2L 3s: Difference between revisions

Revision as of 03:11, 7 November 2016

IMPORTED REVISION FROM WIKISPACES

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This revision was by author xenwolf and made on 2016-11-07 03:11:27 UTC.

The original revision id was 598650408.

The revision comment was: Reverted to Nov 6, 2016 9:01 pm: The problem is that you hide information by changing from "Scale steps" to "Trichord": you don't see the trichord distance any more. So better add another column for the Trichord view.

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

Original Wikitext content:

"Classic" [[pentatonic]]. Perhaps the most common scale in the world.

The [[meantone]] pentatonic scale, in which the generator approximates 4/3 but other intervals in the scale approximate 6/5 and 5/4, has by far the lowest harmonic entropy of all 5-note MOS scales, which explains the worldwide popularity of these scales and their very long history of use. It is also strictly [[Rothenberg propriety|proper]].
||||||||||||~ Generator ||~ Cents ||~ s ||~ L-s ||~ |L-2s| ||~ Scale steps ||~ Comments ||
|| 2\5 ||   ||   ||   ||   ||   || 480 || 240 || 0 || 240 || 1 1 1 1 1 ||=   ||
||   ||   ||   ||   ||   || 11\27 || 488.89 || 222.22 || 44.44 || 177.78 || 6 5 5 6 5 ||= Slendro (insofar as it resembles a MOS)
would be in this region ||
||   ||   ||   ||   || 9\22 ||   || 490.91 || 218.18 || 54.545 || 163.64 || 5 4 4 5 4 ||=   ||
||   ||   ||   ||   ||   || 16\39 || 492.31 || 215.38 || 61.54 || 153.85 || 9 7 7 9 7 ||= No-5's superpyth/dominant is around here ||
||   ||   ||   || 7\17 ||   ||   || 494.12 || 211.76 || 70.59 || 141.18 || 4 3 3 4 3 ||=   ||
||   ||   ||   ||   ||   || 19\46 || 495.65 || 208.7 || 78.26 || 130.435 || 11 8 8 11 8 ||   ||
||   ||   ||   ||   || 12\29 ||   || 496.55 || 206.9 || 82.76 || 124.14 || 7 5 5 7 5 ||=   ||
||   ||   ||   ||   ||   || 17\41 || 497.56 || 204.88 || 87.8 || 117.07 || 10 7 7 10 7 ||= Pythagorean pentatonic is around here ||
||   ||   || 5\12 ||   ||   ||   || 500 || 200 || 100 || 100 || 3 2 2 3 2 ||= Familiar 12-equal pentatonic
(also optimum rank range: L/s=3/2) ||
||   ||   ||   ||   ||   ||   || 502.305 || 195.39 || 111.53 || 83.86 || pi 2 pi 2 2 ||   ||
||   ||   ||   ||   ||   || 18\43 || 502.33 || 195.35 || 111.63 || 83.72 || 11 7 7 11 7 ||   ||
||   ||   ||   ||   || 13\31 ||   || 503.23 || 193.55 || 116.13 || 77.42 || 8 5 5 8 5 ||= Optimal meantone pentatonic
is around here ||
||   ||   ||   ||   ||   ||   || 1200/(4-phi) || 192.43 || 118.93 || 73.50 || phi 1 1 phi 1 ||= Golden meantone ||
