16edo: Difference between revisions

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<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 20:23:51 UTC</tt>.

: This revision was by author [[User:TallKite|TallKite]] and made on <tt>2016-12-25 20:31:03 UTC</tt>.

: The original revision id was <tt>~~602808950~~</tt>.

: The original revision id was <tt>602809000</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.

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=Intervals=

16edo can be notated with conventional notation, including the staff, note 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~~. 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.

16edo can be notated with conventional notation, including the staff, note names, relative notation, etc. in two ways. The first 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 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. Sharp is lower in pitch than flat, major is narrower than minor~~, etc~~. 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 16edo "on the fly".

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. 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 16edo "on the fly".

|| Degree || Cents ||= Approximate

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<h1 id="toc1"><a name="Intervals"></a>Intervals</h1>

16edo can be notated with conventional notation, including the staff, note 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~~. 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.

16edo can be notated with conventional notation, including the staff, note names, relative notation, etc. in two ways. The first 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 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. Sharp is lower in pitch than flat, major is narrower than minor~~, etc~~. 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 16edo &quot;on the fly&quot;.

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. 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 16edo &quot;on the fly&quot;.

@@ 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 20:23:51 UTC</tt>.<br>
+: This revision was by author [[User:TallKite|TallKite]] and made on <tt>2016-12-25 20:31:03 UTC</tt>.<br>
-: The original revision id was <tt>602808950</tt>.<br>
+: The original revision id was <tt>602809000</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 18: / Line 18: @@
 =Intervals=
-edo can be notated with conventional notation, including the staff, note 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. 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 be notated with conventional notation, including the staff, note names, relative notation, etc. in two ways. The first 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 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. Sharp is lower in pitch than flat, major is narrower than minor, etc. 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 16edo "on the fly".
+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. 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 16edo "on the fly".
 || Degree || Cents ||= Approximate
@@ Line 242: / Line 242: @@
 &lt;!-- ws:start:WikiTextHeadingRule:5:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc1"&gt;&lt;a name="Intervals"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:5 --&gt;Intervals&lt;/h1&gt;
   &lt;br /&gt;
-edo can be notated with conventional notation, including the staff, note 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. 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 be notated with conventional notation, including the staff, note 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 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 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. Sharp is lower in pitch than flat, major is narrower than minor, etc. 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 16edo &amp;quot;on the fly&amp;quot;.&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. 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 16edo &amp;quot;on the fly&amp;quot;.&lt;br /&gt;
 &lt;br /&gt;