Kite Guitar Scales: Difference between revisions

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<br>

</tt>

Five of the seven za modes are formed from this collection:

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<br>

</tt>

In both cases, the D is fuzzy. But the two dorian scales and the two locrian scales are not from these lattices, and are not actually modes of the other scales.

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If N goes into 41 X times with a remainder of Y, then the near-N-edo scale has steps YL and (N-Y)s, where L=X+1 and s=X. This near-N-edo scale is altered slightly so that there are only 3 odd numbers, and the rest are even. This avoids an awkward scale, but also tends to make the intervals well tuned. For example, the unaltered whole-tone scale would have thirds of mostly 14/11 with some 5/4, but the the altered one has thirds of mostly 5/4 with some 9/7.

The alteration produces only 1 additional step size which is either 1 edostep larger than L or else 1 edostep smaller than s. If this new step size occurs more than once, the 3 step sizes are named L, m and s. If it only occurs once, the new step is named either XL or xs for extra large/small~~. Thus almost all steps are within the L-to-s range, and the L/s ratio still describes the sound of the scale~~. The new step occurs more than once for near-edos 8 and 12-17, and not at all for near-edos 11 and 19.

The alteration is done so that it produces only 1 additional step size which is either 1 edostep larger than L or else 1 edostep smaller than s. If possible (and it often is), the alteration is done so that this new step size occurs only once. This is ideal because almost all steps are within the L-to-s range, and the L/s ratio still describes the overall sound of the scale. If the new step size occurs more than once, the 3 step sizes are named L, m and s. If it only occurs once, the new step size is named either XL or xs for extra large/small. The new step occurs more than once for near-edos 8 and 12-17, and not at all for near-edos 11 and 19.

{| class="wikitable"

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!# of 5ths

!moves

!~~notes~~

!as chords

|-

!3

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Line 780:

|3L 3m 2s

|1.5

|

|0

| +3, +2, -4

|2 dim7 tetrads

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=== Hexatonic (whole tone) ===

There are no off-5ths ~~(no perfect 5ths either)~~, ~~so there is~~ no motivation for fuzziness. There are six modes. Each mode is a pair of augmented triads. The three 4thward modes have a triad 3 frets above the tonic triad, and the three 5thward modes have it below. All six modes sound similar and are not named individually.

There are no perfect 5ths, only tritones. Thus there are no off-5ths, and no motivation for fuzziness. There is only one scale which distributes the 3 large steps equally. There are six modes of this scale. Each mode is a pair of augmented triads. The three 4thward modes have a triad 3 frets above the tonic triad, and the three 5thward modes have it below. All six modes sound similar and are not named individually.

The whole-tone scale is very comfortable to play physically with its alternating +3 and -3 moves. It only spans 4-5 frets and each string has exactly two notes.

{| class="wikitable center-all"

!subgroup

!~~name~~

!category

! colspan="7" |scale

!as augmented triads

Line 1,009:

Line 1,011:

|P15 vM26 ~374

|6675-665

|}

=== Octotonic ===

The 3rd step size occurs twice in these scales, making them less near-equal and less MOS-like than the other near-equal scales so far. Every scale contains a section of 2L 1m, making that section identical to an equi-heptatonic tetrachord. For example, the first scale in the table below has P5 ~6 ^m7 P8, as does the equi-minor scale. Every scale also contains a section of 2L 1s, making a down-4th, and thus an up-5th upon octave inversion. But this does not motivate fuzziness, because octotonic chords are naturally constructed from stacking "octa-thirds", i.e. using every other note of the scale. Chords avoid both perfect and off-perfect 5ths in favor of the dim 5th. The down-4th is likewise avoided.

Because of the prominence of the "octa-5th" (i.e. tritone) in octatonic chords, this interval plays a role analogous to the perfect 5th in other scales. Every octotonic scale contains eight tritones. The most consonant tritone is the dim 5th. Of course all eight tritones can't be dim 5ths without fuzziness, but half of them can be. In particular, the tonic chord can be a dim7 chord that contains two dim 5ths. The only two such chords that are playable are the ^dim7 and vdim7 chords. If we require that the remaining four notes of the scale make another such chord, there are only two near-equal octotonic scales. Each has two main modes, depending on which of the dim7 chords is considered to be the tonic chord.

{| class="wikitable center-all"

!subgroup

!name

! colspan="9" |scale

!as dim7 tetrads

!edosteps

!step sizes

!step count

!moves

|-

! rowspan="2" |yaza

(2.3.5.7)

!???

|P1

|^m2

|vm3

|^M3

|d5

|P5

|~6

|^m7

|P8

|Ivdim7 + ^bII^dim7

|4565-4566

| rowspan="2" |6 5 4

L/s = 1.5

| rowspan="2" |3L 3m 2s

or 8L

| rowspan="2" | +3, +2, -4

|-

!???

|P1

|~2

|^m3

|v4

|d5

|^5

|M6

|vM7

|P8

|I^dim7 + vVIIvdim7

|5654-5664

|-

! rowspan="2" |"

!???

|P1

|vM2

|^m3

|^M3

|d5

|vm6

|M6

|^m7

|P8

|I^dim7 + vIIvdim7

|6545-6546

| rowspan="2" |"

|-

!???

