Kite Guitar Scales: Difference between revisions

Line 8:

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 have a plain perfect 5th from the tonic. 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 will be 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.

There are many possible 41edo scales. Those discussed here are those with at least 5 notes, and which have a plain perfect 5th from the tonic. 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 plain/mid 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 will be 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 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.

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Step sizes can also be dual, leading to near-MOS scales (see below).

The dualness of a specific note can often be understood by viewing the scale as arising from [[Alternating generator property|alternating generators]]. For example, the downmajor scale with a dual 2nd can be seen as a chain of alternating upminor and downmajor 3rds: vM2 - P4 - vM6 - P1 - vM3 - P5 - vM7 - M2. The chain comes very close to closing after 7 steps, making a 7-note scale with one dual note, the major 2nd.

* upminor/downmajor generators: ^m3 and vM3

* upmajor/downminor generators: vm3 and ^M3

* upminor/downmajor pentatonic generators: ^m3 and vM2

* upmajor/downminor pentatonic generators: vm3 and ^M2

== The Format ==

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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 dual 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.

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.

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 uses both +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!

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!moves

|-

! ~~rowspan="2" |~~ya

!ya (2.3.5)

(2.3.5)

!downmajor

|P1

Line 102:

Line 108:

| rowspan="2" | +3, -1, -3

|-

!"

!upminor

|P1

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Line 120:

|11 6 7 - 11 6

|-

! ~~rowspan="2" |~~za

!za (2.3.7)

(2.3.7)

!downminor

|P1

Line 133:

Line 139:

| rowspan="2" | +4, -2, -3

|-

!"

!upmajor

|P1

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Line 239:

!moves

|-

! ~~rowspan="2" |~~ya

!ya (2.3.5)

(2.3.5)

!downmajor

|P1

Line 251:

Line 257:

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

|-

!"

!upminor

|P1

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Line 270:

|7467-476

|-

! ~~rowspan="2" |~~za

!za (2.3.7)

(2.3.7)

!downminor

|P1

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Line 288:

| rowspan="2" | +4, +1, -3

|-

!"

!upmajor

|P1

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|8:9:10:11:12:13:14:'''15'''

|7665-54'''44'''

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

| rowspan="4" |7 6 5 4

L/s = 2 ~~or 1.75~~

L/s = 1.75

'''or'''

8 7 6 5 4

L/s = 2

|-

!harminor

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Line 470:

|18/(18:16:'''15''':14:13:12:11:10)

|7'''44'''45-566

~~| rowspan="2" |"~~

|-

!subharminor

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For an even scale with small steps that's not awkward, see the next section.

=== Decatonic - the semitonal scale (2L 7s 1xs) ===

=== Decatonic - the semitonal scale or twin pentatonic scale (2L 7s 1xs) ===

Is there an easily playable chromatic-sounding scale with nearly equal steps? One such is the decatonic scale. 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 section on 19-tone scales.

If the steps are nearly equal, it follows that every other note will make a nearly-equal pentatonic scale. Thus these scales consist of two intertwined za pentatonic scales ~~which are (usually?)~~ either ~~both~~ upmajor or ~~both~~ downminor. The ~~scales~~ are named after the "one" of the non-tonic scale, similar to how octotonic scales are named.

If the steps are nearly equal, it follows that every other note will make a nearly-equal pentatonic scale. Thus these scales consist of two intertwined za pentatonic scales. If we further require that the two scales be either upmajor or downminor, there are only 3 such scales, each with two primary modes. The modes are named after the "one" of the non-tonic scale, similar to how octotonic scales are named.

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.

The twin downminor scale consists of two downminor pentatonic scales, offset from each other by two frets. Likewise with the twin upmajor scale. The twin downminor's down-7 mode is (12:13:14:15:16:17:18)/12 plus (12:13:14:15:16)/8, except that prime 17 isn't well tuned.

{| class="wikitable center-all"

!subgroup

Line 1,217:

Line 1,229:

! rowspan="2" |yazala

(2.3.5.7.11)

!down-7 ~~downminor~~

!twin downminor down-7

|P1

|~2

|vm3

|vM3

|~~(v)4~~

|P4

|d5

|P5

Line 1,229:

Line 1,241:

|vM7

|P8

|544-~~434~~-5444

|544-434-5444

| rowspan="2" |5 4 3

L/s = 1.67

Line 1,238:

Line 1,250:

| rowspan="2" | +2, -4, -5

|-

!upflat-2 ~~downminor~~

!twin downminor upflat-2

|P1

|^m2

Line 1,244:

Line 1,256:

|vM3

|P4

|~~(v)~~A4

|A4

|P5

|^m6

Line 1,250:

Line 1,262:

|vM7

|P8

|454-~~443~~-4544

|454-443-4544

|-

! rowspan="2" |"

!down-7 ~~upmajor~~

!twin upmajor down-7

|P1

|m2

|~~(^)~~M2

|M2

|^m3

|^M3

Line 1,270:

Line 1,282:

| rowspan="2" |"

|-

!~~(more to come)~~

!twin upmajor upflat-2

|

|P1

|

|^m2

|

|M2

|

|^m3

|

|^M3

|

|~4

|

|P5

|

|^m6

|

|^M6

|

|~7

|

|P8

|

|434-445-4445

|-

! rowspan="2" |"

!"

