Kite's ups and downs notation: Difference between revisions

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In C: C C^ Dbv Db Db^ D D^ Ebv Eb Eb^ E E^ Fv F F^ F# Gb Gb^ G etc.

JI associations: Perfect = white, major = fifthward white, minor = fourthward white, downmajor = yellow, upminor = green, downminor = blue, upmajor = red, double-downmajor = double-upminor = jade or amber.

==[[image:Tibia in G with ^v, rygb 2.jpg width="800" height="957"]]==  

=__Chord names in other EDOs__=  

(8, 11b, 13 and 18)

Another is to switch from heptatonic notation to some other type. Pentatonic notation is a natural fit, in the sense that no ups or downs are needed, for 8edo, 13edo and 18edo, but not 11edo.

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Ups and Downs is a notation system developed by &lt;a class="wiki_link" href="/KiteGiedraitis"&gt;Kite&lt;/a&gt; that works with almost all EDOs and rank 2 tunings. It only adds 3 symbols to standard notation, so it's very easy to learn. The name comes from the up symbol &amp;quot;^&amp;quot; and the down symbol &amp;quot;v&amp;quot;.&lt;br /&gt;

This is in addition to the trivial EDOs, 2, 3, 4 and 6, which can be notated with standard notation as a subset of 12-EDO. The fifth is defined as the nearest approximation to 3/2. There is a little leeway to this in certain EDOs like 18 which have two possible fifths with nearly equal accuracy.&lt;br /&gt;

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The above diagram is actually a section of the Stern-Brocot tree. The tree usually has ratios, not octave fractions (i.e. 4/7, not 4\7 as above). Also it's usually arranged vertically with nodes of the same &amp;quot;generation&amp;quot; occurring at the same height. For example, 5\9 and 7\12 are both children of 4\7, and would usually be level with each other. Here the nodes are arranged vertically by denominator, i.e., the EDO itself. This version of the Stern-Brocot tree is the scale tree. The colored regions of the tree are what I call &lt;strong&gt;kites&lt;/strong&gt;, and The heptatonic kite is blue and the pentatonic kite is orange. Every kite has a head (4\7 for the blue kite), a central spine (8\14, 12\21, etc.), a fifthward side on the right (7\12, 11\19, etc.) and a fourthward side on the left (5\9, 9\16, etc.). Every node on a spine is a &lt;strong&gt;spinal&lt;/strong&gt; node. Every non-spinal node is part of three kites. It's the head of one kite and on the side of two others.&lt;br /&gt;

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In C: C C^ Dbv Db Db^ D D^ Ebv Eb Eb^ E E^ Fv F F^ F# Gb Gb^ G etc.&lt;br /&gt;

JI associations: Perfect = white, major = fifthward white, minor = fourthward white, downmajor = yellow, upminor = green, downminor = blue, upmajor = red, double-downmajor = double-upminor = jade or amber.&lt;br /&gt;

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In chord names, the mid symbol &amp;quot;~&amp;quot; means &amp;quot;exactly midway between major and minor&amp;quot;, hence neutral. This only applies to even-chroma edos. In chroma-2 edos (10, 17, 24, etc.), upminor equals downmajor, and &amp;quot;mid&amp;quot; replaces both terms. In chroma-4 edos (20, 27, 34, etc.), mid replaces both double-upminor and double-downmajor. In 11-edo and 18b-edo, mid replaces both upmajor and downminor.&lt;br /&gt;

0-3-6-9 = D Fv A Cv = D.~7 = &amp;quot;D dot mid seven&amp;quot;, or D Fv A Bb = D~(b6) = &amp;quot;D mid flat-six&amp;quot;&lt;br /&gt;

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In 22edo, the major chord is 0-8-13 = 0¢-436¢-709¢. In 19edo, it's 0-6-11 = 0¢-379¢-695¢. The two chords sound quite different, because &amp;quot;major 3rd&amp;quot; is defined only in terms of the fifth, not in terms of what JI ratios it approximates. To describe the sound of the chord, color notation can be used. 22edo major chords sound red and 19edo major chords sound yellow.&lt;br /&gt;

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To summarize an EDO, a scale fragment from C to D is shown, including C# and Db. Examples:&lt;br /&gt;

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  (12, 17, 19, 22, 24, 26, 27, 29, 31-34, and all edos 36 or higher)&lt;br /&gt;

All regular EDOs use the usual chain of fifths: m2 - m6 - m3 - m7 - P4 - P1 - P5 - M2 - M6 - M3 - M7 etc.&lt;br /&gt;

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  (7, 14, 21, 28 and 35)&lt;br /&gt;

All perfect EDOs use the same circle of 7 fifths: P4 - P1 - P5 - P2 - P6 - P3 - P7 - P4 - P1 etc.&lt;br /&gt;

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  (9, 11, 13b, 16, 18b and 23)&lt;br /&gt;

All fourthwards EDOs use the usual chain of fifths: m2 - m6 - m3 - m7 - P4 - P1 - P5 - M2 - M6 - M3 - M7 etc.&lt;br /&gt;

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  (5, 10, 15, 20, 25 and 30)&lt;br /&gt;

All pentatonic EDOs use the usual chain of fifths: m2 - m6 - m3 - m7 - P4 - P1 - P5 - M2 - M6 - M3 - M7 etc.&lt;br /&gt;

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  (8, 11b, 13 and 18)&lt;br /&gt;

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Another is to switch from heptatonic notation to some other type. Pentatonic notation is a natural fit, in the sense that no ups or downs are needed, for 8edo, 13edo and 18edo, but not 11edo.&lt;br /&gt;

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Solfege (do-re-mi) can be adapted to indicate sharp/flat and up/down:&lt;br /&gt;

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Ups and downs can be used to notate rank-2 scales. First we must distinguish between edos and sizing frameworks. For example, keyboards with 7 white keys and 5 black keys, and fretted instruments with 12 frets per octave, predate the use of 12edo by many centuries. Such instruments use a 12-tone framework. Traditional Western notation uses a 7-note naming framework and a 12-tone sizing framework. (See the first chapter of part V of Kite's book for more on frameworks.)&lt;br /&gt;

Ups and downs can also be used when naming fractional octave rank-2 tunings. These tunings have multiple genchains. Each genchain has a different &amp;quot;height&amp;quot;; one is up, another is down, etc. See &lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/Naming%20Rank-2%20Scales#Kite%20Giedraitis%20method-Fractional-octave%20periods"&gt;xenharmonic.wikispaces.com/Naming+Rank-2+Scales&lt;/a&gt;&lt;br /&gt;

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The main reason to use ups and downs is to allow fifth-generated heptatonic notation in frameworks and EDOs that aren't fully compatible with such a notation, i.e. those not on the sides of the 4\7 kite. The main reason to use a generator other than a fifth is to use a notation more compatible with one's chosen framework or EDO. Thus there is little reason to use ups and downs in such a situation.&lt;br /&gt;