A328229 Decimal expansion of 2^(7/12).

1, 4, 9, 8, 3, 0, 7, 0, 7, 6, 8, 7, 6, 6, 8, 1, 4, 9, 8, 7, 9, 9, 2, 8, 0, 7, 3, 2, 0, 2, 9, 7, 9, 5, 7, 9, 6, 3, 0, 2, 1, 5, 1, 5, 5, 3, 7, 3, 1, 7, 4, 6, 8, 7, 6, 4, 4, 1, 0, 2, 3, 8, 4, 4, 1, 0, 5, 1, 5, 7, 7, 0, 9, 4, 1, 9, 9, 1, 8, 7, 2, 0, 6, 9, 1, 0, 4, 9, 7, 9, 6, 9, 7, 8, 2, 4, 3, 5, 4, 6, 9

Offset

1,2

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.

Links

Table of n, a(n) for n=1..101.

Wikipedia, Twelfth root of two.

Index entries for algebraic numbers, degree 12.

Index entries for sequences based on music.

Formula

Equals A010774^7. - Michel Marcus, Oct 08 2019

Example

1.498307076876681498...

Mathematica

First@ RealDigits[2^(7/12), 10, 105] (* Michael De Vlieger, Oct 25 2019 *)

Prog

(PARI) sqrtn(2^7, 12) \\ Michel Marcus, Oct 08 2019

Crossrefs

Frequency ratios of musical intervals:

Perfect unison: 2^(0/12) = 1.0000000000

Minor second: 2^(1/12) = 1.0594630943... (A010774)

Major second: 2^(2/12) = 1.1224620483... (A010768)

Minor third: 2^(3/12) = 1.1892071150... (A010767)

Major third: 2^(4/12) = 1.2599210498... (A002580)

Perfect fourth: 2^(5/12) = 1.3348398541... (A329216)

Aug. fourth/

Dim. fifth: 2^(6/12) = 1.4142135623... (A002193)

Perfect fifth: 2^(7/12) = 1.4983070768... (this sequence)

Minor sixth: 2^(8/12) = 1.5874010519... (A005480)

Major sixth: 2^(9/12) = 1.6817928305... (A011006)

Minor seventh: 2^(10/12) = 1.7817974362... (A329219)

Major seventh: 2^(11/12) = 1.8877486253... (A329220)

Perfect octave: 2^(12/12) = 2.0000000000

Cf. A103922, A328228.

Cf. A395980 (Pythagorean "wolf fifth"), A395981 (quarter-comma meantone "wolf fifth").

Sequence in context: A388778 A397008 A215617 * A366174 A198548 A134902

Adjacent sequences: A328226 A328227 A328228 * A328230 A328231 A328232

Keyword

nonn,cons

Author

Daniel Hoyt, Oct 08 2019

Extensions

a(17) ff. corrected by Georg Fischer, Apr 04 2020

Status

approved