Pergen names: 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:TallKite|TallKite]] and made on <tt>2017-11-18 09:23:19 UTC</tt>.

: This revision was by author [[User:TallKite|TallKite]] and made on <tt>2017-11-18 09:31:39 UTC</tt>.

: The original revision id was <tt>~~621915599~~</tt>.

: The original revision id was <tt>621915787</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.

Line 20:

For example, srutal could be {P8/2, M2/2}, but P5 is preferred because it is unsplit. Or it could be {P8/2, P12}, but P5 is preferred because it is smaller. Or it could be {P8/2, P4}, but P5 is always preferred over P4. Note that P5/2 is __not__ preferred over P4/2. For example, decimal is {P8/2, P4/2}, not {P8/2, P5/2}.

||||~ pergen ~~name~~ ||||||||~ example temperaments ||

||||~ pergen set ||||||||~ example temperaments ||

||~ written ||~ spoken ||~ comma(s) ||~ name ||||~ color name ||

||= {P8, P5} ||= fifth-based ||= 81/80 ||= meantone ||= green ||= gT ||

Line 39:

For non-standard prime groups, the period uses the first prime only, and the multi-gen uses the first two primes only. [[Kite's color notation|Color notation ]]is used to indicate primes higher than 3. For example, 2.5.7 with 50/49 tempered out is {P8/2, y3} = half-octave, yellow-third.

Rank-3 pergen sets have three intervals, any of which may be split. The unsplit 2.3.5... subgroup is {P8, P5, y3} = fifth-and-third-based. 2.3.5.7 with 50/49 tempered out is {P8/2, P5, y3} = half-octave fifth-and-third.

Rank-3 pergen sets have three intervals, any of which may be split. The unsplit 2.3.5... subgroup is {P8, P5, y3} = fifth-and-third-based. 2.3.5.7 with 50/49 tempered out is {P8/2, P5, y3}. If one knows that the rank is 3, it can be called half-octave, otherwise it's called half-octave fifth-and-third, to distinguish it from {P8/2, P5}. The color name of a temperament indicates the rank. This is the deep reddish temperament. The name has two explicit colors, red and yellow, and two implicit colors, clear and white (primes 2 and 3). 4 colors minus 1 comma equals rank-3.

Rank-4 temperaments have pergen sets of four intervals. Rank-1 temperaments could have pergen sets of one, such as {P8/12} for 12-edo or {P12/13} for 13-ed3, but there's no particular reason to do so.

Line 84:

<tr>

<th colspan="2">pergen ~~name~~

<th colspan="2">pergen set

</th>

<th colspan="4">example temperaments

Line 289:

For non-standard prime groups, the period uses the first prime only, and the multi-gen uses the first two primes only. <a class="wiki_link" href="/Kite%27s%20color%20notation">Color notation </a>is used to indicate primes higher than 3. For example, 2.5.7 with 50/49 tempered out is {P8/2, y3} = half-octave, yellow-third.

Rank-3 pergen sets have three intervals, any of which may be split. The unsplit 2.3.5... subgroup is {P8, P5, y3} = fifth-and-third-based. 2.3.5.7 with 50/49 tempered out is {P8/2, P5, y3} = half-octave fifth-and-third.

Rank-3 pergen sets have three intervals, any of which may be split. The unsplit 2.3.5... subgroup is {P8, P5, y3} = fifth-and-third-based. 2.3.5.7 with 50/49 tempered out is {P8/2, P5, y3}. If one knows that the rank is 3, it can be called half-octave, otherwise it's called half-octave fifth-and-third, to distinguish it from {P8/2, P5}. The color name of a temperament indicates the rank. This is the deep reddish temperament. The name has two explicit colors, red and yellow, and two implicit colors, clear and white (primes 2 and 3). 4 colors minus 1 comma equals rank-3.

Rank-4 temperaments have pergen sets of four intervals. Rank-1 temperaments could have pergen sets of one, such as {P8/12} for 12-edo or {P12/13} for 13-ed3, but there's no particular reason to do so.

