Kite Guitar Scales: Difference between revisions

Every scale can be thought of as a chord, e.g. the 12edo major pentatonic scale is a 6add9 pentad. Many pentads and heptads have an innate comma which 41edo does not temper out. Thus many Kite Guitar scales are "fuzzy", meaning a scale degree may vary by 1 edostep, in order to avoid a wolf 5th. In the tables below, a note that may be either a M2 or a vM2 is indicated by (v)M2. In general, major scales have a fuzzy 2nd and minor scales have a fuzzy 4th. But it depends on the chord progression. For example, Iv - IVv - Vv7 - Iv requires a major scale with a fuzzy 4th.  

 

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.

Each scale has steps of various sizes, shown as a series of edosteps. A dash separates the P1-P5 section of the scale from the P5-P8 section. The edosteps that can be swapped due to fuzziness are underlined. For example, in the first pentatonic scale, downing the 2nd makes <u>7 6</u> 11 - 6 7 become <u>6 7</u> 11 - 6 7. This chart translates the edostep sizes into 41-edo notation:

The step sizes column shows the sizes used. Two modes of a scale will have the same step sizes, so modes are also grouped by step sizes. The largest-to-smallest ratio L/s indicates how even the scale is. For example, the downminor heptatonic scale has a very large L/s ratio of 8/2 = 4, giving it a lopsided feel. But the downminor ''pentatonic'' scale has a very small L/s ratio of only 9/7 = 1.29, giving it an even [[5-edo|equipentatonic]] feel.  

Harmonic and subharmonic scales are contiguous segments of the harmonic and subharmonic series respectively. They are never fuzzy. Harmonic and subharmonic may be abbreviated as har- and subhar-, e.g. harmajor pentatonic. Pentatonic scales use (sub)harmonics 5-10, and heptatonic scales use (sub)harmonics 7-14. In harmonic scales, the step sizes get smaller as you ascend. In subharmonic scales, they get larger. In general, given a choice between an Ls sequence and an sL sequence, the first is often more otonal, and more consonant. For example, P1-M2-vM3 vs. P1-vM2-vM3, or P1-vm3-P4 vs. P1-^M2-P4, or even P1-vM3-P5 vs. P1-^m3-P5. (One exception: P4-d5-P5 is more otonal that P4-A4-P5.) Likewise for the choice between LLs and LsL and sLL, or between Lss and sLs and ssL, the first is generally more consonant.

The moves column is perhaps the most practical information in the table. It says how many frets to move up or down as you ascend the scale. Positive numbers refer to forward moves that move up the fretboard on a single string. Negative numbers refer to backwards moves that move up a string, then down the fretboard. The moves are not listed in order of size. Rather, forwards moves are listed, then backwards moves. In each category, they are listed by how often they occur in the scale. Assuming no excess string-hopping, there will always be 3 backwards moves per octave. If there are only two sizes of back moves, the first one occurs twice and the second one once.  

To see how this works, consider the two za pentatonic scales. Their two main moves are +4 and -2. Any short sequence of moves that alternates between +4 and -2 will be some fragment of these scales.  

The za scales are nearly [[5-edo|equipentatonic]], dividing the P4 into two nearly equal steps of ^M2 and vm3 (8 and 9). They can also be thought of as a fuzzy 2L3s MOS scale.

| rowspan="2" |11 7 6,

| rowspan="2" |2L 1m 2s,

| rowspan="2" |9 8 7,

| rowspan="2" |2L 2m 1s,

These are named after the triad implied by the 3rd and 5th, minus the up or down. Note that the harmonic ''major'' scale contains a down''minor'' 7th, and the harmonic ''minor'' scale contains a down''major'' 6th. Likewise with the subharmajor and subharminor scales. A harmonic diminished pentatonic scale would be P1 ^m3 d5 ^m6 ^m7 P8 = 5:6:7:8:9. But it's not very plausible, and would be heard as one of the other modes.  

| rowspan="2" |11 9 8 7 6,

All five of these scales are "anti-[[MOS scale|MOS]]", meaning that each scale step has a unique size. There are too many moves to list.  

As with chords, adding up or down to a scale name affects the 3rd, 6th and 7th. However, there are fuzzy notes not implied by the name.  

| rowspan="2" |7 6 4,

| rowspan="2" |3L 2M 2s,

|74<u>6-7</u>476

| rowspan="2" |8 7 2,

| rowspan="2" |2L 3M 2s,

In the edosteps column, the '''bolded''' numbers are those that would merge into one step if the 15th harmonic were excluded. Thus '''44''' would become 8. One of the hallmarks of harmonic and subharmonic scales is that each step has a unique size. Unfortunately, in 41edo, these scales do not have unique step sizes.   

| rowspan="2" |8(='''44''') 7 6 5 4,

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:

To be consistent, the two dorian scales should have a fuzzy tonic. To avoid this, and to provide all six triads, there are ''two'' fuzzy notes. Note that the 6th of the <u>up</u>dorian scale can be <u>downed</u>.

To be consistent, the uplocrian or downlocrian scale should have an upflat or downflat 5th. To get a plain flat 5th, and thus a more consonant 5:6:7 or 7/(7:6:5) tonic triad, the 5th is fuzzy as well as the 3rd.

| rowspan="5" |7 6 4,

| rowspan="5" |3L 2M 2s,

| rowspan="5" |+3, +2, -3

|74<u>6-7</u>476

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|7 6 5 4

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|8 7 6 4 3

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| rowspan="5" |8 7 2,

| rowspan="5" |2L 3M 2s,

| rowspan="5" |+4, +1, -3

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|8 7 5 2

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|8 7 6 3 2

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| rowspan="3" |7 6 5,

"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. 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 (steps of 2, 3 and 4, L/s ratio of 2). The obvious uneven scale is the [[Duodene|harmonic duodene]], with 3 fuzzy notes to avoid wolf 5ths.

|(5) 4 3 2,

L/s = 2 or 2.5

|}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.

| rowspan="2" |5 4 3,

| rowspan="2" |2L 7m 1s,

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