2L 5s: Difference between revisions

Line 1:

<h2>IMPORTED REVISION FROM WIKISPACES</h2>

This is an imported revision from Wikispaces. The revision metadata is included below for reference:

: This revision was by author [[User:~~genewardsmith~~|~~genewardsmith~~]] and made on <tt>2011-03-~~11 00~~:58:56 UTC</tt>.

: This revision was by author [[User:keenanpepper|keenanpepper]] and made on <tt>2011-04-25 04:56:13 UTC</tt>.

: The original revision id was <tt>~~209509152~~</tt>.

: The original revision id was <tt>222632434</tt>.

: The revision comment was: <tt></tt>

The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.

<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">2L 5s refers to a Moment of Symmetry scale with two large steps and five small steps. Common names for such a tuning are mavila and anti-diatonic. The generator is a sharp fourth (or flat fifth), falling between 3\7 (3 degrees of [[7edo]]) and 1\2 (1 degree of [[2edo]] -- the half-octave tritone that appears in every even-numbered edo).

<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">2L 5s refers to a Moment of Symmetry scale with two large steps and five small steps. Common names for such a tuning are mavila and anti-diatonic. The generator is a sharp fourth (or flat fifth), falling between 3\7 (3 degrees of [[7edo]]) and 1\2 (1 degree of [[2edo]] — the half-octave tritone that appears in every even-numbered edo).

The word "mavila" is used in different ways by different folks. Not every user of the word would consider every 2L 5s scale an instance of "mavila." In particular, between 13\29 and 14\31, and centered on 9\20, is the albitonic scale for the score temperament [[chromatic pair]], which is not intended to be treated as having any kind of fifth, flat or otherwise.

~~Generalized form~~ in ~~seven modes:~~

In terms of harmonic entropy, the most significant minimum is at [[Meantone family|Liese]]/Triton, in which the generator is about 7/5 and three of them make a 3/1.

||||||||||||||~ generator in degrees of an [[edo]] ||~ generator in cents ||~ scale ||~ L in cents ||~ s in cents ||~ L to s ratio ||~ comments ||

~~s s L s s s L~~

||= 3\7 ||= ||= ||= ||= || || ||= 514.3 ||= 1 1 1 1 1 1 1 ||= 171.4 ||= 171.4 ||= 1.00 ||= ||

~~s L s s s L s~~

||= ||= ||= ||= ||= 13\30 || || ||= 520.0 ||= 4 4 5 4 4 4 5 ||= 200.0 ||= 160.0 ||= 1.25 ||= ||

~~L s s s L s s~~

||= ||= ||= ||= 10\23 ||= || || ||= 521.7 ||= 3 3 4 3 3 3 4 ||= 208.7 ||= 156.5 ||= 1.33 ||= Mavila is in this general region ||

~~s s s L s s L~~

||= ||= ||= ||= ||= 17\39 || || ||= 523.1 ||= 5 5 7 5 5 5 7 ||= 215.4 ||= 153.8 ||= 1.40 ||= ||

~~s s L s s L s~~

||= ||= ||= 7\16 ||= ||= || || ||= 525.0 ||= 2 2 3 2 2 2 3 ||= 225.0 ||= 150.0 ||= 1.50 ||= ||

~~s L s s L s s~~

||= ||= ||= ||= ||= 18\41 || || ||= 526.8 ||= 5 5 8 5 5 5 8 ||= 234.1 ||= 146.3 ||= 1.60 ||= ||

~~L s s L s s s~~

||= ||= ||= ||= 11\25 ||= || || ||= 528.0 ||= 3 3 5 3 3 3 5 ||= 240.0 ||= 144.0 ||= 1.67 ||= ||

||= ||= ||= ||= ||= 15\34 || || ||= 529.4 ||= 4 4 7 4 4 4 7 ||= 247.1 ||= 141.2 ||= 1.75 ||= ||

||||||||||~ generator in degrees of an [[edo]] ||~ generator in cents ||~ scale ||~ L in cents ||~ s in cents ||~ L to s ratio ||

||= ||= 4\9 ||= ||= ||= || || ||= 533.3 ||= 1 1 2 1 1 1 2 ||= 266.7 ||= 133.3 ||= 2.00 ||= Boundary of propriety (generators