||   ||   ||   ||   ||   || 21\50 || 504 || 192 || 120 || 72 || 13 8 8 13 8 ||=   ||
||   ||   ||   || 8\19 ||   ||   || 505.26 || 189.47 || 126.32 || 63.16 || 5 3 3 5 3 ||=   ||
||   ||   ||   ||   ||   || 19\45 || 506.67 || 186.67 || 133.33 || 53.33 || 12 7 7 12 7 ||   ||
||   ||   ||   ||   ||   ||   || 507.18 || 185.64 || 135.9 || 49.74 || √3 1 √3 1 1 ||   ||
||   ||   ||   ||   || 11\26 ||   || 507.69 || 184.615 || 138.46 || 46.15 || 7 4 4 7 4 ||   ||
||   ||   ||   ||   ||   || 14\33 || 509.09 || 181.82 || 145.455 || 36.36 || 9 5 5 9 5 ||   ||
||   || 3\7 ||   ||   ||   ||   || 514.29 || 171.43 || 171.43 || 0 || 2 1 1 2 1 ||= (Boundary of propriety: smaller
generators than this are strictly proper) ||
||   ||   ||   ||   ||   || 13\30 || 520 || 160 || 200 || 40 || 9 4 4 9 4 ||   ||
||<   ||<   ||<   ||<   ||< 10\23 ||<   ||< 521.74 ||< 156.52 ||< 208.7 ||< 52.17 ||< 7 3 3 7 3 ||<   ||
||   ||   ||   ||   ||   || 17\39 || 523.08 || 153.84 || 215.385 || 61.54 || 12 5 5 12 5 ||   ||
||   ||   ||   || 7\16 ||   ||   || 525 || 150 || 225 || 75 || 5 2 2 5 2 ||= 5-note subset of pelog (insofar as it
resembles a MOS) would be in this region ||
||   ||   ||   ||   ||   || 18\41 || 526.83 || 146.34 || 234.15 || 87.8 || 13 5 5 13 5 ||   ||
||   ||   ||   ||   ||   ||   || 600(25+√5)/31 || 145.7 || 235.75 || 90.05 || phi+1 1 1 phi+1 1 ||   ||
||   ||   ||   ||   || 11\25 ||   || 528 || 144 || 240 || 96 || 8 3 3 8 3 ||   ||
||   ||   ||   ||   ||   ||   || 528.88 || 142.24 || 244.405 || 102.17 || e 1 e 1 1 ||= L/s = e ||
||   ||   ||   ||   ||   || 15\34 || 529.41 || 141.18 || 247.06 || 105.88 || 11 4 4 11 4 ||   ||
||   ||   || 4\9 ||   ||   ||   || 533.33 || 133.33 || 266.67 || 133.33 || 3 1 1 3 1 ||= L/s = 3 ||
||   ||   ||   ||   ||   ||   || 535.36 || 129.26 || 276.835 || 147.57 || pi 1 pi 1 1 ||= <span style="display: block; text-align: center;">L/s = pi</span> ||
||   ||   ||   ||   ||   || 13\29 || 537.93 || 124.14 || 289.655 || 165.52 || 10 3 3 10 3 ||   ||
||   ||   ||   ||   || 9\20 ||   || 540 || 120 || 240 || 180 || 7 2 2 7 2 ||   ||
||   ||   ||   ||   ||   || 14\31 || 541.935 || 116.13 || 309.68 || 193.55 || 11 3 3 11 3 ||   ||
||   ||   ||   || 5\11 ||   ||   || 545.45 || 109.09 || 327.27 || 218.18 || 4 1 1 4 1 ||= L/s = 4 ||
||   ||   ||   ||   ||   || 11\24 || 550 || 100 || 350 || 250 || 9 2 2 9 2 ||   ||
||   ||   ||   ||   || 6\13 ||   || 553.85 || 92.31 || 369.23 || 276.92 || 5 1 1 5 1 ||   ||
||   ||   ||   ||   ||   || 7\15 || 560 || 80 || 480 || 400 || 6 1 1 6 1 ||   ||
|| 1\2 ||   ||   ||   ||   ||   || 600 || 0 || 600 || 600 || 1 0 0 1 0 ||=   ||

