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A schismatic temperament is a musical tuning system that results from tempering the schisma of 32805:32768 (1.9537 cents) to a unison. It is also called the schismic temperament, Helmholtz temperament, or quasi-Pythagorean temperament. ==Construction== In Pythagorean tuning all notes are tuned as a number of perfect fifths (701.96 cents ). The major third above C, E, is considered four fifths above C. This causes the Pythagorean major third, E (407.82 cents ), to differ from the just major third, E (386.31 cents ): the Pythagorean third is sharper than the just third by 21.51 cents (a syntonic comma ). C — G — D — A — E Ellis's "skhismic temperament"〔. 〕 instead uses the note eight fifths ''below'' C, F (384.36 cents ), the Pythagorean diminished fourth or schismatic major third. Though spelled "incorrectly" for a major third, this note is only 1.95 cents (a schisma) flat of E, and thus more in tune than the Pythagorean major third. As Ellis puts it, "the Fifths should be perfect and the Skhisma should be disregarded ()." ::E F :F — C — G — D — A — E — B — F — C In his eighth-schisma "Helmholtzian temperament"〔 the note eight fifths below C is also used as the major third above C. However, in the "skhismic temperament" pure perfect fifths are used to construct an approximate major third, while in the "Helmholtzian temperament" approximate perfect fifths are used to construct a pure major third. To raise the Pythagorean diminished fourth 1.95 cents to a just major third each fifth must be narrowed, or tempered, by 1.95/8 = 0.24 cents. Thus the fifth becomes 701.71 cents instead of 701.96 cents. As Ellis puts it, "the major Thirds are taken perfect, and the Skhisma is disregarded (out )." ::E F :E — C — G — D — A — E — B — F — C Compare vs. . 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Schismatic temperament」の詳細全文を読む スポンサード リンク
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