16edo: 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>2016-11-14 02:39:10 UTC</tt>.

: This revision was by author [[User:TallKite|TallKite]] and made on <tt>2016-11-14 02:45:55 UTC</tt>.

: The original revision id was <tt>~~599358854~~</tt>.

: The original revision id was <tt>599359142</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 17:

=Intervals=

|| Degree || Cents

(coarse, fine)

DMS ||= Approximate

Line 113:

=Hexadecaphonic Notation=

16edo can be notated with conventional notation, including the staff, note names, chord names, relative notation, etc. in two ways. The first preserves the __melodic__ meaning of sharp/flat, major/minor and aug/dim, in that the former is higher pitched than the latter:

16edo can be notated with conventional notation, including the staff, note names, chord names, relative notation, etc. in two ways. The first preserves the __melodic__ meaning of sharp/flat, major/minor and aug/dim, in that the former is always higher pitched than the latter:

||= D ||= ||= E ||= ||= ||= F ||= ||= G ||= ||= A ||= ||= B ||= ||= ||= C ||= ||= D ||

|| ~~__D__~~ || D#/Eb || ~~__E__~~ || _E#_ || ~~_Fb_~~ || ~~__F__~~ || F#/Gb || ~~__G__~~ || G#/Ab || ~~__A__~~ || A#/Bb || ~~__B__~~ || _B#_ || ~~_Cb_~~ || ~~__C__~~ || C#/Db || ~~__D__~~ ||

|| D || D#/Eb || E || E# || Fb || F || F#/Gb || G || G#/Ab || A || A#/Bb || B || B# || Cb || C || C#/Db || D ||

||= P1 ||= A1/d2 ||= m2 ||= M2 ||= m3 ||= M3 ||= A3/d4 ||= P4 ||= A4/d5 ||= P5 ||= A5/d6 ||= m6 ||= M6 ||= m7 ||= M7 ||= A7/d8 ||= P8 ||

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 is to preserve the __harmonic__ meaning of sharp/flat, major/minor and aug/dim, in that the former is further fifthwards on the chain of fifths than the latter:

The second approach is to preserve 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:

||= D ||= ||= E ||= ||= ||= F ||= ||= G ||= ||= A ||= ||= B ||= ||= ||= C ||= ||= D ||

|| ~~__D__~~ || Db/E# || ~~__E__~~ || ~~_Eb_~~ || _F#_ || ~~__F__~~ || Fb/G# || ~~__G__~~ || Gb/A# || ~~__A__~~ || Ab/B# || ~~__B__~~ || ~~_Bb_~~ || _C#_ || ~~__C__~~ || Cb/D# || ~~__D__~~ ||

|| D || Db/E# || E || Eb || F# || F || Fb/G# || G || Gb/A# || A || Ab/B# || B || Bb || C# || C || Cb/D# || D ||

||= P1 ||= d1/~~dA2~~ ||= M2 ||= M2 ||= m3 ||= M3 ||= A3/d4 ||= P4 ||= A4/d5 ||= P5 ||= A5/d6 ||= m6 ||= M6 ||= m7 ||= M7 ||= A7/d8 ||= P8 ||

||= P1 ||= d1/A2 ||= M2 ||= m2 ||= M3 ||= m3 ||= d3/A4 ||= P4 ||= d4/A5 ||= P5 ||= d5/A6 ||= M6 ||= m6 ||= M7 ||= m7 ||= d7/A8 ||= P8 ||

16-EDO notation can be easy utilizing Goldsmith's Circle of keys, nominals, and respective notation. The nominals for a 6 line staff can be switched for Wilson's Beta and Epsilon additions to A-G. Armodue of Italy uses a 4-line staff for 16-EDO.

