2L 5s: Difference between revisions

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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 2.7.11.13 subgroup temperament [[Chromatic pairs#Score|score]], which is not intended to be treated as having any kind of fifth, flat or otherwise.

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 ||~ tetrachord ||~ L in cents ||~ s in cents ||~ L to s ratio ||~ comments ||
||= 3\7 ||=   ||=   ||=   ||=   ||   ||   ||= 514.3 ||= 1 1 1 ||= 171.4 ||= 171.4 ||= 1.00 ||=   ||
||=   ||=   ||=   ||=   ||= 13\30 ||   ||   ||= 520.0 ||= 4 4 5 ||= 200.0 ||= 160.0 ||= 1.25 ||= Mavila extends from here... ||
||=   ||=   ||=   ||= 10\23 ||=   ||   ||   ||= 521.7 ||= 3 3 4 ||= 208.7 ||= 156.5 ||= 1.33 ||=   ||
||=   ||=   ||=   ||=   ||= 17\39 ||   ||   ||= 523.1 ||= 5 5 7 ||= 215.4 ||= 153.8 ||= 1.40 ||=   ||
||=   ||=   ||= 7\16 ||=   ||=   ||   ||   ||= 525.0 ||= 2 2 3 ||= 225.0 ||= 150.0 ||= 1.50 ||= Mavila in Armodue
Optimum rank range (L/s=3/2) ||
||=   ||=   ||=   ||=   ||= 18\41 ||   ||   ||= 526.8 ||= 5 5 8 ||= 234.1 ||= 146.3 ||= 1.60 ||=   ||
||   ||   ||   ||   ||   ||   ||   ||= 1200*5/(13-phi) ||= 1 1 phi ||= 235.7 ||= 145.7 ||= phi ||= Golden mavila ||
||   ||   ||   ||   ||   || 29\66 ||   ||= 527.3 ||= 8 8 13 ||= 236.4 ||= 145.5 ||= 1.62 ||=   ||
||=   ||=   ||=   ||= 11\25 ||=   ||   ||   ||= 528.0 ||= 3 3 5 ||= 240.0 ||= 144.0 ||= 1.67 ||=   ||
||=   ||=   ||=   ||=   ||= 15\34 ||   ||   ||= 529.4 ||= 4 4 7 ||= 247.1 ||= 141.2 ||= 1.75 ||= ...to somewhere around here ||
||=   ||= 4\9 ||=   ||=   ||=   ||   ||   ||= 533.3 ||= 1 1 2 ||= 266.7 ||= 133.3 ||= 2.00 ||= Boundary of propriety (generators
smaller than this are proper) ||
||=   ||=   ||=   ||=   ||= 13\29 ||   ||   ||= 537.9 ||= 3 3 7 ||= 289.7 ||= 124.1 ||= 2.33 ||=   ||
||=   ||=   ||=   ||= 9\20 ||=   ||   ||   ||= 540.0 ||= 2 2 5 ||= 300.0 ||= 120.0 ||= 2.50 ||=   ||
||=   ||=   ||=   ||=   ||= 14\31 ||   ||   ||= 541.9 ||= 3 3 8 ||= 309.7 ||= 116.1 ||= 2.66 ||=   ||
||   ||   ||   ||   ||   ||   ||   ||= 545.2 ||= 1 1 2.97 ||= 325.9 ||= 109.6 ||= 2.97 ||= L/s = 3/2^(1/75) ||
||=   ||=   ||= 5\11 ||=   ||=   ||   ||   ||= 545.5 ||= 1 1 3 ||= 327.3 ||= 109.1 ||= 3.00 ||= L/s = 3 ||
||   ||   ||   ||   ||   ||   ||   ||= 545.7 ||= 1 1 3.03 ||= 328.65 ||= 108.5 ||= 3.03 ||= <span style="display: block; text-align: center;">L/s = 3*2^(1/75)</span> ||
||=   ||=   ||=   ||=   ||= 11\24 ||   ||   ||= 550.0 ||= 2 2 7 ||= 350.0 ||= 100.0 ||= 3.50 ||=   ||
||=   ||=   ||=   ||= 6\13 ||=   ||   ||   ||= 553.8 ||= 1 1 4 ||= 369.2 ||= 92.3 ||= 4.00 ||= Thuja is optimal around here
L/s = 4 ||
||=   ||=   ||=   ||=   ||= 7\15 ||   ||   ||= 560.0 ||= 1 1 5 ||= 400.0 ||= 80.0 ||= 5.00 ||= ie. (11/8)^5 = 5/1 ||
||=   ||=   ||=   ||=   ||=   ||= 8\17 ||=   ||= 564.7 ||= 1 1 6 ||= 423.5 ||= 70.6 ||= 6.00 ||=   ||
||=   ||=   ||=   ||=   ||=   ||=   ||= 9\19 ||= 568.4 ||= 1 1 7 ||= 442.1 ||= 63.2 ||= 7.00 ||= Liese/Triton is around here ||
||= 1\2 ||=   ||=   ||=   ||=   ||   ||   ||= 600.0 ||= 0 0 1 ||= 600.0 ||= 0 ||= — ||=   ||

Original HTML content:

<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).<br />
<br />
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 2.7.11.13 subgroup temperament <a class="wiki_link" href="/Chromatic%20pairs#Score">score</a>, which is not intended to be treated as having any kind of fifth, flat or otherwise.<br />
<br />
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.<br />


<table class="wiki_table">
    <tr>
        <th colspan="7">generator in degrees of an <a class="wiki_link" href="/edo">edo</a><br />
</th>
        <th>generator in cents<br />
</th>
        <th>tetrachord<br />
</th>
        <th>L in cents<br />
</th>
        <th>s in cents<br />
</th>
        <th>L to s ratio<br />
</th>
        <th>comments<br />
</th>
    </tr>
    <tr>
        <td style="text-align: center;">3\7<br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td style="text-align: center;">514.3<br />
</td>
        <td style="text-align: center;">1 1 1<br />
</td>
