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# Tech 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 to know what frequencies the things you want to accentuate (or suppress) operate in.

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 (ofrequently also referred to as singing) 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 or band also operate in that range. But of that, more later...

## 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 to the next one by an equal amount. Each musical 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 the 12th root of 2 (12√2). For ordinary mortals this means taking the value of any note and multiplying it by 1.0594 to get the adjacent higher note (each is 12√2 more than the previous note) or dividing it by 1.0594 to get adjacent lower note (each is 12√2 less than the previous note).

Since each semi-tone is 12√2 more that the previous one by summing these differences the pitch (frequency) doubles over an octave. Thus, the same note in each octave, say C, is always twice the frequency of the previous octave. For example, C3 is 131 Hz and C4 is 262 Hz (any minor deviation from 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 special 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 (up to 5 decimal places by user selection). Finally, the table uses equal tempering with a base of A4 = 440Hz. Again, the calculator will let you change this base frequency.

 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 18795 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 13290 26579 A 28 55 110 220 440 880 1760 3520 7040 14080 28160 A# 29 58 117 233 466 932 1865 3729 7459 14917 29834 B 31 62 123 247 494 988 1976 3951 7902 15804 31608

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, for example, 66 keys or 76 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 (International Standard Pitch) to A4=448Hz depending on the effect the musician wants.

3. What is ubiquitously referred to as '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 clubs or discos in which case you will be lucky to hear anything at all.

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

## Audio Frequencies

A list of frequencies generated 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.

Note: We are now crediting reader input. Apologies to all previous contributors for the grievous oversight. Table augmented by contributions from - Thomas Wildman - many thanks.

 Keyboard Instruments Instrument Fundamental Harmonics dB(SPL) Notes Piano A0 (28 Hz) to C8 (4,186 Hz or 4.1 kHz) 60 - 100 Organ C0 (16 Hz) to A9 (7,040 Hz) 35 - 110 some are said to be capable of C-1 (8 Hz) Wind - without a reed Instrument Fundamental Harmonics dB(SPL) Notes 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 Tenor E2 (82 Hz) to D5 (587 Hz) Exceptionally F5 (698 Hz). Bb fundamental, sometimes F. Contrabass E1 (41 Hz) to E4 (330 Hz) F fundamental, sometimes Bb. Bass C1 (33 Hz) to C5 (523 Hz) Can start around Bb0 (A#0 - 29Hz). Bb fundamental. Trumpet E3 (165 Hz) to B5 (988 Hz) 55 - 95 Tuba (Bass) F1 (44 Hz) to F4 (349 Hz) Many play around Bb0 (A#0 - 29Hz) String Instruments Instrument Fundamental Harmonics dB(SPL) Notes Violin G3 (196 Hz) - G7 (3,136 Hz) (G-D-E-A) (or C8 (4,186 Hz?) to 10 kHz 42 - 95 Viola C3 (131 Hz) - D6 (1,175 Hz) Cello C2 (65 Hz) - B5 (988 Hz (C5)) to 8kHz Double Bass E1 (41 Hz) to B3 (247 Hz) 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 #1 369.63Hz, #1 25th Fret 1,396.91Hz (1.39 KHz) Guitar (Bass) 4 string E1 (41 Hz) to C4 (262 Hz). 15kHz. 5 string Bass normally starts at B0 (31 Hz) but tops out at the same C4 value. Guitar (Electric) E2 (82 Hz) to F6 (1,397 Hz) (Open #6 82.41 Hz (E2), Open #1 369.63 Hz (E4), #1 25th Fret 1,396.91 Hz (1.39 kHz) (F6) Unlimited! 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. Note: When using a slide with a guitar the note frequency at any single fret position does not change from that produced by a finger but the instrument's timbre does, due to the reduced dampening effect of the slide over the human finger. In particular, the sustain (of the ADSR envelope) is much longer and there is more power in the higher harmonics. This latter effect may give the impression the note has a higher frequency. Slide technique, however, typically involves moving the slide back and forth on the frets to literally slide from one note to another thus continually changing frequency to produce its distinctive effect. Percussion Instruments (things you hit) Instrument Fundamental Harmonics dB(SPL) Notes Drums (Timpani) 90Hz - 180Hz Bass (Kick) Drum 60Hz - 100Hz 35 - 115 Some sources quote a low of 30Hz Snare Drum 120 Hz - 250 Hz Toms 60 Hz - 210 Hz 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) Notes 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) Saxophone Tenor G#2 (104 Hz) to E5 (659 Hz) Bb fundamental. Barritone C2 (65 Hz) to A4 (440 Hz) Eb fundamental. Humans (You and me - well, sometimes in our case) Instrument Fundamental Harmonics dB(SPL) Notes 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 or club 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 300hz - 5 kHz Humans are not uniformly sensitive to sound across the frequency spectrum. The most sensitivity is from approximately 300 Hz to 5 kHz with a particularly sensitive spot round 2 - 4 kHz (this phenomenon 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. Sound Power dB(SPL) rating for some common sounds. 10 - leaves rustling in a breeze 20 - whisper 30 - quiet conversation 50/55 - ambient office 70 - city street 80 - noisy office 100 - pneumatic drill (at 3m or 10 feet) 120 - jet take off 120 - pain threshold (See also Loudness and Sound Power) 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 Avi Kaplan of Pentatonix has been recorded down to F1 (44Hz)

