lt;/a&gt;&lt;/u&gt;&lt;br /&gt;
&lt;br /&gt;
6 6 6 6 6 6 6 3&lt;br /&gt;
6 3 6 6 6 6 6 6: &lt;u&gt;&lt;a class="wiki_link" href="/45edo"&gt;45edo&lt;/a&gt;&lt;/u&gt;&lt;br /&gt;
&lt;br /&gt;
7 7 7 7 7 7 7 3&lt;br /&gt;
7 3 7 7 7 7 7 7: &lt;u&gt;&lt;a class="wiki_link" href="/52edo"&gt;52edo&lt;/a&gt;&lt;/u&gt;&lt;/body&gt;&lt;/html&gt;</pre></div>
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