Kite Guitar Scales: Difference between revisions

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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.

~~Most~~ [[MOS scale|MOS scales]] are ~~awkward~~. ~~The only non~~-~~awkward~~ MOS ~~scales that contain~~ a perfect 5th ~~are those~~ from the [[Magic|Laquinyo]] temperament, which ~~are generated by the downmajor 3rd. These~~ have a small step of one fret. They have either a very lopsided L/s ratio or more than 12 notes. ~~Besides these, the least awkward MOS scales with a 5th~~ are the ~~plain pentatonics: P1 M2 M3 P5 M6 P8 (major), or P1 m3 P4 P5 m7 P8 (minor), or the two thirdless modes~~.

[[MOS scale|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 [[Magic|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, 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.

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 [[Essential tempering commas|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. Step sizes can also be fuzzy, leading to fuzzy MOS scales.

== The Format ==

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|^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 7647-674. Downing the 2nd makes 6747-674. ~~The~~ two underlined step sizes ~~almost always~~ differ by one, ~~something like 4 6 becoming 5 5 rarely occurs~~. ~~Hence~~ the fuzziness rarely affects the ~~overall step sizes~~. The only exceptions are the dorian ~~and~~ locrian ~~scales~~ and ~~the~~ dodecatonic scales, all of which are problematic anyway.

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 [[5-edo|equipentatonic]] feel.

The ~~steps~~ column analyzes the scale by the usual MOS notation of how many large and small steps there are. Some scales 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.

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.

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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. ~~Assuming no excess~~ string-~~hopping~~, there ~~will always be~~ 3 ~~backward~~ moves ~~per octave. There are~~ at most only two sizes of ~~backward moves,~~ the ~~first one occuring twice and the second one once~~.

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. 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, and at most 2 secondary backwards moves. 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 ~~main~~ 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 ~~the two~~ za pentatonic ~~scales~~. And +3 and -3 moves, with some +2 moves, evoke the ya heptatonic modes. 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 ~~other~~ moves.

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. And +3 and -3 moves, with some secondary +2 moves, evoke the ya heptatonic modes. 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 ==

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!edosteps

!step sizes

!~~steps~~

!step count

!moves

|-

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!edosteps

!step sizes

!~~steps~~

!step count

|-

! rowspan="2" |yaza

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|9 11 - 6 7 8

|}

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

All five of these scales are "anti-[[MOS scale|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 ==

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!edosteps

!step sizes

!~~steps~~

!step count

!moves

|-

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!edosteps

!step sizes

!~~steps~~

!step count

!moves

|-

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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 7467-747 can become 7467-657.

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.

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.

{| class="wikitable center-all"

|+

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!edosteps

!step sizes

!~~steps~~

!step count

!moves

|-

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|P8

|^m37^4 P415M26 vM6

|7467-747

|7467-746

|7 6 (5) 4

|varies

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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 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 modes by widening the two smallest steps by 1 ~~edostep~~, from an upminor 2nd to a mid 2nd. The tonic triad is never altered by the widening, thus ~~the~~ equi-lydian ~~scale is~~ the same as ~~the~~ equi-major ~~one. The step sizes are 1L4m2s (L=7~~, ~~m=6, s=5). Treating~~ the ~~sole large step~~ as ~~a fuzzy medium step, they are fuzzy 5L2s MOS scales~~.

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.

~~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.

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).

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!edosteps

!step sizes

!~~steps~~

!step count

!moves

|-

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| rowspan="2" |"

|-

!?

!equi-mid ~4

|P1

|vM2

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|6675-665

|}

Unfortunately, obvious near-equal scales like P1 ~2 ~3 P4 P5 ~6 ~7 P8 = 5757-575 are very awkward to play.

=== 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 ~~drive~~ one ~~near~~ the nut and run out of ~~room~~. Thus some of the -5 moves will have to be +8 frets but -1 string.

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.

{| class="wikitable center-all"

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!edosteps

!step sizes

!~~steps~~

!step count

!moves

|-

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| +2, -5

|}

The obvious uneven scale is the [[Duodene|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 obvious uneven scale is the [[Duodene|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.

{| class="wikitable center-all"

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!edosteps

!step sizes

!~~steps~~

!step count

!moves

|-

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!edosteps

!step sizes

!~~steps~~

!step count

!moves

|-

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=== Nineteen-tone - The chromatic scale ===

Let's continue the analysis ~~started in~~ 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. Using the full 19 note scale is somewhat overkill, unless your song is about bumblebees.

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 ~~steps are so small that they really can~~'t ~~be said to~~ imply any prime subgroup. The L/s ratio is 1.5 ~~and the steps are 3L 16s~~. The moves are +1 and -5. If there are 6 or 7 notes per string, it's a MOS scale of the [[Magic|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.