From a [[3-limit]] perspective, just make a chain of four 4/3's and octave-reduce, and you end up with pentatonic.

From a [[5-limit]] perspective, the most interesting temperaments with this kind of pentatonic scale are [[meantone]] and [[Pelogic family|mavila]].

There is also the interesting 2.3.7 temperament that tempers out [[64_63|64/63]] ("no-fives [[dominant]]").

Original HTML content:

<html><head><title>2L 3s</title></head><body>&quot;Classic&quot; <a class="wiki_link" href="/pentatonic">pentatonic</a>. Perhaps the most common scale in the world.<br />
<br />
The <a class="wiki_link" href="/meantone">meantone</a> pentatonic scale, in which the generator approximates 4/3 but other intervals in the scale approximate 6/5 and 5/4, has by far the lowest harmonic entropy of all 5-note MOS scales, which explains the worldwide popularity of these scales and their very long history of use. It is also strictly <a class="wiki_link" href="/Rothenberg%20propriety">proper</a>.<br />


<table class="wiki_table">
    <tr>
        <th colspan="6">Generator<br />
</th>
        <th>Cents<br />
</th>
        <th>s<br />
</th>
        <th>L-s<br />
</th>
        <th>|L-2s|<br />
</th>
        <th>Scale steps<br />
</th>
        <th>Comments<br />
</th>
    </tr>
    <tr>
        <td>2\5<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>480<br />
</td>
        <td>240<br />
</td>
        <td>0<br />
</td>
        <td>240<br />
</td>
        <td>1 1 1 1 1<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>11\27<br />
</td>
        <td>488.89<br />
</td>
        <td>222.22<br />
</td>
        <td>44.44<br />
</td>
        <td>177.78<br />
</td>
        <td>6 5 5 6 5<br />
</td>
        <td style="text-align: center;">Slendro (insofar as it resembles a MOS)<br />
would be in this region<br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>9\22<br />
</td>
        <td><br />
</td>
        <td>490.91<br />
</td>
        <td>218.18<br />
</td>
        <td>54.545<br />
</td>
        <td>163.64<br />
</td>
        <td>5 4 4 5 4<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>16\39<br />
</td>
        <td>492.31<br />
</td>
        <td>215.38<br />
</td>
        <td>61.54<br />
</td>
        <td>153.85<br />
</td>
        <td>9 7 7 9 7<br />
</td>
        <td style="text-align: center;">No-5's superpyth/dominant is around here<br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>7\17<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>494.12<br />
</td>
        <td>211.76<br />
</td>
        <td>70.59<br />
</td>
        <td>141.18<br />
</td>
        <td>4 3 3 4 3<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>19\46<br />
</td>
        <td>495.65<br />
</td>
        <td>208.7<br />
</td>
        <td>78.26<br />
</td>
        <td>130.435<br />
</td>
        <td>11 8 8 11 8<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>12\29<br />
</td>
        <td><br />
</td>
        <td>496.55<br />
</td>
        <td>206.9<br />
</td>
        <td>82.76<br />
</td>
        <td>124.14<br />
</td>
        <td>7 5 5 7 5<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>17\41<br />
</td>
        <td>497.56<br />
</td>
        <td>204.88<br />
</td>
        <td>87.8<br />
</td>
        <td>117.07<br />
</td>
        <td>10 7 7 10 7<br />
</td>
        <td style="text-align: center;">Pythagorean pentatonic is around here<br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td>5\12<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>500<br />
</td>
        <td>200<br />
</td>
        <td>100<br />
</td>
        <td>100<br />
</td>
        <td>3 2 2 3 2<br />
</td>
        <td style="text-align: center;">Familiar 12-equal pentatonic<br />
(also optimum rank range: L/s=3/2)<br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>502.305<br />
</td>
        <td>195.39<br />
</td>
        <td>111.53<br />
</td>
        <td>83.86<br />
</td>
        <td>pi 2 pi 2 2<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>18\43<br />
</td>
        <td>502.33<br />
</td>
        <td>195.35<br />
</td>
        <td>111.63<br />
</td>
        <td>83.72<br />
</td>
        <td>11 7 7 11 7<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>13\31<br />
</td>
        <td><br />
</td>
        <td>503.23<br />
</td>
        <td>193.55<br />
</td>
        <td>116.13<br />
</td>
        <td>77.42<br />
</td>
        <td>8 5 5 8 5<br />
</td>
        <td style="text-align: center;">Optimal meantone pentatonic<br />
is around here<br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>1200/(4-phi)<br />
</td>
        <td>192.43<br />
</td>
        <td>118.93<br />
</td>
        <td>73.50<br />
</td>
        <td>phi 1 1 phi 1<br />
</td>
        <td style="text-align: center;">Golden meantone<br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>21\50<br />
</td>
        <td>504<br />
</td>
        <td>192<br />
</td>
        <td>120<br />
</td>
        <td>72<br />
</td>
        <td>13 8 8 13 8<br />
</td>
        <td style="text-align: center;"><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>8\19<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>505.26<br />
</td>
        <td>189.47<br />
</td>
        <td>126.32<br />
</td>
        <td>63.16<br />
</td>
        <td>5 3 3 5 3<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>19\45<br />
</td>
        <td>506.67<br />
</td>
        <td>186.67<br />
</td>
        <td>133.33<br />
</td>
        <td>53.33<br />
</td>
        <td>12 7 7 12 7<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>507.18<br />
</td>
        <td>185.64<br />
</td>
        <td>135.9<br />
</td>
        <td>49.74<br />
</td>
        <td>√3 1 √3 1 1<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>11\26<br />
</td>
        <td><br />
</td>
        <td>507.69<br />
</td>
