Huygens vs meanpop: Difference between revisions

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In meanpop, 11/8 is represented by the doubly diminished fifth, for example C-Gbb. This is in the opposite direction along the circle of fifths - 13 fifths down.

In 13–limit, they extend by the 105/104 comma. Alternatively meantone extends into grosstone by 144/143.

Can meantone and meanpop be combined into a single temperament? Yes! It works wonderfully and that temperament is [[31edo|31edo]]. In 31edo the circle of fifths closes perfectly after 31 fifths, so Ex and Gbb are the same note. (In other words, the interval of the ''quadruply diminished third'' is tuned to 0 cents, if that makes any sense to you.) This makes everything much simpler and results in 121/120 and 243/242 being tempered out, so that 12/11~11/10 is a "neutral second" (exactly half of a minor third), and 11/9 is a "neutral third" (exactly half of a perfect fifth). Keep in mind that neither of these things are true in either meantone or meanpop.

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 In meanpop, 11/8 is represented by the doubly diminished fifth, for example C-Gbb. This is in the opposite direction along the circle of fifths - 13 fifths down.
+In 13–limit, they extend by the 105/104 comma. Alternatively meantone extends into grosstone by 144/143.
 Can meantone and meanpop be combined into a single temperament? Yes! It works wonderfully and that temperament is [[31edo|31edo]]. In 31edo the circle of fifths closes perfectly after 31 fifths, so Ex and Gbb are the same note. (In other words, the interval of the ''quadruply diminished third'' is tuned to 0 cents, if that makes any sense to you.) This makes everything much simpler and results in 121/120 and 243/242 being tempered out, so that 12/11~11/10 is a "neutral second" (exactly half of a minor third), and 11/9 is a "neutral third" (exactly half of a perfect fifth). Keep in mind that neither of these things are true in either meantone or meanpop.