Kite Guitar Scales: Difference between revisions

|}

=== The seven diatonic modes ===

{| class="wikitable center-all"

|+

!name

! colspan="8" |scale

!edosteps

!step sizes

|-

!downlydian

|P1

|P15M26 vM637vA4 A4

|76<u>83</u>-<u>67</u>4

|-

!downmajor (ya)

|P1

|P415M2 vM2637

|<u>76</u>47-674

|-

!downmixolydian

|P1

|vm7 m7P415M2 vM263

|<u>76</u>47-6<u>38</u>

|-

!updorian

|P1

|^m37^4 P415M26 ^M6

|74<u>67</u>-<u>83</u>6

|-

!upminor (ya)

|P1

|^m637^4 P415M2

|74<u>67</u>-476

|-

!upphrygian

|P1

|m2 ^m2637 m7P415

|<u>38</u>67-4<u>76</u>

|-

!uplocrian

|P1

|d5m2 ^m2637 m7P41

|<u>38</u>63-8<u>76</u>

|-

!uplydian

|P1

|P15M26 ^M637^A4 A4

|78<u>63</u>-<u>87</u>2

|-

!upmajor (za)

|P1

|P415M2 ^M2637

|<u>78</u>27-872

|-

!upmixolydian

|P1

|(◇)^m7

|P8

|<u>78</u>27-8<u>36</u>

|-

!downminor (za)

|P1

|vm637v4 P415M2

|72<u>87</u>-278

|-

!downphrygian

|P1

|m2 vm2637 m7P415

|<u>36</u>87-2<u>78</u>

|-

!downdorian

|P1

|P8

|vm37v4 P415M26 vM6

|-

!downlocrian

|P1

|P4

|vm6

|P8

|}

   D ----- A ----- E ----- B

       \ /    \ /    \ /    \

       ^F ---- ^C ---- ^G ---- ^D

<tt>

     ------- ------- -------

   vF  \ / vC  \ / vG  \ / vD  \

       D ----- A ----- E ----- B

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

|^m7

|P8

|74<u>67</u>-476

|-

|^m37^4 P415M26 vM6

|74<u>67</u>-<u>74</u>6

|varies

|varies

|d5 ^d5^m263 m37P41

|4<u>67</u> <u>3-8</u>67

|varies

|varies

|vm7

|P8

|72<u>87</u>-278

|-

|vm37v4 P415M26 vM6

|72<u>87</u>-<u>72</u>8

|varies

|varies

|varies

|}

Certain Asian music uses very "lopsided" scales such as P1 M3 P4 P5 M7 P8 (SE Asia) and P1 M2 m3 P5 m6 P8 (Japan). While there is a certain charm to these, scales with equal or roughly equal sizes are also attractive. The only such 12edo scales are the whole tone scale and the full 12-note gamut. Since 41 is a prime number, it has no strictly equal scales. But there are many nearly-equal scales, or near-edos.   

|1L 2s

|1.16

| -0, --1

|an aug triad

|2L 1s '''1xs'''

|1.1

| +5, -1, -2

|a dim6 or dim7 tetrad

|'''1XL''' 3L 2s

|1.17

| +3, +4, -3

|2 aug triads

|3L 3m '''2s'''

|1.5

| +3, +2, -4

|2 dim6/dim7 tetrads

|3 aug triads

|-

|5 4 3

|2L 7s '''1xs'''

|-

!11

|8L 3s

|1.33

| +2, -5

|

|-

|4 3 2

|7L 3m '''2s'''

|

| +2, +1, -5

|-

!19

|3L 16s

|

| +1, -5

These near-equal scales can be used to translate music from a small edo to the Kite guitar.

Tritonic scales are augmented triads. Both moves hop strings, hence have a negative sign. The moves are -0 and --1, meaning same fret up 1 string, and up 1 fret up 1 string.  

Both augmented and dim6/dim7 chords are discussed on the [[Kite Guitar Chord Shapes (downmajor tuning)|chords page]].

We've already seen how the upmajor and downminor pentatonic scales are nearly equi-pentatonic. See also Checkerboard[5] in the eleven-tone section.

There are no perfect 5ths, only tritones. Thus there are no off-5ths, and no motivation for dual-ness. 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.  

|m7

|P8

|678-767

|-

|m7

|P8

|876-767

|-

|^m7

|P8

|767-876

|-

|^m7

|P8

|787-676

|}

These are reminiscent of [[7edo|7-edo]]. The 4th is divided into three nearly equal steps of two vM2's and a ~2 (6 6 5), thus it's also reminiscent of the third-4th [[pergen]] and the [[Porcupine|Triyo]] temperament. Unfortunately, obvious near-equal scales like P1 ~2 ~3 P4 P5 ~6 ~7 P8 = 5757-575 are very awkward to play.  