        <td>184.615<br />
</td>
        <td>138.46<br />
</td>
        <td>46.15<br />
</td>
        <td>7 4 4 7 4<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>14\33<br />
</td>
        <td>509.09<br />
</td>
        <td>181.82<br />
</td>
        <td>145.455<br />
</td>
        <td>36.36<br />
</td>
        <td>9 5 5 9 5<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td>3\7<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>514.29<br />
</td>
        <td>171.43<br />
</td>
        <td>171.43<br />
</td>
        <td>0<br />
</td>
        <td>2 1 1 2 1<br />
</td>
        <td style="text-align: center;">(Boundary of propriety: smaller<br />
generators than this are strictly proper)<br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>13\30<br />
</td>
        <td>520<br />
</td>
        <td>160<br />
</td>
        <td>200<br />
</td>
        <td>40<br />
</td>
        <td>9 4 4 9 4<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td style="text-align: left;"><br />
</td>
        <td style="text-align: left;"><br />
</td>
        <td style="text-align: left;"><br />
</td>
        <td style="text-align: left;"><br />
</td>
        <td style="text-align: left;">10\23<br />
</td>
        <td style="text-align: left;"><br />
</td>
        <td style="text-align: left;">521.74<br />
</td>
        <td style="text-align: left;">156.52<br />
</td>
        <td style="text-align: left;">208.7<br />
</td>
        <td style="text-align: left;">52.17<br />
</td>
        <td style="text-align: left;">7 3 3 7 3<br />
</td>
        <td style="text-align: left;"><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>17\39<br />
</td>
        <td>523.08<br />
</td>
        <td>153.84<br />
</td>
        <td>215.385<br />
</td>
        <td>61.54<br />
</td>
        <td>12 5 5 12 5<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>7\16<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>525<br />
</td>
        <td>150<br />
</td>
        <td>225<br />
</td>
        <td>75<br />
</td>
        <td>5 2 2 5 2<br />
</td>
        <td style="text-align: center;">5-note subset of pelog (insofar as it<br />
resembles a MOS) would be in this region<br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>18\41<br />
</td>
        <td>526.83<br />
</td>
        <td>146.34<br />
</td>
        <td>234.15<br />
</td>
        <td>87.8<br />
</td>
        <td>13 5 5 13 5<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>600(25+√5)/31<br />
</td>
        <td>145.7<br />
</td>
        <td>235.75<br />
</td>
        <td>90.05<br />
</td>
        <td>phi+1 1 1 phi+1 1<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>11\25<br />
</td>
        <td><br />
</td>
        <td>528<br />
</td>
        <td>144<br />
</td>
        <td>240<br />
</td>
        <td>96<br />
</td>
        <td>8 3 3 8 3<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>528.88<br />
</td>
        <td>142.24<br />
</td>
        <td>244.405<br />
</td>
        <td>102.17<br />
</td>
        <td>e 1 e 1 1<br />
</td>
        <td style="text-align: center;">L/s = e<br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>15\34<br />
</td>
        <td>529.41<br />
</td>
        <td>141.18<br />
</td>
        <td>247.06<br />
</td>
        <td>105.88<br />
</td>
        <td>11 4 4 11 4<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td>4\9<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>533.33<br />
</td>
        <td>133.33<br />
</td>
        <td>266.67<br />
</td>
        <td>133.33<br />
</td>
        <td>3 1 1 3 1<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>535.36<br />
</td>
        <td>129.26<br />
</td>
        <td>276.835<br />
</td>
        <td>147.57<br />
</td>
        <td>pi 1 pi 1 1<br />
</td>
        <td style="text-align: center;"><span style="display: block; text-align: center;">L/s = pi</span><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>13\29<br />
</td>
        <td>537.93<br />
</td>
        <td>124.14<br />
</td>
        <td>289.655<br />
</td>
        <td>165.52<br />
</td>
        <td>10 3 3 10 3<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>9\20<br />
</td>
        <td><br />
</td>
        <td>540<br />
</td>
        <td>120<br />
</td>
        <td>240<br />
</td>
        <td>180<br />
</td>
        <td>7 2 2 7 2<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>14\31<br />
</td>
        <td>541.935<br />
</td>
        <td>116.13<br />
</td>
        <td>309.68<br />
</td>
        <td>193.55<br />
</td>
        <td>11 3 3 11 3<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>5\11<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>545.45<br />
</td>
        <td>109.09<br />
</td>
        <td>327.27<br />
</td>
        <td>218.18<br />
</td>
        <td>4 1 1 4 1<br />
</td>
        <td style="text-align: center;">L/s = 4<br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>11\24<br />
</td>
        <td>550<br />
</td>
        <td>100<br />
</td>
        <td>350<br />
</td>
        <td>250<br />
</td>
        <td>9 2 2 9 2<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>6\13<br />
</td>
        <td><br />
</td>
        <td>553.85<br />
</td>
        <td>92.31<br />
</td>
        <td>369.23<br />
</td>
        <td>276.92<br />
</td>
        <td>5 1 1 5 1<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>7\15<br />
</td>
        <td>560<br />
</td>
        <td>80<br />
</td>
        <td>480<br />
</td>
        <td>400<br />
</td>
        <td>6 1 1 6 1<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>1\2<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>600<br />
</td>
        <td>0<br />
</td>
        <td>600<br />
</td>
        <td>600<br />
</td>
        <td>1 0 0 1 0<br />
</td>
        <td style="text-align: center;"><br />
</td>
    </tr>
</table>

