16edo: Difference between revisions
Wikispaces>xenwolf **Imported revision 602817456 - Original comment: ** |
Wikispaces>xenwolf **Imported revision 602817514 - Original comment: ** |
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<h2>IMPORTED REVISION FROM WIKISPACES</h2> | <h2>IMPORTED REVISION FROM WIKISPACES</h2> | ||
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br> | This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br> | ||
: This revision was by author [[User:xenwolf|xenwolf]] and made on <tt>2016-12-26 10: | : This revision was by author [[User:xenwolf|xenwolf]] and made on <tt>2016-12-26 10:48:29 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>602817514</tt>.<br> | ||
: The revision comment was: <tt></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> | The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br> | ||
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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". | 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 | ||
Ratios* |||| | Ratios* ||||~ Melodic names, | ||
major wider than minor |||| | major wider than minor ||||~ Harmonic names, | ||
major narrower | major narrower | ||
than minor || | than minor ||~ Interval Names | ||
Just || | Just ||~ Interval | ||
Names | Names | ||
Simplified || | Simplified || | ||
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16edo chords can be named using us and downs. Using harmonic interval names, the names are easy to find, but they bear little relationship to the sound. 4:5:6 is a minor chord and 10:12:15 is a major chord! Using melodic names, the chord names will match the sound, but finding the name is much more complicated. First change sharps to flats, then find every interval from the root, then exchange major for minor and aug for dim, then name the chord from the intervals. (See [[xenharmonic/Ups and Downs Notation#Other%20EDOs|xenharmonic.wikispaces.com/Ups+and+Downs+Notation#Other%20EDOs]]). | 16edo chords can be named using us and downs. Using harmonic interval names, the names are easy to find, but they bear little relationship to the sound. 4:5:6 is a minor chord and 10:12:15 is a major chord! Using melodic names, the chord names will match the sound, but finding the name is much more complicated. First change sharps to flats, then find every interval from the root, then exchange major for minor and aug for dim, then name the chord from the intervals. (See [[xenharmonic/Ups and Downs Notation#Other%20EDOs|xenharmonic.wikispaces.com/Ups+and+Downs+Notation#Other%20EDOs]]). | ||
|| | ||~ chord ||~ JI ratios ||||||~ harmonic name ||||||~ melodic name || | ||
||= 0-5-9 ||= 4:5:6 ||= D F A ||= Dm ||= D minor ||= D F A ||= D ||= D major || | ||= 0-5-9 ||= 4:5:6 ||= D F A ||= Dm ||= D minor ||= D F A ||= D ||= D major || | ||
||= 0-4-9 ||= 10:12:15 ||= D F# A ||= D ||= D major ||= D Fb A ||= Dm ||= D minor || | ||= 0-4-9 ||= 10:12:15 ||= D F# A ||= D ||= D major ||= D Fb A ||= Dm ||= D minor || | ||
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<table class="wiki_table"> | <table class="wiki_table"> | ||
<tr> | <tr> | ||
< | <th>Degree<br /> | ||
</ | </th> | ||
< | <th>Cents<br /> | ||
</ | </th> | ||
< | <th>Approximate<br /> | ||
Ratios*<br /> | Ratios*<br /> | ||
</ | </th> | ||
< | <th colspan="2">Melodic names, <br /> | ||
major wider than minor<br /> | major wider than minor<br /> | ||
</ | </th> | ||
< | <th colspan="2">Harmonic names,<br /> | ||
major narrower<br /> | major narrower<br /> | ||
than minor<br /> | than minor<br /> | ||
</ | </th> | ||
< | <th>Interval Names<br /> | ||
Just<br /> | Just<br /> | ||
</ | </th> | ||
< | <th>Interval<br /> | ||
Names<br /> | Names<br /> | ||
Simplified<br /> | Simplified<br /> | ||
</ | </th> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
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<table class="wiki_table"> | <table class="wiki_table"> | ||
<tr> | <tr> | ||
< | <th>chord<br /> | ||
</ | </th> | ||
< | <th>JI ratios<br /> | ||
</ | </th> | ||
< | <th colspan="3">harmonic name<br /> | ||
</ | </th> | ||
< | <th colspan="3">melodic name<br /> | ||
</ | </th> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||