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

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What’s the proper count of brackets though? Well, the total count of brackets on the multicomma and multimap for a temperament must always sum to the dimensionality of the system from which you tempered. It’s the same thing as <math>d - n = r</math>, just phrased as <math>r + n = d</math>, and where <math>r</math> should be the bracket count for the multimap and <math>n</math> should be the bracket count for the multicomma. So with 5-limit meantone, with dimensionality 3, there should be 3 total pairs of brackets. If 2 are on the multimap, then only 1 are on the multicomma.

=== more on duals ===

Note the Pascal’s triangle shape to the numbers in Figure 6b. Also note that the mirrored results within each dimensionality are reverses of each other. Sometimes that means they’re identical, like <math>+-+-+</math> and <math>+-+-+</math>; other times not, like <math>+-++-+-+-+</math> and <math>+-+-+-++-+</math>.

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 What’s the proper count of brackets though? Well, the total count of brackets on the multicomma and multimap for a temperament must always sum to the dimensionality of the system from which you tempered. It’s the same thing as <span><math>d - n = r</math></span>, just phrased as <span><math>r + n = d</math></span>, and where <span><math>r</math></span> should be the bracket count for the multimap and <span><math>n</math></span> should be the bracket count for the multicomma. So with 5-limit meantone, with dimensionality 3, there should be 3 total pairs of brackets. If 2 are on the multimap, then only 1 are on the multicomma.
+=== more on duals ===
 Note the Pascal’s triangle shape to the numbers in Figure 6b. Also note that the mirrored results within each dimensionality are reverses of each other. Sometimes that means they’re identical, like <span><math>+-+-+</math></span> and <span><math>+-+-+</math></span>; other times not, like <span><math>+-++-+-+-+</math></span> and <span><math>+-+-+-++-+</math></span>.