Digital Audio Stuff - Frequency Ranges

One of the earliest techniques one stumbles accross in the manipulation of Audio is the concept of equalization (EQ), both when mixing multiple tracks to create an audio output or when trying to fix up existing recordings. Equalization allows all kinds of magic such as the ability to pull out voice from a lot of background noise (perhaps that should read music not noise). But in order to work the magic you have got to know what frequencies the things you want to accentuate (or suppress) work on. This is our evolving effort to bring all of this stuff into a single page. Since a lot of digital audio is concerned with music we start with the basic frequencies for just over 10 octaves covering the human hearing range. Most musical instruments and even human voices are defined by the range of notes they can make, thus, for instance, a female soprano is expected to be able to output maximum power (or sing even) in the range C4 to C6 - though many will be able to accomplish higher, lower or both - from the table below we see this range corresponds to 262 Hz to 1047 Hz. So, if we want to pull out a soprano voice from the background these are frequencies we would concentrate on. It is not, however, as simple as that due to harmonics and the fact that most of the instruments in an orchestra also operate in that range. But of that more later...

Contents

Musical Notes by Frequency
Frequency Ranges of Things
Fundamentals and Harmonics and Overtones...

Musical Notes by Frequency

The following table shows the frequency of musical notes for 10+ Octaves covering a bit more than the range of human hearing (nominally 20Hz to 20KHz). This table is based on what is called the American Standard Pitch where the note A4 = 440Hz (used as a base or tuning frequency). There is also a less frequently used (and older) International Standard Pitch where A4 = 435 Hz. Each standard uses what is called an equal tempered interval, that is, each note is related the next one by an equal amount. Each octave is comprised of 12 semi-tones (C, C#, D, D#, E, F, F#, G, G#, A, A#, B) thus the even tempered interval is 2¹² - or for ordinary mortals take the value of any note and multiply it by 1.0594 to get the next higher one (each is 1/12 more than the previous one) or divide it by 1.0594 to get next lower one (each is 1/12 less than the previous one). Since each semi-tone is, magically, 1/12 more that the previous it thus represents a doubling of the pitch over the octave. Thus the same note in each octave, say C, is always twice the value of the previous one. For example C3 is 131 Hz and C4 is 262 Hz (any minor deviation for this rule in the table below is simply the result of rounding errors).

Note: All figures shown are in Hz with decimal points omitted - numbers are rounded up - for clarity and thus may differ marginally from the values shown in tables which show the decimal points in all their natural glory. In defense of our simplification technique we plead a hatred of unnecessary detail. Further, if you need those decimal points you are doing something very weird and probably should not be reading these pages. However, if you are really, really interested in decimal points (and lots of them) use our Acoustic Calculator.

Note	0	1	2	3	4	5	6	7	8	9	10
C	16	33	65	131	262	523	1047	2093	4186	8372	16744
C#	17	35	69	139	277	554	1109	2217	4435	8870	17740
D	18	37	73	147	294	587	1175	2349	4699	9397	18794
D#	19	39	78	156	311	622	1245	2489	4978	9956	19912
E	21	41	82	165	330	659	1319	2637	5274	10548	21096
F	22	44	87	175	349	698	1397	2794	5588	11175	22351
F#	23	46	93	185	370	740	1480	2960	5920	11840	23680
G	25	49	98	196	392	784	1568	3136	6272	12544	25088
G#	26	52	104	208	415	831	1661	3322	6645	13229	26580
A	28	55	110	220	440	880	1760	3520	7040	14080	28159
A#	29	58	117	233	466	932	1864	3729	7459	14917	29832
B	31	62	123	247	493	988	1976	3951	7902	15804	31604

Notes:

1. A standard piano keyboard (88 keys) goes from A0 to C8 (no don't ask why). There are other keyboard instruments with a variety of numbers of keys.

2. Most instruments are tuned to A4=440Hz, however concert pianos are apparently tuned to A4=442Hz (no idea why). Various other instruments can be tuned from A4=435Hz to A4=448Hz depending on the effect the musician wants.

3. Middle C = C4 = 262 Hz. The Treble Clef is normally G4 (392Hz). The Bass Clef is normally F3 (175Hz).

4. Theoretically, the range of human hearing is 20Hz to 20KHz meaning that the lowest and highest notes we can hear are E0 to D10#. However once out of the first flush of youth we practically have a hearing range of ~50Hz to around 15/16KHz (G1# to C10/C10#). Unless many years were spent in noisy discos in which case you will be lucky to hear anything at all.

5. C# (C sharp) = D^b (D flat), D# (D sharp) = E^b (E flat), F# (F sharp) = G^b (G flat), G# (G sharp) = A^b (A flat) , A# (A sharp) = B^b (B flat). We show the # version in all cases in the table above (for brevity) which probably has already sent real musicians into a paroxysm of teeth-gnashing.

Audio Frequencies

A list of frequencies used by things that make noises - like humans and musical instruments - but other stuff as well. As well as the fundamental frequency most instruments have harmonics and overtones which are noted where known. But assembling this stuff is both tedious and incredibly difficult (it is unknown in some cases, horribly contentious in others or just buried in some obscure place even the search engines can't find). If you can add information use the links at the top or bottom of the page to email us. The world will be grateful. That's it. Grateful.

