Kite Guitar Scales: Difference between revisions

Line 63:

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 near-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 fluid version of the s step, making a 2L 3s near-MOS scale. Near-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 fluid. 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.

Harmonic and subharmonic scales are contiguous segments of the harmonic and subharmonic series respectively. They are never fluid. Harmonic and subharmonic may be abbreviated as har- and subhar-, e.g. harmajor. 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 dual notes not implied by the name. Harmonic and subharmonic scales are named after the tonic triad, minus the up or down.

Line 152:

|}

=== ~~Harmonic~~ and ~~subharmonic~~ scales ===

=== Pentharmonic and pentsubharmonic scales ===

These scales are named after the triad implied by the 3rd and 5th, minus the up or down. Note that the ~~har~~''major'' scale contains a down''minor'' 7th, and the ~~har~~''minor'' scale contains a down''major'' 6th. Likewise with the subharmajor and subharminor scales. A ~~hardim 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.

These scales are named after the triad implied by the 3rd and 5th, minus the up or down. Note that the penthar''major'' scale contains a down''minor'' 7th, and the penthar''minor'' scale contains a down''major'' 6th. Likewise with the subharmajor and subharminor scales. A penthardim scale would be P1 ^m3 d5 ^m6 ^m7 P8 = 5:6:7:8:9:10. But it's not very plausible, and would be heard as one of the other modes.

{| class="wikitable left-9 center-all"

|+

Line 166:

! rowspan="2" |yaza

(2.3.5.7)

!~~harmajor~~

!pentharmajor

|P1

|M2

Line 179:

| rowspan="2" |1XL 1L 1m 1s 1xs

|-

!~~harminor~~

!pentharminor

|P1

|vm3

Line 190:

|-

! rowspan="3" |"

!~~subharmajor~~

!pentsubharmajor

|P1

|M2

Line 202:

| rowspan="3" |"

|-

!~~subharminor~~

!pentsubharminor

|P1

|^m3

Line 212:

|11 6 7 - 8 9

|-

!~~subhardim~~

!pentsubhardim

|P1

|vm3

Line 413:

=== 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.

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 octharmonic 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. Each scale contains the similarly-named pentatonic scale, e.g. the harmajor scale contains the pentharmajor 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.

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.

{| class="wikitable left-11 center-all"

|+

!name

! colspan="9" |scale

! colspan="8" |scale

!as a chord

!edosteps

Line 432:

|~6

|vm7

~~|'''vM7'''~~

|P8

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

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

|7665-~~54'''44'''~~

|7665-548

| rowspan="4" |~~7 6 5 4~~

| rowspan="4" |8 7 6 5 4

~~L/s = 1.75~~

~~'''or'''~~

8 7 6 5 4

L/s = 2

|-

Line 449:

Line 442:

|~2

|vm3

~~|'''vM3'''~~

|P4

|P5

Line 455:

Line 447:

|~7

|P8

| style="text-align: left" |12:13:14~~:'''15'''~~:16:18:20:22

| style="text-align: left" |12:13:14:16:18:20:22

|~~54'''44'''7~~-665

|5487-665

|-

!subharmajor

|P1

|M2

~~|'''^m3'''~~

|^M3

|~4

Line 468:

Line 459:

|^m7

|P8

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

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

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

|7845-566

|-

!subharminor

Line 477:

Line 468:

|P4

|P5

~~|'''^m6'''~~

|^M6

|~7

|P8

| style="text-align: left" |24/(24:22:20:18:16~~:'''15'''~~:14:13)

| style="text-align: left" |24/(24:22:20:18:16:14:13)

|5667-~~'''44'''45~~

|5667-845

|}

Octharmonic scales can have two 3rds. If so, the scale is named after the one that isn't derived from harmonic 15. This ensures that the octharminor scale contains the harminor scale.

{| class="wikitable left-11 center-all"

|+

!name

! colspan="9" |scale

!as a chord

!edosteps

!step sizes

|-

!octharmajor

|P1

|M2

|vM3

|~4

|P5

|~6

|vm7

|vM7

|P8

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

|7665-5444

| rowspan="4" |7 6 5 4

L/s = 1.75

|-

!octharminor

|P1

|~2

|vm3

|vM3

|P4

|P5

|vM6

|~7

|P8

| style="text-align: left" |12:13:14:15:16:18:20:22

|54447-665

|-

!octsubharmajor

|P1

|M2

|^m3

|^M3

|~4

|P5

|~6

|^m7

|P8

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

|74445-566

|-

!octsubharminor

|P1

|~2

|^m3

|P4

|P5

|^m6

|^M6

|~7

|P8

| style="text-align: left" |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 3rd, 6th and 7th are all grouped together on on end of the genchain of 5ths, and upping or downing them only breaks the genchain of 5ths once. Hence there is only one wolf 5th, and only one note becomes dual to avoid it. But with the other five modes, the chain gets broken twice, and there are two wolf 5ths, and two dual notes. The dual notes are chosen to get six similar triads with a P5. The scales are all yaza except where noted. Most of these scales are not actually modes of each other.

