Kite's ups and downs notation: Difference between revisions

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=== Enharmonic equivalents ===

Conventionally, in C you use D# instead of Eb when you have a Gaug chord. You have the freedom to spell your notes how you like, to make your chords look right. Likewise, in 22-edo, Db can be spelled ^C or vB# or even ^^B (double-up B).

Conventionally, in C you use D# instead of Eb when you have a Gaug chord. You have the freedom to spell your notes how you like, to make your chords look right. Likewise, in 22-edo, Db can be spelled ^C or vB# or even ^^B (double-up B, or '''dup''' B for short).

From the [[Pergen|pergens]] article: "Conventional notation is generated by the octave and the 5th, and the notation (not the tuning itself) is rank-2. Each additional pair of accidentals increases the notation's rank by one, analogous to adding primes to a JI subgroup. Enharmonic intervals are like commas in that each one reduces the notation's rank by one (assuming they are linearly independent). Obviously, the notation's rank must match the actual tuning's rank. Therefore the minimum number of enharmonics needed always equals the difference between the notation's rank and the tuning's rank."

Since 22edo is rank-1, and conventional notation plus ups and downs is rank-3, two enharmonic intervals are needed to define the notation: v3A1 and vm2. Either interval can be added to or subtracted from any note to respell the note. For example, ^C + vm2 = Db and ^^Eb + v3A1 = vE. Any combination of these two enharmonic intervals is also an enharmonic interval, for example their sum v4M2. Thus ^^F = vvG.

Since 22edo is rank-1, and conventional notation plus ups and downs is rank-3, two enharmonic intervals are needed to define the notation: v3A1 and vm2. Either interval can be added to or subtracted from any note to respell the note. For example, ^C + vm2 = Db and ^^Eb + v3A1 = vE. Any combination of these two enharmonic intervals is also an enharmonic interval, for example their sum v4M2. Thus ^^F = vvG (double-down G, or '''dud''' G for short).

=== Staff Notation ===

Line 414:

|-

|P1

| ^P1/vM2

| ^1/vM2

| M2

| ~2

Line 456:

|-

|P1

| ^P1/vm2

| ^1/vm2

| m2

| ~2

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* C ^E G = C^ = "C up" or "C upmajor"

* C vE G = Cv = "C down" or "C downmajor" (in EDOs 10, 17, 24, 31, etc., C~ = "C mid")

* C vvE G = Cvv = "C double-down" (in EDOs 20, 27, 34, 41, etc., C~ = "C mid", in EDOs 25, 32, 39, 46, etc. C^~ = "C upmid")

* C vvE G = Cvv = "C double-down" or "C dud" (in EDOs 20, 27, 34, 41, etc., C~ = "C mid", in EDOs 25, 32, 39, 46, etc. C^~ = "C upmid")

This table shows how altering the 3rd or the 5th affects the name of the triad. The conventional abbreviations for aug and dim are + and o. These are rather cryptic, and can be replaced with the more obvious and intuitive a and d. Likewise the symbols Δ and − can be replaced with M and m.

{| class="wikitable" style="text-align:center;"

@@ Line 65: / Line 65: @@
 === Enharmonic equivalents ===
-Conventionally, in C you use D# instead of Eb when you have a Gaug chord. You have the freedom to spell your notes how you like, to make your chords look right. Likewise, in 22-edo, Db can be spelled ^C or vB# or even ^^B (double-up B).
+Conventionally, in C you use D# instead of Eb when you have a Gaug chord. You have the freedom to spell your notes how you like, to make your chords look right. Likewise, in 22-edo, Db can be spelled ^C or vB# or even ^^B (double-up B, or '''dup''' B for short).
 From the [[Pergen|pergens]] article: "Conventional notation is generated by the octave and the 5th, and the notation (not the tuning itself) is rank-2. Each additional pair of accidentals increases the notation's rank by one, analogous to adding primes to a JI subgroup. Enharmonic intervals are like commas in that each one reduces the notation's rank by one (assuming they are linearly independent). Obviously, the notation's rank must match the actual tuning's rank. Therefore the minimum number of enharmonics needed always equals the difference between the notation's rank and the tuning's rank."
-Since 22edo is rank-1, and conventional notation plus ups and downs is rank-3, two enharmonic intervals are needed to define the notation: v<sup>3</sup>A1 and vm2. Either interval can be added to or subtracted from any note to respell the note. For example, ^C + vm2 = Db and ^^Eb + v<sup>3</sup>A1 = vE. Any combination of these two enharmonic intervals is also an enharmonic interval, for example their sum v<sup>4</sup>M2. Thus ^^F = vvG.
+Since 22edo is rank-1, and conventional notation plus ups and downs is rank-3, two enharmonic intervals are needed to define the notation: v<sup>3</sup>A1 and vm2. Either interval can be added to or subtracted from any note to respell the note. For example, ^C + vm2 = Db and ^^Eb + v<sup>3</sup>A1 = vE. Any combination of these two enharmonic intervals is also an enharmonic interval, for example their sum v<sup>4</sup>M2. Thus ^^F = vvG (double-down G, or '''dud''' G for short).
 === Staff Notation ===
@@ Line 414: / Line 414: @@
 |-
 |P1
-|  ^P1/vM2
+| ^1/vM2
 |  M2
 | ~2
@@ Line 456: / Line 456: @@
 |-
 |P1
-|  ^P1/vm2
+| ^1/vm2
 |  m2
 | ~2
@@ Line 830: / Line 830: @@
 * C ^E G = C^ = "C up" or "C upmajor"
 * C vE G = Cv = "C down" or "C downmajor" (in EDOs 10, 17, 24, 31, etc., C~ = "C mid")
-* C vvE G = Cvv = "C double-down" (in EDOs 20, 27, 34, 41, etc., C~ = "C mid", in EDOs 25, 32, 39, 46, etc. C^~ = "C upmid")
+* C vvE G = Cvv = "C double-down" or "C dud" (in EDOs 20, 27, 34, 41, etc., C~ = "C mid", in EDOs 25, 32, 39, 46, etc. C^~ = "C upmid")
 This table shows how altering the 3rd or the 5th affects the name of the triad. The conventional abbreviations for aug and dim are + and o. These are rather cryptic, and can be replaced with the more obvious and intuitive a and d. Likewise the symbols Δ and − can be replaced with M and m.
 {| class="wikitable" style="text-align:center;"