A320304 a(n) is the frequency of MIDI note number n in Hertz, rounded to the nearest integer.

8, 9, 9, 10, 10, 11, 12, 12, 13, 14, 15, 15, 16, 17, 18, 19, 21, 22, 23, 24, 26, 28, 29, 31, 33, 35, 37, 39, 41, 44, 46, 49, 52, 55, 58, 62, 65, 69, 73, 78, 82, 87, 92, 98, 104, 110, 117, 123, 131, 139, 147, 156, 165, 175, 185, 196, 208, 220, 233, 247, 262, 277, 294, 311

Offset: 0

Author

Jianing Song, Oct 10 2018

Keywords

• nonn
• easy

Comments

In electronic music, pitch is often given by MIDI note number. The MIDI number of A_4 (440 Hz) is 69; if a note is k semitones higher than A_4, its MIDI note number is 69 + k, and its frequency is 440*2^(k/12) Hz.

Note that audible notes have MIDI note numbers 16 (20.6017 Hz) to 135 (19912.1270 Hz).

Examples

			MIDI note | Note name | Frequency
  number  |           |    (Hz)
     0    |   C_{-1}  |   8.1758
     1    |  C#_{-1}  |   8.6620
     2    |   D_{-1}  |   9.1770
     3    |  D#_{-1}  |   9.7227
     4    |   E_{-1}  |  10.3009
     5    |   F_{-1}  |  10.9134
     6    |  F#_{-1}  |  11.5623
     7    |   G_{-1}  |  12.2499
     8    |  G#_{-1}  |  12.9782
     9    |   A_{-1}  |  13.7500
    10    |  A#_{-1}  |  14.5676
    11    |   B_{-1}  |  15.4339
    12    |   C_{0}   |  16.3516
		

Links

• Jianing Song, Table of n, a(n) for n = 0..1023
• Wikipedia, Table of note frequencies

Crossrefs

Cf. A144488.

Programs

PARI

a(n) = round(6.875*2^(n/12+1/4))

Formula

a(n) = round(6.875*2^(n/12+1/4)).