|P1

|~2

|vm3

|M3

|d5

|^5

|~6

|^m7

|P8

|Ivdim7 + ^bVII^dim7

|5456-5466

|}

=== Dodecatonic (twelve-tone) ===

@@ Line 487: / Line 487: @@
+<br>
 </tt>
 Five of the seven za modes are formed from this collection:
@@ Line 497: / Line 498: @@
+<br>
 </tt>
 In both cases, the D is fuzzy. But the two dorian scales and the two locrian scales are not from these lattices, and are not actually modes of the other scales.
@@ Line 722: / Line 724: @@
 If N goes into 41 X times with a remainder of Y, then the near-N-edo scale has steps YL and (N-Y)s, where L=X+1 and s=X. This near-N-edo scale is altered slightly so that there are only 3 odd numbers, and the rest are even. This avoids an awkward scale, but also tends to make the intervals well tuned. For example, the unaltered whole-tone scale would have thirds of mostly 14/11 with some 5/4, but the the altered one has thirds of mostly 5/4 with some 9/7.
-The alteration produces only 1 additional step size which is either 1 edostep larger than L or else 1 edostep smaller than s. If this new step size occurs more than once, the 3 step sizes are named L, m and s. If it only occurs once, the new step is named either XL or xs for extra large/small. Thus almost all steps are within the L-to-s range, and the L/s ratio still describes the sound of the scale. The new step occurs more than once for near-edos 8 and 12-17, and not at all for near-edos 11 and 19.
+The alteration is done so that it produces only 1 additional step size which is either 1 edostep larger than L or else 1 edostep smaller than s. If possible (and it often is), the alteration is done so that this new step size occurs only once. This is ideal because almost all steps are within the L-to-s range, and the L/s ratio still describes the overall sound of the scale. If the new step size occurs more than once, the 3 step sizes are named L, m and s. If it only occurs once, the new step size is named either XL or xs for extra large/small. The new step occurs more than once for near-edos 8 and 12-17, and not at all for near-edos 11 and 19.
 {| class="wikitable"
@@ Line 732: / Line 734: @@
 !# of 5ths
 !moves
-!notes
+!as chords
 |-
 !3
@@ Line 778: / Line 780: @@
 |3L 3m 2s
 |1.5
-|
+|0
 | +3, +2, -4
 |2 dim7 tetrads
@@ Line 830: / Line 832: @@
 === Hexatonic (whole tone) ===
-There are no off-5ths (no perfect 5ths either), so there is no motivation for fuzziness. There are six modes. Each mode is a pair of augmented triads. The three 4thward modes have a triad 3 frets above the tonic triad, and the three 5thward modes have it below. All six modes sound similar and are not named individually.
+There are no perfect 5ths, only tritones. Thus there are no off-5ths, and no motivation for fuzziness. There is only one scale which distributes the 3 large steps equally. There are six modes of this scale. Each mode is a pair of augmented triads. The three 4thward modes have a triad 3 frets above the tonic triad, and the three 5thward modes have it below. All six modes sound similar and are not named individually.
 The whole-tone scale is very comfortable to play physically with its alternating +3 and -3 moves. It only spans 4-5 frets and each string has exactly two notes.
 {| class="wikitable center-all"
 !subgroup
-!name
+!category
 ! colspan="7" |scale
 !as augmented triads
@@ Line 1,009: / Line 1,011: @@
 |P15  vM26  ~374
 |6675-665
+|}
+=== Octotonic ===
+The 3rd step size occurs twice in these scales, making them less near-equal and less MOS-like than the other near-equal scales so far. Every scale contains a section of 2L 1m, making that section identical to an equi-heptatonic tetrachord. For example, the first scale in the table below has P5 ~6 ^m7 P8, as does the equi-minor scale. Every scale also contains a section of 2L 1s, making a down-4th, and thus an up-5th upon octave inversion. But this does not motivate fuzziness, because octotonic chords are naturally constructed from stacking "octa-thirds", i.e. using every other note of the scale. Chords avoid both perfect and off-perfect 5ths in favor of the dim 5th. The down-4th is likewise avoided.
+Because of the prominence of the "octa-5th" (i.e. tritone) in octatonic chords, this interval plays a role analogous to the perfect 5th in other scales. Every octotonic scale contains eight tritones. The most consonant tritone is the dim 5th. Of course all eight tritones can't be dim 5ths without fuzziness, but half of them can be. In particular, the tonic chord can be a dim7 chord that contains two dim 5ths. The only two such chords that are playable are the ^dim7 and vdim7 chords. If we require that the remaining four notes of the scale make another such chord, there are only two near-equal octotonic scales. Each has two main modes, depending on which of the dim7 chords is considered to be the tonic chord.
+{| class="wikitable center-all"
+!subgroup
+!name
+! colspan="9" |scale
+!as dim7 tetrads
+!edosteps
+!step sizes
+!step count
+!moves
+|-
+! rowspan="2" |yaza
+(2.3.5.7)
+!???
+|P1
+|^m2
+|vm3
+|^M3
+|d5
+|P5
+|~6
+|^m7
+|P8
+|Ivdim7 + ^bII^dim7
+|4565-4566
+| rowspan="2" |6 5 4
+L/s = 1.5
+| rowspan="2" |3L 3m 2s
+or 8L
+| rowspan="2" | +3, +2, -4
+|-
+!???
+|P1
+|~2
+|^m3
+|v4
+|d5
+|^5
+|M6
+|vM7
+|P8
+|I^dim7 + vVIIvdim7
+|5654-5664
+|-
+! rowspan="2" |"
+!???
+|P1
+|vM2
+|^m3
+|^M3
+|d5
+|vm6
+|M6
+|^m7
+|P8
+|I^dim7 + vIIvdim7
+|6545-6546
+| rowspan="2" |"
+| rowspan="2" |"
+| rowspan="2" |"
+|-
+!???
+|P1
+|~2
+|vm3
+|M3
+|d5
+|^5
+|~6
+|^m7
+|P8
+|Ivdim7 + ^bVII^dim7
+|5456-5466
 |}
 === Dodecatonic (twelve-tone) ===