<br />
From a <a class="wiki_link" href="/3-limit">3-limit</a> perspective, just make a chain of four 4/3's and octave-reduce, and you end up with pentatonic.<br />
<br />
From a <a class="wiki_link" href="/5-limit">5-limit</a> perspective, the most interesting temperaments with this kind of pentatonic scale are <a class="wiki_link" href="/meantone">meantone</a> and <a class="wiki_link" href="/Pelogic%20family">mavila</a>.<br />
<br />
There is also the interesting 2.3.7 temperament that tempers out <a class="wiki_link" href="/64_63">64/63</a> (&quot;no-fives <a class="wiki_link" href="/dominant">dominant</a>&quot;).</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:JosephRuhf|JosephRuhf]] and made on <tt>2016-11-06 17:01:46 UTC</tt>.<br>
+: This revision was by author [[User:xenwolf|xenwolf]] and made on <tt>2016-11-07 03:11:27 UTC</tt>.<br>
-: The original revision id was <tt>598619904</tt>.<br>
+: The original revision id was <tt>598650408</tt>.<br>
-: The revision comment was: <tt></tt><br>
+: The revision comment was: <tt>Reverted to Nov 6, 2016 9:01 pm: The problem is that you hide information by changing from "Scale steps" to "Trichord": you don't see the trichord distance any more. So better add another column for the Trichord view.</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>
@@ Line 9: / Line 9: @@
 The [[meantone]] pentatonic scale, in which the generator approximates 4/3 but other intervals in the scale approximate 6/5 and 5/4, has by far the lowest harmonic entropy of all 5-note MOS scales, which explains the worldwide popularity of these scales and their very long history of use. It is also strictly [[Rothenberg propriety|proper]].
-||||||||||||~ Generator ||~ Cents ||~ s ||~ L-s ||~ |L-2s| ||~ Trichord ||~ Comments ||
+||||||||||||~ Generator ||~ Cents ||~ s ||~ L-s ||~ |L-2s| ||~ Scale steps ||~ Comments ||
-|| 2\5 ||   ||   ||   ||   ||   || 480 || 240 || 0 || 240 || 1 1 ||=   ||
+|| 2\5 ||   ||   ||   ||   ||   || 480 || 240 || 0 || 240 || 1 1 1 1 1 ||=   ||
-||   ||   ||   ||   ||   || 11\27 || 488.89 || 222.22 || 44.44 || 177.78 || 6 5 ||= Slendro pentatonic (insofar as it resembles a MOS) ||
+||   ||   ||   ||   ||   || 11\27 || 488.89 || 222.22 || 44.44 || 177.78 || 6 5 5 6 5 ||= Slendro (insofar as it resembles a MOS)
-||   ||   ||   ||   || 9\22 ||   || 490.91 || 218.18 || 54.545 || 163.64 || 5 4 ||=   ||
+would be in this region ||
-||   ||   ||   ||   ||   || 16\39 || 492.31 || 215.38 || 61.54 || 153.85 || 9 7 ||= No-5's superpyth/dominant is around here ||
+||   ||   ||   ||   || 9\22 ||   || 490.91 || 218.18 || 54.545 || 163.64 || 5 4 4 5 4 ||=   ||
-||   ||   ||   || 7\17 ||   ||   || 494.12 || 211.76 || 70.59 || 141.18 || 4 3 ||=   ||
+||   ||   ||   ||   ||   || 16\39 || 492.31 || 215.38 || 61.54 || 153.85 || 9 7 7 9 7 ||= No-5's superpyth/dominant is around here ||
-||   ||   ||   ||   ||   || 19\46 || 495.65 || 208.7 || 78.26 || 130.435 || 11 8 ||   ||
+||   ||   ||   || 7\17 ||   ||   || 494.12 || 211.76 || 70.59 || 141.18 || 4 3 3 4 3 ||=   ||
-||   ||   ||   ||   || 12\29 ||   || 496.55 || 206.9 || 82.76 || 124.14 || 7 5 ||=   ||
+||   ||   ||   ||   ||   || 19\46 || 495.65 || 208.7 || 78.26 || 130.435 || 11 8 8 11 8 ||   ||
-||   ||   ||   ||   ||   || 17\41 || 497.56 || 204.88 || 87.8 || 117.07 || 10 7 ||= Pythagorean pentatonic is around here ||
+||   ||   ||   ||   || 12\29 ||   || 496.55 || 206.9 || 82.76 || 124.14 || 7 5 5 7 5 ||=   ||
-||   ||   || 5\12 ||   ||   ||   || 500 || 200 || 100 || 100 || 3 2 ||= Familiar 12-equal pentatonic
+||   ||   ||   ||   ||   || 17\41 || 497.56 || 204.88 || 87.8 || 117.07 || 10 7 7 10 7 ||= Pythagorean pentatonic is around here ||
+||   ||   || 5\12 ||   ||   ||   || 500 || 200 || 100 || 100 || 3 2 2 3 2 ||= Familiar 12-equal pentatonic
 (also optimum rank range: L/s=3/2) ||
-||   ||   ||   ||   ||   ||   || 502.305 || 195.39 || 111.53 || 83.86 || pi 2 ||   ||
+||   ||   ||   ||   ||   ||   || 502.305 || 195.39 || 111.53 || 83.86 || pi 2 pi 2 2 ||   ||
-||   ||   ||   ||   ||   || 18\43 || 502.33 || 195.35 || 111.63 || 83.72 || 11 7 ||   ||
+||   ||   ||   ||   ||   || 18\43 || 502.33 || 195.35 || 111.63 || 83.72 || 11 7 7 11 7 ||   ||
-||   ||   ||   ||   || 13\31 ||   || 503.23 || 193.55 || 116.13 || 77.42 || 8 5 ||= Optimal meantone pentatonic
+||   ||   ||   ||   || 13\31 ||   || 503.23 || 193.55 || 116.13 || 77.42 || 8 5 5 8 5 ||= Optimal meantone pentatonic
 is around here ||
-||   ||   ||   ||   ||   ||   || 1200/(4-phi) || 192.43 || 118.93 || 73.50 || phi 1 ||= Golden meantone ||
+||   ||   ||   ||   ||   ||   || 1200/(4-phi) || 192.43 || 118.93 || 73.50 || phi 1 1 phi 1 ||= Golden meantone ||
-||   ||   ||   ||   ||   || 21\50 || 504 || 192 || 120 || 72 || 13 8 ||=   ||
+||   ||   ||   ||   ||   || 21\50 || 504 || 192 || 120 || 72 || 13 8 8 13 8 ||=   ||
