Diamond tradeoff: Difference between revisions
Cmloegcmluin (talk | contribs) break up page into sections and add helpful explanation from Keenan Pepper |
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A tuning for a [[rank]]-''r'' [[Prime limit|''p''-limit]] [[regular temperament]] is '''diamond tradeoff''', or '''diamond strict''', if it fits the following definition: we may define the diamond tradeoff tuning range by finding the [[Wikipedia: Convex hull|convex hull]] in [[Vals and Tuning Space|tuning space]] of the set of all tunings with ''r'' [[eigenmonzo subgroup|eigenmonzo]]s chosen as follows: one eigenmonzo 2 (pure octaves tunings) and the rest of the eigenmonzos any set of ''r'' - 1 members of the ''p''-odd limit [[tonality diamond]], whenever such a tuning is defined (this definition based on Gene Ward Smith's). | A tuning for a [[rank]]-''r'' [[Prime limit|''p''-limit]] [[regular temperament]] is '''diamond tradeoff''', or '''diamond strict''', if it fits the following definition: we may define the diamond tradeoff tuning range by finding the [[Wikipedia: Convex hull|convex hull]] in [[Vals and Tuning Space|tuning space]] of the set of all tunings with ''r'' [[eigenmonzo subgroup|eigenmonzo]]s chosen as follows: one eigenmonzo 2 (pure octaves tunings) and the rest of the eigenmonzos any set of ''r'' - 1 members of the ''p''-odd limit [[tonality diamond]], whenever such a tuning is defined (this definition is based on Gene Ward Smith's one). | ||
== Original name == | == Original name == | ||