note-frequencies.md

Note Frequencies

🡪 iicaras

For a concert pitch of $\textup{A}_4 = 440 \textup{ hz}$, frequencies for each pitch in 12-TET are calculated using the equation

$$f_x = 2^{\tfrac{x}{12 \textup{ st}}}f_{\textup{A}_4},$$

with $[x] = \textup{ st}$ (semitones) and $x \in \mathbb{Z}$ ¹. The table below gives the frequency for each note between C0 and B10.

def get_note_frequencies():
    return {['A', 'A#', 'B', 'C', 'C#', 'D', 'D#', 'E', 'F', 'F#', 'G', 'G#'][n % 12] + str(int((n - 3) / 12)) : 440 / (2 ** 5) * 2 ** (n / 12) for n in range(3, 111)}

Note	Frequency [Hz]	Semitones from A4 (st)
C0	16.351597831287414	-57
C#0	17.323914436054505	-56
D0	18.354047994837973	-55
D#0	19.445436482630058	-54
E0	20.60172230705437	-53
F0	21.826764464562743	-52
F#0	23.12465141947715	-51
G0	24.49971474885933	-50
G#0	25.95654359874657	-49
A0	27.5	-48
A#0	29.13523509488062	-47
B0	30.867706328507758	-46
C1	32.70319566257483	-45
C#1	34.64782887210901	-44
D1	36.70809598967595	-43
D#1	38.890872965260115	-42
E1	41.20344461410874	-41
F1	43.653528929125486	-40
F#1	46.2493028389543	-39
G1	48.99942949771866	-38
G#1	51.91308719749314	-37
A1	55	-36
A#1	58.27047018976124	-35
B1	61.7354126570155	-34
C2	65.40639132514966	-33
C#2	69.29565774421802	-32
D2	73.41619197935188	-31
D#2	77.78174593052023	-30
E2	82.4068892282175	-29
F2	87.30705785825097	-28
F#2	92.4986056779086	-27
G2	97.99885899543733	-26
G#2	103.82617439498628	-25
A2	110	-24
A#2	116.54094037952248	-23
B2	123.470825314031	-22
C3	130.8127826502993	-21
C#3	138.59131548843604	-20
D3	146.83238395870376	-19
D#3	155.56349186104046	-18
E3	164.813778456435	-17
F3	174.61411571650194	-16
F#3	184.9972113558172	-15
G3	195.99771799087466	-14
G#3	207.65234878997256	-13
A3	220	-12
A#3	233.0818807590449	-11
B3	246.94165062806212	-10
C4	261.6255653005986	-9
C#4	277.1826309768721	-8
D4	293.66476791740763	-7
D#4	311.1269837220809	-6
E4	329.62755691286986	-5
F4	349.22823143300394	-4
F#4	369.9944227116344	-3
G4	391.9954359817492	-2
G#4	415.3046975799452	-1
A4	440	0
A#4	466.1637615180898	1
B4	493.88330125612424	2
C5	523.2511306011972	3
C#5	554.3652619537442	4
D5	587.3295358348153	5
D#5	622.2539674441618	6
E5	659.2551138257397	7
F5	698.4564628660079	8
F#5	739.9888454232688	9
G5	783.9908719634984	10
G#5	830.6093951598904	11
A5	880	12
A#5	932.3275230361796	13
B5	987.7666025122485	14
C6	1046.5022612023945	15
C#6	1108.7305239074883	16
D6	1174.6590716696305	17
D#6	1244.5079348883237	18
E6	1318.5102276514795	19
F6	1396.9129257320158	20
F#6	1479.9776908465376	21
G6	1567.9817439269968	22
G#6	1661.2187903197807	23
A6	1760	24
A#6	1864.6550460723593	25
B6	1975.533205024497	26
C7	2093.004522404789	27
C#7	2217.4610478149766	28
D7	2349.318143339261	29
D#7	2489.0158697766474	30
E7	2637.020455302959	31
F7	2793.8258514640315	32
F#7	2959.955381693075	33
G7	3135.9634878539937	34
G#7	3322.4375806395615	35
A7	3520	36
A#7	3729.3100921447212	37
B7	3951.0664100489917	38
C8	4186.009044809578	39
C#8	4434.922095629955	40
D8	4698.636286678519	41
D#8	4978.031739553295	42
E8	5274.040910605921	43
F8	5587.65170292806	44
F#8	5919.91076338615	45
G8	6271.926975707992	46
G#8	6644.875161279119	47
A8	7040	48
A#8	7458.6201842894425	49
B8	7902.132820097983	50
C9	8372.018089619156	51
C#9	8869.84419125991	52
D9	9397.272573357039	53
D#9	9956.06347910659	54
E9	10548.081821211843	55
F9	11175.30340585612	56
F#9	11839.8215267723	57
G9	12543.853951415984	58
G#9	13289.750322558239	59
A9	14080	60
A#9	14917.240368578885	61
B9	15804.265640195967	62
C10	16744.036179238312	63
C#10	17739.68838251982	64
D10	18794.545146714077	65
D#10	19912.12695821318	66
E10	21096.163642423686	67
F10	22350.60681171224	68
F#10	23679.6430535446	69
G10	25087.707902831968	70
G#10	26579.500645116477	71
A10	28160	72
A#10	29834.48073715777	73
B10	31608.53128039193	74

Bibliography

Footnotes

1. iicaras, ‘harmonics.md’, Gist. Accessed: Jan. 12, 2025. [Online]. Available: https://gist.github.com/iicaras/9acfe1b65d2f3555211deeb3eec95e1b ↩