Kite Guitar Scales: Difference between revisions

Line 726:

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 is bolded in the table below. It occurs more than once for near-edos 8 and 12-17, and not at all for near-edos 11 and 19.

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 is '''bolded''' in the table below. It occurs more than once for near-edos 8 and 12-17, and not at all for near-edos 11 and 19.

{| class="wikitable"

Line 830:

Tritonic scales are augmented triads. The moves are -0 and --1, meaning same fret up 1 string, and up 1 fret up 1 string. Tetratonic scales are dim6/dim7 tetrads. Both augmented and dim6/dim7 chords are discussed on the [[Kite Guitar Chord Shapes (downmajor tuning)|chords page]].

=== Pentatonic ===

=== Pentatonic (2L 2s '''1xs''') ===

We've already seen how the upmajor and downminor pentatonic scales are nearly equi-pentatonic.

=== Hexatonic (whole tone) ===

=== Hexatonic (whole tone) ('''1XL''' 3L 2s) ===

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.

Line 920:

|787-676

|}

=== Heptatonic ===

=== Heptatonic ('''1XL''' 4L 2s) ===

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

Line 1,015:

|}

=== Octotonic ===

=== Octotonic (3L 3m 2s) ===

The [[Bohlen-Pierce]] or B-P 13-edt scale is a non-octave scale that is contained in 41-edo. (Technically, the 41edo scale is 13-edt stretched by half a cent.) B-P has only one step size, 5 edosteps = ~2. These steps are very near to one-eighth of an octave, so it can be thought of as a near-8edo scale. Unfortunately B-P is very awkward to play on the Kite guitar. It also has the wolfy ^5 and v8 intervals.

Line 1,154:

|}

=== Dodecatonic (twelve-tone) ===

=== Dodecatonic (twelve-tone) (7L 3m 2s) ===

"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.

Line 1,230:

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

=== Decatonic - the semitonal scale ===

=== Decatonic - the semitonal 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.

Line 1,408:

|}

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

=== Nineteen-tone - The chromatic scale (3L 16s) ===

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 [[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 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

@@ Line 726: / Line 726: @@
 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 is bolded in the table below. It occurs more than once for near-edos 8 and 12-17, and not at all for near-edos 11 and 19.
+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 is '''bolded''' in the table below. It occurs more than once for near-edos 8 and 12-17, and not at all for near-edos 11 and 19.
 {| class="wikitable"
@@ Line 830: / Line 830: @@
 Tritonic scales are augmented triads. The moves are -0 and --1, meaning same fret up 1 string, and up 1 fret up 1 string. Tetratonic scales are dim6/dim7 tetrads. Both augmented and dim6/dim7 chords are discussed on the [[Kite Guitar Chord Shapes (downmajor tuning)|chords page]].
-=== Pentatonic ===
+=== Pentatonic (2L 2s '''1xs''') ===
 We've already seen how the upmajor and downminor pentatonic scales are nearly equi-pentatonic.
-=== Hexatonic (whole tone) ===
+=== Hexatonic (whole tone) ('''1XL''' 3L 2s) ===
 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.
@@ Line 920: / Line 920: @@
 |787-676
 |}
-=== Heptatonic ===
+=== Heptatonic ('''1XL''' 4L 2s) ===
 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. Unfortunately, obvious near-equal scales like P1 ~2 ~3 P4 P5 ~6 ~7 P8 = 5757-575 are very awkward to play.
@@ Line 1,015: / Line 1,015: @@
 |}
-=== Octotonic ===
+=== Octotonic (3L 3m 2s) ===
 The [[Bohlen-Pierce]] or B-P 13-edt scale is a non-octave scale that is contained in 41-edo. (Technically, the 41edo scale is 13-edt stretched by half a cent.) B-P has only one step size, 5 edosteps = ~2. These steps are very near to one-eighth of an octave, so it can be thought of as a near-8edo scale. Unfortunately B-P is very awkward to play on the Kite guitar. It also has the wolfy ^5 and v8 intervals.
@@ Line 1,154: / Line 1,154: @@
 |}
-=== Dodecatonic (twelve-tone) ===
+=== Dodecatonic (twelve-tone) (7L 3m 2s) ===
 "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.
@@ Line 1,230: / Line 1,230: @@
 For an even scale with small steps that's not awkward, see the next section.
-=== Decatonic - the semitonal scale ===
+=== Decatonic - the semitonal 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.
@@ Line 1,408: / Line 1,408: @@
 |}
-=== Nineteen-tone - The chromatic scale ===
+=== Nineteen-tone - The chromatic scale (3L 16s) ===
 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 [[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 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