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单词 Diesis
释义

Diesis

The musical interval by which an octave exceeds three major thirds,


Taking Continued Fraction Convergents of gives the increasing accurateapproximations of octaves and major thirds: 1/3, 9/28, 19/59, 47/146, 207/643, 1289/4004, ...(Sloane's A046103and A046104). Other near equalities of octaves and major thirds having


with are given in the following table.

RatioRatio
9 280.99035203141043231.012011267
10311.014120481133511.002247414
18560.98079714621223790.9925777621
19 591.0043362781233821.016399628
28870.99464647281314070.983001403
29901.0185179881324101.006593437
371150.98505015491414380.9968818549
381181.0086913591504660.9872639701
47 1460.99895953611514691.010958305
561740.98932160591604971.001204611
571771.0130653241695250.9915450208
662051.0032913021705281.015342101
752330.99361157911785530.9819786256
762361.0174582571795561.005546113
842610.98402524581885840.9958446353
852641.0076418521895871.019744907
942920.99792015481976120.9862367575
1033200.98829225251986151.00990644

See also Comma of Didymus, Comma of Pythagoras, Schisma


References

Sloane, N. J. A.A046103 andA046104 in ``An On-Line Version of the Encyclopedia of Integer Sequences.''http://www.research.att.com/~njas/sequences/eisonline.html.


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