The Pythagorean limma and Pythagorean apotome are enharmonic equivalents ( chromatic semitones ) and only a Pythagorean comma apart, in contrast to diatonic and chromatic semitones in meantone temperament and 5-limit just intonation.
42.
The Locrian major scale has a circle of four major and two minor thirds, along with a diminished third, which in septimal meantone temperament approximates a septimal major second of ratio 8 / 7.
43.
Pythagorean tuning also had a second problem, which meantone temperament does not solve, which is the problem of below " ), which is restricted because both have a broken circle of fifths.
44.
As you say, in equal temperament, it's the same as a perfect fifth, but in extended meantone temperament, for example, it's much narrower than a perfect fifth.
45.
Traditional Indian systems of 22 [ ruti; Indonesian gamelan music; Thai, Burmese, and African music, and music using just intonation, meantone temperament or other alternative tunings may be considered microtonal"
46.
The standard proposed to the Acoustical Society of America explicitly states a logarithmic scale for frequency, which excludes meantone temperament, and the base frequency it uses gives A 4 a frequency of exactly 440 Hz.
47.
In tuning systems that are based on a cycle of fifths, such as Pythagorean tuning and meantone temperament, these alternatives are labelled as " diatonic " or " chromatic " intervals.
48.
He did this by first recapitulating a conventional known temperament of his time, and then he compared that with his new scheme ( which actually had been approximately conceived ( quarter-comma ) meantone temperament.
49.
Silbermann's non-negotiable style was not welcome everywhere, an important example of an opponent being Johann Sebastian Bach, who, unlike Silbermann who tuned in meantone temperament, preferred a more flexible tuning.
50.
In meantone temperament, this effect is even more pronounced ( the fifth over the break in the circle is known as the Wolf interval, as its intense beating was likened to a " howling " ).
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