Val: Difference between revisions
Cmloegcmluin (talk | contribs) →Shorthand notation: note that wart notation is relative to pure-octave tuning |
Cmloegcmluin (talk | contribs) m →Vals in JI subgroups: add link to concept of vanish / temper out |
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Note that the notion of a "patent val" for a subgroup val may not agree with the patent val on a prime limit. For instance, [[13edo]]'s "2.9.5 [[patent val]]" can be written as "2.9.5 {{val| 13 41 30 }}, because the best approximation to 2 is 13 steps, the best approximation to 9 is 41 steps, and the best approximation to 5 is 30 steps. Note that, however, the patent val on the 2.3.5 subgroup instead maps 3/1 to 21 steps, so that the "induced 9" from the 2.3.5 patent val is not the same as the "direct 9" from the 2.9.5 patent val. | Note that the notion of a "patent val" for a subgroup val may not agree with the patent val on a prime limit. For instance, [[13edo]]'s "2.9.5 [[patent val]]" can be written as "2.9.5 {{val| 13 41 30 }}, because the best approximation to 2 is 13 steps, the best approximation to 9 is 41 steps, and the best approximation to 5 is 30 steps. Note that, however, the patent val on the 2.3.5 subgroup instead maps 3/1 to 21 steps, so that the "induced 9" from the 2.3.5 patent val is not the same as the "direct 9" from the 2.9.5 patent val. | ||
This notation is also used for subgroup monzos; e.g. [[81/80]] on the 2.9.5 subgroup is "2.9.5 {{monzo| -4 2 -1 }}", and it is thus easy to see that the 2.9.5 13p val above | This notation is also used for subgroup monzos; e.g. [[81/80]] on the 2.9.5 subgroup is "2.9.5 {{monzo| -4 2 -1 }}", and it is thus easy to see that the 2.9.5 13p val above makes 81/80 [[vanish]]: | ||
⟨13, 41, 30|2^-4, 9^2, 5^-1⟩ = 13*-4 + 41*2 + 30*-1 = 0. | ⟨13, 41, 30|2^-4, 9^2, 5^-1⟩ = 13*-4 + 41*2 + 30*-1 = 0. | ||