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<td>Degree

</td>

<td>Cents

<td>Cents

(coarse, fine)

DMS

Line 727:

Line 725:

<h1 id="toc4"><a name="Hexadecaphonic Notation"></a>Hexadecaphonic Notation</h1>

16edo can be notated with conventional notation, including the staff, note names, chord names, relative notation, etc. in two ways. The first preserves the melodic meaning of sharp/flat, major/minor and aug/dim, in that the former is higher pitched than the latter:~~ ~~

16edo can be notated with conventional notation, including the staff, note names, chord names, relative notation, etc. in two ways. The first preserves the melodic meaning of sharp/flat, major/minor and aug/dim, in that the former is always higher pitched than the latter:

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</tr>

<tr>

<td~~><u~~>D~~~~

<td>D

</td>

<td>D#/Eb

</td>

<td~~><u~~>E~~~~

<td>E

</td>

<td>_E#_

<td>E#

</td>

<td>~~_Fb_~~

<td>Fb

</td>

<td~~><u~~>F~~~~

<td>F

</td>

<td>F#/Gb

</td>

<td~~><u~~>G~~~~

<td>G

</td>

<td>G#/Ab

</td>

<td~~><u~~>A~~~~

<td>A

</td>

<td>A#/Bb

</td>

<td~~><u~~>B~~~~

<td>B

</td>

<td>_B#_

<td>B#

</td>

<td>~~_Cb_~~

<td>Cb

</td>

<td~~><u~~>C~~~~

<td>C

</td>

<td>C#/Db

</td>

<td~~><u~~>D~~~~

<td>D

</td>

</tr>

Line 844:

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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 is to preserve the harmonic meaning of sharp/flat, major/minor and aug/dim, in that the former is further fifthwards on the chain of fifths than the latter:~~ ~~

The second approach is to preserve 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:

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</tr>

<tr>

<td~~><u~~>D~~~~

<td>D

</td>

<td>Db/E#

</td>

<td~~><u~~>E~~~~

<td>E

</td>

<td>~~_Eb_~~

<td>Eb

</td>

<td>_F#_

<td>F#

</td>

<td~~><u~~>F~~~~

<td>F

</td>

<td>Fb/G#

</td>

<td~~><u~~>G~~~~

<td>G

</td>

<td>Gb/A#

</td>

<td~~><u~~>A~~~~

<td>A

</td>

<td>Ab/B#

</td>

<td~~><u~~>B~~~~

<td>B

</td>

<td>~~_Bb_~~

<td>Bb

</td>

<td>_C#_

<td>C#

</td>

<td~~><u~~>C~~~~

<td>C

</td>

<td>Cb/D#

</td>

<td~~><u~~>D~~~~

<td>D

</td>

</tr>

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<td style="text-align: center;">P1