## Frequencies, Harmonics and Under Tones

This table was conributed by DJ Adi Abhishek. It is the most comprehensive we have ever seen and must have taken enormous work to put together. A truly remarkable (IOHO) piece of work.

The terms Under and Over tone are explained here. Ali quotes a frequency range for most sounds (different manufacturers, human characteristics) and then uses a single Fundamental Frequency for calculation of Under and Over tones.

We have made minor editing changes to Ali's originally supplied table and one significant change. The significant change is that the column headed Harmonics (2nd - 6th) was originally labelled Harmonic Over Tones. We made the change since, as harmonics, they all represent integer multiples of the Fundamental Frequency (a.k.a. 1st Harmonic). Overtones are not always integer multiples.

 SOUND FREQUENCYRANGE FUNDAMENTALFREQUENCY HARMONICS (2nd - 6th) HARMONIC UNDER TONES Kick Drum 60 250 155 310 465 620 775 930 77.50 51.67 38.75 31.00 25.83 Toms 60 210 135 270 405 540 675 810 67.50 45 33.75 27.00 22.50 Snare 120 250 185 370 555 740 925 1110 92.50 61.67 46.25 37.00 30.83 Cymbal/Hi-hat 3000 5000 4000 8000 12000 16000 20000 24000 2000 1333.33 1000.00 800.00 666.67 Electric Guitar 82 1397 739.50 1479 2218.50 2958 3697.50 4437 369.75 246.50 184.88 147.90 123.25 Bass Guitar 41 262 151.50 303 454.5 606 757.50 909 75.75 50.50 37.88 30.30 25.25 Acoustic Guitar 82 1397 739.50 1479 2218.50 2958 3697.50 4437 369.75 246.50 184.88 147.90 123.25 Mandolin 136 1320 728 1456 2184 2912 3640 4368 364 242.67 182.00 145.60 121.33 Tenor Sax 104 659 381.50 763 1144.50 1526 1907.50 2289 190.75 127.17 95.38 76.30 63.58 Alto Sax 150 800 475 950 1425 1900 2375 2850 237.50 158.33 118.75 95.00 79.17 Harmonica Various 180 3100 1640 3280 4920 6560 8200 9840 820 546.67 410.00 328.00 273.33 Vocal (Baritone) 87 349 218 436 654 872 1090 1308 109 72.67 54.50 43.60 36.33 Vocal (Tenor) 130 523 326.50 653 979.50 1306 1632.50 1959 163.25 108.83 81.63 65.30 54.42 Vocal (Alto) 180 700 440 880 1320 1760 2200 2640 220 146.67 110.00 88.00 73.33 Vocal (Soprano) 250 1300 775 1550 2325 3100 3875 4650 387.50 258.33 193.75 155.00 129.17 Violin 196 4186 2191 4382 6573 8764 10955 13146 1095.50 730.33 547.75 438.20 365.17 Viola 315 1175 745 1490 2235 2980 3725 4470 372.50 248.33 186.25 149.00 124.17 Cello 65 988 526.50 1053 1579.50 