Kite Guitar: Difference between revisions

Line 508:

|

|}

The downadd7no5 chord has 5/4 and 16/9. Surprisingly, this chord is also intervallic odd-limit 9. The interval from 5/4 up to 16/9 is 64/45. But because 41edo tempers out the [[225/224|Ruyoyo]] comma, ~~it becomes~~ 10/7. The high-3 voicing inverts this into an even smoother 7/5. Note that adding the 5th would increase the odd-limit to 27. In chord names, alterations are enclosed in parentheses, and additions are set off with a comma (the punctuation mark, not the interval!) In general, the comma is spoken as "add". Thus C-down add-seven is Cv,7 = C vE G Bb. Compare with C down-seven = Cv7 = C vE G vBb.

The downadd7no5 chord has 5/4 and 16/9. Surprisingly, this chord is also intervallic odd-limit 9. The interval from 5/4 up to 16/9 is 64/45. But because 41edo tempers out the [[225/224|Ruyoyo]] comma of only 8¢, 64/45 is equivalent to 10/7. The high-3 voicing inverts this into an even smoother 7/5. Note that adding the 5th would increase the odd-limit to 27. In chord names, alterations are enclosed in parentheses, and additions are set off with a comma (the punctuation mark, not the interval!) In general, the comma is spoken as "add". Thus C-down add-seven is Cv,7 = C vE G Bb. Compare with C down-seven = Cv7 = C vE G vBb.

The downmajor7sus4 chord (odd-limit 15) also has an innate ruyoyo comma. ~~Its vM7 is a 5~~/~~4 above the 5th, making it~~ 15/8~~. But it's also~~ 7/5 ~~above the 4th, making it 28/15~~. Its homonym is the sus2addb5 chord F2,b5 = F G Cb C. Cb is enharmonically equivalent to vB. In chord names, "(b5)" means alter the 5th by flattening it, but ",b5" means add a flat 5th alongside the perfect 5th.

The downmajor7sus4 chord (odd-limit 15) also has an innate ruyoyo comma. The interval from 4/3 up to 15/8 is 45/32, equivalent to 7/5. Its homonym is the sus2addb5 chord F2,b5 = F G Cb C. In 41-edo, Cb is enharmonically equivalent to vB. In chord names, "(b5)" means alter the 5th by flattening it, but ",b5" means add a flat 5th alongside the perfect 5th.

The down7flat5 chord (odd-limit 9) is also innate-ruyoyo. ~~Its b5 is a~~ 7/5, ~~but also~~ 9/8 ~~above the 3rd (ratio 5/4), making it a 45/32~~. Its homonym is the downadd7upflat5 chord Gbv,7(^b5) = Gb vBb ^Dbb Fb. The upflat five is enharmonically equivalent to an aug 4th = 10/7.

The down7flat5 chord (odd-limit 9) is also innate-ruyoyo. The interval from 5/4 up to 7/5 is 28/25, equivalent to 9/8. Its homonym is the downadd7upflat5 chord Gbv,7(^b5) = Gb vBb ^Dbb Fb. The upflat five is enharmonically equivalent to an aug 4th = 10/7.

Other innate-ruyoyo chords of odd-limit 15 are Cv,b5, C^m,b5 and Cvm,b5.

{| class="wikitable"

!chord type

Line 589:

Line 591:

|1 3 4 . 2

|}

11th chords include the vM9,v#11 (frets 4 4 3 3 2 2), vM11 (4 4 3 3 2 0), v11 (4 4 3 1 2 0), and ^m11 (4 3 3 2 2 1). All ~~but~~ the ~~first of these~~ contain a wolf 11th. Rather than 8/3, the vM11 and v11 chords have 21/8, and the ^m11 chord has 27/10~~. The first chord's v#11th is 45/16, which is equivalent to 14/5, because 41edo tempers out the [[225/224|Ruyoyo]] comma. Thus the chord's intervallic odd limit is only 15~~.

'''11th chords''' include the vM9,v#11 (frets 4 4 3 3 2 2), vM11 (4 4 3 3 2 0), v11 (4 4 3 1 2 0), and ^m11 (4 3 3 2 2 1). The first chord's v#11th is 45/16, which is equivalent to 14/5. Thus the chord's intervallic odd limit is only 15. All the other chords contain a wolf 11th. Rather than 8/3, the vM11 and v11 chords have 21/8, and the ^m11 chord has 27/10.

