Gallery of omnitetrachordal scales: Difference between revisions
m →Scales with 3 step sizes: added 46-tone |
m →Definitions and formulas: {{Navbox scale gallery}} |
||
| (5 intermediate revisions by 4 users not shown) | |||
| Line 954: | Line 954: | ||
ABAABCAABAABCAABA | ABAABCAABAABCAABA | ||
2L+5M+10s - | 2L+5M+10s - sMssMLssMssMLssMs | ||
2L+10M+5s - | 2L+10M+5s - MsMMsLMMsMMsLMMsM | ||
5L+2M+10s - | 5L+2M+10s - sLssLMssLssLMssLs | ||
10L+2M+5s - | 10L+2M+5s - LsLLsMLLsLLsMLLsL | ||
ABACABCABACABCABC ([[Fokker block]]) | ABACABCABACABCABC ([[Fokker block]]) | ||
| Line 970: | Line 970: | ||
ABCABCAABCABCAABC ([[Fokker block]]) | ABCABCAABCABCAABC ([[Fokker block]]) | ||
5L+7M+5s | 5L+7M+5s - MLsMLsMMLsMLsMMLs, sLMMsLMsLMMsLMsLM | ||
7L+5M+5s | 7L+5M+5s - LMsLMsLLMsLMsLLMs, sMLLsMLsMLLsMLsML | ||
== 19 tones == | == 19 tones == | ||
| Line 1,041: | Line 1,041: | ||
'''"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 ). | ||
| Line 1,090: | Line 1,090: | ||
'''"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:scales | [[Category:Omnitetrachordal]] | ||
[[Category:Lists of scales]] | |||