cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Previous Showing 11-14 of 14 results.

A046102 Denominators of convergents to the comma of Pythagoras.

Original entry on oeis.org

1, 1, 3, 7, 24, 31, 179, 389, 9126, 18641, 46408, 65049, 111457, 6195184, 6306641, 31421748, 100571885, 131993633, 232565518, 3620476403, 3853041921, 38297853692, 80448749305, 440541600217, 3164239950824, 3604781551041
Offset: 1

Views

Author

Eric W. Weisstein

Keywords

Links

Crossrefs

Cf. A005664.

Programs

  • Mathematica
    Denominator[ Table[ ContinuedFraction[ Log[ 2 ]/Log[ 3/2 ], i ]//Normal, {i, 30} ] ]

Formula

a(n) = A005663(n) - A005664(n). - T. D. Noe, Oct 12 2007

A112732 Denominators of the convergents to the continued fraction for log_2(5)/4.

Original entry on oeis.org

1, 2, 5, 7, 12, 19, 31, 174, 205, 789, 2572, 3361, 9294, 12655, 97879, 7647217, 15392313, 207747286, 1054128743, 2316004772, 24214176463, 74958534161, 174131244785, 3557583429861, 3731714674646, 14752727453799, 77495351943641
Offset: 0

Views

Author

Gene Ward Smith, Dec 31 2005

Keywords

Comments

This is the fifth of 1/4-comma meantone temperament and hence of significance in music theory, as these represent equal divisions of the octave in which the circle of fifths nearly closes. The sequence is therefore closely related to A005664.

Links

Crossrefs

Cf. A005664.

Programs

  • Mathematica
    Rest[Denominator[Convergents[(Log[5]/(4 Log[2])),50]]] (* Peter J. C. Moses, Oct 05 2014 *)
Rest[Convergents[Log2[5]/4,50]//Denominator] (* Harvey P. Dale, May 12 2025 *)

A206788 Denominators of semiconvergents to log_2(3), which equals log(3)/log(2).

Original entry on oeis.org

1, 1, 2, 3, 5, 7, 12, 17, 29, 41, 53, 94, 147, 200, 253, 306, 359, 665, 971, 1636, 2301, 2966, 3631, 4296, 4961, 5626, 6291, 6956, 7621, 8286, 8951, 9616, 10281, 10946, 11611, 12276, 12941, 13606, 14271, 14936, 15601, 16266, 31867, 47468, 79335, 111202, 190537
Offset: 1

Views

Author

Keenan Pepper, Feb 12 2012

Keywords

Comments

These are also equal divisions of the octave that have good approximations of the 3rd harmonic (and hence other Pythagorean intervals such as 3/2, 4/3, 9/8 etc.).
The semiconvergents are important musically as the cardinalities of MOS scales of Pythagorean tuning.

Links

Crossrefs

Cf. A028507 (continued fraction expansion), A005664 (denominators of convergents).

A328228 Simple continued fraction expansion of 2^(7/12).

Original entry on oeis.org

1, 2, 147, 5, 1, 3, 5, 4, 4, 1, 1, 159, 6, 1, 1, 1, 4, 1, 2, 1, 2, 3, 1, 8, 15, 47, 1, 103, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 2, 1, 10, 3, 1, 2, 1, 2, 4, 1, 1, 1, 9, 28, 2, 4, 2, 2, 5, 1, 3, 1, 1, 2, 1, 1, 1, 52, 6, 2, 6, 1, 5, 94, 3, 6, 26, 1, 6, 5, 1, 3, 109
Offset: 0

Views

Author

Daniel Hoyt, Oct 08 2019

Keywords

Comments

2^(7/12) is the multiplier with respect to a base frequency to produce a perfect fifth interval in an equal tempered chromatic scale.
This constant is of interest because it is close to the just intonation perfect fifth coefficient of 1.5 (continued fraction [1, 2]). It is the closest to just intonation of the chromatic scale divisions other than the octaves (2*frequency), and unison (1*frequency). The perfect fifth is the most consonant division of the chromatic scale.

Links

Crossrefs

Cf. A005664, A103922, A328229.

Programs

Previous Showing 11-14 of 14 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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