Kite Guitar Scales: Difference between revisions

== Overview ==

There are many possible 41edo scales. Those discussed here are those with at least 5 notes, and which contain a plain perfect 5th. Scales that are awkward to play on the Kite guitar are avoided. An awkward scale has a step which requires a jump of more than four frets. Thus plain minor 2nds and 3rds are avoided. A scale naturally hops from one string to the next as it goes up or down. Unlike other guitars, the Kite guitar doesn't let one hop freely. For example, the 3-limit scale fragment P1 M2 M3 P4 requires 3 hops, 2 upward and 1 downward. Any scale which doesn't have exactly three upward hops per octave is awkward, because the downward hop will always be at least 6 frets, and usually 7 or more. Almost every scale with a low prime limit and/or a low odd limit is not awkward.  

Intervals can also be thought of as fuzzy. For example, a fuzzy major 2nd can be either a M2 or a vM2. Thus the downmajor scale 7647-674 is a fuzzy 5L2s MOS scale.

== Pentatonic Scales ==

Every pentatonic scale has 5 modes, but only those modes with a non-fuzzy 5th are listed.  

=== Major and minor scales ===

{| class="wikitable left-9 center-all"

|+

! colspan="6" |scale

!as a chord

|-

! rowspan="2" |ya

|P8

|v6,(v)9 chord

|-

!upminor

|P8

| style="text-align: left" |^m7,(^)11 chord

|-

! rowspan="2" |za

|P8

|vm7,(v)11 chord

|-

!upmajor

|P8

| style="text-align: left" |^6,(^)9 chord

|}

! colspan="6" |scale

!as a chord

|-

! rowspan="2" |yaza

|P8

|v9 = 8:9:10:12:14

|-

!harmonic minor

|P8

| style="text-align: left" |vm6,11 = 6:7:8:9:10

|-

! rowspan="3" |"

|P8

|^9 = 9/(9:8:7:6:5)

| rowspan="3" |"

| rowspan="3" |"

|P8

| style="text-align: left" |^m6,11 = 12/(12:10:9:8:7)

|-

!subharmonic diminished

|P8

| style="text-align: left" |vm7(b5),vm6 = 14/(14:12:10:9:8)

|}

== Heptatonic Scales ==

=== Major and minor scales ===

{| class="wikitable center-all"

|+

!name

! colspan="8" |scale

|-

! rowspan="2" |ya

|vM7

|P8

|-

!upminor

|^m7

|P8

|-

! rowspan="2" |za

(2.3.7)

!upmajor

|P1

|^M7

|P8

|}

=== Harmonic and subharmonic scales ===

These all have the same prime subgroup, yazalatha (2.3.5.7.11.13). They use harmonics 7-14. Adding the 15th harmonic (the '''bolded''' note) makes an octotonic scale that uses harmonics 8-16. Again, the scales are named after the triad implied by the 3rd and 5th, minus the up or down. If there are two 3rds, the unbolded one is used. Each scale contains the similarly-named pentatonic scale, e.g. the harmajor scale contains the harmajor pentatonic scale. Subhardim = 14/(14:13:12:11:10:9:8) is a theoretical possibility.  

{| class="wikitable left-11 center-all"

|+

! colspan="9" |scale

!as a chord

|-

!harmonic major

|P8

|8:9:10:11:12:13:14:'''15'''

|-

!harmonic minor

|P8

| style="text-align: left" |12:13:14:'''15''':16:18:20:22

|-

!subharmonic major

|P8

|18/(18:16:'''15''':14:13:12:11:10)

| rowspan="2" |"

|-

|P8

| style="text-align: left" |24/(24:22:20:18:16:'''15''':14:13)

|}

=== The seven diatonic modes ===

Generalizing major and minor to 41edo is fairly straightforward. Some of the other modes are tricky. Five of the seven ya modes are formed from this collection of notes:

       \ /    \ /    \ /    \

       ^F ---- ^C ---- ^G ---- ^D

</tt>

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

   vF  \ / vC  \ / vG  \ / vD  \

       D ----- A ----- E ----- B

</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.

!name

! colspan="8" |scale

|-

! rowspan="5" |ya

|P8

|P15M26 vM637vA4

|-

!downmajor

|P8

|P415M2 vM2637

|-

!downmixolydian

|P8

|m7P415 v5vM263

|-

!upminor

|P8

|^m637^4 P415M2

|-

!upphrygian

|P8

|^m2637 m7P415

|-

!"

|P8

|

|-

!"

|P8

|

|-

! rowspan="5" |za

|^M7

|P8

|-

!upmajor

|^M7

|P8

|-

!upmixolydian

|m7

|P8

|-

!downminor

|vm7

|P8

|-

!downphrygian

|(v)m7

|P8

|-

!yaza

|P8

|

|-

!"

|P8

|

|}

It would also be possible to define the modes based on the harmonic and subharmonic scales. For example, the downmixolydian scale could be P1 M2 vM3 P4 P5 vM6 vm7 P8, which contains a 4:5:6:7:9 chord. But this scale has two wolf 5ths.

=== Heptatonic ===

As can be seen from the [[:File:41-edo spiral.png|41-edo spiral of 5ths]], the upminor scale occupies two arms of the 41edo spiral of 5ths. Only one fuzzy note is needed to avoid wolf fifths. But these scales occupy three arms, and would need two fuzzy notes.   

!name

! colspan="8" |scale

!as edosteps

|-

! rowspan="3" |yala

|~7

|P8

|(8:9:10:11:12)/8 + (9:10:11:12)/6

|P152  vM263  ~74

|-

!equi-mid

|~7

|P8

|(9:10:11:12)/9 + (8:9:10:11:12)/6

|P415  vM26  ~37

|-

!equi-dorian

|^m7

|P8

|65<u>67</u>-656

|-

! rowspan="2" |"

|^m7

|P8

|12/(12:11:10:9:8) + 18/(12:11:10:9)

|~26  ^m37^4  P415

| rowspan="2" |"

|-

|~7

|P8

|6675-665

|}

!name

! colspan="13" |scale

|-

!ya

|P8

|A4^m2637  m7P415M2  vM2637vA4

|}Is there an easily playable chromatic-sounding scale with nearly equal steps? Imagine such a scale expressed in edosteps. To avoid awkward string-hopping, we need three odd numbers and the rest even. If the even number is 8, we get the equipentatonic scales, because one-eighth of 41 is about 5. If the even number is 6, we get the equiheptatonic scales, because one-sixth of 41 is about 7. The next even number is 4, which makes a decatonic scale.

! colspan="11" |scale

!as edosteps

|-

! rowspan="2" |yalaza

|vM7

|P8

|-

!twin downminor #2

|vm3

|vM3

|P5

|^m6

|vM7

|P8

|-

! rowspan="2" |"

|P8

|344-454-4454

| rowspan="2" |"

| rowspan="2" |"

|-

!

|

|

|

|

| rowspan="2" |"

| rowspan="2" |"

|-

!

|

|