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Kite's ups and downs notation: Difference between revisions

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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>
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: This revision was by author [[User:TallKite|TallKite]] and made on <tt>2016-08-03 20:41:53 UTC</tt>.<br>
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As we've seen, 19-EDO doesn't require ups and downs. Let the keyspan of the octave in an EDO be K1 and the keyspan of the fifth be K2. For example, in 12-EDO, K1 = 12 and K2 = 7. The stepspan is one less than the degree. For our usual heptatonic framework, the stepspan of the octave S1 is 7 and the stepspan of the fifth S2 is 4. In order for ups and downs to be unnecessary, S1 * K2 - S2 * K1 = +/-1. Examples of EDOs that don't need ups and downs are 5, 12, 19, 26, 33, 40, etc. (every 7th EDO). There are 4 other such EDOs, 7, 9, 16 and 23. All other EDOs need ups and downs.
As we've seen, 19-EDO doesn't require ups and downs. Let the keyspan of the octave in an EDO be K1 and the keyspan of the fifth be K2. For example, in 12-EDO, K1 = 12 and K2 = 7. The stepspan is one less than the degree. For our usual heptatonic framework, the stepspan of the octave S1 is 7 and the stepspan of the fifth S2 is 4. In order for ups and downs to be unnecessary, S1 * K2 - S2 * K1 = +/-1. Examples of EDOs that don't need ups and downs are 5, 12, 19, 26, 33, 40, etc. (every 7th EDO). There are 4 other such EDOs, 7, 9, 16 and 23. All other EDOs need ups and downs.
When applied to actual notes (absolute notation), the mid symbol "~"means "neither up nor down". But in relative notation it means "exactly midway between major and minor", hence neutral. In other words, mid is a quality like major or perfect. This only applies to certain "neutral EDOs" in which the sharp equals an even number of EDOsteps. For example, in every seventh EDO (10edo, 17edo, 24edo, 31edo, etc.), a sharp is two EDOsteps, upminor equals downmajor, and "mid" replaces both terms. In 20edo, 27edo, 34edo, 41edo, etc., a sharp is four EDOsteps, and mid replaces both double-upminor and double-downmajor.


**__17-EDO__:** (2 keys per sharp/flat)
**__17-EDO__:** (2 keys per sharp/flat)
Black and white keys: C * * D * * E F * * G * * A * * B C
Black and white keys: C * * D * * E F * * G * * A * * B C
Relative notation: P1 m2 vM2 M2 m3 vM3 M3 P4 d5 vP5 P5 m6 vM6 M6 m7 vM7 M7 P8
Relative notation: 1 m2 ~2 M2 m3 ~3 M3 4 d5 v5 5 m6 ~6 M6 m7 ~7 M7 8 (1, 4, 5 and 8 are assumed to be perfect)
or with upminors instead of downmajors: P1 m2 ^m2 M2 m3 ^m3 M3 P4 d5 ^d5 P5 m6 ^m6 M6 m7 ^m7 M7 P8
The d5 could instead be an A4: P4 ^P4 A4 P5 or P4 vA4 A4 P5
The d5 could instead be an A4: P4 ^P4 A4 P5 or P4 vA4 A4 P5
Many other variations are possible, much freedom of spelling.
Many other variations are possible, much freedom of spelling.
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&lt;br /&gt;
&lt;br /&gt;
As we've seen, 19-EDO doesn't require ups and downs. Let the keyspan of the octave in an EDO be K1 and the keyspan of the fifth be K2. For example, in 12-EDO, K1 = 12 and K2 = 7. The stepspan is one less than the degree. For our usual heptatonic framework, the stepspan of the octave S1 is 7 and the stepspan of the fifth S2 is 4. In order for ups and downs to be unnecessary, S1 * K2 - S2 * K1 = +/-1. Examples of EDOs that don't need ups and downs are 5, 12, 19, 26, 33, 40, etc. (every 7th EDO). There are 4 other such EDOs, 7, 9, 16 and 23. All other EDOs need ups and downs.&lt;br /&gt;
As we've seen, 19-EDO doesn't require ups and downs. Let the keyspan of the octave in an EDO be K1 and the keyspan of the fifth be K2. For example, in 12-EDO, K1 = 12 and K2 = 7. The stepspan is one less than the degree. For our usual heptatonic framework, the stepspan of the octave S1 is 7 and the stepspan of the fifth S2 is 4. In order for ups and downs to be unnecessary, S1 * K2 - S2 * K1 = +/-1. Examples of EDOs that don't need ups and downs are 5, 12, 19, 26, 33, 40, etc. (every 7th EDO). There are 4 other such EDOs, 7, 9, 16 and 23. All other EDOs need ups and downs.&lt;br /&gt;
&lt;br /&gt;
When applied to actual notes (absolute notation), the mid symbol &amp;quot;~&amp;quot;means &amp;quot;neither up nor down&amp;quot;. But in relative notation it means &amp;quot;exactly midway between major and minor&amp;quot;, hence neutral. In other words, mid is a quality like major or perfect. This only applies to certain &amp;quot;neutral EDOs&amp;quot; in which the sharp equals an even number of EDOsteps. For example, in every seventh EDO (10edo, 17edo, 24edo, 31edo, etc.), a sharp is two EDOsteps, upminor equals downmajor, and &amp;quot;mid&amp;quot; replaces both terms. In 20edo, 27edo, 34edo, 41edo, etc., a sharp is four EDOsteps, and mid replaces both double-upminor and double-downmajor.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;strong&gt;&lt;u&gt;17-EDO&lt;/u&gt;:&lt;/strong&gt; (2 keys per sharp/flat)&lt;br /&gt;
&lt;strong&gt;&lt;u&gt;17-EDO&lt;/u&gt;:&lt;/strong&gt; (2 keys per sharp/flat)&lt;br /&gt;
Black and white keys: C * * D * * E F * * G * * A * * B C&lt;br /&gt;
Black and white keys: C * * D * * E F * * G * * A * * B C&lt;br /&gt;
Relative notation: P1 m2 vM2 M2 m3 vM3 M3 P4 d5 vP5 P5 m6 vM6 M6 m7 vM7 M7 P8&lt;br /&gt;
Relative notation: 1 m2 ~2 M2 m3 ~3 M3 4 d5 v5 5 m6 ~6 M6 m7 ~7 M7 8 (1, 4, 5 and 8 are assumed to be perfect)&lt;br /&gt;
or with upminors instead of downmajors: P1 m2 ^m2 M2 m3 ^m3 M3 P4 d5 ^d5 P5 m6 ^m6 M6 m7 ^m7 M7 P8&lt;br /&gt;
The d5 could instead be an A4: P4 ^P4 A4 P5 or P4 vA4 A4 P5&lt;br /&gt;
The d5 could instead be an A4: P4 ^P4 A4 P5 or P4 vA4 A4 P5&lt;br /&gt;
Many other variations are possible, much freedom of spelling.&lt;br /&gt;
Many other variations are possible, much freedom of spelling.&lt;br /&gt;
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