Kite Guitar Scales
Printable charts for the downmajor tuning of the Kite Guitar. One is of scale degrees, the other is of the three main heptatonic scales. In the latter, some scale degrees appear more than once. In general, use the one that agrees with the current chord.
Overview
This is the practical guide to Kite Guitar scales. See also Kite Giedraitis's Categorizations of 41edo Scales, which is more theoretical.
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.
MOS (moment of symmetry) scales have only two step sizes, with the less frequent steps evenly distributed throughout the scale. MOS scales are an important part of microtonal scale theory. But almost every 41-edo MOS scale with a perfect 5th is awkward. The only exception is scales from the Laquinyo temperament, which have a small step of only one fret. They have either a very lopsided L/s ratio or more than 12 notes. They are discussed further in the Nineteen-tone section.
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, majorish scales have a fuzzy 2nd and minorish scales have a fuzzy 4th. But it depends on the chord progression. For example, Iv - IVv - Vv7 - Iv requires a downmajor scale with a fuzzy 4th. Step sizes can also be fuzzy, leading to fuzzy MOS scales (see below).
The Format
The modes of a scale are grouped together. Not every mode is shown. Often two scales are modes only because of the fuzzy notes, e.g. downmajor and upminor. Two modes of a scale will use the same prime subgroup, so modes are grouped by subgroup. Subgroups are explained on the theoretical scales page: Kite Giedraitis's Categorizations of 41edo Scales.
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. An odd number always hops a string, an even number never does. This chart translates the edostep sizes into 41-edo notation:
edosteps | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 |
---|---|---|---|---|---|---|---|---|---|---|
name | vm2 | m2 | ^m2 | ~2 | vM2 | M2 | ^M2 | vm3 | m3 | ^m3 |
The edosteps that are affected by fuzziness are underlined. For example, the downmajor scale is P1 (v)M2 vM3 P4 P5 vM6 vM7 P8. The edosteps are listed as if the 2nd were plain: 7647-674. Downing the 2nd makes 6747-674. Almost always, the two underlined step sizes differ by only one, and upping or downing merely swaps the two numbers. Therefore the fuzziness rarely affects the moves (see below). The only exceptions are the dorian, locrian and dodecatonic scales, all of which are problematic anyway.
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 equipentatonic feel.
The step count column analyzes the scale by the usual MOS notation of how many large and small steps there are. Some scales also have m for medium, and even XL for extra large and xs for extra small. Most scales are not actually MOS, but a fuzzy MOS. For example, the first two pentatonic scales are 2L 1m 2s, where L=11, m=7 and s=6. The single m step can be thought of as a fuzzy version of the s step, making a fuzzy 2L 3s MOS scale. Fuzzy MOS scales are listed as alternates, e.g. "2L 1m 2s or 2L 3s".
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. But P1-^m2-M2 is better than P1-m2-M2.) Likewise for the choice between LLs and LsL and sLL, or between Lss and sLs and ssL, the first is generally more consonant.
Scales are loosely named similarly to how chords are named. Adding up or down to a scale name affects the 3rd, 6th and 7th. However, there are usually fuzzy notes not implied by the name. Harmonic and subharmonic scales are named after the tonic triad, minus the up or down.
Some scales are listed as chains of 5ths. For example, the downmajor scale is P1 (v)M2 vM3 P4 P5 vM6 vM7 P8. There are two chains: P4-P1-P5-M2 and vM2-vM6-vM3-vM7. This is condensed to P415M2 vM2637. Here the two chains overlap on a fuzzy note. However, the near-equidistant heptatonic scales do not, and have a wolf 5th.
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, forward moves are listed, then backward moves. In each category, they are listed by how often they occur in the scale. In case of a tie, the largest step size is listed first. The first move in the list is the primary forward move, and the first negative number is the primary backward move. All other moves are secondary. Because there are only 3 string-hops in an octave, there are at most 3 backwards moves. There are at most 2 secondary backwards moves, and usually only 1. A scale that doesn't have any secondary moves (i.e. has only two step sizes) is usually one of the rare MOS scales.