        <td style="text-align: center;">171.4<br />
</td>
        <td style="text-align: center;">171.4<br />
</td>
        <td style="text-align: center;">1.00<br />
</td>
        <td style="text-align: center;"><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;"><br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td style="text-align: center;">13\30<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td style="text-align: center;">520.0<br />
</td>
        <td style="text-align: center;">4 4 5<br />
</td>
        <td style="text-align: center;">200.0<br />
</td>
        <td style="text-align: center;">160.0<br />
</td>
        <td style="text-align: center;">1.25<br />
</td>
        <td style="text-align: center;">Mavila extends from here...<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;"><br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td style="text-align: center;">10\23<br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td style="text-align: center;">521.7<br />
</td>
        <td style="text-align: center;">3 3 4<br />
</td>
        <td style="text-align: center;">208.7<br />
</td>
        <td style="text-align: center;">156.5<br />
</td>
        <td style="text-align: center;">1.33<br />
</td>
        <td style="text-align: center;"><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;"><br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td style="text-align: center;">17\39<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td style="text-align: center;">523.1<br />
</td>
        <td style="text-align: center;">5 5 7<br />
</td>
        <td style="text-align: center;">215.4<br />
</td>
        <td style="text-align: center;">153.8<br />
</td>
        <td style="text-align: center;">1.40<br />
</td>
        <td style="text-align: center;"><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;"><br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td style="text-align: center;">7\16<br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td style="text-align: center;">525.0<br />
</td>
        <td style="text-align: center;">2 2 3<br />
</td>
        <td style="text-align: center;">225.0<br />
</td>
        <td style="text-align: center;">150.0<br />
</td>
        <td style="text-align: center;">1.50<br />
</td>
        <td style="text-align: center;">Mavila in Armodue<br />
Optimum rank range (L/s=3/2)<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;"><br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td style="text-align: center;">18\41<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td style="text-align: center;">526.8<br />
</td>
        <td style="text-align: center;">5 5 8<br />
</td>
        <td style="text-align: center;">234.1<br />
</td>
        <td style="text-align: center;">146.3<br />
</td>
        <td style="text-align: center;">1.60<br />
</td>
        <td style="text-align: center;"><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td style="text-align: center;">1200*5/(13-phi)<br />
</td>
        <td style="text-align: center;">1 1 phi<br />
</td>
        <td style="text-align: center;">235.7<br />
</td>
        <td style="text-align: center;">145.7<br />
</td>
        <td style="text-align: center;">phi<br />
</td>
        <td style="text-align: center;">Golden mavila<br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>29\66<br />
</td>
        <td><br />
</td>
        <td style="text-align: center;">527.3<br />
</td>
        <td style="text-align: center;">8 8 13<br />
</td>
        <td style="text-align: center;">236.4<br />
</td>
        <td style="text-align: center;">145.5<br />
</td>
        <td style="text-align: center;">1.62<br />
</td>
        <td style="text-align: center;"><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;"><br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td style="text-align: center;">11\25<br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td style="text-align: center;">528.0<br />
</td>
        <td style="text-align: center;">3 3 5<br />
</td>
        <td style="text-align: center;">240.0<br />
