MOS scale: Difference between revisions
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: The period of this temperament is 1\gcd(''X'', ''Y''), and the rational ''a''/''b'' is very closely related to the [[step ratio]] of the corresponding MOS scale, because 1{{val| ''X'' ...}} + 0{{val| ''Y'' ...}} is the L = 1, s = 0 tuning while 0{{val| ''X'' ...}} + 1{{val| ''Y'' ...}} is the L = 1, s = 1 tuning and 1{{val| ''X'' ...}} + 1{{val| ''Y'' ...}} is the L = 2, s = 1 tuning, so that L = ''a'' + ''b'' and s = ''b'' and therefore: | : The period of this temperament is 1\gcd(''X'', ''Y''), and the rational ''a''/''b'' is very closely related to the [[step ratio]] of the corresponding MOS scale, because 1{{val| ''X'' ...}} + 0{{val| ''Y'' ...}} is the L = 1, s = 0 tuning while 0{{val| ''X'' ...}} + 1{{val| ''Y'' ...}} is the L = 1, s = 1 tuning and 1{{val| ''X'' ...}} + 1{{val| ''Y'' ...}} is the L = 2, s = 1 tuning, so that L = ''a'' + ''b'' and s = ''b'' and therefore: | ||
: 1/([[step ratio]]) = ''s''/''L'' = (''a'' + ''b'') | : 1/([[step ratio]]) = ''s''/''L'' = ''b''/(''a'' + ''b'') implying [[step ratio]] = (''a'' + ''b'')/''b'' >= 1 for [[Wikipedia:Natural number|natural]] ''a'' and ''b'', where if ''b'' = 0 then the step ratio is infinite, corresponding to the [[collapsed]] tuning. | ||
* Every MOS scale has two ''child MOS'' scales. The two children of the MOS scale ''a''L ''b''s are ({{nowrap|''a'' + ''b''}})L ''a''s (generated by generators of soft-of-basic ''a''L ''b''s) and ''a''L ({{nowrap|''a'' + ''b''}})s (generated by generators of hard-of-basic ''a''L'' b''s). | * Every MOS scale has two ''child MOS'' scales. The two children of the MOS scale ''a''L ''b''s are ({{nowrap|''a'' + ''b''}})L ''a''s (generated by generators of soft-of-basic ''a''L ''b''s) and ''a''L ({{nowrap|''a'' + ''b''}})s (generated by generators of hard-of-basic ''a''L'' b''s). | ||