</td>

<td style="text-align: center;">d1/~~dA2~~

<td style="text-align: center;">d1/A2

</td>

<td style="text-align: center;">M2

</td>

<td style="text-align: center;">M2

<td style="text-align: center;">m2

</td>

<td style="text-align: center;">M3

</td>

<td style="text-align: center;">m3

</td>

<td style="text-align: center;">~~M3<br~~ /~~>~~

<td style="text-align: center;">d3/A4

~~</td>~~

~~<td style="text-align: center;">A3/d4~~

</td>

<td style="text-align: center;">P4

</td>

<td style="text-align: center;">A4/d5

<td style="text-align: center;">d4/A5

</td>

<td style="text-align: center;">P5

</td>

<td style="text-align: center;">A5/d6

<td style="text-align: center;">d5/A6

</td>

<td style="text-align: center;">M6

</td>

<td style="text-align: center;">m6

</td>

<td style="text-align: center;">M6

<td style="text-align: center;">M7

</td>

<td style="text-align: center;">m7

</td>

<td style="text-align: center;">~~M7<br~~ /~~>~~

<td style="text-align: center;">d7/A8

~~</td>~~

~~<td style="text-align: center;">A7/d8~~

</td>

<td style="text-align: center;">P8

@@ 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>2016-11-14 02:39:10 UTC</tt>.<br>
+: This revision was by author [[User:TallKite|TallKite]] and made on <tt>2016-11-14 02:45:55 UTC</tt>.<br>
-: The original revision id was <tt>599358854</tt>.<br>
+: The original revision id was <tt>599359142</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 17: / Line 17: @@
 =Intervals=
 || Degree || Cents
 (coarse, fine)
 DMS ||= Approximate
@@ Line 113: / Line 113: @@
 =Hexadecaphonic Notation=
-edo can be notated with conventional notation, including the staff, note names, chord names, relative notation, etc. in two ways. The first preserves the __melodic__ meaning of sharp/flat, major/minor and aug/dim, in that the former is higher pitched than the latter:
+edo can be notated with conventional notation, including the staff, note names, chord names, relative notation, etc. in two ways. The first preserves the __melodic__ meaning of sharp/flat, major/minor and aug/dim, in that the former is always higher pitched than the latter:
 ||= D ||=   ||= E ||=   ||=   ||= F ||=   ||= G ||=   ||= A ||=   ||= B ||=   ||=   ||= C ||=   ||= D ||
-|| __D__ || D#/Eb || __E__ || _E#_ || _Fb_ || __F__ || F#/Gb || __G__ || G#/Ab || __A__ || A#/Bb || __B__ || _B#_ || _Cb_ || __C__ || C#/Db || __D__ ||
+|| D || D#/Eb || E || E# || Fb || F || F#/Gb || G || G#/Ab || A || A#/Bb || B || B# || Cb || C || C#/Db || D ||
 ||= P1 ||= A1/d2 ||= m2 ||= M2 ||= m3 ||= M3 ||= A3/d4 ||= P4 ||= A4/d5 ||= P5 ||= A5/d6 ||= m6 ||= M6 ||= m7 ||= M7 ||= A7/d8 ||= P8 ||
 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 is to preserve the __harmonic__ meaning of sharp/flat, major/minor and aug/dim, in that the former is further fifthwards on the chain of fifths than the latter:
+The second approach is to preserve 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:
 ||= D ||=   ||= E ||=   ||=   ||= F ||=   ||= G ||=   ||= A ||=   ||= B ||=   ||=   ||= C ||=   ||= D ||
-|| __D__ || Db/E# || __E__ || _Eb_ || _F#_ || __F__ || Fb/G# || __G__ || Gb/A# || __A__ || Ab/B# || __B__ || _Bb_ || _C#_ || __C__ || Cb/D# || __D__ ||
+|| D || Db/E# || E || Eb || F# || F || Fb/G# || G || Gb/A# || A || Ab/B# || B || Bb || C# || C || Cb/D# || D ||
-||= P1 ||= d1/dA2 ||= M2 ||= M2 ||= m3 ||= M3 ||= A3/d4 ||= P4 ||= A4/d5 ||= P5 ||= A5/d6 ||= m6 ||= M6 ||= m7 ||= M7 ||= A7/d8 ||= P8 ||
+||= P1 ||= d1/A2 ||= M2 ||= m2 ||= M3 ||= m3 ||= d3/A4 ||= P4 ||= d4/A5 ||= P5 ||= d5/A6 ||= M6 ||= m6 ||= M7 ||= m7 ||= d7/A8 ||= P8 ||
 -EDO notation can be easy utilizing Goldsmith's Circle of keys, nominals, and respective notation. The nominals for a 6 line staff can be switched for Wilson's Beta and Epsilon additions to A-G. Armodue of Italy uses a 4-line staff for 16-EDO.
@@ Line 269: / Line 267: @@
          &lt;td&gt;Degree&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;Cents &lt;br /&gt;
+         &lt;td&gt;Cents&lt;br /&gt;
 (coarse, fine)&lt;br /&gt;
 DMS&lt;br /&gt;
@@ Line 727: / Line 725: @@
 &lt;!-- ws:start:WikiTextHeadingRule:11:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc4"&gt;&lt;a name="Hexadecaphonic Notation"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:11 --&gt;Hexadecaphonic Notation&lt;/h1&gt;
   &lt;br /&gt;
-edo can be notated with conventional notation, including the staff, note names, chord names, relative notation, etc. in two ways. The first preserves the &lt;u&gt;melodic&lt;/u&gt; meaning of sharp/flat, major/minor and aug/dim, in that the former is higher pitched than the latter:&lt;br /&gt;
+edo can be notated with conventional notation, including the staff, note names, chord names, relative notation, etc. in two ways. The first preserves the &lt;u&gt;melodic&lt;/u&gt; meaning of sharp/flat, major/minor and aug/dim, in that the former is always higher pitched than the latter:&lt;br /&gt;
-&lt;br /&gt;
@@ Line 769: / Line 766: @@
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td&gt;&lt;u&gt;D&lt;/u&gt;&lt;br /&gt;