To see how this works, consider the two ya pentatonic scales. Their two primary moves are +3 and -1. Any short sequence of moves that alternates between +3 and -1 (or -3 and +1 if descending) will be some fragment of these scales. Likewise +4 and -2 moves evoke a za pentatonic feel. For longer sequences, one's natural inclination to stay in the same region of the fretboard, and to repeat at the octave, will guide one when to include the secondary moves.
There is a saying in the arts, "learn the rules, then break them." Often a striking melody is striking because it doesn't conform to a standard scale. Don't be afraid to experiment!
Pentatonic Scales
Every pentatonic scale has 5 modes, but only those modes with a non-fuzzy 5th are listed.
Major and minor scales
The za scales are nearly equipentatonic, dividing the P4 into two nearly equal steps of 8 and 9 edosteps (^M2 and vm3). Since one is a 2nd and the other a 3rd, this can conflict with one's categorical perception of intervals. Best to think of them both as "penta-2nds".
subgroup | name | scale | as a chord | as chains of 5ths | edosteps | step sizes | step count | moves | |||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|
ya
(2.3.5) |
downmajor | P1 | (v)M2 | vM3 | P5 | vM6 | P8 | v6,(v)9 chord | P15M2 vM263 | 7 6 11 - 6 11 | 11 7 6
L/s = 1.83 |
2L 1m 2s
or 2L 3s |
+3, -1, -3 |
upminor | P1 | ^m3 | (^)4 | P5 | ^m7 | P8 | ^m7,(^)11 chord | ^m37^4 P415 | 11 6 7 - 11 6 | ||||
za
(2.3.7) |
downminor | P1 | vm3 | (v)4 | P5 | vm7 | P8 | vm7,(v)11 chord | vm37v4 P415 | 9 8 7 - 9 8 | 9 8 7
L/s = 1.29 |
2L 2m 1s
or 2L 3s or 5L |
+4, -2, -3 |
upmajor | P1 | (^)M2 | ^M3 | P5 | ^M6 | P8 | ^6,(^)9 chord | P15M2 ^M263 | 7 8 9 - 8 9 |
Harmonic and subharmonic scales
Note that the harmonic major scale contains a downminor 7th, and the harmonic minor scale contains a downmajor 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.
subgroup | name | nickname | scale | as a chord | edosteps | step sizes | step count | |||||
---|---|---|---|---|---|---|---|---|---|---|---|---|
yaza
(2.3.5.7) |
harmonic major | harmajor | P1 | M2 | vM3 | P5 | vm7 | P8 | v9 = 8:9:10:12:14 | 7 6 11 - 9 8 | 11 9 8 7 6
L/s = 1.83 |
1XL 1L 1m 1s 1xs |
harmonic minor | harminor | P1 | vm3 | P4 | P5 | vM6 | P8 | vm6,11 = 6:7:8:9:10 | 9 8 7 - 6 11 | |||
" | subharmonic major | subharmajor | P1 | M2 | ^M3 | P5 | ^m7 | P8 | ^9 = 9/(9:8:7:6:5) | 7 8 9 - 11 6 | " | " |
subharmonic minor | subharminor | P1 | ^m3 | P4 | P5 | ^M6 | P8 | ^m6,11 = 12/(12:10:9:8:7) | 11 6 7 - 8 9 | |||
subharmonic diminished | subhardim | P1 | vm3 | d5 | vm6 | vm7 | P8 | vm7(b5),vm6 = 14/(14:12:10:9:8) | 9 11 - 6 7 8 |
All five of these scales are "anti-MOS", meaning that each scale step has a unique size. There are many secondary moves, and thus too many types of moves to list. These scales are half ya, half za.
