Gallery of omnitetrachordal scales: Difference between revisions
m →Scales with 3 step sizes: the 9-note scale was only weakly OTC |
m →Definitions and formulas: {{Navbox scale gallery}} |
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== 8 notes == | == 8 notes == | ||
ABCABCAB ([[Fokker block]]) | |||
2L+3M+3s - LMsMsLMs, sMLsMsML | 2L+3M+3s - LMsMsLMs, sMLsMsML | ||
== 10 tones == | == 10 tones == | ||
ABACABACAB (3-[[SN scale|SN]]) | |||
2L+ | 2L+3M+5s - sMsLsMsMsL | ||
5L+2M+3s - LsLMLsLsLm | 2L+5M+3s - MsMLMsMsML | ||
5L+2M+3s - LsLMLsLsLm | |||
== 11 tones == | == 11 tones == | ||
2L+3M+6s - sMsLsMssMsL ( | ABACABACABA (3-[[SN scale|SN]]) | ||
2L+3M+6s - sMsLsMssMsL | |||
2L+6M+3s - MsMLMsMMsML | |||
ABCAABCAABA | |||
2L+3M+6s - sMLssMssMLs, sLMssMssLMs | |||
2L+6M+3s - MsLMMsMMsLM, MLsMMsMMLsM | |||
== 12 tones == | |||
ABABCABABCAB ([[Fokker block]]) | |||
5L+2M+5s - LsLsMLsLsLsM, MsLsLsLMsLsL | |||
5L+5M+2s - LMLMsLMLMLMs, sMLMLMLsMLML | |||
== 13 tones == | == 13 tones == | ||
ABACAABACAABA | |||
2L+3M+8s - sMsLssMssMsLs, sLsMssMssLsMs | 2L+3M+8s - sMsLssMssMsLs, sLsMssMssLsMs | ||
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== 14 tones == | == 14 tones == | ||
ABABACABABACAB (3-[[SN scale|SN]]) | |||
5L+7M+2s - MLMsMLMLMLMsML | 5L+2M+7s - sLsMsLsLsLsMsL | ||
5L+7M+2s - MLMsMLMLMLMsML | |||
== 15 tones == | == 15 tones == | ||
ABAACAABAACAABA (3-[[SN scale|SN]]) | |||
2L+ | 2L+3M+10s - sMssLssMssMssLs | ||
10L+2M+3s - LsLLMLLsLLsLLML | 2L+5M+3s - MsMMLMMsMMsMMLM | ||
10L+2M+3s - LsLLMLLsLLsLLML | |||
== 17 tones == | == 17 tones == | ||
ABAABACABAABACABA (3-[[SN scale|SN]]) | |||
2L+ | 2L+5M+10s - sMsLsMssMssMsLsMs | ||
5L+2M+10s - sLsMsLssLssLsMsLs ( | 2L+10M+5s - MsMLMsMMsMMsMLMsM | ||
5L+2M+10s - sLsMsLssLssLsMsLs | |||
10L+2M+5s - LsLMLsLLsLLsLMLsL | |||
ABAABCAABAABCAABA | |||
2L+5M+10s - sMssMLssMssMLssMs | |||
2L+10M+5s - MsMMsLMMsMMsLMMsM | |||
5L+2M+10s - sLssLMssLssLMssLs | |||
10L+2M+5s - LsLLsMLLsLLsMLLsL | |||
ABACABCABACABCABC ([[Fokker block]]) | |||
5L+7M+5s - MLMsMLsMLsMLMsMLs, sLMsMLMsLMsLMsMLM | 5L+7M+5s - MLMsMLsMLsMLMsMLs, sLMsMLMsLMsLMsMLM | ||
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7L+5M+5s - LMLsLMsLMsLMLsLMs, sMLsLMLsMLsMLsLML | 7L+5M+5s - LMLsLMsLMsLMLsLMs, sMLsLMLsMLsMLsLML | ||
ABCABCAABCABCAABC ([[Fokker block]]) | |||
5L+7M+5s - MLsMLsMMLsMLsMMLs, sLMMsLMsLMMsLMsLM | |||
7L+5M+5s - LMsLMsLLMsLMsLLMs, sMLLsMLsMLLsMLsML | |||
== 19 tones == | == 19 tones == | ||
ABCBAABAABCBAABAABA (3-[[SN scale|SN]]) | |||
ABA=9/8 | ABA=9/8 | ||
ABCBA=32/27, BC=256/243 | ABCBA=32/27, BC=256/243 | ||
10L+2M+7s: LsMsLLsLLsMsLLsLLsL | |||
ABCABCABABCABCABCAB ([[Fokker block]]) | |||
== 20 tones == | |||
ABACABABABABABACABAB | |||
== 22 tones == | == 22 tones == | ||
ABABCABABABABABABCABAB | |||
ACABBACABACABBACABACAB | |||
AbcbAbcbAAbcbAbcbAbcbA<ul><li>[[OTC_JI_22_sruti_scale|22-tone Indian 'sruti' scale]]</li></ul> | AbcbAbcbAAbcbAbcbAbcbA<ul><li>[[OTC_JI_22_sruti_scale|22-tone Indian 'sruti' scale]]</li></ul> | ||
----- | ----- | ||
== 24 tones == | |||
ACABABACABACABABACABACAB (3-[[SN scale|SN]]) | |||
MET-24 has this structure as 5L+12M+7s: MLMsMsMLMsMLMsMsMLMsMLMs | |||
AABAAABAACAABAAABAACAABA (3-[[SN scale|SN]]) | |||
== 29 tones == | |||
BABBABABBABCBABBABABBABCBABBA (3-[[SN scale|SN]]) | |||
2L+10m+17s: smsmssmsLsmssmsmssmsLsmssmsms | |||
== 31 tones == | |||
BABBCBBABABBABABBCBBABABBABABBA (3-[[SN scale|SN]]) | |||
10L+19m+2s: mLmmLmsmLmmLmmLmLmmLmmLmsmLmmLm | |||
10L+2m+19s: sLssLsmsLssLssLsLssLssLsmsLssLs | |||
== 41 tones == | |||
BABCBABBABBABCBABBABCBABBABBABCBABBABCBAB (3-[[SN scale|SN]]) | |||
5L+12M+24s: sMsLsMssMssMsLsMssMsLsMssMssMsLsMssMsLsMs | |||
BBABBBABBABBBABBCBBABBBABBABBBABBCBBABBBA (3-[[SN scale|SN]]) | |||
29L+2M+10s: LsLLLsLLMLLsLLLsLLsLLLsLLsLLLsLLMLLsLLLsL | |||
2L+29M+10s: MsMMMsMMLMMsMMMsMMsMMMsMMsMMMsMMLMMsMMMsM | |||
== 46 tones == | |||
CACACBCACACACBCACACCACACBCACACACBCACACCACACBCA (3-[[SN scale|SN]]) | |||
== 72 tones == | |||
ABAABABABAABABACABABAABABABAABABAABABABAABABAABABABAABABACABABAABABABAAB (3-[[SN scale|SN]]) | |||
29L+2M+41s: sLssLsLsLssLsLsMsLsLssLsLsLssLsLssLsLsLssLsLssLsLsLssLsLsMsLsLssLsLsLssL | |||
2L+29M+41s: sMssMsMsMssMsMsLsMsMssMsMsMssMsMssMsMsMssMsMssMsMsMssMsMsLsMssMsMsMssM | |||
=Definitions and formulas= | =Definitions and formulas= | ||
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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:scales | [[Category:Omnitetrachordal]] | ||
[[Category:Lists of scales]] | |||