||= 3\7 ||= ||= ||= ||= ||= 514.3 ||= 1 1 1 1 1 1 1 ||= 171.4 ||= 171.4 ||= 1.00 ||

smaller than this are proper) ||

||= ||= ||= ||= ||= 13\30 ||= 520.0 ||= 4 4 5 4 4 4 5 ||= 200.0 ||= 160.0 ||= 1.25 ||

||= ||= ||= ||= ||= 13\29 || || ||= 537.9 ||= 3 3 7 3 3 3 7 ||= 289.7 ||= 124.1 ||= 2.33 ||= ||

||= ||= ||= ||= 10\23 ||= ||= 521.7 ||= 3 3 4 3 3 3 4 ||= 208.7 ||= 156.5 ||= 1.33 ||

||= ||= ||= ||= 9\20 ||= || || ||= 540.0 ||= 2 2 5 2 2 2 5 ||= 300.0 ||= 120.0 ||= 2.50 ||= ||

||= ||= ||= ||= ||= 17\39 ||= 523.1 ||= 5 5 7 5 5 5 7 ||= 215.4 ||= 153.8 ||= 1.40 ||

||= ||= ||= ||= ||= 14\31 || || ||= 541.9 ||= 3 3 8 3 3 3 8 ||= 309.7 ||= 116.1 ||= 2.66 ||= ||

||= ||= ||= 7\16 ||= ||= ||= 525.0 ||= 2 2 3 2 2 2 3 ||= 225.0 ||= 150.0 ||= 1.50 ||

||= ||= ||= 5\11 ||= ||= || || ||= 545.5 ||= 1 1 3 1 1 1 3 ||= 327.3 ||= 109.1 ||= 3.00 ||= ||

||= ||= ||= ||= ||= 18\41 ||= 526.8 ||= 5 5 8 5 5 5 8 ||= 234.1 ||= 146.3 ||= 1.60 ||

||= ||= ||= ||= ||= 11\24 || || ||= 550.0 ||= 2 2 7 2 2 2 7 ||= 350.0 ||= 100.0 ||= 3.50 ||= ||

||= ||= ||= ||= 11\25 ||= ||= 528.0 ||= 3 3 5 3 3 3 5 ||= 240.0 ||= 144.0 ||= 1.67 ||

||= ||= ||= ||= 6\13 ||= || || ||= 553.8 ||= 1 1 4 1 1 1 4 ||= 369.2 ||= 92.3 ||= 4.00 ||= ||

||= ||= ||= ||= ||= 15\34 ||= 529.4 ||= 4 4 7 4 4 4 7 ||= 247.1 ||= 141.2 ||= 1.75 ||

||= ||= ||= ||= ||= 7\15 || || ||= 560.0 ||= 1 1 5 1 1 1 5 ||= 400.0 ||= 80.0 ||= 5.00 ||= ||

||= ||= 4\9 ||= ||= ||= ||= 533.3 ||= 1 1 2 1 1 1 2 ||= 266.7 ||= 133.3 ||= 2.00 ||

||= ||= ||= ||= ||= ||= 8\17 ||= ||= 564.7 ||= 1 1 6 1 1 1 6 ||= 423.5 ||= 70.6 ||= 6.00 ||= ||

||= ||= ||= ||= ||= 13\29 ||= 537.9 ||= 3 3 7 3 3 3 7 ||= 289.7 ||= 124.1 ||= 2.33 ||

||= ||= ||= ||= ||= ||= ||= 9\19 ||= 568.4 ||= 1 1 7 1 1 1 7 ||= 442.1 ||= 63.2 ||= 7.00 ||= Liese/Triton is around here ||

||= ||= ||= ||= 9\20 ||= ||= 540.0 ||= 2 2 5 2 2 2 5 ||= 300.0 ||= 120.0 ||= 2.50 ||

||= 1\2 ||= ||= ||= ||= || || ||= 600.0 ||= 0 0 1 0 0 0 1 ||= 600.0 ||= 0 ||= — ||= ||</pre></div>

||= ||= ||= ||= ||= 14\31 ||= 541.9 ||= 3 3 8 3 3 3 8 ||= 309.7 ||= 116.1 ||= 2.66 ||