</td>
        <td style="text-align: center;">144.0<br />
</td>
        <td style="text-align: center;">1.67<br />
</td>
        <td style="text-align: center;"><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;"><br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td style="text-align: center;">15\34<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td style="text-align: center;">529.4<br />
</td>
        <td style="text-align: center;">4 4 7<br />
</td>
        <td style="text-align: center;">247.1<br />
</td>
        <td style="text-align: center;">141.2<br />
</td>
        <td style="text-align: center;">1.75<br />
</td>
        <td style="text-align: center;">...to somewhere around here<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;"><br />
</td>
        <td style="text-align: center;">4\9<br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td style="text-align: center;">533.3<br />
</td>
        <td style="text-align: center;">1 1 2<br />
</td>
        <td style="text-align: center;">266.7<br />
</td>
        <td style="text-align: center;">133.3<br />
</td>
        <td style="text-align: center;">2.00<br />
</td>
        <td style="text-align: center;">Boundary of propriety (generators<br />
smaller than this are proper)<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;"><br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td style="text-align: center;">13\29<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td style="text-align: center;">537.9<br />
</td>
        <td style="text-align: center;">3 3 7<br />
</td>
        <td style="text-align: center;">289.7<br />
</td>
        <td style="text-align: center;">124.1<br />
</td>
        <td style="text-align: center;">2.33<br />
</td>
        <td style="text-align: center;"><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;"><br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td style="text-align: center;">9\20<br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td style="text-align: center;">540.0<br />
</td>
        <td style="text-align: center;">2 2 5<br />
</td>
        <td style="text-align: center;">300.0<br />
</td>
        <td style="text-align: center;">120.0<br />
</td>
        <td style="text-align: center;">2.50<br />
</td>
        <td style="text-align: center;"><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;"><br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td style="text-align: center;">14\31<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td style="text-align: center;">541.9<br />
</td>
        <td style="text-align: center;">3 3 8<br />
</td>
        <td style="text-align: center;">309.7<br />
</td>
        <td style="text-align: center;">116.1<br />
</td>
        <td style="text-align: center;">2.66<br />
</td>
        <td style="text-align: center;"><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td style="text-align: center;">545.2<br />
</td>
        <td style="text-align: center;">1 1 2.97<br />
</td>
        <td style="text-align: center;">325.9<br />
</td>
        <td style="text-align: center;">109.6<br />
</td>
        <td style="text-align: center;">2.97<br />
</td>
        <td style="text-align: center;">L/s = 3/2^(1/75)<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;"><br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td style="text-align: center;">5\11<br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td style="text-align: center;">545.5<br />
</td>
        <td style="text-align: center;">1 1 3<br />
</td>
        <td style="text-align: center;">327.3<br />
</td>
        <td style="text-align: center;">109.1<br />
</td>
        <td style="text-align: center;">3.00<br />
</td>
        <td style="text-align: center;">L/s = 3<br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td style="text-align: center;">545.7<br />
</td>
        <td style="text-align: center;">1 1 3.03<br />
</td>
        <td style="text-align: center;">328.65<br />
</td>
        <td style="text-align: center;">108.5<br />
</td>
