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A329219
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Decimal expansion of 2^(10/12) = 2^(5/6).
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3
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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
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OFFSET
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1,2
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COMMENTS
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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.
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LINKS
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FORMULA
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Equals Product_{k>=0} (1 + (-1)^k/(6*k + 1)). - Amiram Eldar, Jul 25 2020
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EXAMPLE
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1.78179743...
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PROG
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(PARI) default(realprecision, 100); 2^(10/12)
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CROSSREFS
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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
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KEYWORD
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AUTHOR
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STATUS
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approved
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