2L 3s
IMPORTED REVISION FROM WIKISPACES
This is an imported revision from Wikispaces. The revision metadata is included below for reference:
- This revision was by author keenanpepper and made on 2011-04-05 19:18:06 UTC.
- The original revision id was 217504062.
- The revision comment was:
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.
||||||||||~ Generator || ||~ Cents ||~ Scale steps ||~ Comments ||
|| 2\5 || || || || || || 480 || 1 1 1 1 1 ||= Slendro (insofar as it resembles a MOS)
would be in this region ||
|| || || || || 9\22 || || 490.91 || 5 4 4 5 4 || ||
|| || || || 7\17 || || || 494.12 || 4 3 3 4 3 || ||
|| || || || || 12\29 || || 496.55 || 7 5 5 7 5 || ||
|| || || || || || 17\41 || 497.56 || 10 7 7 10 7 ||= Pythagorean pentatonic is around here ||
|| || || 5\12 || || || || 500 || 3 2 2 3 2 ||= Familiar 12-equal pentatonic ||
|| || || || || 13\31 || || 503.23 || 8 5 5 8 5 ||= Optimal meantone pentatonic
is around here ||
|| || || || 8\19 || || || 505.26 || 5 3 3 5 3 || ||
|| || 3\7 || || || || || 514.29 || 2 1 1 2 1 || ||
|| || || || 7\16 || || || 525 || 5 2 2 5 2 ||= Pelog (insofar as it resembles a MOS)
would be in this region ||
|| || || 4\9 || || || || 533.33 || 3 1 1 3 1 || ||
|| || || || 5\11 || || || 545.45 || 4 1 1 4 1 || ||
|| 1\2 || || || || || || 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 [[mavila]].
There is also the interesting 2.3.7 temperament that tempers out 64/63 ("no-fives [[dominant]]").
Original HTML content:
<html><head><title>2L 3s</title></head><body>"Classic" pentatonic. Perhaps the most common scale in the world.<br />
<br />
<table class="wiki_table">
<tr>
<th colspan="5">Generator<br />
</th>
<td><br />
</td>
<th>Cents<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>1 1 1 1 1<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>5 4 4 5 4<br />
</td>
<td><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>4 3 3 4 3<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>7 5 5 7 5<br />
</td>
<td><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>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>3 2 2 3 2<br />
</td>
<td style="text-align: center;">Familiar 12-equal pentatonic<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>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>8\19<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>505.26<br />
</td>
<td>5 3 3 5 3<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>2 1 1 2 1<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>5 2 2 5 2<br />
</td>
<td style="text-align: center;">Pelog (insofar as it resembles a MOS)<br />
would be in this region<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>3 1 1 3 1<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>4 1 1 4 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>1 0 0 1 0<br />
</td>
<td><br />
</td>
</tr>
</table>
<br />
From a 3-limit perspective, just make a chain of four 4/3's and octave-reduce, and you end up with pentatonic.<br />
<br />
From a 5-limit 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="/mavila">mavila</a>.<br />
<br />
There is also the interesting 2.3.7 temperament that tempers out 64/63 ("no-fives <a class="wiki_link" href="/dominant">dominant</a>").</body></html>