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 &gt; 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 &gt; 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 &gt; 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> &gt; 1, then P<span style="vertical-align: sub;">b</span> &lt; 1 ).
In this case the value '''P''' is given, where P = L/s.  For a perfect scale, P &gt; 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> &gt; 1, then P<span style="vertical-align: sub;">b</span> &lt; 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:omnitetrachordal]]
 
{{Navbox scale gallery}}
[[Category:Omnitetrachordal]]
[[Category:Lists of scales]]
[[Category:Lists of scales]]
[[Category:todo:add_definition]]