Douglas Blumeyer's RTT How-To: Difference between revisions

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We’ve made it to a critical point here: we are now able to explain why RTT is called “regular” temperament theory. Regular here is a mathematical term, and I don’t have a straightforward definition of it for you, but it apparently refers to the fact that all intervals in the tuning are combinations of only these specified generators. So there you go.

Note well: this is not to say that {{val|1 1 0}} or {{val|0 1 4}} are the generators for meantone. These are generator mappings. They describe behavior of the generators. But they are not themselves the generators. It can get confusing, because it's certainly tempting to say {{val|1 1 0}} "is" the octave or the period and that {{val|0 1 4}} "is" the fifth or the generator, because {{monzo|1 0 0}} maps to {{monzo|1 0}} and {{monzo|-1 1 0}} maps to {{monzo|0 1}}. And maybe when the context is clear it may even be acceptable to say that. I suppose if "2/1 maps to one of the first generator (and zero of the second generator)" it may be to some extent acceptable to say that the first generator "is 2/1". ~~But~~ some folks may be less tolerant of such stretches of the ~~concepts~~.

Note well: this is not to say that {{val|1 1 0}} or {{val|0 1 4}} are the generators for meantone. These are generator mappings. They describe behavior of the generators. But they are not themselves the generators. It can get confusing, because it's certainly tempting to say {{val|1 1 0}} "is" the octave or the period and that {{val|0 1 4}} "is" the fifth or the generator, because {{monzo|1 0 0}} maps to {{monzo|1 0}} and {{monzo|-1 1 0}} maps to {{monzo|0 1}}. And maybe when the context is clear it may even be acceptable to say that. I suppose if "2/1 maps to one of the first generator (and zero of the second generator)" it may be to some extent acceptable to say that the first generator "is 2/1". And if we're looking at this mapping and you ask me, "which generator is the octave?" I'd be hard-pressed to find a better answer than "it's the {{val|1 1 0}} one", but some folks may be less tolerant of such stretches of the terminology.

=== JI as a temperament ===

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 We’ve made it to a critical point here: we are now able to explain why RTT is called “regular” temperament theory. Regular here is a mathematical term, and I don’t have a straightforward definition of it for you, but it apparently refers to the fact that all intervals in the tuning are combinations of only these specified generators. So there you go.
-Note well: this is not to say that {{val|1 1 0}} or {{val|0 1 4}} are the generators for meantone. These are generator mappings. They describe behavior of the generators. But they are not themselves the generators. It can get confusing, because it's certainly tempting to say {{val|1 1 0}} "is" the octave or the period and that {{val|0 1 4}} "is" the fifth or the generator, because {{monzo|1 0 0}} maps to {{monzo|1 0}} and {{monzo|-1 1 0}} maps to {{monzo|0 1}}. And maybe when the context is clear it may even be acceptable to say that. I suppose if "2/1 maps to one of the first generator (and zero of the second generator)" it may be to some extent acceptable to say that the first generator "is 2/1". But some folks may be less tolerant of such stretches of the concepts.
+Note well: this is not to say that {{val|1 1 0}} or {{val|0 1 4}} are the generators for meantone. These are generator mappings. They describe behavior of the generators. But they are not themselves the generators. It can get confusing, because it's certainly tempting to say {{val|1 1 0}} "is" the octave or the period and that {{val|0 1 4}} "is" the fifth or the generator, because {{monzo|1 0 0}} maps to {{monzo|1 0}} and {{monzo|-1 1 0}} maps to {{monzo|0 1}}. And maybe when the context is clear it may even be acceptable to say that. I suppose if "2/1 maps to one of the first generator (and zero of the second generator)" it may be to some extent acceptable to say that the first generator "is 2/1". And if we're looking at this mapping and you ask me, "which generator is the octave?" I'd be hard-pressed to find a better answer than "it's the {{val|1 1 0}} one", but some folks may be less tolerant of such stretches of the terminology.
 === JI as a temperament ===