        <td style="text-align: center;">3.03<br />
</td>
        <td style="text-align: center;"><span style="display: block; text-align: center;">L/s = 3*2^(1/75)</span><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;"><br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td style="text-align: center;">11\24<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td style="text-align: center;">550.0<br />
</td>
        <td style="text-align: center;">2 2 7<br />
</td>
        <td style="text-align: center;">350.0<br />
</td>
        <td style="text-align: center;">100.0<br />
</td>
        <td style="text-align: center;">3.50<br />
</td>
        <td style="text-align: center;"><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;"><br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td style="text-align: center;">6\13<br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td style="text-align: center;">553.8<br />
</td>
        <td style="text-align: center;">1 1 4<br />
</td>
        <td style="text-align: center;">369.2<br />
</td>
        <td style="text-align: center;">92.3<br />
</td>
        <td style="text-align: center;">4.00<br />
</td>
        <td style="text-align: center;">Thuja is optimal around here<br />
L/s = 4<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;"><br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td style="text-align: center;">7\15<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td style="text-align: center;">560.0<br />
</td>
        <td style="text-align: center;">1 1 5<br />
</td>
        <td style="text-align: center;">400.0<br />
</td>
        <td style="text-align: center;">80.0<br />
</td>
        <td style="text-align: center;">5.00<br />
</td>
        <td style="text-align: center;">ie. (11/8)^5 = 5/1<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;"><br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td style="text-align: center;">8\17<br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td style="text-align: center;">564.7<br />
</td>
        <td style="text-align: center;">1 1 6<br />
</td>
        <td style="text-align: center;">423.5<br />
</td>
        <td style="text-align: center;">70.6<br />
</td>
        <td style="text-align: center;">6.00<br />
</td>
        <td style="text-align: center;"><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;"><br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td style="text-align: center;">9\19<br />
</td>
        <td style="text-align: center;">568.4<br />
</td>
        <td style="text-align: center;">1 1 7<br />
</td>
        <td style="text-align: center;">442.1<br />
</td>
        <td style="text-align: center;">63.2<br />
</td>
        <td style="text-align: center;">7.00<br />
</td>
        <td style="text-align: center;">Liese/Triton is around here<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">1\2<br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td style="text-align: center;">600.0<br />
</td>
        <td style="text-align: center;">0 0 1<br />
</td>
        <td style="text-align: center;">600.0<br />
</td>
        <td style="text-align: center;">0<br />
</td>
        <td style="text-align: center;">—<br />
</td>
        <td style="text-align: center;"><br />
</td>
    </tr>
</table>

</body></html>

@@ 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:keenanpepper|keenanpepper]] and made on <tt>2012-11-24 13:16:20 UTC</tt>.<br>
+: This revision was by author [[User:JosephRuhf|JosephRuhf]] and made on <tt>2015-02-10 23:19:22 UTC</tt>.<br>
-: The original revision id was <tt>385547970</tt>.<br>
+: The original revision id was <tt>540550588</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>
@@ Line 11: / Line 11: @@
 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 ||
+||||||||||||||~ generator in degrees of an [[edo]] ||~ generator in cents ||~ tetrachord ||~ L in cents ||~ s in cents ||~ L to s ratio ||~ comments ||
-||= 3\7 ||=   ||=   ||=   ||=   ||   ||   ||= 514.3 ||= 1 1 1 1 1 1 1 ||= 171.4 ||= 171.4 ||= 1.00 ||=   ||
