Kite Guitar Scales: Difference between revisions

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Certain Asian music uses very "lopsided" scales such as P1 M3 P4 P5 M7 P8 (SE Asia) and P1 M2 m3 P5 m6 P8 (Japan). While there is a certain charm to these, scales with equal or roughly equal sizes are also attractive. The only such 12edo scales are the whole tone scale and the full 12-note gamut. Since 41 is a prime number, it has no strictly equal scales. But there are many nearly-equal scales, or near-edos.

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~~, but~~ 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.

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 L-to-s range, and the 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 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 occurs more than once for near-edos 8 and 12-17, and not at all for near-edos 11 and 19.

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 Certain Asian music uses very "lopsided" scales such as P1 M3 P4 P5 M7 P8 (SE Asia) and P1 M2 m3 P5 m6 P8 (Japan). While there is a certain charm to these, scales with equal or roughly equal sizes are also attractive. The only such 12edo scales are the whole tone scale and the full 12-note gamut. Since 41 is a prime number, it has no strictly equal scales. But there are many nearly-equal scales, or near-edos.
-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, but 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.
+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 L-to-s range, and the 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 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 occurs more than once for near-edos 8 and 12-17, and not at all for near-edos 11 and 19.
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