-||   ||   ||   || 8\19 ||   ||   || 505.26 || 189.47 || 126.32 || 63.16 || 5 3 ||=   ||
+||   ||   ||   || 8\19 ||   ||   || 505.26 || 189.47 || 126.32 || 63.16 || 5 3 3 5 3 ||=   ||
-||   ||   ||   ||   ||   || 19\45 || 506.67 || 186.67 || 133.33 || 53.33 || 12 7 ||   ||
+||   ||   ||   ||   ||   || 19\45 || 506.67 || 186.67 || 133.33 || 53.33 || 12 7 7 12 7 ||   ||
-||   ||   ||   ||   ||   ||   || 507.18 || 185.64 || 135.9 || 49.74 || √3 1 ||   ||
+||   ||   ||   ||   ||   ||   || 507.18 || 185.64 || 135.9 || 49.74 || √3 1 √3 1 1 ||   ||
-||   ||   ||   ||   || 11\26 ||   || 507.69 || 184.615 || 138.46 || 46.15 || 7 4 ||   ||
+||   ||   ||   ||   || 11\26 ||   || 507.69 || 184.615 || 138.46 || 46.15 || 7 4 4 7 4 ||   ||
-||   ||   ||   ||   ||   || 14\33 || 509.09 || 181.82 || 145.455 || 36.36 || 9 5 ||   ||
+||   ||   ||   ||   ||   || 14\33 || 509.09 || 181.82 || 145.455 || 36.36 || 9 5 5 9 5 ||   ||
-||   || 3\7 ||   ||   ||   ||   || 514.29 || 171.43 || 171.43 || 0 || 2 1 ||= (Boundary of propriety: smaller
+||   || 3\7 ||   ||   ||   ||   || 514.29 || 171.43 || 171.43 || 0 || 2 1 1 2 1 ||= (Boundary of propriety: smaller
 generators than this are strictly proper) ||
-||   ||   ||   ||   ||   || 13\30 || 520 || 160 || 200 || 40 || 9 4 ||   ||
+||   ||   ||   ||   ||   || 13\30 || 520 || 160 || 200 || 40 || 9 4 4 9 4 ||   ||
-||&lt;   ||&lt;   ||&lt;   ||&lt;   ||&lt; 10\23 ||&lt;   ||&lt; 521.74 ||&lt; 156.52 ||&lt; 208.7 ||&lt; 52.17 ||&lt; 7 3 ||&lt;   ||
+||&lt;   ||&lt;   ||&lt;   ||&lt;   ||&lt; 10\23 ||&lt;   ||&lt; 521.74 ||&lt; 156.52 ||&lt; 208.7 ||&lt; 52.17 ||&lt; 7 3 3 7 3 ||&lt;   ||
-||   ||   ||   ||   ||   || 17\39 || 523.08 || 153.84 || 215.385 || 61.54 || 12 5 ||   ||
+||   ||   ||   ||   ||   || 17\39 || 523.08 || 153.84 || 215.385 || 61.54 || 12 5 5 12 5 ||   ||
-||   ||   ||   || 7\16 ||   ||   || 525 || 150 || 225 || 75 || 5 2 ||= &lt;span style="display: block; text-align: center;"&gt;Pelog pentatonic (insofar as it resembles a MOS)&lt;/span&gt; ||
+||   ||   ||   || 7\16 ||   ||   || 525 || 150 || 225 || 75 || 5 2 2 5 2 ||= 5-note subset of pelog (insofar as it
-||   ||   ||   ||   ||   || 18\41 || 526.83 || 146.34 || 234.15 || 87.8 || 13 5 ||   ||
+resembles a MOS) would be in this region ||
-||   ||   ||   ||   ||   ||   || 600(25+√5)/31 || 145.7 || 235.75 || 90.05 || phi+1 1 ||   ||
+||   ||   ||   ||   ||   || 18\41 || 526.83 || 146.34 || 234.15 || 87.8 || 13 5 5 13 5 ||   ||
-||   ||   ||   ||   || 11\25 ||   || 528 || 144 || 240 || 96 || 8 3 ||   ||
+||   ||   ||   ||   ||   ||   || 600(25+√5)/31 || 145.7 || 235.75 || 90.05 || phi+1 1 1 phi+1 1 ||   ||
-||   ||   ||   ||   ||   ||   || 528.88 || 142.24 || 244.405 || 102.17 || e 1 ||= L/s = e ||
+||   ||   ||   ||   || 11\25 ||   || 528 || 144 || 240 || 96 || 8 3 3 8 3 ||   ||
-||   ||   ||   ||   ||   || 15\34 || 529.41 || 141.18 || 247.06 || 105.88 || 11 4 ||   ||
+||   ||   ||   ||   ||   ||   || 528.88 || 142.24 || 244.405 || 102.17 || e 1 e 1 1 ||= L/s = e ||
-||   ||   || 4\9 ||   ||   ||   || 533.33 || 133.33 || 266.67 || 133.33 || 3 1 ||= L/s = 3 ||
+||   ||   ||   ||   ||   || 15\34 || 529.41 || 141.18 || 247.06 || 105.88 || 11 4 4 11 4 ||   ||
-||   ||   ||   ||   ||   ||   || 535.36 || 129.26 || 276.835 || 147.57 || pi 1 ||= &lt;span style="display: block; text-align: center;"&gt;L/s = pi&lt;/span&gt; ||
+||   ||   || 4\9 ||   ||   ||   || 533.33 || 133.33 || 266.67 || 133.33 || 3 1 1 3 1 ||= L/s = 3 ||
-||   ||   ||   ||   ||   || 13\29 || 537.93 || 124.14 || 289.655 || 165.52 || 10 3 ||   ||
+||   ||   ||   ||   ||   ||   || 535.36 || 129.26 || 276.835 || 147.57 || pi 1 pi 1 1 ||= &lt;span style="display: block; text-align: center;"&gt;L/s = pi&lt;/span&gt; ||
-||   ||   ||   ||   || 9\20 ||   || 540 || 120 || 240 || 180 || 7 2 ||   ||
+||   ||   ||   ||   ||   || 13\29 || 537.93 || 124.14 || 289.655 || 165.52 || 10 3 3 10 3 ||   ||
-||   ||   ||   ||   ||   || 14\31 || 541.935 || 116.13 || 309.68 || 193.55 || 11 3 ||   ||
+||   ||   ||   ||   || 9\20 ||   || 540 || 120 || 240 || 180 || 7 2 2 7 2 ||   ||
-||   ||   ||   || 5\11 ||   ||   || 545.45 || 109.09 || 327.27 || 218.18 || 4 1 ||= L/s = 4 ||
+||   ||   ||   ||   ||   || 14\31 || 541.935 || 116.13 || 309.68 || 193.55 || 11 3 3 11 3 ||   ||
-||   ||   ||   ||   ||   || 11\24 || 550 || 100 || 350 || 250 || 9 2 ||   ||
+||   ||   ||   || 5\11 ||   ||   || 545.45 || 109.09 || 327.27 || 218.18 || 4 1 1 4 1 ||= L/s = 4 ||
-||   ||   ||   ||   || 6\13 ||   || 553.85 || 92.31 || 369.23 || 276.92 || 5 1 ||   ||
+||   ||   ||   ||   ||   || 11\24 || 550 || 100 || 350 || 250 || 9 2 2 9 2 ||   ||
-||   ||   ||   ||   ||   || 7\15 || 560 || 80 || 480 || 400 || 6 1 ||   ||
+||   ||   ||   ||   || 6\13 ||   || 553.85 || 92.31 || 369.23 || 276.92 || 5 1 1 5 1 ||   ||