+||= 3\7 ||=   ||=   ||=   ||=   ||   ||   ||= 514.3 ||= 1 1 1 ||= 171.4 ||= 171.4 ||= 1.00 ||=   ||
-||=   ||=   ||=   ||=   ||= 13\30 ||   ||   ||= 520.0 ||= 4 4 5 4 4 4 5 ||= 200.0 ||= 160.0 ||= 1.25 ||= Mavila extends from here... ||
+||=   ||=   ||=   ||=   ||= 13\30 ||   ||   ||= 520.0 ||= 4 4 5 ||= 200.0 ||= 160.0 ||= 1.25 ||= Mavila extends from here... ||
-||=   ||=   ||=   ||= 10\23 ||=   ||   ||   ||= 521.7 ||= 3 3 4 3 3 3 4 ||= 208.7 ||= 156.5 ||= 1.33 ||=   ||
+||=   ||=   ||=   ||= 10\23 ||=   ||   ||   ||= 521.7 ||= 3 3 4 ||= 208.7 ||= 156.5 ||= 1.33 ||=   ||
-||=   ||=   ||=   ||=   ||= 17\39 ||   ||   ||= 523.1 ||= 5 5 7 5 5 5 7 ||= 215.4 ||= 153.8 ||= 1.40 ||=   ||
+||=   ||=   ||=   ||=   ||= 17\39 ||   ||   ||= 523.1 ||= 5 5 7 ||= 215.4 ||= 153.8 ||= 1.40 ||=   ||
-||=   ||=   ||= 7\16 ||=   ||=   ||   ||   ||= 525.0 ||= 2 2 3 2 2 2 3 ||= 225.0 ||= 150.0 ||= 1.50 ||= Mavila in Armodue
+||=   ||=   ||= 7\16 ||=   ||=   ||   ||   ||= 525.0 ||= 2 2 3 ||= 225.0 ||= 150.0 ||= 1.50 ||= Mavila in Armodue
 Optimum rank range (L/s=3/2) ||
-||=   ||=   ||=   ||=   ||= 18\41 ||   ||   ||= 526.8 ||= 5 5 8 5 5 5 8 ||= 234.1 ||= 146.3 ||= 1.60 ||=   ||
+||=   ||=   ||=   ||=   ||= 18\41 ||   ||   ||= 526.8 ||= 5 5 8 ||= 234.1 ||= 146.3 ||= 1.60 ||=   ||
-||   ||   ||   ||   ||   ||   ||   ||= 1200*5/(13-phi) ||= 1 1 phi 1... ||= 235.7 ||= 145.7 ||= phi ||= Golden mavila ||
+||   ||   ||   ||   ||   ||   ||   ||= 1200*5/(13-phi) ||= 1 1 phi ||= 235.7 ||= 145.7 ||= phi ||= Golden mavila ||
-||   ||   ||   ||   ||   || 29\66 ||   ||= 527.3 ||= 8 8 13... ||= 236.4 ||= 145.5 ||= 1.62 ||=   ||
+||   ||   ||   ||   ||   || 29\66 ||   ||= 527.3 ||= 8 8 13 ||= 236.4 ||= 145.5 ||= 1.62 ||=   ||
-||=   ||=   ||=   ||= 11\25 ||=   ||   ||   ||= 528.0 ||= 3 3 5 3 3 3 5 ||= 240.0 ||= 144.0 ||= 1.67 ||=   ||
+||=   ||=   ||=   ||= 11\25 ||=   ||   ||   ||= 528.0 ||= 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 ||= ...to somewhere around here ||
+||=   ||=   ||=   ||=   ||= 15\34 ||   ||   ||= 529.4 ||= 4 4 7 ||= 247.1 ||= 141.2 ||= 1.75 ||= ...to somewhere around here ||
-||=   ||= 4\9 ||=   ||=   ||=   ||   ||   ||= 533.3 ||= 1 1 2 1 1 1 2 ||= 266.7 ||= 133.3 ||= 2.00 ||= Boundary of propriety (generators
+||=   ||= 4\9 ||=   ||=   ||=   ||   ||   ||= 533.3 ||= 1 1 2 ||= 266.7 ||= 133.3 ||= 2.00 ||= Boundary of propriety (generators
 smaller than this are proper) ||
-||=   ||=   ||=   ||=   ||= 13\29 ||   ||   ||= 537.9 ||= 3 3 7 3 3 3 7 ||= 289.7 ||= 124.1 ||= 2.33 ||=   ||
+||=   ||=   ||=   ||=   ||= 13\29 ||   ||   ||= 537.9 ||= 3 3 7 ||= 289.7 ||= 124.1 ||= 2.33 ||=   ||
-||=   ||=   ||=   ||= 9\20 ||=   ||   ||   ||= 540.0 ||= 2 2 5 2 2 2 5 ||= 300.0 ||= 120.0 ||= 2.50 ||=   ||
+||=   ||=   ||=   ||= 9\20 ||=   ||   ||   ||= 540.0 ||= 2 2 5 ||= 300.0 ||= 120.0 ||= 2.50 ||=   ||
-||=   ||=   ||=   ||=   ||= 14\31 ||   ||   ||= 541.9 ||= 3 3 8 3 3 3 8 ||= 309.7 ||= 116.1 ||= 2.66 ||=   ||
+||=   ||=   ||=   ||=   ||= 14\31 ||   ||   ||= 541.9 ||= 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 ||= L/s = 3 ||
+||   ||   ||   ||   ||   ||   ||   ||= 545.2 ||= 1 1 2.97 ||= 325.9 ||= 109.6 ||= 2.97 ||= L/s = 3/2^(1/75) ||
-||=   ||=   ||=   ||=   ||= 11\24 ||   ||   ||= 550.0 ||= 2 2 7 2 2 2 7 ||= 350.0 ||= 100.0 ||= 3.50 ||=   ||
+||=   ||=   ||= 5\11 ||=   ||=   ||   ||   ||= 545.5 ||= 1 1 3 ||= 327.3 ||= 109.1 ||= 3.00 ||= L/s = 3 ||
-||=   ||=   ||=   ||= 6\13 ||=   ||   ||   ||= 553.8 ||= 1 1 4 1 1 1 4 ||= 369.2 ||= 92.3 ||= 4.00 ||= Thuja is optimal around here
+||   ||   ||   ||   ||   ||   ||   ||= 545.7 ||= 1 1 3.03 ||= 328.65 ||= 108.5 ||= 3.03 ||= &lt;span style="display: block; text-align: center;"&gt;L/s = 3*2^(1/75)&lt;/span&gt; ||
+||=   ||=   ||=   ||=   ||= 11\24 ||   ||   ||= 550.0 ||= 2 2 7 ||= 350.0 ||= 100.0 ||= 3.50 ||=   ||
+||=   ||=   ||=   ||= 6\13 ||=   ||   ||   ||= 553.8 ||= 1 1 4 ||= 369.2 ||= 92.3 ||= 4.00 ||= Thuja is optimal around here
 L/s = 4 ||
-||=   ||=   ||=   ||=   ||= 7\15 ||   ||   ||= 560.0 ||= 1 1 5 1 1 1 5 ||= 400.0 ||= 80.0 ||= 5.00 ||= ie. (11/8)^5 = 5/1 ||
