A221363 Decimal expansion of the Pythagorean comma.

1, 0, 1, 3, 6, 4, 3, 2, 6, 4, 7, 7, 0, 5, 0, 7, 8, 1, 2, 5

Offset

1,4

Comments

In musical tuning, the Pythagorean comma is 12 fifths / 7 octaves = (3/2)^12 / 2^7.

References

Larry Baggett, In the Dark on the Sunny Side: A Memoir of an Out-of-Sight Mathematician, Mathematical Association of America, 2012, p. 78.

Dave Benson, Music: A Mathematical Offering. Cambridge: Cambridge University Press (2006): 164.

J. H. Conway and R. K. Guy, The Book of Numbers, New York: Springer-Verlag, 1995, p. 257.

Links

Table of n, a(n) for n=1..20.

Peter A. Frazer, Temperament, Midicode, January 2010.

Eric Weisstein's World of Music, Comma of Pythagoras

Wikipedia, Pythagorean comma

OEIS index entry for music

The multi-faceted reach of the OEIS: Music

Formula

A229948/A229943 - Omar E. Pol, Oct 25 2013

Example

3^12 / 2^19 = 531441/524288 = 1.0136432647705078125

Mathematica

RealDigits[N[31441/524288, 50]][[1]]

Crossrefs

Cf. A005663, A005664, A010774, A046102.

Sequence in context: A011307 A243625 A321872 * A245943 A245557 A197071

Adjacent sequences: A221360 A221361 A221362 * A221364 A221365 A221366

Keyword

nonn,cons,easy,fini,full

Author

Jonathan Sondow, Jan 19 2013

Status

approved