Cross-domain temperament merging: Difference between revisions

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''For a map-merge'', then, because the output temperament will deal only with tempered commas shared by every input temperament, then its interval basis only needs to include the formal primes that are present in all of the input interval bases. Here's why: a comma built using a formal prime that isn't shared by all input temperaments couldn't even be ''built'' in all input temperaments, yet alone tempered out by all of them. And so, to build the set of commas that are tempered out by all temperaments, we only need the building blocks that can be found in all of them. In mathematical terms, we must find the intersection of the input interval bases.

[[File:Map-merge across interval bases.png|450px|thumb|left|A map-merge across interval bases gives a comma-intersection and an interval basis intersection (for purposes of illustrating this concept, the results are not being canonicalized).]]

[[File:Comma-merge across interval bases.png|450px|thumb|right|A comma-merge across interval bases gives a map-intersection and an interval basis merge (for purposes of illustrating this concept, the results are not being canonicalized).]]

== 2. Convert the input temperaments to the output interval basis ==

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 ''For a map-merge'', then, because the output temperament will deal only with tempered commas shared by every input temperament, then its interval basis only needs to include the formal primes that are present in all of the input interval bases. Here's why: a comma built using a formal prime that isn't shared by all input temperaments couldn't even be ''built'' in all input temperaments, yet alone tempered out by all of them. And so, to build the set of commas that are tempered out by all temperaments, we only need the building blocks that can be found in all of them. In mathematical terms, we must find the intersection of the input interval bases.
+[[File:Map-merge across interval bases.png|450px|thumb|left|A map-merge across interval bases gives a comma-intersection and an interval basis intersection (for purposes of illustrating this concept, the results are not being canonicalized).]]
+[[File:Comma-merge across interval bases.png|450px|thumb|right|A comma-merge across interval bases gives a map-intersection and an interval basis merge (for purposes of illustrating this concept, the results are not being canonicalized).]]
 == 2. Convert the input temperaments to the output interval basis ==