+||=   ||=   ||=   ||=   ||= 7\15 ||   ||   ||= 560.0 ||= 1 1 5 ||= 400.0 ||= 80.0 ||= 5.00 ||= ie. (11/8)^5 = 5/1 ||
-||=   ||=   ||=   ||=   ||=   ||= 8\17 ||=   ||= 564.7 ||= 1 1 6 1 1 1 6 ||= 423.5 ||= 70.6 ||= 6.00 ||=   ||
+||=   ||=   ||=   ||=   ||=   ||= 8\17 ||=   ||= 564.7 ||= 1 1 6 ||= 423.5 ||= 70.6 ||= 6.00 ||=   ||
-||=   ||=   ||=   ||=   ||=   ||=   ||= 9\19 ||= 568.4 ||= 1 1 7 1 1 1 7 ||= 442.1 ||= 63.2 ||= 7.00 ||= Liese/Triton is around here ||
+||=   ||=   ||=   ||=   ||=   ||=   ||= 9\19 ||= 568.4 ||= 1 1 7 ||= 442.1 ||= 63.2 ||= 7.00 ||= Liese/Triton is around here ||
-||= 1\2 ||=   ||=   ||=   ||=   ||   ||   ||= 600.0 ||= 0 0 1 0 0 0 1 ||= 600.0 ||= 0 ||= — ||=   ||</pre></div>
+||= 1\2 ||=   ||=   ||=   ||=   ||   ||   ||= 600.0 ||= 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;
@@ Line 50: / Line 52: @@
          &lt;th&gt;generator in cents&lt;br /&gt;
 &lt;/th&gt;
-         &lt;th&gt;scale&lt;br /&gt;
+         &lt;th&gt;tetrachord&lt;br /&gt;
 &lt;/th&gt;
          &lt;th&gt;L in cents&lt;br /&gt;
@@ Line 78: / Line 80: @@
          &lt;td style="text-align: center;"&gt;514.3&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;1 1 1 1 1 1 1&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;1 1 1&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;171.4&lt;br /&gt;
@@ Line 106: / Line 108: @@
          &lt;td style="text-align: center;"&gt;520.0&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;4 4 5 4 4 4 5&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;4 4 5&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;200.0&lt;br /&gt;
@@ Line 134: / Line 136: @@
          &lt;td style="text-align: center;"&gt;521.7&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;3 3 4 3 3 3 4&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;3 3 4&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;208.7&lt;br /&gt;
@@ Line 162: / Line 164: @@
          &lt;td style="text-align: center;"&gt;523.1&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;5 5 7 5 5 5 7&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;5 5 7&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;215.4&lt;br /&gt;
@@ Line 190: / Line 192: @@
          &lt;td style="text-align: center;"&gt;525.0&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;2 2 3 2 2 2 3&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;2 2 3&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;225.0&lt;br /&gt;
@@ Line 219: / Line 221: @@
          &lt;td style="text-align: center;"&gt;526.8&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;5 5 8 5 5 5 8&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;5 5 8&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;234.1&lt;br /&gt;
@@ Line 247: / Line 249: @@
          &lt;td style="text-align: center;"&gt;1200*5/(13-phi)&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;1 1 phi 1...&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;1 1 phi&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;235.7&lt;br /&gt;
@@ Line 275: / Line 277: @@
          &lt;td style="text-align: center;"&gt;527.3&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;8 8 13...&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;8 8 13&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;236.4&lt;br /&gt;
@@ Line 303: / Line 305: @@
          &lt;td style="text-align: center;"&gt;528.0&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;3 3 5 3 3 3 5&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;3 3 5&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;240.0&lt;br /&gt;
@@ Line 331: / Line 333: @@
          &lt;td style="text-align: center;"&gt;529.4&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;4 4 7 4 4 4 7&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;4 4 7&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;247.1&lt;br /&gt;
@@ Line 359: / Line 361: @@
          &lt;td style="text-align: center;"&gt;533.3&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;1 1 2 1 1 1 2&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;1 1 2&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;266.7&lt;br /&gt;
