Kite Guitar: Difference between revisions
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→Scale Shapes: renamed the harmonic & subharmonic scales, added some paragraphs. |
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There are many possible scales. Those listed here are select ones with a low prime limit and/or a low odd limit. | There are many possible scales. Those listed here are select ones with a low prime limit and/or a low odd limit. | ||
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 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. Harmonic and subharmonic scales are not fuzzy. | 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 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. Harmonic and subharmonic scales, which are segments of the harmonic and subharmonic series, are not fuzzy. | ||
The modes of a scale are grouped together. Not every mode is shown. Two modes of a scale will use the same prime subgroup, so modes are grouped by subgroup. | The modes of a scale are grouped together. Not every mode is shown. Two modes of a scale will use the same prime subgroup, so modes are grouped by subgroup. | ||
Each scale has steps of various sizes, shown in the far right columns. Two modes of a scale will have the same step sizes, so modes are also grouped by step sizes. The | Each scale has steps of various sizes, shown in the far right columns as both intervals and edosteps. Two modes of a scale will have the same step sizes, so modes are also grouped by step sizes. The largest-to-smallest ratio can be calculated directly from the edosteps. For example, the downminor and upmajor heptatonic scales have a very large L/s ratio of 8/2 = 4, giving them a lopsided feel. But the downminor/upmajor <u>pentatonic</u> scales have a very small L/s ratio of only 9/7 = 1.29, giving them a 5-edo-ish feel. | ||
Harmonic and subharmonic may be abbreviated as har- and sub-, e.g. harmajor pentatonic. | |||
=== Pentatonic Scales === | === Pentatonic Scales === | ||
Every pentatonic scale has 5 modes, but only those modes with a non-fuzzy | Every pentatonic scale has 5 modes, but only those modes with a non-fuzzy 5th are listed. The harmonic and subharmonic scales are named after the triad implied by the 3rd and 5th, minus the up or down. Note that the harmonic/subharmonic <u>major</u> scales contain a <u>minor</u> 7th, and the harmonic/subharmonic <u>minor</u> scales contain a <u>major</u> 6th. A harmonic diminished 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. | ||
{| class="wikitable" | {| class="wikitable" | ||
|+ | |+ | ||
| Line 239: | Line 241: | ||
|P8 | |P8 | ||
|v6,(v)9 chord | |v6,(v)9 chord | ||
| rowspan="2" |vM2 M2 ^m3 | | rowspan="2" |vM2, M2, ^m3 | ||
| rowspan="2" |6 7 11 | | rowspan="2" |6 7 11 | ||
|- | |- | ||
| Line 261: | Line 263: | ||
|P8 | |P8 | ||
|vm7,(v)11 chord | |vm7,(v)11 chord | ||
| rowspan="2" |M2 ^M2 vm3 | | rowspan="2" |M2, ^M2, vm3 | ||
| rowspan="2" |7 8 9 | | rowspan="2" |7 8 9 | ||
|- | |- | ||
| Line 275: | Line 277: | ||
! rowspan="2" |yaza | ! rowspan="2" |yaza | ||
(2.3.5.7) | (2.3.5.7) | ||
!harmonic | !harmonic major | ||
|P1 | |P1 | ||
|M2 | |M2 | ||
| Line 283: | Line 285: | ||
|P8 | |P8 | ||
|v9 = 8:9:10:12:14 | |v9 = 8:9:10:12:14 | ||
| rowspan="2" |vM2 M2 ^M2 | | rowspan="2" |vM2, M2, ^M2, | ||
vm3 ^m3 | vm3, ^m3 | ||
| rowspan="2" |6 7 8 9 11 | | rowspan="2" |6 7 8 9 11 | ||
|- | |- | ||
!harmonic | !harmonic minor | ||
|P1 | |P1 | ||
|vm3 | |vm3 | ||
| Line 296: | Line 298: | ||
