A328228 Simple continued fraction expansion of 2^(7/12).

1, 2, 147, 5, 1, 3, 5, 4, 4, 1, 1, 159, 6, 1, 1, 1, 4, 1, 2, 1, 2, 3, 1, 8, 15, 47, 1, 103, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 2, 1, 10, 3, 1, 2, 1, 2, 4, 1, 1, 1, 9, 28, 2, 4, 2, 2, 5, 1, 3, 1, 1, 2, 1, 1, 1, 52, 6, 2, 6, 1, 5, 94, 3, 6, 26, 1, 6, 5, 1, 3, 109

Offset: 0

Author

Daniel Hoyt, Oct 08 2019

Keywords

• nonn
• cofr

Comments

2^(7/12) is the multiplier with respect to a base frequency to produce a perfect fifth interval in an equal tempered chromatic scale.

This constant is of interest because it is close to the just intonation perfect fifth coefficient of 1.5 (continued fraction [1, 2]). It is the closest to just intonation of the chromatic scale divisions other than the octaves (2*frequency), and unison (1*frequency). The perfect fifth is the most consonant division of the chromatic scale.

Links

• Wikipedia, Twelfth root of two
• Index entries for sequences based on music

Crossrefs

Cf. A005664, A103922, A328229.

Programs

Maple

convert(2^(7/12), confrac,100); # Robert Israel, Oct 24 2019

Mathematica

ContinuedFraction[2^(7/12), 82] (* Michael De Vlieger, Oct 25 2019 *)

PARI

contfrac(sqrtn(2^7, 12)) \\ Michel Marcus, Oct 09 2019