|^m7

|P8

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

|-

|~6

|^m7

|~26  ^m37^4  P415

|56<u>67</u>-566

|vM6

|~7

|P15  vM26  ~374

|6675-665

|}

The [[Bohlen-Pierce]] or B-P 13-edt scale is a non-octave scale that is contained in 41-edo. (Technically, the 41edo scale is 13-edt stretched by half a cent.) B-P has only one step size, 5 edosteps = ~2. These steps are very near to one-eighth of an octave, so it can be thought of as a near-8edo scale. Unfortunately B-P is very awkward to play on the Kite guitar. It also has the wolfy ^5, v8 and M10 intervals. As with the other scales, we can avoid the wolves by shifting some of the notes by a single edostep. We must shift three notes, and shifting one more also makes the scale non-awkward. Instead of 13 equal steps 5 5 5 5 5 5 5 5 5 5 5 5 5, we have 5 6 4 5 6 4 5 6 4 5 6 4 5. The moves are +3 +2 -4. This scale now includes a perfect 8ve, which implies an octave-repeating version of it that is 5 6 4 5 6 4 5 6. This is one form of the octotonic 3L 3m 2s scale.

!name

! colspan="9" |scale

!edosteps

!step sizes

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

or 8L

|-

!down-7

|5456-5466

|-

!up-3 up

|P1

See also Checkerboard[8] in the eleven-tone section.

"The Flight of the Bumblebee" has simple 5-limit triads, but a scale that is clearly dodecatonic. The evenly-spaced 12edo scale is quite fitting for this piece, nicely evoking the random movements of flying insects. How would this piece translate to the Kite Guitar? Poorly, because the scale would be either very awkward to play (all plain notes, lots of hopping between strings), or very uneven, with an L/s ratio of at least 2.  

|3434-343-

34343

L/s = 1.33

|5L 7s

|4<u>34</u>2-4<u>43</u>-

42<u>43</u>4

L/s = 2.5

|}

For an even scale with small steps that's not awkward, see the next section.

Is there an easily playable chromatic-sounding scale with nearly equal steps? One such is the decatonic scale. The precise term for these scales is not chromatic but '''semitonal''', because the steps are roughly the size of a 12edo semitone. '''Trientonal''' ("by third-tones") or '''fretwise''' refers to movement by a single fret, see the section on 19-tone scales. '''Microtonal''' refers to movement by a half-fret, see the final section. '''Chromatic''' includes semitonal, trientonal/fretwise, and microtonal.  

|454-443-4544

|-

!twin upmajor down-7

|P1

| rowspan="2" |"

|-

|P1

|^m2

|}

This scale is notable for not needing a 3rd step size or a 3rd move. It gets its name from the fact that it uses every other fret of each string, and each string's notes are offset by one fret from the neighboring strings. Thus the scale chart looks like an actual checkerboard. It's a [[MOS scale]] generated by the ^M3, which is 15\41. The complete genchain containing all 11 modes runs from -10 generators to +10:

(2.3.5.7.11)

!#1

|^M2

|~3

|P1 ... m6

|444-3444-344-3

L/s = 1.33

| rowspan="11" | +2, -5

|-

!#2

|^M2

|'''~3'''

|m7

|M7

|444-344-3444-3

|-

!#3

|^M2

|'''^m3'''

|m7

|'''M7'''

|44-3444-3444-3

|-

!#4

|^M2

|^m3

|m7

|'''vM7'''

|44-3444-344-34

|-

!#5

|'''^M2'''

|^m3

|-

!#6

|'''M2'''

|^m3

|-

!#7

|M2

|^m3

|'''vm7'''

|vM7

|4-3444-344-344

|-

!#8

|P1

|M2

|^m3

!#9

|P1

|M2

|^m3

!#10

|P1

|M2

|^m3

!#11

|P1

|M2

|^m3

* 1 step = minorish 2nd = 88¢ or 117¢

There's not much to say about these scales. All the modes sound fairly similar, and there's not much reason to name them individually. Using the full 19 note scale is somewhat overkill, unless your song is about bumblebees.  

|}

These scales use step sizes of 1 and 2 edosteps only. They are quite awkward to play, with much string-hopping and fret-leaping. If there are only 3 small steps, it is a 22-note MOS or MODMOS of Laquinyo.

See the discussion at [[Kite Giedraitis's Categorizations of 41edo Scales]].

{| class="wikitable"

|8 3

| +4, -5

|-

| rowspan="5" |Laquinyo

| rowspan="5" |(P8, P12/5)

| rowspan="5" |vM3

|7 = 3L 4s

| rowspan="5" |fretwise scales

|-

|9 2

| +1, -2

|-

|7 2

| +1, -3

|-

|5 2

| +1, -4

|-

|3 2

| +1, -5

| rowspan="3" |Checkerboard

| rowspan="3" |(P8, c⁶P5/18)

| rowspan="3" |^M3

|5 = 3L 2s

|11 4

| +2, -1

|-

|8 = 3L 5s

| +2, -3

|-

|4 3

| +2, -5

|(P8, P5)

|17\41

|5 = 2L 3s

|10 7