||= ||= ||= 5\11 ||= ||= ||= 545.5 ||= 1 1 3 1 1 1 3 ||= 327.3 ||= 109.1 ||= 3.00 ||

||= ||= ||= ||= ||= 11\24 ||= 550.0 ||= 2 2 7 2 2 2 7 ||= 350.0 ||= 100.0 ||= 3.50 ||

||= ||= ||= ||= 6\13 ||= ||= 553.8 ||= 1 1 4 1 1 1 4 ||= 369.2 ||= 92.3 ||= 4.00 ||

||= ||= ||= ||= ||= 7\15 ||= 560.0 ||= 1 1 5 1 1 1 5 ||= 400.0 ||= 80.0 ||= 5.00 ||

||= 1\2 ||= ||= ||= ||= ||= 600.0 ||= 0 0 1 0 0 0 1 ||= 600.0 ||= 0 ||= -- ||</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"><html><head><title>2L 5s</title></head><body>2L 5s refers to a Moment of Symmetry scale with two large steps and five small steps. Common names for such a tuning are mavila and anti-diatonic. The generator is a sharp fourth (or flat fifth), falling between 3\7 (3 degrees of <a class="wiki_link" href="/7edo">7edo</a>) and 1\2 (1 degree of <a class="wiki_link" href="/2edo">2edo</a> -- the half-octave tritone that appears in every even-numbered edo).

<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"><html><head><title>2L 5s</title></head><body>2L 5s refers to a Moment of Symmetry scale with two large steps and five small steps. Common names for such a tuning are mavila and anti-diatonic. The generator is a sharp fourth (or flat fifth), falling between 3\7 (3 degrees of <a class="wiki_link" href="/7edo">7edo</a>) and 1\2 (1 degree of <a class="wiki_link" href="/2edo">2edo</a> — the half-octave tritone that appears in every even-numbered edo).

The word &quot;mavila&quot; is used in different ways by different folks. Not every user of the word would consider every 2L 5s scale an instance of &quot;mavila.&quot; In particular, between 13\29 and 14\31, and centered on 9\20, is the albitonic scale for the score temperament <a class="wiki_link" href="/chromatic%20pair">chromatic pair</a>, which is not intended to be treated as having any kind of fifth, flat or otherwise.

~~Generalized form in seven modes:~~

In terms of harmonic entropy, the most significant minimum is at <a class="wiki_link" href="/Meantone%20family">Liese</a>/Triton, in which the generator is about 7/5 and three of them make a 3/1.

~~s s L s s s L<br~~ /~~>~~

~~s L s s s L s ~~

~~L s s s L s s ~~

~~s s s L s s L ~~

~~s s L s s L s ~~

~~s L s s L s s<br~~ /~~>~~

~~L s s L s s s<br~~ /~~>~~

<tr>

<th colspan="5">generator in degrees of an <a class="wiki_link" href="/edo">edo</a>

<th colspan="7">generator in degrees of an <a class="wiki_link" href="/edo">edo</a>

</th>

<th>generator in cents

Line 68:

Line 53:

</th>

<th>L to s ratio

</th>

<th>comments

</th>

</tr>

Line 80:

Line 67:

</td>

</td>

<td>

</td>

<td>

</td>

<td style="text-align: center;">514.3

Line 90:

Line 81:

</td>

<td style="text-align: center;">1.00

</td>

</td>

</tr>

Line 102:

Line 95:

</td>

<td style="text-align: center;">13\30

</td>

<td>

</td>

<td>

</td>

<td style="text-align: center;">520.0

Line 112:

Line 109:

</td>

<td style="text-align: center;">1.25

</td>

</td>

</tr>

Line 124:

Line 123:

</td>

</td>

<td>

</td>

<td>

</td>

<td style="text-align: center;">521.7

Line 134:

Line 137:

</td>

<td style="text-align: center;">1.33

</td>

<td style="text-align: center;">Mavila is in this general region

</td>

</tr>

Line 146:

Line 151:

</td>

<td style="text-align: center;">17\39

</td>

<td>

</td>

<td>

</td>

<td style="text-align: center;">523.1

Line 156:

Line 165:

</td>

<td style="text-align: center;">1.40

</td>

</td>

</tr>

Line 168:

Line 179:

</td>

</td>

<td>

</td>

<td>

</td>

<td style="text-align: center;">525.0

Line 178:

Line 193:

</td>

<td style="text-align: center;">1.50

</td>

</td>

</tr>

Line 190:

Line 207:

</td>

<td style="text-align: center;">18\41

</td>

<td>

</td>

<td>

</td>

<td style="text-align: center;">526.8

Line 200:

Line 221:

</td>

<td style="text-align: center;">1.60

</td>

</td>

</tr>

Line 212:

Line 235:

</td>

</td>

<td>

</td>

<td>

</td>

<td style="text-align: center;">528.0

Line 222:

Line 249:

</td>

<td style="text-align: center;">1.67

</td>

</td>

</tr>

Line 234:

Line 263:

</td>

<td style="text-align: center;">15\34

</td>

<td>

</td>

<td>

</td>

<td style="text-align: center;">529.4

Line 244:

Line 277:

</td>

<td style="text-align: center;">1.75

</td>

</td>

</tr>

Line 256:

Line 291:

</td>

</td>

<td>

</td>

<td>

</td>

<td style="text-align: center;">533.3

Line 266:

Line 305:

</td>

<td style="text-align: center;">2.00

</td>

<td style="text-align: center;">Boundary of propriety (generators

smaller than this are proper)

</td>

</tr>

Line 278:

Line 320:

</td>

<td style="text-align: center;">13\29

</td>

<td>

</td>

<td>

</td>

<td style="text-align: center;">537.9

Line 288:

Line 334:

</td>

<td style="text-align: center;">2.33

</td>

</td>

</tr>

Line 300:

Line 348:

</td>

</td>

<td>

</td>

<td>

</td>

<td style="text-align: center;">540.0

Line 310:

Line 362:

</td>

<td style="text-align: center;">2.50

</td>

</td>

</tr>

Line 322:

Line 376:

</td>

<td style="text-align: center;">14\31

</td>

<td>

</td>

<td>

</td>

<td style="text-align: center;">541.9

Line 332:

Line 390:

</td>

<td style="text-align: center;">2.66

</td>

</td>

</tr>

Line 344:

Line 404:

</td>

</td>

<td>

</td>

<td>

</td>

<td style="text-align: center;">545.5

Line 354:

Line 418:

</td>

<td style="text-align: center;">3.00

</td>

</td>

</tr>

Line 366:

Line 432:

</td>

<td style="text-align: center;">11\24

</td>

<td>

</td>

<td>

</td>

<td style="text-align: center;">550.0

Line 376:

Line 446:

</td>

<td style="text-align: center;">3.50

</td>

</td>

</tr>

Line 388:

Line 460:

</td>

</td>

<td>

</td>

<td>

</td>

<td style="text-align: center;">553.8

Line 398:

Line 474:

</td>

<td style="text-align: center;">4.00

</td>

</td>

</tr>

Line 410:

Line 488:

</td>

<td style="text-align: center;">7\15

</td>

<td>

</td>

<td>

</td>

<td style="text-align: center;">560.0

Line 420:

Line 502:

</td>

<td style="text-align: center;">5.00

</td>

</td>

</tr>

<tr>

</td>

</td>

</td>

</td>

</td>

<td style="text-align: center;">8\17

</td>

</td>

<td style="text-align: center;">564.7

</td>

<td style="text-align: center;">1 1 6 1 1 1 6

</td>

<td style="text-align: center;">423.5

</td>

<td style="text-align: center;">70.6

</td>

<td style="text-align: center;">6.00

</td>

</td>

</tr>

<tr>

</td>

</td>

</td>

</td>

</td>

</td>

<td style="text-align: center;">9\19

</td>

<td style="text-align: center;">568.4

</td>

<td style="text-align: center;">1 1 7 1 1 1 7

</td>

<td style="text-align: center;">442.1

</td>

<td style="text-align: center;">63.2

</td>

<td style="text-align: center;">7.00

</td>

<td style="text-align: center;">Liese/Triton is around here

</td>

</tr>

Line 432:

Line 572:

</td>

</td>

<td>

</td>

<td>

</td>

<td style="text-align: center;">600.0

Line 441:

Line 585:

<td style="text-align: center;">0

</td>

<td style="text-align: center;">--

<td style="text-align: center;">—

</td>

</td>

</tr>

@@ Line 1: / Line 1: @@
 <h2>IMPORTED REVISION FROM WIKISPACES</h2>
 This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
-: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-03-11 00:58:56 UTC</tt>.<br>
+: This revision was by author [[User:keenanpepper|keenanpepper]] and made on <tt>2011-04-25 04:56:13 UTC</tt>.<br>
-: The original revision id was <tt>209509152</tt>.<br>
+: The original revision id was <tt>222632434</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">2L 5s refers to a Moment of Symmetry scale with two large steps and five small steps. Common names for such a tuning are mavila and anti-diatonic. The generator is a sharp fourth (or flat fifth), falling between 3\7 (3 degrees of [[7edo]]) and 1\2 (1 degree of [[2edo]] -- the half-octave tritone that appears in every even-numbered edo).
+<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">2L 5s refers to a Moment of Symmetry scale with two large steps and five small steps. Common names for such a tuning are mavila and anti-diatonic. The generator is a sharp fourth (or flat fifth), falling between 3\7 (3 degrees of [[7edo]]) and 1\2 (1 degree of [[2edo]] — the half-octave tritone that appears in every even-numbered edo).
 The word "mavila" is used in different ways by different folks. Not every user of the word would consider every 2L 5s scale an instance of "mavila." In particular, between 13\29 and 14\31, and centered on 9\20, is the albitonic scale for the score temperament [[chromatic pair]], which is not intended to be treated as having any kind of fifth, flat or otherwise.
-Generalized form in seven modes:
+In terms of harmonic entropy, the most significant minimum is at [[Meantone family|Liese]]/Triton, in which the generator is about 7/5 and three of them make a 3/1.
+||||||||||||||~ generator in degrees of an [[edo]] ||~ generator in cents ||~ scale ||~ L in cents ||~ s in cents ||~ L to s ratio ||~ comments ||
-s s L s s s L
+||= 3\7 ||=   ||=   ||=   ||=   ||   ||   ||= 514.3 ||= 1 1 1 1 1 1 1 ||= 171.4 ||= 171.4 ||= 1.00 ||=   ||
-s L s s s L s
+||=   ||=   ||=   ||=   ||= 13\30 ||   ||   ||= 520.0 ||= 4 4 5 4 4 4 5 ||= 200.0 ||= 160.0 ||= 1.25 ||=   ||
-L s s s L s s
+||=   ||=   ||=   ||= 10\23 ||=   ||   ||   ||= 521.7 ||= 3 3 4 3 3 3 4 ||= 208.7 ||= 156.5 ||= 1.33 ||= Mavila is in this general region ||
-s s s L s s L
+||=   ||=   ||=   ||=   ||= 17\39 ||   ||   ||= 523.1 ||= 5 5 7 5 5 5 7 ||= 215.4 ||= 153.8 ||= 1.40 ||=   ||
-s s L s s L s
+||=   ||=   ||= 7\16 ||=   ||=   ||   ||   ||= 525.0 ||= 2 2 3 2 2 2 3 ||= 225.0 ||= 150.0 ||= 1.50 ||=   ||
-s L s s L s s
+||=   ||=   ||=   ||=   ||= 18\41 ||   ||   ||= 526.8 ||= 5 5 8 5 5 5 8 ||= 234.1 ||= 146.3 ||= 1.60 ||=   ||
-L s s L s s s
+||=   ||=   ||=   ||= 11\25 ||=   ||   ||   ||= 528.0 ||= 3 3 5 3 3 3 5 ||= 240.0 ||= 144.0 ||= 1.67 ||=   ||
+||=   ||=   ||=   ||=   ||= 15\34 ||   ||   ||= 529.4 ||= 4 4 7 4 4 4 7 ||= 247.1 ||= 141.2 ||= 1.75 ||=   ||
-||||||||||~ generator in degrees of an [[edo]] ||~ generator in cents ||~ scale ||~ L in cents ||~ s in cents ||~ L to s ratio ||
+||=   ||= 4\9 ||=   ||=   ||=   ||   ||   ||= 533.3 ||= 1 1 2 1 1 1 2 ||= 266.7 ||= 133.3 ||= 2.00 ||= Boundary of propriety (generators
-||= 3\7 ||=   ||=   ||=   ||=   ||= 514.3 ||= 1 1 1 1 1 1 1 ||= 171.4 ||= 171.4 ||= 1.00 ||
+smaller than this are proper) ||
-||=   ||=   ||=   ||=   ||= 13\30 ||= 520.0 ||= 4 4 5 4 4 4 5 ||= 200.0 ||= 160.0 ||= 1.25 ||
+||=   ||=   ||=   ||=   ||= 13\29 ||   ||   ||= 537.9 ||= 3 3 7 3 3 3 7 ||= 289.7 ||= 124.1 ||= 2.33 ||=   ||
-||=   ||=   ||=   ||= 10\23 ||=   ||= 521.7 ||= 3 3 4 3 3 3 4 ||= 208.7 ||= 156.5 ||= 1.33 ||
+||=   ||=   ||=   ||= 9\20 ||=   ||   ||   ||= 540.0 ||= 2 2 5 2 2 2 5 ||= 300.0 ||= 120.0 ||= 2.50 ||=   ||
