Radical interval: Difference between revisions
Equal divisions implying an equave is a common misconception. Correct wording. Clarify a few things. style and formatting improvements |
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By multiplying each monzo entry by the [[cent]] value of the corresponding prime and adding the results together (which can be represented, if the monzo is treated as a vector, by a dot product with the [[just tuning map]] in cents 1200⋅{{val| log<sub>2</sub>(2) log<sub>2</sub>(3) … log<sub>2</sub>(''p'') }}) the value in cents of a fractional monzo may be obtained, just as with an ordinary monzo. For instance, in the above example {{nowrap| (1/13)⋅1200 - (1/13)⋅1200⋅log<sub>2</sub>(3) + (7/26)⋅1200⋅log<sub>2</sub>(5) {{=}} 696.1648 cents }}. | By multiplying each monzo entry by the [[cent]] value of the corresponding prime and adding the results together (which can be represented, if the monzo is treated as a vector, by a dot product with the [[just tuning map]] in cents 1200⋅{{val| log<sub>2</sub>(2) log<sub>2</sub>(3) … log<sub>2</sub>(''p'') }}) the value in cents of a fractional monzo may be obtained, just as with an ordinary monzo. For instance, in the above example {{nowrap| (1/13)⋅1200 - (1/13)⋅1200⋅log<sub>2</sub>(3) + (7/26)⋅1200⋅log<sub>2</sub>(5) {{=}} 696.1648 cents }}. | ||
Vectors in [[interval space]], where the coefficients are allowed to be real numbers, do not uniquely correspond to intervals, whereas monzos do. Fractional monzos do also; for each fractional monzo there is one and only one ''n''-th root of a positive rational number which corresponds to it. | Vectors in [[monzos and interval space|interval space]], where the coefficients are allowed to be real numbers, do not uniquely correspond to intervals, whereas monzos do. Fractional monzos do also; for each fractional monzo there is one and only one ''n''-th root of a positive rational number which corresponds to it. | ||
== Tunings in terms of radical intervals == | == Tunings in terms of radical intervals == | ||