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

0,1

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).

Links

Jianing Song, Table of n, a(n) for n = 0..1023

Wikipedia, Table of note frequencies

Formula

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

Example

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

Prog

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

Crossrefs

Cf. A144488.

Sequence in context: A358519 A256923 A347219 * A217292 A004164 A004449

Adjacent sequences: A320301 A320302 A320303 * A320305 A320306 A320307

Keyword

nonn,easy

Author

Jianing Song, Oct 10 2018

Status

approved