@@ 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:TallKite|TallKite]] and made on <tt>2017-11-18 09:23:19 UTC</tt>.<br>
+: This revision was by author [[User:TallKite|TallKite]] and made on <tt>2017-11-18 09:31:39 UTC</tt>.<br>
-: The original revision id was <tt>621915599</tt>.<br>
+: The original revision id was <tt>621915787</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 20: / Line 20: @@
 For example, srutal could be {P8/2, M2/2}, but P5 is preferred because it is unsplit. Or it could be {P8/2, P12}, but P5 is preferred because it is smaller. Or it could be {P8/2, P4}, but P5 is always preferred over P4. Note that P5/2 is __not__ preferred over P4/2. For example, decimal is {P8/2, P4/2}, not {P8/2, P5/2}.
-||||~ pergen name ||||||||~ example temperaments ||
+||||~ pergen set ||||||||~ example temperaments ||
 ||~ written ||~ spoken ||~ comma(s) ||~ name ||||~ color name ||
 ||= {P8, P5} ||= fifth-based ||= 81/80 ||= meantone ||= green ||= gT ||
@@ Line 39: / Line 39: @@
 For non-standard prime groups, the period uses the first prime only, and the multi-gen uses the first two primes only. [[Kite's color notation|Color notation ]]is used to indicate primes higher than 3. For example, 2.5.7 with 50/49 tempered out is {P8/2, y3} = half-octave, yellow-third.
-Rank-3 pergen sets have three intervals, any of which may be split. The unsplit 2.3.5... subgroup is {P8, P5, y3} = fifth-and-third-based. 2.3.5.7 with 50/49 tempered out is {P8/2, P5, y3} = half-octave fifth-and-third.
+Rank-3 pergen sets have three intervals, any of which may be split. The unsplit 2.3.5... subgroup is {P8, P5, y3} = fifth-and-third-based. 2.3.5.7 with 50/49 tempered out is {P8/2, P5, y3}. If one knows that the rank is 3, it can be called half-octave, otherwise it's called half-octave fifth-and-third, to distinguish it from {P8/2, P5}. The color name of a temperament indicates the rank. This is the deep reddish temperament. The name has two explicit colors, red and yellow, and two implicit colors, clear and white (primes 2 and 3). 4 colors minus 1 comma equals rank-3.
 Rank-4 temperaments have pergen sets of four intervals. Rank-1 temperaments could have pergen sets of one, such as {P8/12} for 12-edo or {P12/13} for 13-ed3, but there's no particular reason to do so.
@@ Line 84: / Line 84: @@
 &lt;table class="wiki_table"&gt;
      &lt;tr&gt;
-         &lt;th colspan="2"&gt;pergen name&lt;br /&gt;
+         &lt;th colspan="2"&gt;pergen set&lt;br /&gt;
 &lt;/th&gt;
          &lt;th colspan="4"&gt;example temperaments&lt;br /&gt;
@@ Line 289: / Line 289: @@
 For non-standard prime groups, the period uses the first prime only, and the multi-gen uses the first two primes only. &lt;a class="wiki_link" href="/Kite%27s%20color%20notation"&gt;Color notation &lt;/a&gt;is used to indicate primes higher than 3. For example, 2.5.7 with 50/49 tempered out is {P8/2, y3} = half-octave, yellow-third.&lt;br /&gt;
 &lt;br /&gt;
-Rank-3 pergen sets have three intervals, any of which may be split. The unsplit 2.3.5... subgroup is {P8, P5, y3} = fifth-and-third-based. 2.3.5.7 with 50/49 tempered out is {P8/2, P5, y3} = half-octave fifth-and-third.&lt;br /&gt;
+Rank-3 pergen sets have three intervals, any of which may be split. The unsplit 2.3.5... subgroup is {P8, P5, y3} = fifth-and-third-based. 2.3.5.7 with 50/49 tempered out is {P8/2, P5, y3}. If one knows that the rank is 3, it can be called half-octave, otherwise it's called half-octave fifth-and-third, to distinguish it from {P8/2, P5}. The color name of a temperament indicates the rank. This is the deep reddish temperament. The name has two explicit colors, red and yellow, and two implicit colors, clear and white (primes 2 and 3). 4 colors minus 1 comma equals rank-3.&lt;br /&gt;
 &lt;br /&gt;
 Rank-4 temperaments have pergen sets of four intervals. Rank-1 temperaments could have pergen sets of one, such as {P8/12} for 12-edo or {P12/13} for 13-ed3, but there's no particular reason to do so.&lt;br /&gt;