Keyboard Instruments
Instrument	Fundamental	Harmonics	dB(SPL)
Piano	A0 (28 Hz) to C8 (4,186 Hz or 4.1 KHz)		60 - 100
Organ	C0 (16 Hz) (some are said to be cabable of C-1 (8 Hz)) to A9 (7,040 KHz)		35 - 110
Wind - without a reed
Instrument	Fundamental	Harmonics	dB(SPL)
Concert Flute	C4 (262 Hz) to B6 (1,976 Hz) (Some start at B3 (247 Hz))
French Horn	A2 (110 Hz) to A5 (880 Hz)
Picolo	C5 (523 Hz) to B7 (3,951 Hz)
Trombone	E2 (82 Hz) to B4 (493 Hz)
Trumpet	E3 (165 Hz) to B5 (988 Hz)		55 - 95
Tuba (Bass)	F1 (44 Hz) to F4 (349 Hz)
String Instruments
Instrument	Fundamental	Harmonics	dB(SPL)
Violin	G3 (196 Hz) - G7 (3,136 Hz) (G-D-E-A) (or C8 (4,186 Hz?)	Harmonics to 10 KHz	42 - 95
Viola	C3 (315 Hz) - D6 (1,175 Hz)
Cello	C2 (65 Hz) - B5 (988 Hz (C5))	Harmonics/overtones to 8Khz
Double Bass	E1 (41 Hz) to B3 (247 Hz)	Harmonics/overtones to 7Khz
Guitar (Acoustic)	E2 (82 Hz) to F6 (1,397 Hz) Standard tuning of E A D G B E. (Open #6 82.407Hz, Open #1 880Hz, #1 25th Fret 1,396.91Hz (1.39 KHz)
Guitar (Bass)	4 string E1 (41 Hz) to C4 (262 Hz). 5 string Bass normally starts at B0 (31 Hz) but tops out at the same C4 value.	Harmonics up to 15KHz.
Guitar (Electric)	E2 (82 Hz) to F6 (1,397 Hz) (Open #6 82.407Hz, Open #1 880Hz, #1 25th Fret 1,396.91 Hz (1.39 KHz) Same range as for acoustic guitars but electric guitars have more harmonics and effects and these can go way over 20KHz. But, since you cannot hear them (unless you claim to be an audiophile) - who cares.		Unlimited!
Percussion Instruments (things you hit)
Instrument	Fundamental	Harmonics	dB(SPL)
Drums (Timpani)	90Hz - 180Hz
Bass (Kick) Drum	60Hz - 100Hz		35 - 115
Snare Drum	1 KHz - 2 KHz
Toms	150 Hz - 2 KHz
Cymbal - Hi-hat	3 KHz - 5 KHz		4 - 110
Xylophone	700 Hz - 3.5 KHz
Wind (Reed or Woodwind) Instruments
Instrument	Fundamental	Harmonics	dB(SPL)
Bandoneon	Descant (right) side G3 (196 Hz) to A6 (1,750 Hz). Bass (left) side C3 (131 Hz) to A5# (932 Hz)
Clarinet	E3 (165 Hz) to G6 (1,568 Hz) (C7 sometimes possible (2,093 Hz)
Humans (You and me - well sometimes)
Instrument	Fundamental	Harmonics	dB(SPL)
Hi-Fi	50 Hz - 15 KHz. Originally thought to be the range of human hearing and still may be depending on your age. Now revised as shown below.
Human Hearing	20Hz - 20KHz. Unless you spent a lot of your adolescence in a disco in which case it is now probably squat. Audiophiles are supposed to be able to hear above 20KHz - or perhaps they only think they can. Over the age of 50 (some research suggests it may be even lower than that) most people are limited to a range of ~50 Hz to 15/16 KHz.
Hearing Sensitivity	Humans are not uniformly sensitive to sound accross the frequency spectrum. The most sensitivity is from approximately 300 Hz to 5 KHz with a particularly sensitive spot round 2 - 4 KHz (this phenomena is described by the Fletcher-Munson curves). This means that for many instruments we can be more sensitive to the effects of the 2nd, 3rd or higher harmonics (and equivalent overtones) not the fundamental. A doubling in sound power/energy results in a 3 dB(SPL) increase, 10 times power sound power/energy results in 10 dB(SPL) increase but humans preceive 10 dB(SPL) as only double the loudness.		10 - leaves in a breeze 20 - whisper 30 - quiet conversation 50/55 - ambient in office 70 - city street 80 - noisy office 100 - pneumatic drill(3m) 120 - jet take off 120 - pain threshold
Soprano	C4 (262 Hz) to C6 (1,047 Hz).
Mezzo-Soprano	A3 (110 Hz) to A5(880 Hz) (exceptions G3 (196 Hz) to C6(1,047 Hz))
Contralto	F3 (175 Hz) to F5 (698 Hz)
Countertenor	Male voice. Normally sings in the Contralto or Mezzo-Soprano range - exceptionally the soprano range.
Tenor	C3 (130 Hz) to C5 (523 Hz) (F5 (698 Hz) as extreme)
Baritone	F2 (87 Hz) to F4 (349 Hz)
Bass	F2 (87 Hz) to E4 (330 Hz)	Harmonics to 12KHz

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