31edo/Individual degrees: Difference between revisions
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A single step of 31-edo is about 38.71¢. Intervals around this size are called ''dieses'' (singular '''diesis'''). In 31 it is equivalent to the difference between one octave and three stacked major thirds (C to E, to G♯, to B♯, but {{nowrap|B♯ ≠ C}}), or four minor thirds (C to E♭ to G♭ to B𝄫 to {{nowrap|D𝄫 ≠ C}}). In the [[11-limit]], the diesis stands in for just ratios {{nowrap|56:55 (31.19)|55:54 (31.77¢)|49:48 (39.70¢)|45:44 (38.91¢)|36:35 (48.77¢)|33:32 (53.27¢)}}, and others. The diesis is a defining sound of 31edo; when it does not appear directly in a scale, it often shows up as the difference between two or more intervals of a similar size. Demonstrated in [[SpiralProgressions]]. | A single step of 31-edo is about 38.71¢. Intervals around this size are called ''dieses'' (singular '''diesis'''). In 31 it is equivalent to the difference between one octave and three stacked major thirds (C to E, to G♯, to B♯, but {{nowrap|B♯ ≠ C}}), or four minor thirds (C to E♭ to G♭ to B𝄫 to {{nowrap|D𝄫 ≠ C}}). In the [[11-limit]], the diesis stands in for just ratios {{nowrap|56:55 (31.19)|55:54 (31.77¢)|49:48 (39.70¢)|45:44 (38.91¢)|36:35 (48.77¢)|33:32 (53.27¢)}}, and others. The diesis is a defining sound of 31edo; when it does not appear directly in a scale, it often shows up as the difference between two or more intervals of a similar size. Demonstrated in [[SpiralProgressions]]. | ||
== 2\31 – minor semitone, chromatic semitone, small minor 2nd or downminor 2nd == | == 2\31 – minor semitone, chromatic semitone, small minor 2nd, or downminor 2nd == | ||
The difference between a major and minor third. The more "expressive" of the "half steps," and the larger of 31's two "microtones". In meantone, it is the ''chromatic semitone'', the interval that distinguishes major and minor intervals of the same generic interval class (e.g. thirds). 2\31 stands in for just ratios {{nowrap|28:27 (62.96¢)|25:24 (70.67¢)|22:21 (80.54¢)|21:20 (84.45¢)}}, and others. Generates [[Valentine|valentine temperament]]—aka [[Armodue theory#Semi-equalized Armodue|semi-equalized Armodue]]. | The difference between a major and minor third. The more "expressive" of the "half steps," and the larger of 31's two "microtones". In meantone, it is the ''chromatic semitone'', the interval that distinguishes major and minor intervals of the same generic interval class (e.g. thirds). 2\31 stands in for just ratios {{nowrap|28:27 (62.96¢)|25:24 (70.67¢)|22:21 (80.54¢)|21:20 (84.45¢)}}, and others. Generates [[Valentine|valentine temperament]]—aka [[Armodue theory#Semi-equalized Armodue|semi-equalized Armodue]]. | ||