=== Sixth chords ===

@@ Line 508: / Line 508: @@
 |
 |}
-The downadd7no5 chord has 5/4 and 16/9. Surprisingly, this chord is also intervallic odd-limit 9. The interval from 5/4 up to 16/9 is 64/45. But because 41edo tempers out the [[225/224|Ruyoyo]] comma, it becomes 10/7. The high-3 voicing inverts this into an even smoother 7/5. Note that adding the 5th would increase the odd-limit to 27. In chord names, alterations are enclosed in parentheses, and additions are set off with a comma (the punctuation mark, not the interval!) In general, the comma is spoken as "add". Thus C-down add-seven is Cv,7 = C vE G Bb. Compare with C down-seven = Cv7 = C vE G vBb.
+The downadd7no5 chord has 5/4 and 16/9. Surprisingly, this chord is also intervallic odd-limit 9. The interval from 5/4 up to 16/9 is 64/45. But because 41edo tempers out the [[225/224|Ruyoyo]] comma of only 8¢, 64/45 is equivalent to 10/7. The high-3 voicing inverts this into an even smoother 7/5. Note that adding the 5th would increase the odd-limit to 27. In chord names, alterations are enclosed in parentheses, and additions are set off with a comma (the punctuation mark, not the interval!) In general, the comma is spoken as "add". Thus C-down add-seven is Cv,7 = C vE G Bb. Compare with C down-seven = Cv7 = C vE G vBb.
-The downmajor7sus4 chord (odd-limit 15) also has an innate ruyoyo comma. Its vM7 is a 5/4 above the 5th, making it 15/8. But it's also 7/5 above the 4th, making it 28/15. Its homonym is the sus2addb5 chord F2,b5 = F G Cb C. Cb is enharmonically equivalent to vB. In chord names, "(b5)" means alter the 5th by flattening it, but ",b5" means add a flat 5th alongside the perfect 5th.
+The downmajor7sus4 chord (odd-limit 15) also has an innate ruyoyo comma. The interval from 4/3 up to 15/8 is 45/32, equivalent to 7/5. Its homonym is the sus2addb5 chord F2,b5 = F G Cb C. In 41-edo, Cb is enharmonically equivalent to vB. In chord names, "(b5)" means alter the 5th by flattening it, but ",b5" means add a flat 5th alongside the perfect 5th.
-The down7flat5 chord (odd-limit 9) is also innate-ruyoyo. Its b5 is a 7/5, but also 9/8 above the 3rd (ratio 5/4), making it a 45/32. Its homonym is the downadd7upflat5 chord Gbv,7(^b5) = Gb vBb ^Dbb Fb. The upflat five is enharmonically equivalent to an aug 4th = 10/7.
+The down7flat5 chord (odd-limit 9) is also innate-ruyoyo. The interval from 5/4 up to 7/5 is 28/25, equivalent to 9/8. Its homonym is the downadd7upflat5 chord Gbv,7(^b5) = Gb vBb ^Dbb Fb. The upflat five is enharmonically equivalent to an aug 4th = 10/7.
+Other innate-ruyoyo chords of odd-limit 15 are Cv,b5, C^m,b5 and Cvm,b5.
 {| class="wikitable"
 !chord type
@@ Line 589: / Line 591: @@
 |1 3 4 . 2
 |}
-th chords include the vM9,v#11 (frets 4 4 3 3 2 2), vM11 (4 4 3 3 2 0), v11 (4 4 3 1 2 0), and ^m11 (4 3 3 2 2 1). All but the first of these contain a wolf 11th. Rather than 8/3, the vM11 and v11 chords have 21/8, and the ^m11 chord has 27/10. The first chord's v#11th is 45/16, which is equivalent to 14/5, because 41edo tempers out the [[225/224|Ruyoyo]] comma. Thus the chord's intervallic odd limit is only 15.
+'''11th chords''' include the vM9,v#11 (frets 4 4 3 3 2 2), vM11 (4 4 3 3 2 0), v11 (4 4 3 1 2 0), and ^m11 (4 3 3 2 2 1). The first chord's v#11th is 45/16, which is equivalent to 14/5. Thus the chord's intervallic odd limit is only 15. All the other chords contain a wolf 11th. Rather than 8/3, the vM11 and v11 chords have 21/8, and the ^m11 chord has 27/10.
 === Sixth chords ===