|vm6,11 = 6:7:8:9:10 | |vm6,11 = 6:7:8:9:10 | ||
|- | |- | ||
! rowspan=" | ! rowspan="3" |" | ||
!subharmonic | !subharmonic major | ||
|P1 | |P1 | ||
|M2 | |M2 | ||
| Line 305: | Line 307: | ||
|P8 | |P8 | ||
|^9 = 9/(9:8:7:6:5) | |^9 = 9/(9:8:7:6:5) | ||
| rowspan=" | | rowspan="3" |vM2, M2, ^M2, | ||
vm3 ^m3 | vm3, ^m3 | ||
| rowspan=" | | rowspan="3" |6 7 8 9 11 | ||
|- | |- | ||
!subharmonic | !subharmonic minor | ||
|P1 | |P1 | ||
|^m3 | |^m3 | ||
| Line 318: | Line 320: | ||
|P8 | |P8 | ||
|^m6,11 = 12/(12:10:9:8:7) | |^m6,11 = 12/(12:10:9:8:7) | ||
|- | |||
!subharmonic diminished | |||
|P1 | |||
|vm3 | |||
|d5 | |||
|vm6 | |||
|vm7 | |||
|P8 | |||
|vm7(b5),vm6 = 14/(14:12:10:9:8) | |||
|} | |} | ||
=== Heptatonic Scales === | === Heptatonic Scales === | ||
Only a few of the modes are listed. See also the octotonic scales that omit the 15th harmonic. | |||
{| class="wikitable" | {| class="wikitable" | ||
|+ | |+ | ||
| Line 339: | Line 351: | ||
|vM7 | |vM7 | ||
|P8 | |P8 | ||
| rowspan="2" |^m2 vM2 M2 | | rowspan="2" |^m2, vM2, M2 | ||
| rowspan="2" |4 6 7 | | rowspan="2" |4 6 7 | ||
|- | |- | ||
| Line 363: | Line 375: | ||
|vm7 | |vm7 | ||
|P8 | |P8 | ||
| rowspan="2" |vm2 M2 ^M2 | | rowspan="2" |vm2, M2, ^M2 | ||
| rowspan="2" |2 7 8 | | rowspan="2" |2 7 8 | ||
|- | |- | ||
| Line 378: | Line 390: | ||
=== Octatonic Scales === | === Octatonic Scales === | ||
The prime subgroup for all these scales is yazalatha (2.3.5.7.11.13). Omitting the bolded note makes a heptatonic scale that uses harmonics 7-14. | The prime subgroup for all these scales is yazalatha (2.3.5.7.11.13). Omitting the 15th harmonic (the '''bolded''' note) makes a heptatonic scale that uses harmonics 7-14. | ||
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 harmonic major octotonic scale contains the harmonic major pentatonic scale. | |||
One of the hallmarks of harmonic and subharmonic scales is that each step has a unique size. Unfortunately, while 41edo approximates the individual harmonics quite well, these scales do not have unique step sizes. The step sizes run 7 6 6 5 5 4 4 4. The heptatonic scales are better, 8 7 6 6 5 5 4. Only the pentatonic scales have unique step sizes. | |||
{| class="wikitable" | {| class="wikitable" | ||
|+ | |+ | ||
| Line 386: | Line 402: | ||
! colspan="2" |step sizes | ! colspan="2" |step sizes | ||
|- | |- | ||
!harmonic | !harmonic major | ||
|P1 | |P1 | ||
|M2 | |M2 | ||
| Line 396: | Line 412: | ||
|'''vM7''' | |'''vM7''' | ||
|P8 | |P8 | ||
|8:9:10:11:12:13:14:15 | |8:9:10:11:12:13:14:'''15''' | ||
| rowspan="2" |A1 | | rowspan="2" |A1/^m2, ~2, vM2, M2 | ||
| rowspan="2" |4 5 6 7 | | rowspan="2" |4 5 6 7 | ||
|- | |- | ||
!harmonic | !harmonic minor | ||
|P1 | |P1 | ||
|~2 | |~2 | ||
| Line 410: | Line 426: | ||
|~7 | |~7 | ||
|P8 | |P8 | ||
|12:13:14:15:16:18:20:22 | |12:13:14:'''15''':16:18:20:22 | ||
|- | |- | ||
!subharmonic | !subharmonic major | ||
|P1 | |P1 | ||
|M2 | |M2 | ||
| Line 422: | Line 438: | ||
|^m7 | |^m7 | ||
|P8 | |P8 | ||
|18/(18:16:15:14:13:12:11:10) | |18/(18:16:'''15''':14:13:12:11:10) | ||
| rowspan="2" |A1 | | rowspan="2" |A1/^m2, ~2, vM2, M2 | ||
| rowspan="2" |4 5 6 7 | | rowspan="2" |4 5 6 7 | ||
|- | |- | ||
!subharmonic | !subharmonic minor | ||
|P1 | |P1 | ||
|~2 | |~2 | ||
| Line 436: | Line 452: | ||
|~7 | |~7 | ||
|P8 | |P8 | ||
|24/(24:22:20:18:16:15:14:13) | |24/(24:22:20:18:16:'''15''':14:13) | ||
|} | |} | ||
== Relative and Absolute Tab == | == Relative and Absolute Tab == | ||