@@ Line 63: / Line 63: @@
 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 near-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 fluid version of the s step, making a 2L 3s near-MOS scale. Near-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 fluid. 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.
+Harmonic and subharmonic scales are contiguous segments of the harmonic and subharmonic series respectively. They are never fluid. Harmonic and subharmonic may be abbreviated as har- and subhar-, e.g. harmajor. 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 dual notes not implied by the name. Harmonic and subharmonic scales are named after the tonic triad, minus the up or down.
@@ Line 152: / Line 152: @@
 |}
-=== Harmonic and subharmonic scales ===
+=== Pentharmonic and pentsubharmonic scales ===
-These scales are named after the triad implied by the 3rd and 5th, minus the up or down. Note that the har''major'' scale contains a down''minor'' 7th, and the har''minor'' scale contains a down''major'' 6th. Likewise with the subharmajor and subharminor scales. A hardim 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.
+These scales are named after the triad implied by the 3rd and 5th, minus the up or down. Note that the penthar''major'' scale contains a down''minor'' 7th, and the penthar''minor'' scale contains a down''major'' 6th. Likewise with the subharmajor and subharminor scales. A penthardim scale would be P1 ^m3 d5 ^m6 ^m7 P8 = 5:6:7:8:9:10. But it's not very plausible, and would be heard as one of the other modes.
 {| class="wikitable left-9 center-all"
 |+
@@ Line 166: / Line 166: @@
 ! rowspan="2" |yaza
 (2.3.5.7)
-!harmajor
+!pentharmajor
 |P1
 |M2
@@ Line 179: / Line 179: @@
 | rowspan="2" |1XL 1L 1m 1s 1xs
 |-
-!harminor
+!pentharminor
 |P1
 |vm3
@@ Line 190: / Line 190: @@
 |-
 ! rowspan="3" |"
-!subharmajor
+!pentsubharmajor
 |P1
 |M2
@@ Line 202: / Line 202: @@
 | rowspan="3" |"
 |-
-!subharminor
+!pentsubharminor
 |P1
 |^m3
@@ Line 212: / Line 212: @@
 |11 6 7 - 8 9
 |-
-!subhardim
+!pentsubhardim
 |P1
 |vm3
@@ Line 413: / Line 413: @@
 === 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.
+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 octharmonic 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. Each scale contains the similarly-named pentatonic scale, e.g. the harmajor scale contains the pentharmajor 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.
+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.
 {| class="wikitable left-11 center-all"
 |+
 !name
-! colspan="9" |scale
+! colspan="8" |scale
 !as a chord
 !edosteps
@@ Line 432: / Line 432: @@
 |~6
 |vm7
-|'''vM7'''
 |P8
-|8:9:10:11:12:13:14:'''15'''
+|8:9:10:11:12:13:14
-|7665-54'''44'''
+|7665-548
-| rowspan="4" |7 6 5 4
+| rowspan="4" |8 7 6 5 4
-L/s = 1.75
-'''or'''
-7 6 5 4
 L/s = 2
 |-
@@ Line 449: / Line 442: @@
 |~2
 |vm3
-|'''vM3'''
 |P4
 |P5
@@ Line 455: / Line 447: @@
 |~7
 |P8
-| style="text-align: left" |12:13:14:'''15''':16:18:20:22
+| style="text-align: left" |12:13:14:16:18:20:22
-|54'''44'''7-665
+|5487-665
 |-
 !subharmajor
 |P1
 |M2
-|'''^m3'''
 |^M3
 |~4
@@ Line 468: / Line 459: @@
 |^m7
 |P8
-|18/(18:16:'''15''':14:13:12:11:10)
+|18/(18:16:14:13:12:11:10)
-|7'''44'''45-566
+|7845-566
 |-
 !subharminor
@@ Line 477: / Line 468: @@
 |P4
 |P5
-|'''^m6'''
 |^M6
 |~7
 |P8
-| style="text-align: left" |24/(24:22:20:18:16:'''15''':14:13)
+| style="text-align: left" |24/(24:22:20:18:16:14:13)
-|5667-'''44'''45
+|5667-845
 |}
+Octharmonic scales can have two 3rds. If so, the scale is named after the one that isn't derived from harmonic 15. This ensures that the octharminor scale contains the harminor scale.
+{| class="wikitable left-11 center-all"
+|+
+!name
+! colspan="9" |scale
+!as a chord
+!edosteps
+!step sizes
+|-
+!octharmajor
+|P1
+|M2
+|vM3
+|~4
+|P5
+|~6
+|vm7
+|vM7
+|P8
+|8:9:10:11:12:13:14:15
+|7665-5444
+| rowspan="4" |7 6 5 4
+L/s = 1.75
+|-
+!octharminor
+|P1
+|~2
+|vm3
+|vM3
+|P4
+|P5
+|vM6
+|~7
+|P8
+| style="text-align: left" |12:13:14:15:16:18:20:22
+|54447-665
+|-
+!octsubharmajor
+|P1
+|M2
+|^m3
+|^M3
+|~4
+|P5
+|~6
+|^m7
+|P8
+|18/(18:16:15:14:13:12:11:10)
+|74445-566
+|-
+!octsubharminor
+|P1
+|~2
+|^m3
+|P4
+|P5
+|^m6
+|^M6
+|~7
+|P8
+| style="text-align: left" |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 3rd, 6th and 7th are all grouped together on on end of the genchain of 5ths, and upping or downing them only breaks the genchain of 5ths once. Hence there is only one wolf 5th, and only one note becomes dual to avoid it. But with the other five modes, the chain gets broken twice, and there are two wolf 5ths, and two dual notes. The dual notes are chosen to get six similar triads with a P5. The scales are all yaza except where noted. Most of these scales are not actually modes of each other.