A230437 -id:A230437 - cp's OEIS frontend

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

Offset: 1

Omar E. Pol, Oct 25 2013

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.

			1.053497942386831275720164609...

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.

Wikipedia, Semitone
OEIS index entry for music
The multi-faceted reach of the OEIS: Music

Cf. A010774, A221363, A229948, A230437.

RealDigits[256/243,10,120][[1]] (* Harvey P. Dale, Jul 17 2019 *)

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

A229948 Decimal expansion of 2187/2048, the Pythagorean apotome.

Original entry on oeis.org

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

Offset: 1

Omar E. Pol, Oct 25 2013

The Pythagorean apotome 2187/2048 (also called the apotome Pythagorica) is one of the musical intervals.

			1.06787109375

Wikipedia, Semitone
OEIS index entry for music
The multi-faceted reach of the OEIS: Music

Cf. A010774, A221363, A229943, A230437.

A221363 * A229943 = (3^12/2^19)*(2^8/3^5) = 3^7/2^11 = 2187/2048.

cp's OEIS Frontend

A229943 Decimal expansion of 256/243, the Pythagorean semitone.

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