Kite's Genchain mode numbering: Difference between revisions

← Older edit Newer edit →

VisualWikitext

@@ 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>2016-09-25 08:24:56 UTC</tt>.<br>
+: This revision was by author [[User:TallKite|TallKite]] and made on <tt>2016-09-25 21:35:23 UTC</tt>.<br>
-: The original revision id was <tt>593234434</tt>.<br>
+: The original revision id was <tt>593267764</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 307: / Line 307: @@
 L 4th Meantone [5] add +2, +5
+Sensi is a good example because it's nether heptatonic nor fifth-generated. Here's a Sensi [8] MOS and MODMOS in both heptatonic and octotonic notation. The generator, a heptatonic 3rd or octotonic 4th, is chroma-negative. In 19edo, generator = 7\19, L = 3\19, and s = 2\19.
-Using the numbers 1-5 both as note names and as scale degrees, we get this genchain:
+|| notation || scale name || sL pattern || example in C || genchain ||
-...5# 3# 1# 4# 2# 5 3 1 4 2 5b 3b 1b 4b 2b bb5...
+|| heptatonic || 5th Sensi [8] || sL sL ssLs || C Db Eb E# Gb G# A B C || Gb B Eb G# __**C**__ E# A Db ||
-...-5 -3 -1 -4 -2 5 3 1 4 2 +5 +3 +1 +4 +2 ++5...
+|| octotonic || 5th Sensi [8] || sL sL ssLs || C D E# F G# H A B# C || G# B# E# H __**C**__ F A D ||
-and these standard modes:
+|| heptatonic || 5th Sensi [8] +7 || sL sL sssL || C Db Eb E# Gb G# A Bb C || Gb * Eb G# __**C**__ E# A Db * Bb ||
-1st Meantone [5] = 1 2 +3 4 +5 1
+|| octotonic || 5th Sensi [8] +8 ||&lt; sL sL sssL || C D E# F G# H A B C || G# * E# H __**C**__ F A D * B ||
-2nd Meantone [5] = 1 2 3 4 +5 1
+Heptatonic fifth-based notation:
-3rd Meantone [5] = 1 2 3 4 5 1
+C - C# - Db - D - D# - Eb - E - E#/Fb - F - F# - Gb - G - G# - Ab - A - A# - Bb - B - B#/Cb - C
-4th Meantone [5] = 1 -2 3 4 5 1
+Octotonic fourth-based notation:
-5th Meantone [5] = 1 -2 3 -4 5 1
+C - C#/Db - D - D#/Eb - E - E# - Fb - F - F#/Gb - G - G# - Hb - H - H#/Ab - A - A#/Bb - B - B# - Cb -C
-The initial "1" is the tonic of the scale.
-The A C B D F E G A scale becomes 1 2 -2 3 4 +5 5 1, which has 3 possible names:
-3rd Meantone [5] add -2, +5
-2nd Meantone [5] add -2, -5
-4th Meantone [5] add +2, +5
@@ Line 1,707: / Line 1,701: @@
 L 4th Meantone [5] add +2, +5&lt;br /&gt;
 &lt;br /&gt;
-&lt;br /&gt;
+Sensi is a good example because it's nether heptatonic nor fifth-generated. Here's a Sensi [8] MOS and MODMOS in both heptatonic and octotonic notation. The generator, a heptatonic 3rd or octotonic 4th, is chroma-negative. In 19edo, generator = 7\19, L = 3\19, and s = 2\19.&lt;br /&gt;
-Using the numbers 1-5 both as note names and as scale degrees, we get this genchain:&lt;br /&gt;
-...5# 3# 1# 4# 2# 5 3 1 4 2 5b 3b 1b 4b 2b bb5...&lt;br /&gt;
-...-5 -3 -1 -4 -2 5 3 1 4 2 +5 +3 +1 +4 +2 ++5...&lt;br /&gt;
+&lt;table class="wiki_table"&gt;
-and these standard modes:&lt;br /&gt;
+    &lt;tr&gt;
-1st Meantone [5] = 1 2 +3 4 +5 1&lt;br /&gt;
+        &lt;td&gt;notation&lt;br /&gt;
-2nd Meantone [5] = 1 2 3 4 +5 1&lt;br /&gt;
+&lt;/td&gt;
-3rd Meantone [5] = 1 2 3 4 5 1&lt;br /&gt;
+        &lt;td&gt;scale name&lt;br /&gt;
-4th Meantone [5] = 1 -2 3 4 5 1&lt;br /&gt;
+&lt;/td&gt;
-5th Meantone [5] = 1 -2 3 -4 5 1&lt;br /&gt;
+        &lt;td&gt;sL pattern&lt;br /&gt;
-The initial &amp;quot;1&amp;quot; is the tonic of the scale.&lt;br /&gt;
+&lt;/td&gt;
-&lt;br /&gt;
+        &lt;td&gt;example in C&lt;br /&gt;
-The A C B D F E G A scale becomes 1 2 -2 3 4 +5 5 1, which has 3 possible names:&lt;br /&gt;
+&lt;/td&gt;
-3rd Meantone [5] add -2, +5&lt;br /&gt;
+        &lt;td&gt;genchain&lt;br /&gt;
-2nd Meantone [5] add -2, -5&lt;br /&gt;
+&lt;/td&gt;
-4th Meantone [5] add +2, +5&lt;br /&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;heptatonic&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;5th Sensi [8]&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;sL sL ssLs&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;C Db Eb E# Gb G# A B C&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;Gb B Eb G# &lt;u&gt;&lt;strong&gt;C&lt;/strong&gt;&lt;/u&gt; E# A Db&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;octotonic&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;5th Sensi [8]&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;sL sL ssLs&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;C D E# F G# H A B# C&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;G# B# E# H &lt;u&gt;&lt;strong&gt;C&lt;/strong&gt;&lt;/u&gt; F A D&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;heptatonic&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;5th Sensi [8] +7&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;sL sL sssL&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;C Db Eb E# Gb G# A Bb C&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;Gb * Eb G# &lt;u&gt;&lt;strong&gt;C&lt;/strong&gt;&lt;/u&gt; E# A Db * Bb&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;octotonic&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;5th Sensi [8] +8&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: left;"&gt;sL sL sssL&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;C D E# F G# H A B C&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;G# * E# H &lt;u&gt;&lt;strong&gt;C&lt;/strong&gt;&lt;/u&gt; F A D * B&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+&lt;/table&gt;
+Heptatonic fifth-based notation:&lt;br /&gt;
+C - C# - Db - D - D# - Eb - E - E#/Fb - F - F# - Gb - G - G# - Ab - A - A# - Bb - B - B#/Cb - C&lt;br /&gt;
+Octotonic fourth-based notation:&lt;br /&gt;
+C - C#/Db - D - D#/Eb - E - E# - Fb - F - F#/Gb - G - G# - Hb - H - H#/Ab - A - A#/Bb - B - B# - Cb -C&lt;br /&gt;
 &lt;br /&gt;
 &lt;br /&gt;