Gallery of omnitetrachordal scales: Difference between revisions
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'''"Dual"''' refers to the "inverse" of a L+s scale pattern, where every L is replaced by s, and vice versa. For example, <tt> sLssL </tt> and <tt> LsLLs </tt> are duals. If a scale is OTC, its dual is often OTC as well, but not always! | '''"Dual"''' refers to the "inverse" of a L+s scale pattern, where every L is replaced by s, and vice versa. For example, <tt> sLssL </tt> and <tt> LsLLs </tt> are duals. If a scale is OTC, its dual is often OTC as well, but not always! | ||
'''"Perfect"''' means that values for L and s exist such that L > s and that every mode of the scale will contain a perfect (just) 3/2 or 4/3 (or both). (See also [[Eigenmonzo_subgroup|Eigenmonzo subgroup]].) | '''"Perfect"''' means that values for L and s exist such that L > s and that every mode of the scale will contain a perfect (just) 3/2 or 4/3 (or both). (See also [[Eigenmonzo_subgroup|Eigenmonzo subgroup]], or [[unchanged-interval basis]].) | ||
In this case the value '''P''' is given, where P = L/s. For a perfect scale, P > 1. Note that if a scale "a" is perfect (P<span style="vertical-align: sub;">a</span> = L/s), its dual "b" will have the value P<span style="vertical-align: sub;">b</span> = s/L = 1/P<span style="vertical-align: sub;">a</span>, and therefore must be imperfect (if P<span style="vertical-align: sub;">a</span> > 1, then P<span style="vertical-align: sub;">b</span> < 1 ). | In this case the value '''P''' is given, where P = L/s. For a perfect scale, P > 1. Note that if a scale "a" is perfect (P<span style="vertical-align: sub;">a</span> = L/s), its dual "b" will have the value P<span style="vertical-align: sub;">b</span> = s/L = 1/P<span style="vertical-align: sub;">a</span>, and therefore must be imperfect (if P<span style="vertical-align: sub;">a</span> > 1, then P<span style="vertical-align: sub;">b</span> < 1 ). | ||
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'''"L/s range"''': For any L+s scale pattern, the ratio L/s may range from 1 (L=s, in which case the scale is (L+s)edo ) to ~infinity (s=0, in which case the scale is (L)edo ). A note such as "full L/s range is good" simply means that the approximation of 3/2 or 4/3 is reasonable across the entire range; no other assessment of the scale's "goodness" is intended. | '''"L/s range"''': For any L+s scale pattern, the ratio L/s may range from 1 (L=s, in which case the scale is (L+s)edo ) to ~infinity (s=0, in which case the scale is (L)edo ). A note such as "full L/s range is good" simply means that the approximation of 3/2 or 4/3 is reasonable across the entire range; no other assessment of the scale's "goodness" is intended. | ||
[[Category: | |||
{{Navbox scale gallery}} | |||
[[Category:Omnitetrachordal]] | |||
[[Category:Lists of scales]] | [[Category:Lists of scales]] | ||