A329220 Decimal expansion of 2^(11/12).

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

Offset: 1

Author

Jianing Song, Nov 08 2019

Keywords

• nonn
• easy
• cons

Comments

2^(11/12) is the ratio of the frequencies of the pitches in a major seventh (e.g., D4-C#5) in 12-tone equal temperament.

Links

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

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... (A329219)

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

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

Programs

Mathematica

First[RealDigits[2^(11/12), 10, 100]] (* Paolo Xausa, Apr 28 2024 *)

PARI

default(realprecision, 100); 2^(11/12)

Formula

Equals 2/A010774.

Equals Product_{k>=0} (1 + (-1)^k/(12*k + 1)). - Amiram Eldar, Jul 29 2020