-||=   ||=   ||=   ||=   ||= 17\39 ||= 523.1 ||= 5 5 7 5 5 5 7 ||= 215.4 ||= 153.8 ||= 1.40 ||
+||=   ||=   ||=   ||=   ||= 14\31 ||   ||   ||= 541.9 ||= 3 3 8 3 3 3 8 ||= 309.7 ||= 116.1 ||= 2.66 ||=   ||
-||=   ||=   ||= 7\16 ||=   ||=   ||= 525.0 ||= 2 2 3 2 2 2 3 ||= 225.0 ||= 150.0 ||= 1.50 ||
+||=   ||=   ||= 5\11 ||=   ||=   ||   ||   ||= 545.5 ||= 1 1 3 1 1 1 3 ||= 327.3 ||= 109.1 ||= 3.00 ||=   ||
-||=   ||=   ||=   ||=   ||= 18\41 ||= 526.8 ||= 5 5 8 5 5 5 8 ||= 234.1 ||= 146.3 ||= 1.60 ||
+||=   ||=   ||=   ||=   ||= 11\24 ||   ||   ||= 550.0 ||= 2 2 7 2 2 2 7 ||= 350.0 ||= 100.0 ||= 3.50 ||=   ||
-||=   ||=   ||=   ||= 11\25 ||=   ||= 528.0 ||= 3 3 5 3 3 3 5 ||= 240.0 ||= 144.0 ||= 1.67 ||
+||=   ||=   ||=   ||= 6\13 ||=   ||   ||   ||= 553.8 ||= 1 1 4 1 1 1 4 ||= 369.2 ||= 92.3 ||= 4.00 ||=   ||
-||=   ||=   ||=   ||=   ||= 15\34 ||= 529.4 ||= 4 4 7 4 4 4 7 ||= 247.1 ||= 141.2 ||= 1.75 ||
+||=   ||=   ||=   ||=   ||= 7\15 ||   ||   ||= 560.0 ||= 1 1 5 1 1 1 5 ||= 400.0 ||= 80.0 ||= 5.00 ||=   ||
-||=   ||= 4\9 ||=   ||=   ||=   ||= 533.3 ||= 1 1 2 1 1 1 2 ||= 266.7 ||= 133.3 ||= 2.00 ||
+||=   ||=   ||=   ||=   ||=   ||= 8\17 ||=   ||= 564.7 ||= 1 1 6 1 1 1 6 ||= 423.5 ||= 70.6 ||= 6.00 ||=   ||
-||=   ||=   ||=   ||=   ||= 13\29 ||= 537.9 ||= 3 3 7 3 3 3 7 ||= 289.7 ||= 124.1 ||= 2.33 ||
+||=   ||=   ||=   ||=   ||=   ||=   ||= 9\19 ||= 568.4 ||= 1 1 7 1 1 1 7 ||= 442.1 ||= 63.2 ||= 7.00 ||= Liese/Triton is around here ||
-||=   ||=   ||=   ||= 9\20 ||=   ||= 540.0 ||= 2 2 5 2 2 2 5 ||= 300.0 ||= 120.0 ||= 2.50 ||
+||= 1\2 ||=   ||=   ||=   ||=   ||   ||   ||= 600.0 ||= 0 0 1 0 0 0 1 ||= 600.0 ||= 0 ||= — ||=   ||</pre></div>
-||=   ||=   ||=   ||=   ||= 14\31 ||= 541.9 ||= 3 3 8 3 3 3 8 ||= 309.7 ||= 116.1 ||= 2.66 ||
-||=   ||=   ||= 5\11 ||=   ||=   ||= 545.5 ||= 1 1 3 1 1 1 3 ||= 327.3 ||= 109.1 ||= 3.00 ||
-||=   ||=   ||=   ||=   ||= 11\24 ||= 550.0 ||= 2 2 7 2 2 2 7 ||= 350.0 ||= 100.0 ||= 3.50 ||
-||=   ||=   ||=   ||= 6\13 ||=   ||= 553.8 ||= 1 1 4 1 1 1 4 ||= 369.2 ||= 92.3 ||= 4.00 ||
-||=   ||=   ||=   ||=   ||= 7\15 ||= 560.0 ||= 1 1 5 1 1 1 5 ||= 400.0 ||= 80.0 ||= 5.00 ||
-||= 1\2 ||=   ||=   ||=   ||=   ||= 600.0 ||= 0 0 1 0 0 0 1 ||= 600.0 ||= 0 ||= -- ||</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;2L 5s&lt;/title&gt;&lt;/head&gt;&lt;body&gt;2L 5s refers to a Moment of Symmetry scale with two large steps and five small steps. Common names for such a tuning are mavila and anti-diatonic. The generator is a sharp fourth (or flat fifth), falling between 3\7 (3 degrees of &lt;a class="wiki_link" href="/7edo"&gt;7edo&lt;/a&gt;) and 1\2 (1 degree of &lt;a class="wiki_link" href="/2edo"&gt;2edo&lt;/a&gt; -- the half-octave tritone that appears in every even-numbered edo).&lt;br /&gt;
+<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;2L 5s&lt;/title&gt;&lt;/head&gt;&lt;body&gt;2L 5s refers to a Moment of Symmetry scale with two large steps and five small steps. Common names for such a tuning are mavila and anti-diatonic. The generator is a sharp fourth (or flat fifth), falling between 3\7 (3 degrees of &lt;a class="wiki_link" href="/7edo"&gt;7edo&lt;/a&gt;) and 1\2 (1 degree of &lt;a class="wiki_link" href="/2edo"&gt;2edo&lt;/a&gt; — the half-octave tritone that appears in every even-numbered edo).&lt;br /&gt;
 &lt;br /&gt;
 The word &amp;quot;mavila&amp;quot; is used in different ways by different folks. Not every user of the word would consider every 2L 5s scale an instance of &amp;quot;mavila.&amp;quot; In particular, between 13\29 and 14\31, and centered on 9\20, is the albitonic scale for the score temperament &lt;a class="wiki_link" href="/chromatic%20pair"&gt;chromatic pair&lt;/a&gt;, which is not intended to be treated as having any kind of fifth, flat or otherwise.&lt;br /&gt;
 &lt;br /&gt;
