Kite's ups and downs notation: Difference between revisions

: This revision was by author [[User:TallKite|TallKite]] and made on <tt>2016-09-29 04:59:53 UTC</tt>.<br>

: The original revision id was <tt>593581682</tt>.<br>

For staff notation, just put an up or down to the left of the note and any standard accidental it might have. To write Db^ followed by Db in the same measure, use the mid sign: Db^ Db~. Or just write Db^ Db. All 22 possible keys can be written out. The tonic is always a mid note, i.e. not up or down. Just as conventionally each black key produces both a sharp key and a flat key (Db major and C# minor), each of the 15 black keys of 22-EDO produces both, and there are 37 possible keys. Double-sharps and double-flats are avoided, as are Fb, Cb, B# and E#. Also Fb^, Cb^, B#v and E#v. This is so that the three black keys between, say, C and D are only notated as some version of C or D, never as some version of B or E. To achieve this, ups and downs are allowed in tonic names and key signatures.

Ups and downs allow us to name any chord easily. First we need an exact definition of major, minor, perfect, etc. that works with all edos. The quality of an interval is defined by its position on the chain of 5ths (or more generally, the chain of generators). Perfect is 0-1 steps away, major/minor are 2-5 steps away, aug/dim are 6-12 steps away, etc.

===__Fourthward EDOs__===  

===__Pentatonic EDOs__===  

(8, 11b, 13 and 18)

__**11edo**__: (generator = 3\11 = perfect 3rd)

&lt;!-- ws:end:WikiTextTocRule:60 --&gt;&lt;!-- ws:start:WikiTextTocRule:61: --&gt;&lt;div style="margin-left: 3em;"&gt;&lt;a href="#Summary of EDO notation--Fourthward EDOs"&gt;Fourthward EDOs&lt;/a&gt;&lt;/div&gt;

&lt;!-- ws:end:WikiTextTocRule:61 --&gt;&lt;!-- ws:start:WikiTextTocRule:62: --&gt;&lt;div style="margin-left: 3em;"&gt;&lt;a href="#Summary of EDO notation--Pentatonic EDOs"&gt;Pentatonic EDOs&lt;/a&gt;&lt;/div&gt;

For staff notation, just put an up or down to the left of the note and any standard accidental it might have. To write Db^ followed by Db in the same measure, use the mid sign: Db^ Db~. Or just write Db^ Db. All 22 possible keys can be written out. The tonic is always a mid note, i.e. not up or down. Just as conventionally each black key produces both a sharp key and a flat key (Db major and C# minor), each of the 15 black keys of 22-EDO produces both, and there are 37 possible keys. Double-sharps and double-flats are avoided, as are Fb, Cb, B# and E#. Also Fb^, Cb^, B#v and E#v. This is so that the three black keys between, say, C and D are only notated as some version of C or D, never as some version of B or E. To achieve this, ups and downs are allowed in tonic names and key signatures.&lt;br /&gt;

Ups and downs allow us to name any chord easily. First we need an exact definition of major, minor, perfect, etc. that works with all edos. The quality of an interval is defined by its position on the chain of 5ths (or more generally, the chain of generators). Perfect is 0-1 steps away, major/minor are 2-5 steps away, aug/dim are 6-12 steps away, etc.&lt;br /&gt;

&lt;!-- ws:start:WikiTextHeadingRule:28:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc14"&gt;&lt;a name="Summary of EDO notation--Fourthward EDOs"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:28 --&gt;&lt;u&gt;Fourthward EDOs&lt;/u&gt;&lt;/h3&gt;

&lt;!-- ws:start:WikiTextHeadingRule:30:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc15"&gt;&lt;a name="Summary of EDO notation--Pentatonic EDOs"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:30 --&gt;&lt;u&gt;Pentatonic EDOs&lt;/u&gt;&lt;/h3&gt;

  (8, 11b, 13 and 18)&lt;br /&gt;

&lt;u&gt;&lt;strong&gt;11edo&lt;/strong&gt;&lt;/u&gt;: (generator = 3\11 = perfect 3rd)&lt;br /&gt;