2106 2632.50 3159 263.25 175.50 131.63 105.30 87.75 Double Bass 41 247 144 288 432 576 720 864 72 48 36.00 28.80 24.00 Piccolo 523 3951 2237 4474 6711 8948 11185 13422 1118.50 745.67 559.25 447.40 372.83 Flute 250 2500 1375 2750 4125 5500 6875 8250 687.50 458.33 343.75 275.00 229.17 Oboe 225 1500 862.50 1725 2587.50 3450 4312.50 5175 431.25 287.50 215.63 172.50 143.75 Clarinet 165 1568 866.50 1733 2599.50 3466 4332.50 5199 433.25 288.83 216.63 173.30 144.42 Accordion 180 1000 590 1180 1770 2360 2950 3540 295 196.67 147.50 118.00 98.33 Bassoon 60 620 340 680 1020 1360 1700 2040 170 113.33 85.00 68.00 56.67 Trumpet 165 988 576.50 1153 1729.50 2306 2882.50 3459 288.25 192.17 144.13 115.30 96.08 Trombone 60 500 280 560 840 1120 1400 1680 140 93.33 70.00 56.00 46.67 French Horn 110 880 495 990 1485 1980 2475 2970 247.50 165 123.75 99.00 82.50 Tuba (Bass) 44 349 196.50 393 589.5 786 982.50 1179 98.25 65.50 49.13 39.30 32.75 Harp 30 7000 3515 7030 10545 14060 17575 21090 1757.50 1171.67 878.75 703.00 585.83 Harpsichord 40 1500 770 1540 2310 3080 3850 4620 385 256.67 192.50 154.00 128.33 Piano 28 4186 2107 4214 6321 8428 10535 12642 1053.50 702.33 526.75 421.40 351.17 Pipe Organ 16 7040 3528 7056 10584 14112 17640 21168 1764 1176 882.00 705.60 588.00 Keyboard / Synth 20 4000 2010 4020 6030 8040 10050 12060 1005 670 502.50 402.00 335.00 Female Voice 250 1000 625 1250 1875 2500 3125 3750 312.50 208.33 156.25 125.00 104.17 Male Voice 100 800 450 900 1350 1800 2250 2700 225 150 112.50 90.00 75.00 Sub Bass 16 60 38 76 114 152 190 228 19 12.67 9.50 7.60 6.33 Concert Flute 262 1976 1119 2238 3357 4476 5595 6714 559.50 373 279.75 223.80 186.50 Xylophone 700 3500 2100 4200 6300 8400 10500 12600 1050 700 525.00 420.00 350.00 Timpani (Drum) 90 180 135 270 405 540 675 810 67.50 45 33.75 27.00 22.50 Contra Bass 41 330 185.50 371 556.50 742 927.50 1113 92.75 61.83 46.38 37.10 30.92 Bass 33 330 181.50 363 544.50 726 907.50 1089 90.75 60.50 45.38 36.30 30.25 Baritone Sax 65 440 252.50 505 757.50 1010 1262.50 1515 126.25 84.17 63.13 50.50 42.08 Soprano 262 1047 654.50 1309 1963.50 2618 3272.50 3927 327.25 218.17 163.63 130.90 109.08 Mezzo Soprano 110 880 495 990 1485 1980 2475 2970 247.50 165 123.75 99.00 82.50 Contra Alto 175 698 436.50 873 1309.50 1746 2182.50 2619 218.25 145.50 109.13 87.30 72.75

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