-Generalized form in seven modes:&lt;br /&gt;
+In terms of harmonic entropy, the most significant minimum is at &lt;a class="wiki_link" href="/Meantone%20family"&gt;Liese&lt;/a&gt;/Triton, in which the generator is about 7/5 and three of them make a 3/1.&lt;br /&gt;
-&lt;br /&gt;
-s s L s s s L&lt;br /&gt;
-s L s s s L s&lt;br /&gt;
-L s s s L s s&lt;br /&gt;
-s s s L s s L&lt;br /&gt;
-s s L s s L s&lt;br /&gt;
-s L s s L s s&lt;br /&gt;
-L s s L s s s&lt;br /&gt;
-&lt;br /&gt;
 &lt;table class="wiki_table"&gt;
      &lt;tr&gt;
-         &lt;th colspan="5"&gt;generator in degrees of an &lt;a class="wiki_link" href="/edo"&gt;edo&lt;/a&gt;&lt;br /&gt;
+         &lt;th colspan="7"&gt;generator in degrees of an &lt;a class="wiki_link" href="/edo"&gt;edo&lt;/a&gt;&lt;br /&gt;
 &lt;/th&gt;
          &lt;th&gt;generator in cents&lt;br /&gt;
@@ Line 68: / Line 53: @@
 &lt;/th&gt;
          &lt;th&gt;L to s ratio&lt;br /&gt;
+&lt;/th&gt;
+        &lt;th&gt;comments&lt;br /&gt;
 &lt;/th&gt;
      &lt;/tr&gt;
@@ Line 80: / Line 67: @@
 &lt;/td&gt;
          &lt;td style="text-align: center;"&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 style="text-align: center;"&gt;514.3&lt;br /&gt;
@@ Line 90: / Line 81: @@
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;1.00&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 102: / Line 95: @@
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;13\30&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 style="text-align: center;"&gt;520.0&lt;br /&gt;
@@ Line 112: / Line 109: @@
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;1.25&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 124: / Line 123: @@
 &lt;/td&gt;
          &lt;td style="text-align: center;"&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 style="text-align: center;"&gt;521.7&lt;br /&gt;
@@ Line 134: / Line 137: @@
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;1.33&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;Mavila is in this general region&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 146: / Line 151: @@
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;17\39&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 style="text-align: center;"&gt;523.1&lt;br /&gt;
@@ Line 156: / Line 165: @@
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;1.40&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 168: / Line 179: @@
 &lt;/td&gt;
          &lt;td style="text-align: center;"&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 style="text-align: center;"&gt;525.0&lt;br /&gt;
@@ Line 178: / Line 193: @@
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;1.50&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 190: / Line 207: @@
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;18\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 style="text-align: center;"&gt;526.8&lt;br /&gt;
@@ Line 200: / Line 221: @@
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;1.60&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 212: / Line 235: @@
 &lt;/td&gt;
          &lt;td style="text-align: center;"&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 style="text-align: center;"&gt;528.0&lt;br /&gt;
@@ Line 222: / Line 249: @@
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;1.67&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 234: / Line 263: @@
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;15\34&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 style="text-align: center;"&gt;529.4&lt;br /&gt;
@@ Line 244: / Line 277: @@
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;1.75&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 256: / Line 291: @@
 &lt;/td&gt;
          &lt;td style="text-align: center;"&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 style="text-align: center;"&gt;533.3&lt;br /&gt;
