13edo: 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>2016-12-25 22:53:14 UTC</tt>.

: This revision was by author [[User:TallKite|TallKite]] and made on <tt>2016-12-25 23:16:42 UTC</tt>.

: The original revision id was <tt>~~602809706~~</tt>.

: The original revision id was <tt>602810166</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 36:

*based on treating 13-EDO as a 2.5.9.11.13.21 subgroup temperament; other approaches are possible.

13edo can also be notated with ups and downs. The notational 5th is the 2nd-best approximation of 3/2, 7\13. ~~Using this~~ 5th allows conventional notation to be used, including the staff, note names, relative notation, etc. in two ways. The first way preserves the __melodic__ meaning of sharp/flat, major/minor and aug/dim, in that sharp is higher pitched than flat, and major/aug is wider than minor/dim. The disadvantage to this approach is that conventional interval arithmetic no longer works. e.g. M2 + M2 isn't M3, and D + M2 isn't E. Chord names are different because C - E - G isn't P1 - M3 - P5.

13edo can also be notated with ups and downs. The notational 5th is the 2nd-best approximation of 3/2, 7\13. This is 56¢ flat of 3/2, and the best approximation is 36¢ sharp, noticeably better. But using the 2nd-best 5th allows conventional notation to be used, including the staff, note names, relative notation, etc. There are two ways to do this. The first way preserves the __melodic__ meaning of sharp/flat, major/minor and aug/dim, in that sharp is higher pitched than flat, and major/aug is wider than minor/dim. The disadvantage to this approach is that conventional interval arithmetic no longer works. e.g. M2 + M2 isn't M3, and D + M2 isn't E. Chord names are different because C - E - G isn't P1 - M3 - P5.

The second approach preserves the __harmonic__ meaning of sharp/flat, major/minor and aug/dim, in that the former is always further fifthwards on the chain of fifths than the latter. Sharp is lower in pitch than flat, and major/aug is narrower than minor/dim. While this approach may seem bizarre at first, interval arithmetic and chord names work as usual. Furthermore, conventional 12edo music can be directly translated to 13edo "on the fly".

||= **Degree** ||= **Cents** ||||||= [[xenharmonic/Ups and Downs Notation|Up/down notation]] with

||= **Degree** ||= **Cents** ||||||= [[xenharmonic/Ups and Downs Notation|Up/down notation]] using the narrow 5th of 7\13,

major wider than minor ||||||= Up/down notation with

with major wider than minor ||||||= Up/down notation using the narrow 5th of 7\13,

major narrower than minor ||

with major narrower than minor ||

||= 0 ||= 0 ||= perfect unison ||= P1 ||= D ||= perfect unison ||= P1 ||= D ||

||= 1 ||= 92 ||= up unison, minor 2nd ||= ^1, m2 ||= D^, E ||= up unison, major 2nd ||= ^1, M2 ||= D^, E ||

Line 504:

*based on treating 13-EDO as a 2.5.9.11.13.21 subgroup temperament; other approaches are possible.

13edo can also be notated with ups and downs. The notational 5th is the 2nd-best approximation of 3/2, 7\13. ~~Using this~~ 5th allows conventional notation to be used, including the staff, note names, relative notation, etc. in two ways. The first way preserves the melodic meaning of sharp/flat, major/minor and aug/dim, in that sharp is higher pitched than flat, and major/aug is wider than minor/dim. The disadvantage to this approach is that conventional interval arithmetic no longer works. e.g. M2 + M2 isn't M3, and D + M2 isn't E. Chord names are different because C - E - G isn't P1 - M3 - P5.

13edo can also be notated with ups and downs. The notational 5th is the 2nd-best approximation of 3/2, 7\13. This is 56¢ flat of 3/2, and the best approximation is 36¢ sharp, noticeably better. But using the 2nd-best 5th allows conventional notation to be used, including the staff, note names, relative notation, etc. There are two ways to do this. The first way preserves the melodic meaning of sharp/flat, major/minor and aug/dim, in that sharp is higher pitched than flat, and major/aug is wider than minor/dim. The disadvantage to this approach is that conventional interval arithmetic no longer works. e.g. M2 + M2 isn't M3, and D + M2 isn't E. Chord names are different because C - E - G isn't P1 - M3 - P5.

The second approach preserves the harmonic meaning of sharp/flat, major/minor and aug/dim, in that the former is always further fifthwards on the chain of fifths than the latter. Sharp is lower in pitch than flat, and major/aug is narrower than minor/dim. While this approach may seem bizarre at first, interval arithmetic and chord names work as usual. Furthermore, conventional 12edo music can be directly translated to 13edo &quot;on the fly&quot;.

Line 516:

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

</td>

<td colspan="3" style="text-align: center;"><a class="wiki_link" href="http://xenharmonic.wikispaces.com/Ups%20and%20Downs%20Notation">Up/down notation</a> ~~with~~

<td colspan="3" style="text-align: center;"><a class="wiki_link" href="http://xenharmonic.wikispaces.com/Ups%20and%20Downs%20Notation">Up/down notation</a> using the narrow 5th of 7\13,

major wider than minor

with major wider than minor

</td>

<td colspan="3" style="text-align: center;">Up/down notation ~~with~~

<td colspan="3" style="text-align: center;">Up/down notation using the narrow 5th of 7\13,