+         &lt;td&gt;D&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;D#/Eb&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;u&gt;E&lt;/u&gt;&lt;br /&gt;
+         &lt;td&gt;E&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;_E#_&lt;br /&gt;
+         &lt;td&gt;E#&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;_Fb_&lt;br /&gt;
+         &lt;td&gt;Fb&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;u&gt;F&lt;/u&gt;&lt;br /&gt;
+         &lt;td&gt;F&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;F#/Gb&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;u&gt;G&lt;/u&gt;&lt;br /&gt;
+         &lt;td&gt;G&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;G#/Ab&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;u&gt;A&lt;/u&gt;&lt;br /&gt;
+         &lt;td&gt;A&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;A#/Bb&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;u&gt;B&lt;/u&gt;&lt;br /&gt;
+         &lt;td&gt;B&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;_B#_&lt;br /&gt;
+         &lt;td&gt;B#&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;_Cb_&lt;br /&gt;
+         &lt;td&gt;Cb&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;u&gt;C&lt;/u&gt;&lt;br /&gt;
+         &lt;td&gt;C&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;C#/Db&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;u&gt;D&lt;/u&gt;&lt;br /&gt;
+         &lt;td&gt;D&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 844: / Line 841: @@
 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 is to preserve the &lt;u&gt;harmonic&lt;/u&gt; meaning of sharp/flat, major/minor and aug/dim, in that the former is further fifthwards on the chain of fifths than the latter:&lt;br /&gt;
+The second approach is to preserve 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:&lt;br /&gt;
-&lt;br /&gt;
@@ Line 886: / Line 882: @@
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td&gt;&lt;u&gt;D&lt;/u&gt;&lt;br /&gt;
+         &lt;td&gt;D&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;Db/E#&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;u&gt;E&lt;/u&gt;&lt;br /&gt;
+         &lt;td&gt;E&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;_Eb_&lt;br /&gt;
+         &lt;td&gt;Eb&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;_F#_&lt;br /&gt;
+         &lt;td&gt;F#&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;u&gt;F&lt;/u&gt;&lt;br /&gt;
+         &lt;td&gt;F&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;Fb/G#&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;u&gt;G&lt;/u&gt;&lt;br /&gt;
+         &lt;td&gt;G&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;Gb/A#&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;u&gt;A&lt;/u&gt;&lt;br /&gt;
+         &lt;td&gt;A&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;Ab/B#&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;u&gt;B&lt;/u&gt;&lt;br /&gt;
+         &lt;td&gt;B&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;_Bb_&lt;br /&gt;
+         &lt;td&gt;Bb&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;_C#_&lt;br /&gt;
+         &lt;td&gt;C#&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;u&gt;C&lt;/u&gt;&lt;br /&gt;
+         &lt;td&gt;C&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;Cb/D#&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;u&gt;D&lt;/u&gt;&lt;br /&gt;
+         &lt;td&gt;D&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 924: / Line 920: @@
          &lt;td style="text-align: center;"&gt;P1&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;d1/dA2&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;d1/A2&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;M2&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;M2&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;m2&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;M3&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;m3&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;M3&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;d3/A4&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td style="text-align: center;"&gt;A3/d4&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;P4&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;A4/d5&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;d4/A5&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;P5&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;A5/d6&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;d5/A6&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;M6&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;m6&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;M6&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;M7&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;m7&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;M7&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;d7/A8&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td style="text-align: center;"&gt;A7/d8&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;P8&lt;br /&gt;