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

There are many possible 41edo scales. Those discussed here are those which are not awkward to play on the Kite guitar. 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. Any scale which doesn't have exactly three hops per octave is awkward. All pentatonic, hexatonic and heptatonic MOS scales are awkward. However 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 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 the chord progression may make other degrees fuzzy. For example, Iv - IVv - Vv7 - Iv requires a fuzzy 4th.

The modes of a scale are grouped together. Not every mode is shown. Two modes of a scale will use the same prime subgroup, so modes are grouped by subgroup.

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 equipentatonic feel.

Harmonic and subharmonic scales are segments of the harmonic and subharmonic series. 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.

See also Kite Giedraitis's Categorizations of 41edo Scales.

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 ^M2 and vm3 (8 and 9).

subgroup	name	scale						as a chord	step sizes
ya (2.3.5)	downmajor	P1	(v)M2	vM3	P5	vM6	P8	v6,(v)9 chord	vM2, M2, ^m3	6 7 11
	upminor	P1	^m3	(^)4	P5	^m7	P8	^m7,(^)11 chord
za (2.3.7)	downminor	P1	vm3	(v)4	P5	vm7	P8	vm7,(v)11 chord	M2, ^M2, vm3	7 8 9
	upmajor	P1	(^)M2	^M3	P5	^M6	P8	^6,(^)9 chord

Harmonic and subharmonic scales

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 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	step sizes
yaza (2.3.5.7)	harmonic major	harmajor	P1	M2	vM3	P5	vm7	P8	v9 = 8:9:10:12:14	vM2, M2, ^M2, vm3, ^m3	6 7 8 9 11
	harmonic minor	harminor	P1	vm3	P4	P5	vM6	P8	vm6,11 = 6:7:8:9:10
"	subharmonic major	subharmajor	P1	M2	^M3	P5	^m7	P8	^9 = 9/(9:8:7:6:5)	"	"
	subharmonic minor	subharminor	P1	^m3	P4	P5	^M6	P8	^m6,11 = 12/(12:10:9:8:7)
	subharmonic diminished	subhardim	P1	vm3	d5	vm6	vm7	P8	vm7(b5),vm6 = 14/(14:12:10:9:8)

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

Heptatonic Scales

Major and minor scales

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. Without these fuzzy notes, downmajor and upminor would not be modes of each other.

subgroup	name	scale								step sizes
ya (2.3.5)	downmajor	P1	(v)M2	vM3	P4	P5	vM6	vM7	P8	^m2, vM2, M2	4 6 7
	upminor	P1	M2	^m3	(^)4	P5	^m6	^m7	P8
za (2.3.7)	upmajor	P1	(^)M2	^M3	P4	P5	^M6	^M7	P8	vm2, M2, ^M2	2 7 8
	downminor	P1	M2	vm3	(v)4	P5	vm6	vm7	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.

name	nickname	scale									as a chord	step sizes
harmonic major	harmajor	P1	M2	vM3	~4	P5	~6	vm7	vM7	P8	8:9:10:11:12:13:14:15	^m2, ~2, vM2, M2, ^M2	4 5 6 7 8
harmonic minor	harminor	P1	~2	vm3	vM3	P4	P5	vM6	~7	P8	12:13:14:15:16:18:20:22
subharmonic major	subharmajor	P1	M2	^m3	^M3	~4	P5	~6	^m7	P8	18/(18:16:15:14:13:12:11:10)	"	"
subharmonic minor	subharminor	P1	~2	^m3	P4	P5	^m6	^M6	~7	P8	24/(24:22:20:18:16:15:14:13)

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. The heptatonic scales run 8 7 6 6 5 5 4. The octotonic step sizes are worse, 7 6 6 5 5 4 4 4. Only the "anti-MOS" pentatonic scales have unique step sizes.

The seven 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:

  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.