major narrower than minor

with major narrower than minor

</td>

</tr>

@@ Line 1: / Line 1: @@
 <h2>IMPORTED REVISION FROM WIKISPACES</h2>
 This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
-: This revision was by author [[User:TallKite|TallKite]] and made on <tt>2016-12-25 22:53:14 UTC</tt>.<br>
+: This revision was by author [[User:TallKite|TallKite]] and made on <tt>2016-12-25 23:16:42 UTC</tt>.<br>
-: The original revision id was <tt>602809706</tt>.<br>
+: The original revision id was <tt>602810166</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 36: / Line 36: @@
 *based on treating 13-EDO as a 2.5.9.11.13.21 subgroup temperament; other approaches are possible.
-edo can also be notated with ups and downs. The notational 5th is the 2nd-best approximation of 3/2, 7\13. Using this 5th allows conventional notation to be used, including the staff, note names, relative notation, etc. in two ways. The first way preserves the __melodic__ meaning of sharp/flat, major/minor and aug/dim, in that sharp is higher pitched than flat, and major/aug is wider than minor/dim. The disadvantage to this approach is that conventional interval arithmetic no longer works. e.g. M2 + M2 isn't M3, and D + M2 isn't E. Chord names are different because C - E - G isn't P1 - M3 - P5.
+edo can also be notated with ups and downs. The notational 5th is the 2nd-best approximation of 3/2, 7\13. This is 56¢ flat of 3/2, and the best approximation is 36¢ sharp, noticeably better. But using the 2nd-best 5th allows conventional notation to be used, including the staff, note names, relative notation, etc. There are two ways to do this. The first way preserves the __melodic__ meaning of sharp/flat, major/minor and aug/dim, in that sharp is higher pitched than flat, and major/aug is wider than minor/dim. The disadvantage to this approach is that conventional interval arithmetic no longer works. e.g. M2 + M2 isn't M3, and D + M2 isn't E. Chord names are different because C - E - G isn't P1 - M3 - P5.
 The second approach preserves the __harmonic__ meaning of sharp/flat, major/minor and aug/dim, in that the former is always further fifthwards on the chain of fifths than the latter. Sharp is lower in pitch than flat, and major/aug is narrower than minor/dim. While this approach may seem bizarre at first, interval arithmetic and chord names work as usual. Furthermore, conventional 12edo music can be directly translated to 13edo "on the fly".
-||= **Degree** ||= **Cents** ||||||= [[xenharmonic/Ups and Downs Notation|Up/down notation]] with
+||= **Degree** ||= **Cents** ||||||= [[xenharmonic/Ups and Downs Notation|Up/down notation]] using the narrow 5th of 7\13,
-major wider than minor ||||||= Up/down notation with
+with major wider than minor ||||||= Up/down notation using the narrow 5th of 7\13,
-major narrower than minor ||
+with major narrower than minor ||
 ||= 0 ||= 0 ||= perfect unison ||= P1 ||= D ||= perfect unison ||= P1 ||= D ||
 ||= 1 ||= 92 ||= up unison, minor 2nd ||= ^1, m2 ||= D^, E ||= up unison, major 2nd ||= ^1, M2 ||= D^, E ||
@@ Line 504: / Line 504: @@
 *based on treating 13-EDO as a 2.5.9.11.13.21 subgroup temperament; other approaches are possible.&lt;br /&gt;
 &lt;br /&gt;
-edo can also be notated with ups and downs. The notational 5th is the 2nd-best approximation of 3/2, 7\13. Using this 5th allows conventional notation to be used, including the staff, note names, relative notation, etc. in two ways. The first way preserves the &lt;u&gt;melodic&lt;/u&gt; meaning of sharp/flat, major/minor and aug/dim, in that sharp is higher pitched than flat, and major/aug is wider than minor/dim. The disadvantage to this approach is that conventional interval arithmetic no longer works. e.g. M2 + M2 isn't M3, and D + M2 isn't E. Chord names are different because C - E - G isn't P1 - M3 - P5.&lt;br /&gt;
+edo can also be notated with ups and downs. The notational 5th is the 2nd-best approximation of 3/2, 7\13. This is 56¢ flat of 3/2, and the best approximation is 36¢ sharp, noticeably better. But using the 2nd-best 5th allows conventional notation to be used, including the staff, note names, relative notation, etc. There are two ways to do this. The first way preserves the &lt;u&gt;melodic&lt;/u&gt; meaning of sharp/flat, major/minor and aug/dim, in that sharp is higher pitched than flat, and major/aug is wider than minor/dim. The disadvantage to this approach is that conventional interval arithmetic no longer works. e.g. M2 + M2 isn't M3, and D + M2 isn't E. Chord names are different because C - E - G isn't P1 - M3 - P5.&lt;br /&gt;
 &lt;br /&gt;
 The second approach preserves the &lt;u&gt;harmonic&lt;/u&gt; meaning of sharp/flat, major/minor and aug/dim, in that the former is always further fifthwards on the chain of fifths than the latter. Sharp is lower in pitch than flat, and major/aug is narrower than minor/dim. While this approach may seem bizarre at first, interval arithmetic and chord names work as usual. Furthermore, conventional 12edo music can be directly translated to 13edo &amp;quot;on the fly&amp;quot;.&lt;br /&gt;
@@ Line 516: / Line 516: @@
          &lt;td style="text-align: center;"&gt;&lt;strong&gt;Cents&lt;/strong&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td colspan="3" style="text-align: center;"&gt;&lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/Ups%20and%20Downs%20Notation"&gt;Up/down notation&lt;/a&gt; with&lt;br /&gt;
+         &lt;td colspan="3" style="text-align: center;"&gt;&lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/Ups%20and%20Downs%20Notation"&gt;Up/down notation&lt;/a&gt; using the narrow 5th of 7\13,&lt;br /&gt;
-major wider than minor&lt;br /&gt;
+with major wider than minor&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td colspan="3" style="text-align: center;"&gt;Up/down notation with&lt;br /&gt;
+         &lt;td colspan="3" style="text-align: center;"&gt;Up/down notation using the narrow 5th of 7\13,&lt;br /&gt;
-major narrower than minor&lt;br /&gt;
+with major narrower than minor&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;