Heptatonic Scales
Major and minor scales
See below for modes of these scales.
subgroup | name | scale | as chains of 5ths | edosteps | step sizes | step count | moves | |||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
ya
(2.3.5) |
downmajor | P1 | (v)M2 | vM3 | P4 | P5 | vM6 | vM7 | P8 | P415M2 vM2637 | 7647-674 | 7 6 4
L/s = 1.75 |
3L 2M 2s
or 5L 2s |
+3, +2, -3 |
upminor | P1 | M2 | ^m3 | (^)4 | P5 | ^m6 | ^m7 | P8 | ^m637^4 P415M2 | 7467-476 | ||||
za
(2.3.7) |
downminor | P1 | M2 | vm3 | (v)4 | P5 | vm6 | vm7 | P8 | vm637v4 P415M2 | 7287-278 | 8 7 2
L/s = 4 |
2L 3M 2s
or 5L 2s |
+4, +1, -3 |
upmajor | P1 | (^)M2 | ^M3 | P4 | P5 | ^M6 | ^M7 | P8 | P415M2 ^M2637 | 7827-872 |
Altered minor scales
The conventional 12-edo melodic minor and harmonic minor scales are MODMOS scales, modified MOS scales. This is a sort of "macro-fuzziness", where one scale step can vary by an entire semitone. The two harmonic downminor scales have an enormous L/s ratio!
subgroup | name | scale | as chains of 5ths | edosteps | step sizes | step count | moves | |||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
ya
(2.3.5) |
harmonic
upminor |
P1 | M2 | ^m3 | P4 | P5 | ^m6 | vM7 | P8 | ^m63 P415M2 vM7 | 7467-494 | 9 7 6 4
L/s = 2.25 |
1XL 2L 1m 3s
or 1L 3m 2s |
+2, +3, -3, -2 |
" | melodic
upminor |
P1 | M2 | ^m3 | P4 | P5 | vM6 | vM7 | P8 | ^m3 P415M2 vM6 vM7 | 7467-674 | 7 6 4
L/s = 1.75 |
3L 2m 2s
or 5L 2s |
+3, +2, -3 |
za
(2.3.7) |
harmonic
downminor |
P1 | M2 | vm3 | P4 | P5 | vm6 | ^M7 | P8 | vm63 P415M2 ^M7 | 7287-2,13,2 | 13 8 7 2
L/s = 6.5 |
1XL 1L 2m 3s
or 1L 3m 3s |
+1, +4, -3, -0 |
" | harmonic
downminor ^#4 |
P1 | M2 | vm3 | ^A4 | P5 | vm6 | ^M7 | P8 | vm63 P15M2 ^M7^A4 | 7,2,13,2-2,13,2 | 13 7 2
L/s = 6.5 |
2L 1m 4s | +1, -0, -3 |
" | melodic
downminor |
P1 | M2 | vm3 | P4 | P5 | ^M6 | ^M7 | P8 | vm3 P415M2 ^M6 ^M7 | 7287-872 | 8 7 2
L/s = 4 |
2L 3m 2s
or 5L 2s |
+4, +1, -3 |
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.
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, especially the octotonic ones.
name | nickname | scale | as a chord | edosteps | step sizes | ||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|
harmonic major | harmajor | P1 | M2 | vM3 | ~4 | P5 | ~6 | vm7 | vM7 | P8 | 8:9:10:11:12:13:14:15 | 7665-5444 | 8(=44) 7 6 5 4
L/s = 2 or 1.75 |
harmonic minor | harminor | P1 | ~2 | vm3 | vM3 | P4 | P5 | vM6 | ~7 | P8 | 12:13:14:15:16:18:20:22 | 54447-665 | |
subharmonic major | subharmajor | P1 | M2 | ^m3 | ^M3 | ~4 | P5 | ~6 | ^m7 | P8 | 18/(18:16:15:14:13:12:11:10) | 74445-566 | " |
subharmonic minor | subharminor | P1 | ~2 | ^m3 | P4 | P5 | ^m6 | ^M6 | ~7 | P8 | 24/(24:22:20:18:16:15:14:13) | 5667-4445 |
The seven diatonic modes
Generalizing major and minor to 41edo is fairly straightforward. The dorian and locrian modes don't translate well. The other five ya modes are formed from this collection of notes:
D ----- A ----- E ----- B \ / \ / \ / \ \ / \ / \ / \ \ / \ / \ / \ ^F ---- ^C ---- ^G ---- ^D
Five of the seven za modes are formed from this collection:
------- ------- ------- \ / \ / \ / \ \ / \ / \ / \ vF \ / vC \ / vG \ / vD \ D ----- A ----- E ----- B
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.
