Recursive structure of MOS scales: Difference between revisions
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Truncate the strings as follows, to get three distinct K-steps in w: | Truncate the strings as follows, to get three distinct K-steps in w: | ||
w1': L ... [lop off the s at the beginning of w1, so | w1': L ... [lop off the s at the beginning of w1, so w1' has k s's] | ||
w2': <L ... sXL ... sXL ... sXL ... ] [lop off one s at the end of w2, so | w2': <L ... sXL ... sXL ... sXL ... ] [lop off one s at the end of w2, so w2' has one fewer s than w3'] | ||
w3': <L ... sXL ... sXL ... sXL ... s> [lop off an L at the beginning of w3, | w3': <L ... sXL ... sXL ... sXL ... s> [lop off an L at the beginning of w3, so w3' has at most k-1 s's] | ||
so this contradicts our original scale being a mos. | so this contradicts our original scale being a mos. | ||