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| For a more mathematically intensive introduction to vals, see [[Vals and tuning space]]. For the characterization of higher-rank temperaments, see [[Mapping]]. | | For a more mathematically intensive introduction to vals, see [[Vals and tuning space]]. For the characterization of higher-rank temperaments, see [[Mapping]]. |
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| === Another example (12edo) ===
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| Consider the 5-limit patent val {{val| 12 19 28 }}. This val tells us that you should view 12 generator steps as mapping to the octave 2/1. Since the temperament which maps 12 generator steps to the octave is 12edo, this means you're describing a val for 12edo.
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| The val {{val| 12 19 28 }}, in addition to saying that 12 steps of 12-equal represents 2/1, also states explicitly that 19 steps of 12-equal represents a tempered 3/1, and 28 steps of 12-equal represents a tempered 5/1.
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| Now assume you'd like to extend 12edo into the 7-limit. If you would like to assume the perspective that the 10 step interval in 12-equal (representing 1000 cents) is a very tempered 7/4, then that means that 7/1, which is 7/4 with two octaves stacked on top, is equal to 10 steps + 12 steps + 12 steps = 34 steps. This decision can hence be represented by using the 7-limit patent val for 12edo: {{val| 12 19 28 34 }}.
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| If for some strange reason you'd instead like to say that 900 cents is 7/4, then that would be represented by the {{val| 12 19 28 33 }} val (notated 12d), and if you'd like to say that 1100 cents is 7/4, that would be represented by the {{val| 12 19 28 35 }} (12dd) val.
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| == Shorthand notations == | | == Shorthand notations == |