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

Author

Jonathan Sondow, Jan 19 2013

Keywords

• nonn
• cons
• easy
• fini
• full

Comments

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

Examples

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

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

• 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

Crossrefs

Cf. A005663, A005664, A010774, A046102.

Programs

Mathematica

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

Formula

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