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.

subgroup	name	scale								step sizes
ya (2.3.5)	downlydian	P1	M2	vM3	vA4	P5	(v)M6	vM7	P8	^m2, vM2, M2	4 6 7
	downmajor	P1	(v)M2	vM3	P4	P5	vM6	vM7	P8
	downmixolydian	P1	vM2	vM3	P4	(v)5	vM6	m7	P8
	upminor	P1	M2	^m3	(^)4	P5	^m6	^m7	P8
	upphrygian	P1	^m2	^m3	P4	P5	^m6	(^)m7	P8
"	updorian	P1	M2	^m3	(^)4	P5	(v)M6	^m7	P8	^m2, ~2, vM2, M2	4 5 6 7
"	uplocrian	P1	^m2	(^)m3	P4	(^)d5	^m6	m7	P8	m2, ^m2, vM2, M2, ^M2	3 4 6 7 8
za (2.3.7)	uplydian	P1	M2	^M3	^A4	P5	(^)M6	^M7	P8	vm2, M2, ^M2	2 7 8
	upmajor	P1	(^)M2	^M3	P4	P5	^M6	^M7	P8
	upmixolydian	P1	^M2	^M3	P4	(^)5	^M6	m7	P8
	downminor	P1	M2	vm3	(v)4	P5	vm6	vm7	P8
	downphrygian	P1	vm2	vm3	P4	P5	vm6	(v)m7	P8
yaza	downdorian	P1	M2	vm3	(v)4	P5	(v)M6	vm7	P8	vm2, ~2, M2, ^M2	2 5 7 8
"	downlocrian	P1	vm2	(v)m3	P4	(v)d5	vm6	m7	P8	vm2, m2, vM2, M2, ^M2	2 3 6 7 8

Near-equiheptatonic scales

These are a cross between the usual modes and the harmonic or subharmonic scales. Obviously they 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.

The two smallest steps of the upminor or downmajor scale are widened by 1 edostep to a mid-2nd.

As can be seen from this picture, 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.

"Middish-major" means a majorish scale that has a few mid notes.

subgroup	name	scale								as edosteps	as (sub)harmonic series fragments	as chain of 5ths	step sizes
yala (2.3.5.11)	middish-major	P1	(v)M2	vM3	~4	P5	vM6	~7	P8	7665-665	(8:9:10:11:12)/8 + (9:10:11:12)/6	P152 vM263 ~74	~2, vM2, M2	5 6 7
	majorish-mid	P1	vM2	~3	P4	P5	vM6	~7	P8	6657-665	(9:10:11:12)/9 + (8:9:10:11:12)/6	P415 vM26 ~37
	majorish-minor	P1	vM2	^m3	(^)4	P5	vM6	^m7	P8	6567-656		^m374 P415 vM26
"	middish-minor	P1	~2	^m3	P4	P5	~6	^m7	P8	5667-566	12/(12:11:10:9:8) + 18/(12:11:10:9)	~26 ^m37 P415	"	"
	?	P1	vM2	~3	~4	P5	vM6	~7	P8	6675-665		P15 vM26 ~374

Dodecatonic

The harmonic duodene, with 3 fuzzy notes to avoid wolf 5ths.

subgroup	name	scale													as chain of 5ths	step sizes
ya (2.3.5)	?	P1	^m2	(v)M2	^m3	vM3	P4	A4/d5	P5	^m6	vM6	(^)m7	vM7	P8	A4-^m2637 m7-P415-M2 vM2637-d5	vvA1, m2, ^m2, (~2)	2 3 4 (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 uneven (steps of 2, 3 and 4, L/s ratio of 2), or very awkward to play (all plain notes, lots of jumping between strings).

Decatonic - Ten is the New Twelve

Is there an easily playable chromatic-sounding scale with nearly even steps? We need three odd numbers and the rest even. If the even number is 6 or 8, we get the equiheptatonic (41/6 is about 7) or equipentatonic (41/8 is about 5) scales. The obvious answer is 4, which makes a decatonic scale.

subgroup	name	scale											as edosteps	as a chord	step sizes
yalaza (2.3.5.7.11)	twin downminor pentatonic #1	P1	~2	vm3	vM3	(v)4	d5	P5	~6	vm7	vM7	P8	544-434-5444	12:13:14:15:16	m2, ^m2, ~2	3 4 5
	twin downminor pentatonic #2	P1	^m2	vm3	vM3	(v)4	A4	P5	^m6	vm7	vM7	P8	454-443-4544
"		P1	m2	M2	^m3	^M3	d5	P5					344-454-4454		"	"
"															"	"