+||   ||   ||   ||   ||   || 7\15 || 560 || 80 || 480 || 400 || 6 1 1 6 1 ||   ||
 || 1\2 ||   ||   ||   ||   ||   || 600 || 0 || 600 || 600 || 1 0 0 1 0 ||=   ||
@@ Line 76: / Line 78: @@
          &lt;th&gt;|L-2s|&lt;br /&gt;
 &lt;/th&gt;
-         &lt;th&gt;Trichord&lt;br /&gt;
+         &lt;th&gt;Scale steps&lt;br /&gt;
 &lt;/th&gt;
          &lt;th&gt;Comments&lt;br /&gt;
@@ Line 102: / Line 104: @@
          &lt;td&gt;240&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;1 1&lt;br /&gt;
+         &lt;td&gt;1 1 1 1 1&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;&lt;br /&gt;
@@ Line 128: / Line 130: @@
          &lt;td&gt;177.78&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;6 5&lt;br /&gt;
+         &lt;td&gt;6 5 5 6 5&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;Slendro pentatonic (insofar as it resembles a MOS)&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;Slendro (insofar as it resembles a MOS)&lt;br /&gt;
+would be in this region&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 154: / Line 157: @@
          &lt;td&gt;163.64&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;5 4&lt;br /&gt;
+         &lt;td&gt;5 4 4 5 4&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;&lt;br /&gt;
@@ Line 180: / Line 183: @@
          &lt;td&gt;153.85&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;9 7&lt;br /&gt;
+         &lt;td&gt;9 7 7 9 7&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;No-5's superpyth/dominant is around here&lt;br /&gt;
@@ Line 206: / Line 209: @@
          &lt;td&gt;141.18&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;4 3&lt;br /&gt;
+         &lt;td&gt;4 3 3 4 3&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;&lt;br /&gt;
@@ Line 232: / Line 235: @@
          &lt;td&gt;130.435&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;11 8&lt;br /&gt;
+         &lt;td&gt;11 8 8 11 8&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;
@@ Line 258: / Line 261: @@
          &lt;td&gt;124.14&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;7 5&lt;br /&gt;
+         &lt;td&gt;7 5 5 7 5&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;&lt;br /&gt;
@@ Line 284: / Line 287: @@
          &lt;td&gt;117.07&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;10 7&lt;br /&gt;
+         &lt;td&gt;10 7 7 10 7&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;Pythagorean pentatonic is around here&lt;br /&gt;
@@ Line 310: / Line 313: @@
          &lt;td&gt;100&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;3 2&lt;br /&gt;
+         &lt;td&gt;3 2 2 3 2&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;Familiar 12-equal pentatonic&lt;br /&gt;
@@ Line 337: / Line 340: @@
          &lt;td&gt;83.86&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;pi 2&lt;br /&gt;
+         &lt;td&gt;pi 2 pi 2 2&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;
@@ Line 363: / Line 366: @@
          &lt;td&gt;83.72&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;11 7&lt;br /&gt;
+         &lt;td&gt;11 7 7 11 7&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;
@@ Line 389: / Line 392: @@
          &lt;td&gt;77.42&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;8 5&lt;br /&gt;
+         &lt;td&gt;8 5 5 8 5&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;Optimal meantone pentatonic&lt;br /&gt;
@@ Line 416: / Line 419: @@
          &lt;td&gt;73.50&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;phi 1&lt;br /&gt;
+         &lt;td&gt;phi 1 1 phi 1&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;Golden meantone&lt;br /&gt;
@@ Line 442: / Line 445: @@
          &lt;td&gt;72&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;13 8&lt;br /&gt;
+         &lt;td&gt;13 8 8 13 8&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;&lt;br /&gt;
@@ Line 468: / Line 471: @@
          &lt;td&gt;63.16&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;5 3&lt;br /&gt;
+         &lt;td&gt;5 3 3 5 3&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;&lt;br /&gt;
@@ Line 494: / Line 497: @@
          &lt;td&gt;53.33&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;12 7&lt;br /&gt;
+         &lt;td&gt;12 7 7 12 7&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;
@@ Line 520: / Line 523: @@
          &lt;td&gt;49.74&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;√3 1&lt;br /&gt;
+         &lt;td&gt;√3 1 √3 1 1&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;
@@ Line 546: / Line 549: @@
          &lt;td&gt;46.15&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;7 4&lt;br /&gt;
+         &lt;td&gt;7 4 4 7 4&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;
@@ Line 572: / Line 575: @@
          &lt;td&gt;36.36&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;9 5&lt;br /&gt;