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 updorian scale can be downed. Note that this fuzziness affects the step sizes, and 7467-746 can become 7467-656. Thus the moves vary.
To be consistent, the two locrian scales 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. Again, this fuzziness affects the step sizes and the moves.
subgroup | name | scale | as chains of 5ths | edosteps | step sizes | step count | moves | |||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
ya
(2.3.5) |
downlydian | P1 | M2 | vM3 | vA4 | P5 | (v)M6 | vM7 | P8 | P15M26 vM637vA4 | 7674-764 | 7 6 4
L/s = 1.75 |
3L 2M 2s
or 5L 2s |
+3, +2, -3 |
downmajor | P1 | (v)M2 | vM3 | P4 | P5 | vM6 | vM7 | P8 | P415M2 vM2637 | 7647-674 | ||||
downmixolydian | P1 | vM2 | vM3 | P4 | (v)5 | vM6 | m7 | P8 | m7P415 v5vM263 | 6747-647 | ||||
upminor | P1 | M2 | ^m3 | (^)4 | P5 | ^m6 | ^m7 | P8 | ^m637^4 P415M2 | 7467-476 | ||||
upphrygian | P1 | ^m2 | ^m3 | P4 | P5 | ^m6 | (^)m7 | P8 | ^m2637 m7P415 | 4767-467 | ||||
" | updorian | P1 | M2 | ^m3 | (^)4 | P5 | (v)M6 | ^m7 | P8 | ^m37^4 P415M26 vM6 | 7467-746 | 7 6 (5) 4 | varies | varies |
" | uplocrian | P1 | ^m2 | (^)m3 | P4 | (^)d5 | ^m6 | m7 | P8 | d5 ^d5^m263 m37P41 | 467 3-867 | (8) 7 6 4 (3) | varies | varies |
za
(2.3.7) |
uplydian | P1 | M2 | ^M3 | ^A4 | P5 | (^)M6 | ^M7 | P8 | P15M26 ^M637^A4 | 7872-782 | 8 7 2
L/s = 4 |
2L 3M 2s
or 5L 2s |
+4, +1, -3 |
upmajor | P1 | (^)M2 | ^M3 | P4 | P5 | ^M6 | ^M7 | P8 | P415M2 ^M2637 | 7827-872 | ||||
upmixolydian | P1 | ^M2 | ^M3 | P4 | (^)5 | ^M6 | m7 | P8 | m7P415 ^5^M263 | 8727-827 | ||||
downminor | P1 | M2 | vm3 | (v)4 | P5 | vm6 | vm7 | P8 | vm637v4 P415M2 | 7287-278 | ||||
downphrygian | P1 | vm2 | vm3 | P4 | P5 | vm6 | (v)m7 | P8 | vm2637 m7P415 | 2787-287 | ||||
yaza | downdorian | P1 | M2 | vm3 | (v)4 | P5 | (v)M6 | vm7 | P8 | vm37v4 P415M26 vM6 | 7287-728 | 8 7 (6) (3) 2 | varies | varies |
" | downlocrian | P1 | vm2 | (v)m3 | P4 | (v)d5 | vm6 | m7 | P8 | d5 vd5vm263 m37P41 | 287 3-687 | " | varies | varies |
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.
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, or near-edos.
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 and 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 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 original L-to-s range, and the original (small) 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.
