A329219 - OEIS

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A329219

Decimal expansion of 2^(10/12) = 2^(5/6).

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

(list; constant; graph; refs; listen; history; text; internal format)

OFFSET

1,2

COMMENTS

2^(10/12) is the ratio of the frequencies of the pitches in a minor seventh (e.g., D4-C5) in 12-tone equal temperament.

LINKS

Table of n, a(n) for n=1..91.

Wikipedia, Equal temperament

Wikipedia, Twelfth root of two

Index entries for sequences based on music

FORMULA

Equals 2/A010768.

Equals Product_{k>=0} (1 + (-1)^k/(6*k + 1)). - Amiram Eldar, Jul 25 2020

EXAMPLE

1.78179743...

MATHEMATICA

First[RealDigits[2^(5/6), 10, 100]] (* Paolo Xausa, Apr 27 2024 *)

PROG

(PARI) default(realprecision, 100); 2^(10/12)

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... (A328229)

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

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

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

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

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

Sequence in context: A019936 A086724 A268979 * A093720 A154216 A258947

Adjacent sequences: A329216 A329217 A329218 * A329220 A329221 A329222

KEYWORD

nonn,easy,cons

AUTHOR

Jianing Song, Nov 08 2019

STATUS

approved