+         &lt;td&gt;9 5 5 9 5&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;
@@ Line 598: / Line 601: @@
          &lt;td&gt;0&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;2 1&lt;br /&gt;
+         &lt;td&gt;2 1 1 2 1&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;(Boundary of propriety: smaller&lt;br /&gt;
@@ Line 625: / Line 628: @@
          &lt;td&gt;40&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;9 4&lt;br /&gt;
+         &lt;td&gt;9 4 4 9 4&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;
@@ Line 651: / Line 654: @@
          &lt;td style="text-align: left;"&gt;52.17&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: left;"&gt;7 3&lt;br /&gt;
+         &lt;td style="text-align: left;"&gt;7 3 3 7 3&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: left;"&gt;&lt;br /&gt;
@@ Line 677: / Line 680: @@
          &lt;td&gt;61.54&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;12 5&lt;br /&gt;
+         &lt;td&gt;12 5 5 12 5&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;
@@ Line 703: / Line 706: @@
          &lt;td&gt;75&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;5 2&lt;br /&gt;
+         &lt;td&gt;5 2 2 5 2&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;&lt;span style="display: block; text-align: center;"&gt;Pelog pentatonic (insofar as it resembles a MOS)&lt;/span&gt;&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;5-note subset of pelog (insofar as it&lt;br /&gt;
+resembles a MOS) would be in this region&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 729: / Line 733: @@
          &lt;td&gt;87.8&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;13 5&lt;br /&gt;
+         &lt;td&gt;13 5 5 13 5&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;
@@ Line 755: / Line 759: @@
          &lt;td&gt;90.05&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;phi+1 1&lt;br /&gt;
+         &lt;td&gt;phi+1 1 1 phi+1 1&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;
@@ Line 781: / Line 785: @@
          &lt;td&gt;96&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;8 3&lt;br /&gt;
+         &lt;td&gt;8 3 3 8 3&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;
@@ Line 807: / Line 811: @@
          &lt;td&gt;102.17&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;e 1&lt;br /&gt;
+         &lt;td&gt;e 1 e 1 1&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;L/s = e&lt;br /&gt;
@@ Line 833: / Line 837: @@
          &lt;td&gt;105.88&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;11 4&lt;br /&gt;
+         &lt;td&gt;11 4 4 11 4&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;
@@ Line 859: / Line 863: @@
          &lt;td&gt;133.33&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;3 1&lt;br /&gt;
+         &lt;td&gt;3 1 1 3 1&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;L/s = 3&lt;br /&gt;
@@ Line 885: / Line 889: @@
          &lt;td&gt;147.57&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;pi 1&lt;br /&gt;
+         &lt;td&gt;pi 1 pi 1 1&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;&lt;span style="display: block; text-align: center;"&gt;L/s = pi&lt;/span&gt;&lt;br /&gt;
@@ Line 911: / Line 915: @@
          &lt;td&gt;165.52&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;10 3&lt;br /&gt;
+         &lt;td&gt;10 3 3 10 3&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;
@@ Line 937: / Line 941: @@
          &lt;td&gt;180&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;7 2&lt;br /&gt;
+         &lt;td&gt;7 2 2 7 2&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;
@@ Line 963: / Line 967: @@
          &lt;td&gt;193.55&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;11 3&lt;br /&gt;
+         &lt;td&gt;11 3 3 11 3&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;
@@ Line 989: / Line 993: @@
          &lt;td&gt;218.18&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;4 1&lt;br /&gt;
+         &lt;td&gt;4 1 1 4 1&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;L/s = 4&lt;br /&gt;
@@ Line 1,015: / Line 1,019: @@
          &lt;td&gt;250&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;9 2&lt;br /&gt;
+         &lt;td&gt;9 2 2 9 2&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;
@@ Line 1,041: / Line 1,045: @@
          &lt;td&gt;276.92&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;5 1&lt;br /&gt;
+         &lt;td&gt;5 1 1 5 1&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;
@@ Line 1,067: / Line 1,071: @@
          &lt;td&gt;400&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;6 1&lt;br /&gt;
+         &lt;td&gt;6 1 1 6 1&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;

2L 3s: Difference between revisions

Revision as of 03:11, 7 November 2016

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