A229943 - OEIS

A229943

Decimal expansion of 256/243, the Pythagorean semitone.

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

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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.

LINKS

Table of n, a(n) for n=1..109.

Wikipedia, Semitone

OEIS index entry for music

The multi-faceted reach of the OEIS: Music

FORMULA

A229948/A221363 = (3^7/2^11)/(3^12/2^19) = 2^8/3^5 = 256/243.

EXAMPLE