@@ Line 266: / Line 305: @@
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;2.00&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;Boundary of propriety (generators&lt;br /&gt;
+smaller than this are proper)&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 278: / Line 320: @@
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;13\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 style="text-align: center;"&gt;537.9&lt;br /&gt;
@@ Line 288: / Line 334: @@
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;2.33&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 300: / Line 348: @@
 &lt;/td&gt;
          &lt;td style="text-align: center;"&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 style="text-align: center;"&gt;540.0&lt;br /&gt;
@@ Line 310: / Line 362: @@
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;2.50&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 322: / Line 376: @@
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;14\31&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 style="text-align: center;"&gt;541.9&lt;br /&gt;
@@ Line 332: / Line 390: @@
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;2.66&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 344: / Line 404: @@
 &lt;/td&gt;
          &lt;td style="text-align: center;"&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 style="text-align: center;"&gt;545.5&lt;br /&gt;
@@ Line 354: / Line 418: @@
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;3.00&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 366: / Line 432: @@
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;11\24&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 style="text-align: center;"&gt;550.0&lt;br /&gt;
@@ Line 376: / Line 446: @@
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;3.50&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 388: / Line 460: @@
 &lt;/td&gt;
          &lt;td style="text-align: center;"&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 style="text-align: center;"&gt;553.8&lt;br /&gt;
@@ Line 398: / Line 474: @@
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;4.00&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 410: / Line 488: @@
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;7\15&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 style="text-align: center;"&gt;560.0&lt;br /&gt;
@@ Line 420: / Line 502: @@
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;5.00&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;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;8\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;564.7&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;1 1 6 1 1 1 6&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;423.5&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;70.6&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;6.00&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;&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\19&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;568.4&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;1 1 7 1 1 1 7&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;442.1&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;63.2&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;7.00&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;Liese/Triton is around here&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 432: / Line 572: @@
 &lt;/td&gt;
          &lt;td style="text-align: center;"&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 style="text-align: center;"&gt;600.0&lt;br /&gt;
@@ Line 441: / Line 585: @@
          &lt;td style="text-align: center;"&gt;0&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;--&lt;br /&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;/tr&gt;