事象の地平線 EVENT HORIZON (micro tuning KIRNBERG microtonal ambient)

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Kirnberger temperament is an irregular temperament developed in the second half of the 18th century by Johann Kirnberger. Kirnberger was a student of Johann Sebastian Bach, held great admiration for his teacher and was one of his principal proponents.[1]

The first Kirnberger temperament, "Kirnberger I", had similarities to Pythagorean temperament, which stressed the importance of perfect fifths all throughout the circle of fifths. A complete circle of perfect fifths is not possible, because when the circle comes to an end at the tone it began, it will have overshot its original pitch. Thus, if one tunes C-G, G-D, D-A, A-E, E-B, B-F♯, F♯-C♯, C♯-G♯ (A♭), A♭-E♭, E♭-B♭, B♭-F, F-C... the new "C" will not be the same frequency as the first. The two "C"s will have a discrepancy of about 23 cents (a comma), which would be unacceptable. This difference between the initial "c" and final "c" that is derived from performing a series of perfect tunings is generally referred to as the Pythagorean comma. In Kirnberger I, the D-A fifth is reduced by a syntonic comma, making the major thirds F-A, C-E, G-B, and D-F pure, though the fifth based on D is a ratio of 40/27 instead of 3/2. Many tuning systems have been developed to "spread around" that comma, that is, to divide that anomalous musical space among the other intervals of the scale.