!downminor + down-3 upmajor

|

|P1

|

|^m2

|

|vm3

|

|vM3

|

|P4

|

|d5

|

|P5

|

|^m6

|

|vm7

|

|vM7

|

|P8

|

|454-434-4544

| rowspan="2" |"

|-

!"

!upmajor + upflat-6 downminor

|

|P1

|

|^m2

|

|M2

|

|^m3

|

|^M3

|

|d5

|

|P5

|

|^m6

|

|^M6

|

|vM7

|

|P8

|

|434-454-4454

|}

The down-7 ~~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.

The twin downminor down-7 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.

{| class="wikitable center-all"

!subgroup

Line 1,333:

Line 1,345:

|vm3

|vM3

|~~(v)4~~

|P4

|d5

|P5

Line 1,340:

Line 1,352:

|vM7

|P8

|544-~~434~~-5444

|544-434-5444

| rowspan="3" |5 4 3

L/s = 1.67

Line 1,358:

Line 1,370:

|vm6

|vM6

|~~(v)~~m7

|m7

|vM7

|P8

|544-45-~~44434~~

|544-45-44434

|-

!down-7 downminor on V

@@ Line 8: / Line 8: @@
 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 have a plain perfect 5th from the tonic. 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 will be 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.
+There are many possible 41edo scales. Those discussed here are those with at least 5 notes, and which have a plain perfect 5th from the tonic. 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 plain/mid 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 will be 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 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.
@@ Line 19: / Line 19: @@
 Step sizes can also be dual, leading to near-MOS scales (see below).
+The dualness of a specific note can often be understood by viewing the scale as arising from [[Alternating generator property|alternating generators]]. For example, the downmajor scale with a dual 2nd can be seen as a chain of alternating upminor and downmajor 3rds: vM2 - P4 - vM6 - P1 - vM3 - P5 - vM7 - M2. The chain comes very close to closing after 7 steps, making a 7-note scale with one dual note, the major 2nd.
+* upminor/downmajor generators: ^m3 and vM3
+* upmajor/downminor generators: vm3 and ^M3
+* upminor/downmajor pentatonic generators: ^m3 and vM2
+* upmajor/downminor pentatonic generators: vm3 and ^M2
 == The Format ==
@@ Line 62: / Line 69: @@
 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 dual 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.
+<u>The moves column is perhaps the most practical information in the table</u>. 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.
+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 uses both +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!
@@ Line 84: / Line 91: @@
 !moves
 |-
-! rowspan="2" |ya
+!ya (2.3.5)
-(2.3.5)
 !downmajor
 |P1
@@ Line 102: / Line 108: @@
 | rowspan="2" | +3, -1, -3
 |-
+!"
 !upminor
 |P1
@@ Line 113: / Line 120: @@
 |11 <u>6 7</u> - 11 6
 |-
-! rowspan="2" |za
+!za (2.3.7)
-(2.3.7)
 !downminor
 |P1
@@ Line 133: / Line 139: @@
 | rowspan="2" | +4, -2, -3
 |-
+!"
 !upmajor
 |P1
@@ Line 232: / Line 239: @@
 !moves
 |-
-! rowspan="2" |ya
+!ya (2.3.5)
-(2.3.5)
 !downmajor
 |P1
@@ Line 251: / Line 257: @@
 | rowspan="2" | +3, +2, -3
 |-
+!"
 !upminor
 |P1
@@ Line 263: / Line 270: @@
 |74<u>67</u>-476
 |-
-! rowspan="2" |za
+!za (2.3.7)
-(2.3.7)
 !downminor
 |P1
@@ Line 282: / Line 288: @@
 | rowspan="2" | +4, +1, -3
 |-
+!"
 !upmajor
 |P1
@@ Line 429: / Line 436: @@
 |8:9:10:11:12:13:14:'''15'''
 |7665-54'''44'''
-| rowspan="2" |8(='''44''') 7 6 5 4
+| rowspan="4" |7 6 5 4
-L/s = 2 or 1.75
