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A229943
Decimal expansion of 256/243, the Pythagorean semitone.
5
1, 0, 5, 3, 4, 9, 7, 9, 4, 2, 3, 8, 6, 8, 3, 1, 2, 7, 5, 7, 2, 0, 1, 6, 4, 6, 0, 9, 0, 5, 3, 4, 9, 7, 9, 4, 2, 3, 8, 6, 8, 3, 1, 2, 7, 5, 7, 2, 0, 1, 6, 4, 6, 0, 9, 0, 5, 3, 4, 9, 7, 9, 4, 2, 3, 8, 6, 8, 3, 1, 2, 7, 5, 7, 2, 0, 1, 6, 4, 6, 0, 9, 0, 5, 3, 4, 9, 7, 9, 4, 2, 3, 8, 6, 8, 3, 1, 2, 7, 5, 7, 2, 0, 1, 6, 4, 6, 0, 9
OFFSET
1,3
COMMENTS
The Pythagorean diatonic semitone is one of the musical intervals. Has a ratio of 256/243, and is often called the Pythagorean limma. It is also sometimes called the Pythagorean minor semitone.
After the initial term the sequence has period 27, repeat: 0, 5, 3, 4, 9, 7, 9, 4, 2, 3, 8, 6, 8, 3, 1, 2, 7, 5, 7, 2, 0, 1, 6, 4, 6, 0, 9.
REFERENCES
J. M. Merino de la Fuente, Las vibraciones de la música, Editorial Club Universitario (2006), 133.
Alberto Rojo, La física en la vida cotidiana, Siglo Veintiuno Editores (2011), 137.
FORMULA
A229948/A221363 = (3^7/2^11)/(3^12/2^19) = 2^8/3^5 = 256/243.
EXAMPLE
1.053497942386831275720164609...
MATHEMATICA
RealDigits[256/243, 10, 120][[1]] (* Harvey P. Dale, Jul 17 2019 *)
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
Omar E. Pol, Oct 25 2013
STATUS
approved