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 [[Magic|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.

{| class="wikitable center-all"

!name

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|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 ~~above~~ scales can be spiced up ~~this way~~.

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.

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!edosteps

!step sizes

!~~steps~~

!step count

!moves

|-

!?

!chromatic

|P1

|vm2

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=== Microtonal scales ===

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

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.

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 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.
-Most [[MOS scale|MOS scales]] are awkward. The only non-awkward MOS scales that contain a perfect 5th are those from the [[Magic|Laquinyo]] temperament, which are generated by the downmajor 3rd. These have a small step of one fret. They have either a very lopsided L/s ratio or more than 12 notes. Besides these, the least awkward MOS scales with a 5th are the plain pentatonics: P1 M2 M3 P5 M6 P8 (major), or P1 m3 P4 P5 m7 P8 (minor), or the two thirdless modes.
+[[MOS scale|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 [[Magic|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, 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.
+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 [[Essential tempering commas|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. Step sizes can also be fuzzy, leading to fuzzy MOS scales.
 == The Format ==
@@ Line 44: / Line 44: @@
 |^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 <u>76</u>47-674. Downing the 2nd makes <u>67</u>47-674. The two underlined step sizes almost always differ by one, something like <u>4 6</u> becoming <u>5 5</u> rarely occurs. Hence the fuzziness rarely affects the overall step sizes. The only exceptions are the dorian and locrian scales and the dodecatonic scales, all of which are problematic anyway.
+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: <u>76</u>47-674. Downing the 2nd makes <u>67</u>47-674. 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 [[5-edo|equipentatonic]] feel.
-The steps column analyzes the scale by the usual MOS notation of how many large and small steps there are. Some scales 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.
+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.
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 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. Assuming no excess string-hopping, there will always be 3 backward moves per octave. There are at most only two sizes of backward moves, the first one occuring twice and the second one once.
+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. 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, and at most 2 secondary backwards moves. 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 main 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 the two za pentatonic scales. And +3 and -3 moves, with some +2 moves, evoke the ya heptatonic modes. 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 other moves.
+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. And +3 and -3 moves, with some secondary +2 moves, evoke the ya heptatonic modes. 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 ==
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 |9 11 - 6 7 8
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-All five of these scales are "anti-[[MOS scale|MOS]]", meaning that each scale step has a unique size. There are too many types of moves to list. These scales are half ya, half za.
+All five of these scales are "anti-[[MOS scale|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 ==
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+<br>
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 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 <u>up</u>dorian scale can be <u>downed</u>. Note that this fuzziness affects the step sizes, and 74<u>67</u>-<u>74</u>7 can become 74<u>67</u>-<u>65</u>7.
+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>. Note that this fuzziness affects the step sizes, and 74<u>67</u>-<u>74</u>6 can become 74<u>67</u>-<u>65</u>6. 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.
+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.
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 |P8
 |^m37^4 P415M26 vM6
-|74<u>67</u>-<u>74</u>7
+|74<u>67</u>-<u>74</u>6
 |7 6 (5) 4
 |varies
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 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 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 modes by widening the two smallest steps by 1 edostep, from an upminor 2nd to a mid 2nd. The tonic triad is never altered by the widening, thus the equi-lydian scale is the same as the equi-major one. The step sizes are 1L4m2s (L=7, m=6, s=5). Treating the sole large step as a fuzzy medium step, they are fuzzy 5L2s MOS scales.
+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.
-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.
+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).
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 | rowspan="2" |"
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-!?
+!equi-mid ~4
 |P1
 |vM2
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 |6675-665
 |}
+Unfortunately, obvious near-equal scales like P1 ~2 ~3 P4 P5 ~6 ~7 P8 = 5757-575 are very awkward to play.
 === 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 drive one near the nut and run out of room. Thus some of the -5 moves will have to be +8 frets but -1 string.
+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.
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 | +2, -5
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-The obvious uneven scale is the [[Duodene|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 obvious uneven scale is the [[Duodene|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.
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 === Nineteen-tone - The chromatic scale ===
-Let's continue the analysis started in 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. Using the full 19 note scale is somewhat overkill, unless your song is about bumblebees.
+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 steps are so small that they really can't be said to imply any prime subgroup. The L/s ratio is 1.5 and the steps are 3L 16s. The moves are +1 and -5. If there are 6 or 7 notes per string, it's a MOS scale of the [[Magic|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.
+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 [[Magic|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.
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 |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 above scales can be spiced up this way.
+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.
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 === Microtonal scales ===
-These use step sizes of 1 and 2 edosteps only. If there are only 3 small steps, it is a 22-note MOS or MODMOS of Laquinyo. With more than 3 small steps, they are quite awkward to play, with much string-hopping and fret-leaping.
+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.