Kite Guitar Scales: Difference between revisions

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.  

 

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 in the far right columns as both intervals and edosteps. Two modes of a scale will have the same step sizes, so modes are also grouped by step sizes. The largest-to-smallest ratio can be calculated directly from the edosteps. 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 [[5-edo|equipentatonic]] feel. It can also be thought of as a fuzzy 2L3s MOS scale.

Harmonic and subharmonic scales are contiguous segments of the harmonic and subharmonic series respectively. They are not 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. Likewise for the choice between LLs and LsL and sLL, or between Lss and sLs and ss, the first is generally more consonant.

All five of these scales are "anti-MOS" in the sense that each scale step has a unique size.  

=== The seven diatonic modes ===

== Near-equidistant Scales ==

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. We've seen how the downminor pentatonic is nearly equi-pentatonic.

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. The 5th is divided into four nearly equal steps, reminiscent of the quarter-5th [[pergen]] and the [[Tetracot|Saquadyo]] temperament.  

These scales can be derived from the seven modes by widening the two smallest steps by 1 edostep, from an upminor 2nd to a mid 2nd. The step sizes are 1L4m2s. Treating the sole large step as an outlier, they are fuzzy 5L2s MOS scales.

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.   

!equi-major

|<u>76</u>65-665

!equi-mid

!equi-dorian

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

|^m37^4 P415 vM26

!equi-minor

|(^)4

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

|~26  ^m37^4 P415

=== Dodecatonic ===

"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 jumping 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.

!ya

!harmonic

|(v)A4

|A4^m2637  m7P415M2 vM2637vA4

|vvA1, m2, ^m2, (~2)

|2 3 4 (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.

!twin downminor #1

!twin downminor #2

!twin upmajor

|(^)M2

|^m6

|^M6

|vM7

|P8