near-edo | step sizes | step count | L/s | # of 5ths | moves | as chords |
---|---|---|---|---|---|---|
3 | 15 13 | 1L 2s | 1.16 | 0 | -0, --1 | an aug triad |
4 | 11 10 9 | 2L 1s 1xs | 1.1 | 0 | +5, -1, -2 | a dim7 tetrad |
5 | 9 8 7 | 2L 2s 1xs | 1.125 | 3-4 | +4, -2, -3 | a za pentad |
6 | 8 7 6 | 1XL 3L 2s | 1.17 | 0 | +3, +4, -3 | 2 aug triads |
7 | 7 6 5 | 1XL 4L 2s | 1.2 | 4-5 | +3, -4, -3 | |
8 | 6 5 4 | 3L 3m 2s | 1.5 | 0 | +3, +2, -4 | 2 dim7 tetrads |
9 | 6 5 4 | 1XL 3L 5s | 1.25 | +2, +3, -4 | 3 aug triads | |
10 | 5 4 3 | 2L 7s 1xs | 1.25 | 5-6 | +2, -4, -5 | 2 za pentads |
11 | 4 3 | 8L 3s | 1.33 | +2, -5 | ||
12 | 4 3 2 | 7L 3m 2s | 2.0 | +2, +1, -5 | ||
19 | 3 2 | 3L 16s | 1.5 | +1, -5 |
Tritonic and Tetratonic
Tritonic scales are augmented triads, discussed here. Tetratonic scales are dim7 tetrads, discussed here.
Pentatonic
We've already seen how the upmajor and downminor pentatonic scales are nearly equi-pentatonic.
Hexatonic (whole tone)
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.
subgroup | category | scale | as augmented triads | edosteps | step sizes | step count | moves | ||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|
yaza
(2.3.5.7) |
4thward
whole-tone |
P1 | vM2 | vM3 | ~4 | vm6 | m7 | P8 | Ivhalf-aug + vIIvaug | 676-787 | 8 7 6
L/s = 1.4 |
1XL 3L 2s
or 4L 2s or 6L |
+3, +4, -3 |
P1 | vM2 | vM3 | A4 | ^m6 | m7 | P8 | Ivaug + vII^aug | 678-767 | |||||
P1 | ^M2 | ^M3 | A4 | ^m6 | m7 | P8 | I^aug + ^IIvhalf-aug | 876-767 | |||||
5thward
whole-tone |
P1 | M2 | vM3 | d5 | vm6 | vm7 | P8 | Ivhalf-aug + vbVII^aug | 767-678 | ||||
P1 | M2 | vM3 | d5 | ^m6 | ^m7 | P8 | Ivaug + ^bVIIvhalf-aug | 767-876 | |||||
P1 | M2 | ^M3 | ~5 | ^m6 | ^m7 | P8 | I^aug + ^bVIIvaug | 787-676 |
Heptatonic
These are reminiscent of 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 Triyo temperament. Unfortunately, obvious near-equal scales like P1 ~2 ~3 P4 P5 ~6 ~7 P8 = 5757-575 are very awkward to play.
The two main scales are equi-major and equi-minor. Equi-minor is somewhat like maqam Huseyni or maqam Bayati. Equi-major is equi-minor octave-inverted.
These scales can be derived from the seven ya modes by widening the two smallest steps by 1 or 2 edosteps, from an upminor 2nd to a mid or downmajor 2nd. The tonic triad is never altered by the widening, thus equi-lydian and equi-mixolydian would be the same as equi-major, and equi-phrygian the same as equi-minor.
The standard downmajor and upminor scales have two chains of 5ths. Only one fuzzy note linking them is needed to avoid a wolf fifth. But these scales have three chains, and would need two fuzzy notes. They are shown here with only one fuzzy note, thus they have a wolf 5th. To avoid the wolf, either the 3rd must be fuzzy, or else there must be a step of 4 edosteps which inflates the L/s ratio and destroys the near-equal feel. The two equi-mid scales each have two wolf 5ths.
These scales are harmonic or subharmonic series fragments. Equi-major is (8:9:10:11:12)/8 plus (9:10:11:12)/6. Equi-mid is (9:10:11:12)/9 + (8:9:10:11:12)/6. Equi-minor is 12/(12:11:10:9:8) + 18/(12:11:10:9).
