Kite Guitar Scales: Difference between revisions
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still a work in progress |
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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. | 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 == | == Pentatonic Scales == | ||
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=== Harmonic and subharmonic scales === | === Harmonic and subharmonic scales === | ||
These all have the same prime subgroup, yazalatha (2.3.5.7.11.13). 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. | 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. | ||
{| class="wikitable left-11 center-all" | {| class="wikitable left-11 center-all" | ||
|+ | |+ | ||
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\ / \ / \ / \ | \ / \ / \ / \ | ||
^F ---- ^C ---- ^G ---- ^D | ^F ---- ^C ---- ^G ---- ^D | ||
</tt> | </tt> | ||
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vF \ / vC \ / vG \ / vD \ | vF \ / vC \ / vG \ / vD \ | ||
D ----- A ----- E ----- B | D ----- A ----- E ----- B | ||
</tt> | </tt> | ||
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=== Near-equiheptatonic scales === | === 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 [[Porcupine|Triyo]] temperament. | These are a cross between the usual modes and the harmonic or subharmonic scales. Obviously they 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 smallest step of the upminor or downmajor scale is widened by 1 edostep to a mid-2nd. | The smallest step of the upminor or downmajor scale is widened by 1 edostep to a mid-2nd. | ||
As can be seen from [[:File:41-edo spiral.png|this picture]], the upminor scale | As can be seen from [[:File:41-edo spiral.png|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. | ||
mid-downmajor - 7 6 6 5 - 6 6 5 --> 6 5 7 6 - 6 5 6 = vM2 ^m3 | mid-downmajor - 7 6 6 5 - 6 6 5 --> 6 5 7 6 - 6 5 6 = vM2 ^m3 | ||
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! rowspan="2" |yala | ! rowspan="2" |yala | ||
(2.3.5.11) | (2.3.5.11) | ||
!mid-major | !mid-major? | ||
|P1 | |P1 | ||
|M2 | |M2 | ||
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|- | |- | ||
! rowspan="2" |" | ! rowspan="2" |" | ||
!mid-minor | !mid-minor? | ||
|P1 | |P1 | ||
|~2 | |~2 | ||
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|} | |} | ||
== | == Dodecatonic == | ||
The [[Duodene|harmonic duodene]], with 3 fuzzy notes to avoid wolf 5ths. | |||
{| class="wikitable center-all" | |||
!subgroup | |||
!name | |||
! colspan="13" |scale | |||
!as chain of 5ths | |||
! colspan="2" |step sizes | |||
|- | |||
! rowspan="2" |ya | |||
(2.3.5) | |||
!? | |||
|P1 | |||
|^m2 | |||
|(v)M2 | |||
|^m3 | |||
|vM3 | |||
|P4 | |||
|vA4/^d5 | |||
|P5 | |||
|^m6 | |||
|vM6 | |||
|(^)m7 | |||
|vM7 | |||
|P8 | |||
|^d5-^m2637 m7-P415-M2 vM2637-vA4 | |||
| rowspan="2" |vvA1, m2, ^m2, (~2) | |||
| rowspan="2" |2 3 4 (5) | |||
|- | |||
!? | |||
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"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). | "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. | 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. | ||