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In classical music from Western culture, a diesis ( ; "difference"; Greek: δίεσις "leak" or "escape"〔Benson, Dave (2006). ''Music: A Mathematical Offering'', p.171. ISBN 0-521-85387-7. Based on the technique of playing the aulos, where pitch is raised a small amount by slightly raising the finger on the lowest closed hole, letting a small amount of air "escape".〕) is either an accidental (see sharp), or a very small musical interval, usually defined as the difference between an octave (in the ratio 2:1) and three justly tuned major thirds (tuned in the ratio 5:4), equal to 128:125 or about 41.06 cents. In 12-tone equal temperament (on a piano for example) three major thirds in a row equal an octave, but three justly-tuned major thirds fall quite a bit narrow of an octave, and the diesis describes the amount by which they are short. For instance, an octave (2:1) spans from C to C', and three justly tuned major thirds (5:4) span from C to B (namely, from C, to E, to G, to B). The difference between C-C' (2:1) and C-B (125:64) is the diesis (128:125). Notice that this coincides with the interval between B and C', also called a diminished second. The diesis is a comma. The above-mentioned 128:125 comma is also known as the lesser diesis, as opposed to a wider comma (648:625) known as greater diesis. As shown in the picture, in the quarter-comma meantone tuning system (a tuning system in which, by definition, major thirds are justly tuned), the diminished second coincides with the diesis. == Alternative definitions == In any tuning system, the deviation of an octave from three major thirds, however large that is, is typically referred to as a diminished second. The diminished second is an interval between pairs of enharmonically equivalent notes; for instance the interval between E and F. As mentioned above, the term ''diesis'' most commonly refers to the diminished second in quarter-comma meantone temperament. Less frequently and less strictly, the same term is also used to refer to a diminished second of any size. In third-comma meantone, the diminished second is typically denoted as a greater diesis (see below). In quarter-comma meantone, since major thirds are justly tuned, the width of the diminished second coincides with the above-mentioned value of 128:125. Notice that 128:125 is larger than a unison (1:1). This means that, for instance, C' is sharper than B. In other tuning systems, the diminished second has different widths, and may be smaller than a unison (e.g. C' may be flatter than B): * a greater diesis above unison (648:625) for third-comma meantone temperament (see below), * a diaschisma above unison (2048:2025) for sixth-comma, * a schisma below unison (32768:32805) for twelfth-comma, and * a Pythagorean comma below unison (524288:531441) for Pythagorean tuning. In eleventh-comma meantone, the diminished second is within 1/716 (0.0014) of a cent above unison, so it closely resembles the 1:1 unison ratio of twelve-tone equal temperament. The word ''diesis'' has also been used to describe a large number of intervals, of varying sizes, but typically around 50 cents. Philolaus used it to describe the interval now usually called a ''limma'', that of a justly tuned perfect fourth (4:3) minus two whole tones (9:8), equal to 256:243 or about 90.22 cents. Rameau, in his ''Treatise on Harmony'' (1722), names 125:148 (, ''recte'' 125:128)〔Corrected in the English edition, ''Treatise on Harmony'', translated with an introduction and notes by Philip Gossett (New York: Dover Publications, Inc., 1971), p. 30. ISBN 0-486-22461-9.〕 as a "minor diesis" and 243:250 as a "major diesis", explaining that the latter may be derived through multiplication of the former by the ratio 15552:15625.〔Jean-Philippe Rameau, ''Traité de l'harmonie réduite à ses principes naturels'' (Paris: Jean-Baptiste-Christophe Ballard, 1722), pp. 26–27.〕 Other theorists have used it for various other intervals. 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「diesis」の詳細全文を読む スポンサード リンク
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