subgroup | name | scale | as chains of 5ths | edosteps | step sizes | step count | moves | |||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
yala
(2.3.5.11) |
equi-major | P1 | (v)M2 | vM3 | ~4 | P5 | vM6 | ~7 | P8 | P152 vM263 ~74 | 7665-665 | 7 6 5
L/s = 1.4 |
1L 4m 2s
or 5L 2s or 7L |
+3, -4, -3 |
equi-mid | P1 | vM2 | ~3 | P4 | P5 | vM6 | ~7 | P8 | P415 vM26 ~37 | 6657-665 | ||||
equi-dorian | P1 | vM2 | ^m3 | (^)4 | P5 | vM6 | ^m7 | P8 | ^m37^4 P415 vM26 | 6567-656 | ||||
" | equi-minor | P1 | ~2 | ^m3 | (^)4 | P5 | ~6 | ^m7 | P8 | ~26 ^m37^4 P415 | 5667-566 | " | " | " |
equi-mid ~4 | P1 | vM2 | ~3 | ~4 | P5 | vM6 | ~7 | P8 | 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.
subgroup | name | scale | as dim7 tetrads | edosteps | step sizes | step count | moves | ||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
yaza
(2.3.5.7) |
??? | P1 | ^m2 | vm3 | ^M3 | d5 | P5 | ~6 | ^m7 | P8 | Ivdim7 + ^bII^dim7 | 4565-4566 | 6 5 4
L/s = 1.5 |
3L 3m 2s
or 8L |
+3, +2, -4 |
??? | P1 | ~2 | ^m3 | v4 | d5 | ^5 | M6 | vM7 | P8 | I^dim7 + vVIIvdim7 | 5654-5664 | ||||
" | ??? | P1 | vM2 | ^m3 | ^M3 | d5 | vm6 | M6 | ^m7 | P8 | I^dim7 + vIIvdim7 | 6545-6546 | " | " | " |
??? | P1 | ~2 | vm3 | M3 | d5 | ^5 | ~6 | ^m7 | P8 | Ivdim7 + ^bVII^dim7 | 5456-5466 |
Dodecatonic (twelve-tone)
"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.
Here is one mode of the 3-limit pythagorean dodecatonic scale, which is the closest one can get to 12-edo on the Kite Guitar. There are 7 small steps of 3 edosteps, each of which requires a string-hop. The moves column is deceptive, because repeated -5 moves will push one to the nut and make one run out of frets. Thus some of the -5 moves will have to be +8 frets but -1 string.
subgroup | name | scale | as a chain of 5ths | edosteps | step sizes | step count | moves | ||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
wa
(2.3) |
3-limit
dodecatonic |
P1 | m2 | M2 | m3 | M3 | P4 | A4 | P5 | m6 | M6 | m7 | M7 | P8 | m2637P415M2637A4 | 3434-343-
34343 |
4 3
L/s = 1.5 |
5L 7s
or 12L |
+2, -5 |
The obvious uneven scale is the harmonic duodene, with 3 fuzzy notes to avoid wolf 5ths. Note that the fuzzy major 2nd and minor 7th affect the step sizes. Both vM2-^m3 and vM6-^m7 are 5 edosteps. The step count and moves are affected as well.
subgroup | name | scale | as chains of 5ths | edosteps | step sizes | ||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
ya
(2.3.5) |
harmonic
duodene |
P1 | ^m2 | (v)M2 | ^m3 | vM3 | P4 | (v)A4 | P5 | ^m6 | vM6 | (^)m7 | vM7 | P8 | A4^m2637 m7P415M2 vM2637vA4 | 4342-443-
42434 |
(5) 4 3 2
L/s = 2.5 |
For an even scale with small steps that's not awkward, see the next section.
Decatonic - the semitonal scale
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. The even numbers should all be the same. The odd numbers should be 1 greater or 1 less. If the even number is 8, we get the near-equipentatonic scales, because one-eighth of 41 is about 5. If the even number is 6, we get the near-equiheptatonic scales, because one-sixth of 41 is about 7. The next even number is 4, which makes a decatonic scale. Thus the saying that on the Kite Guitar, "ten is the new twelve".
However, the term for these scales is not chromatic but semitonal, because the steps are roughly the size of a 12edo semitone. Chromatic refers to movement by a single fret, see the next section.