+L/s = 1.75
+'''or'''
+7 6 5 4
+L/s = 2
 |-
 !harminor
@@ Line 457: / Line 470: @@
 |18/(18:16:'''15''':14:13:12:11:10)
 |7'''44'''45-566
-| rowspan="2" |"
 |-
 !subharminor
@@ Line 1,200: / Line 1,212: @@
 For an even scale with small steps that's not awkward, see the next section.
-=== Decatonic - the semitonal scale (2L 7s 1xs) ===
+=== Decatonic - the semitonal scale or twin pentatonic scale (2L 7s 1xs) ===
 Is there an easily playable chromatic-sounding scale with nearly equal steps? One such is the decatonic scale. 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 section on 19-tone scales.
-If the steps are nearly equal, it follows that every other note will make a nearly-equal pentatonic scale. Thus these scales consist of two intertwined za pentatonic scales which are (usually?) either both upmajor or both downminor. The scales are named after the "one" of the non-tonic scale, similar to how octotonic scales are named.
+If the steps are nearly equal, it follows that every other note will make a nearly-equal pentatonic scale. Thus these scales consist of two intertwined za pentatonic scales. If we further require that the two scales be either upmajor or downminor, there are only 3 such scales, each with two primary modes. The modes are named after the "one" of the non-tonic scale, similar to how octotonic scales are named.
-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.
+The twin downminor scale consists of two downminor pentatonic scales, offset from each other by two frets. Likewise with the twin upmajor scale. The twin downminor's down-7 mode is (12:13:14:15:16:17:18)/12 plus (12:13:14:15:16)/8, except that prime 17 isn't well tuned.
 {| class="wikitable center-all"
 !subgroup
@@ Line 1,217: / Line 1,229: @@
 ! rowspan="2" |yazala
 (2.3.5.7.11)
-!down-7 downminor
+!twin downminor down-7
 |P1
 |~2
 |vm3
 |vM3
-|(v)4
+|P4
 |d5
 |P5
@@ Line 1,229: / Line 1,241: @@
 |vM7
 |P8
-|544-<u>43</u>4-5444
+|544-434-5444
 | rowspan="2" |5 4 3
 L/s = 1.67
@@ Line 1,238: / Line 1,250: @@
 | rowspan="2" | +2, -4, -5
 |-
-!upflat-2 downminor
+!twin downminor upflat-2
 |P1
 |^m2
@@ Line 1,244: / Line 1,256: @@
 |vM3
 |P4
-|(v)A4
+|A4
 |P5
 |^m6
@@ Line 1,250: / Line 1,262: @@
 |vM7
 |P8
-|454-4<u>43</u>-4544
+|454-443-4544
 |-
 ! rowspan="2" |"
-!down-7 upmajor
+!twin upmajor down-7
 |P1
 |m2
-|(^)M2
+|M2
 |^m3
 |^M3
@@ Line 1,270: / Line 1,282: @@
 | rowspan="2" |"
 |-
-!(more to come)
+!twin upmajor upflat-2
-|
+|P1
-|
+|^m2
-|
+|M2
-|
+|^m3
-|
+|^M3
-|
+|~4
-|
+|P5
-|
+|^m6
-|
+|^M6
-|
+|~7
-|
+|P8
-|
+|434-445-4445
 |-
 ! rowspan="2" |"
-!"
+!downminor + down-3 upmajor
-|
+|P1
-|
+|^m2
-|
+|vm3
-|
+|vM3
-|
+|P4
-|
+|d5
-|
+|P5
-|
+|^m6
-|
+|vm7
-|
+|vM7
-|
+|P8
-|
+|454-434-4544
 | rowspan="2" |"
 | rowspan="2" |"
 | rowspan="2" |"
 |-
-!"
+!upmajor + upflat-6 downminor
-|
+|P1
-|
+|^m2
-|
+|M2
-|
+|^m3
-|
+|^M3
-|
+|d5
-|
+|P5
-|
+|^m6
-|
+|^M6
-|
+|vM7
-|
+|P8
-|
+|434-454-4454
 |}
-The down-7 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.
+The twin downminor down-7 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.
 {| class="wikitable center-all"
 !subgroup
@@ Line 1,333: / Line 1,345: @@
 |vm3
 |vM3
-|(v)4
+|P4
 |d5
 |P5
@@ Line 1,340: / Line 1,352: @@
 |vM7
 |P8
-|544-<u>43</u>4-5444
+|544-434-5444
 | rowspan="3" |5 4 3
 L/s = 1.67
@@ Line 1,358: / Line 1,370: @@
 |vm6
 |vM6
-|(v)m7
+|m7
 |vM7
 |P8
-|544-45-44<u>43</u>4
+|544-45-44434
 |-
 !down-7 downminor on V