Andrew Heathwaite's MOS Investigations: Difference between revisions

Line 984:

So I posted to XA: "Ok, thinking it over, A and d are interesting choices to describe the additional steps, since they're so general. "d" is the small step minus one chroma, or s-c. But since the chroma itself is L-s, we can define d directly in terms of L and s as 2s-L. Meanwhile, "A" is the large step plus one chroma, or L+c. Described in terms of L and s, "A" is 2L-s. This allows us to quickly compute c, A, and d quickly, given L and s. As one example, Orwell[9] in 53edo has L=7 and s=5. So c=L-s=7-5=2; d=2s-L=2(5)-7=3; and A=2L-s=2(7)-5=9. Sure enough, a MODMOS of Orwell[9] with all four of these steps can be easily generated. Start with 7 5 7 5 7 5 7 5 5 and shift the second tone up by one chroma (which we computed to be 2\53), producing 9 3 7 5 7 5 7 5 5, which generalizes to AdLsLsLss! (Note that in 53edo Orwell[9] 2s=10 and A=9, not equal; while in 22edo's version of Orwell[9] 2s=4 and A=4, a potential 22edo Orwell pun.) ... ‎(Oh, and another pun is possible here, since c and d are both 1 degree in 22edo but 2 and 3 degrees, respectively, in 53edo.)"

[[Category:MOS scales]]

Revision as of 00:00, 17 July 2018 view source Wikispaces>FREEZE No edit summary ← Older edit		Revision as of 04:49, 15 August 2022 view source Fredg999 category edits (talk \| contribs) autopatrolled, Bots, emailconfirmed 4,330 edits m Categories Newer edit →
Line 984:		Line 984:

	<span style="">So I posted to XA: "Ok, thinking it over, A and d are interesting choices to describe the additional steps, since they're so general. "d" is the small step minus one chroma, or s-c. But since the chroma itself is L-s, we can define d directly in terms of L a</span><span style="">nd s as 2s-L. Meanwhile, "A" is the large step plus one chroma, or L+c. Described in terms of L and s, "A" is 2L-s. This allows us to quickly compute c, A, and d quickly, given L and s. As one example, Orwell[9] in 53edo has L=7 and s=5. So c=L-s=7-5=2; d=2s-L=2(5)-7=3; and A=2L-s=2(7)-5=9. Sure enough, a MODMOS of Orwell[9] with all four of these steps can be easily generated. Start with 7 5 7 5 7 5 7 5 5 and shift the second tone up by one chroma (which we computed to be 2\53), producing 9 3 7 5 7 5 7 5 5, which generalizes to AdLsLsLss! (Note that in 53edo Orwell[9] 2s=10 and A=9, not equal; while in 22edo's version of Orwell[9] 2s=4 and A=4, a potential 22edo Orwell pun.)</span><span style=""> ... ‎(Oh, and another pun is possible here, since c and d are both 1 degree in 22edo but 2 and 3 degrees, respectively, in 53edo.)"</span>		<span style="">So I posted to XA: "Ok, thinking it over, A and d are interesting choices to describe the additional steps, since they're so general. "d" is the small step minus one chroma, or s-c. But since the chroma itself is L-s, we can define d directly in terms of L a</span><span style="">nd s as 2s-L. Meanwhile, "A" is the large step plus one chroma, or L+c. Described in terms of L and s, "A" is 2L-s. This allows us to quickly compute c, A, and d quickly, given L and s. As one example, Orwell[9] in 53edo has L=7 and s=5. So c=L-s=7-5=2; d=2s-L=2(5)-7=3; and A=2L-s=2(7)-5=9. Sure enough, a MODMOS of Orwell[9] with all four of these steps can be easily generated. Start with 7 5 7 5 7 5 7 5 5 and shift the second tone up by one chroma (which we computed to be 2\53), producing 9 3 7 5 7 5 7 5 5, which generalizes to AdLsLsLss! (Note that in 53edo Orwell[9] 2s=10 and A=9, not equal; while in 22edo's version of Orwell[9] 2s=4 and A=4, a potential 22edo Orwell pun.)</span><span style=""> ... ‎(Oh, and another pun is possible here, since c and d are both 1 degree in 22edo but 2 and 3 degrees, respectively, in 53edo.)"</span>

			[[Category:MOS scales]]