The twin downminor scale consists of two downminor pentatonic scales, offset from each other by two frets. Mode #1 is (12:13:14:15:16:17:18)/12 plus (12:13:14:15:16)/8, except that prime 17 isn't well tuned.
subgroup | name | scale | edosteps | step sizes | step count | moves | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
yazala
(2.3.5.7.11) |
twin downminor #1 | P1 | ~2 | vm3 | vM3 | (v)4 | d5 | P5 | ~6 | vm7 | vM7 | P8 | 544-434-5444 | 5 4 3
L/s = 1.67 |
2L 7m 1s
or 2L 8s or 10L |
+2, -4, -5 |
twin downminor #2 | P1 | ^m2 | vm3 | vM3 | P4 | (v)A4 | P5 | ^m6 | vm7 | vM7 | P8 | 454-443-4544 | ||||
" | twin upmajor | P1 | m2 | (^)M2 | ^m3 | ^M3 | d5 | P5 | ^m6 | ^M6 | vM7 | P8 | 344-454-4454 | " | " | " |
(more to come) | ||||||||||||||||
" | " | " | " | " | ||||||||||||
" |
The twin downminor scale works well for the blues. It lacks a M2, so over the V chord, shift the scale so that it's rooted on the 5th. Likewise shift the root to the 4th over the IV chord.
subgroup | name | scale | edosteps | step sizes | step count | moves | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
yazala
(2.3.5.7.11) |
twin downminor on I | P1 | ~2 | vm3 | vM3 | (v)4 | d5 | P5 | ~6 | vm7 | vM7 | P8 | 544-434-5444 | 5 4 3
L/s = 1.67 |
2L 7m 1s
or 2L 8s or 10L |
+2, -4, -5 |
twin downminor on IV | P1 | ~2 | vm3 | vM3 | P4 | ~5 | vm6 | vM6 | (v)m7 | vM7 | P8 | 544-45-44434 | ||||
twin downminor on V | P1 | m2 | M2 | ~3 | v4 | d5 | P5 | ~6 | vm7 | vM7 | P8 | 345-444-5444 |
Nineteen-tone - The chromatic scale
Let's continue the analysis that starts the previous section. The next even number below 4 is 2. This implies many steps of a single fret, and three string-hopping steps of 3 edosteps. (1 edostep is just too small!) This makes a 19-note scale. 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.
The one-fret step implies several different ratios, and doesn't imply any particular prime subgroup. The step count is 3L 16s and the L/s ratio is 1.5. The moves are +1 and -5. If there are 6 or 7 notes per string, it's a MOS scale of the Laquinyo temperament, which has a (P8, P12/5) pergen. If not, it's a MODMOS scale of Laquinyo. For example, the 2nd scale in the table is MODMOS because the large steps are not evenly distributed throughout the scale.
name | scale | edosteps | |||||||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
chromatic | P1 | vm2 | ^m2 | (v)M2 | vm3 | ^m3 | vM3 | ^M3 | P4 | d5 | ~5 | P5 | vm6 | ^m6 | vM6 | vm7 | ^m7 | vM7 | ^M7 | P8 | 223222-22322-2223-2222 |
" | P1 | vm2 | ^m2 | vM2 | ^M2 | ^m3 | vM3 | ^M3 | P4 | ~4 | ~5 | P5 | vm6 | ^m6 | vM6 | ^M6 | ^m7 | vM7 | ^M7 | P8 | 222232-22232-2222-3222 |
Although the full scale is a bit much, pieces of it are nice. Chromatic melodies with movements of a single fret are quite novel and pleasant. 59¢ is just barely large enough to sound like a 2nd and not a quartertone. Any of the 5, 7, and 10-note scales can be spiced up with chromatic movement.
One can make a scale that's not very even, but still quite interesting, by using a smaller MOS, for example 13. This scale is 3 chromatic runs separated by 3 major 2nds.
name | scale | edosteps | step sizes | step count | moves | |||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
chromatic | P1 | vm2 | ^m2 | ^m3 | vM3 | ^M3 | P4 | P5 | vm6 | ^m6 | vM6 | ^M6 | ^M7 | P8 | 2272-227-222272 | 7 2, L/s = 3.5 | 3L 10s | +2, -3 |
Microtonal scales
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.