@@ Line 388: / Line 390: @@
          &lt;td style="text-align: center;"&gt;537.9&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;3 3 7 3 3 3 7&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;3 3 7&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;289.7&lt;br /&gt;
@@ Line 416: / Line 418: @@
          &lt;td style="text-align: center;"&gt;540.0&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;2 2 5 2 2 2 5&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;2 2 5&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;300.0&lt;br /&gt;
@@ Line 444: / Line 446: @@
          &lt;td style="text-align: center;"&gt;541.9&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;3 3 8 3 3 3 8&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;3 3 8&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;309.7&lt;br /&gt;
@@ Line 453: / Line 455: @@
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;&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;&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;545.2&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;1 1 2.97&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;325.9&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;109.6&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;2.97&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;L/s = 3/2^(1/75)&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 472: / Line 502: @@
          &lt;td style="text-align: center;"&gt;545.5&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;1 1 3 1 1 1 3&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;1 1 3&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;327.3&lt;br /&gt;
@@ Line 481: / Line 511: @@
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;L/s = 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;&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;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;545.7&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;1 1 3.03&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;328.65&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;108.5&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;3.03&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;&lt;span style="display: block; text-align: center;"&gt;L/s = 3*2^(1/75)&lt;/span&gt;&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 500: / Line 558: @@
          &lt;td style="text-align: center;"&gt;550.0&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;2 2 7 2 2 2 7&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;2 2 7&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;350.0&lt;br /&gt;
@@ Line 528: / Line 586: @@
          &lt;td style="text-align: center;"&gt;553.8&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;1 1 4 1 1 1 4&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;1 1 4&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;369.2&lt;br /&gt;
@@ Line 557: / Line 615: @@
          &lt;td style="text-align: center;"&gt;560.0&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;1 1 5 1 1 1 5&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;1 1 5&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;400.0&lt;br /&gt;
@@ Line 585: / Line 643: @@
          &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 style="text-align: center;"&gt;1 1 6&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;423.5&lt;br /&gt;
@@ Line 613: / Line 671: @@
          &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 style="text-align: center;"&gt;1 1 7&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;442.1&lt;br /&gt;
@@ Line 641: / Line 699: @@
          &lt;td style="text-align: center;"&gt;600.0&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;0 0 1 0 0 0 1&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;0 0 1&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;600.0&lt;br /&gt;

2L 5s: Difference between revisions

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