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Tech Stuff - Frequency Ranges.html
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Tech Stuff - Frequency Ranges.html
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<!DOCTYPE html>
<html lang="en-us">
<head>
<meta http-equiv="Content-Type" content="text/html; charset=utf-8">
<link rel="icon" href="http://www.zytrax.com/favicon.ico">
<title>Tech Stuff - Frequency Ranges</title>
<meta name="description" content="Zytrax Tech Stuff - audio introduction, frequencies of 10 octaves, frequencies of common sounds and instruments, table listing frequency ranges, overtones and undertones for many instruments. American Standard Pitch, Internation Standard Pitch, equal tempering and equal temperment.">
<meta name="keywords" content="ZYTRAX, Tech Stuff, octaves, American Standard Pitch, Internation Standard Pitch, equal tempering, equal temperment, timbre, pitch, fundamental frequency, harmonics">
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<h1>Tech Stuff - Frequency Ranges</h1>
<p>One of the earliest techniques one stumbles accross in the manipulation of Audio is the concept of <a href="glossary.html#equalization" class="t-db">equalization (EQ)</a>, 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.<p>
<p>This is our evolving effort to bring all of this stuff into a single page.</p>
<p>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.</p>
<p>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... </p>
<h3 id="contents">Contents</h3>
<p><a href="#notes" class="t-db">Musical Notes by Frequency</a><br>
<a href="#frequencies" class="t-db">Frequency Ranges of Things</a><br>
<a href="#contribution" class="t-db">Contributed Frequency, Harmonics and Under Tones Table</a><br>
<a href="sound.html" class="t-db">Fundamentals and Harmonics and Overtones...</a><br>
</p>
<h2 id="notes">Musical Notes by Frequency</h2>
<p>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.<p>
<p>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 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 1/12 more than the previous note) or dividing it by 1.0594 to get adjacent lower note (each is 1/12 less than the previous note).</p>
<p>Since each semi-tone is, magically, 1/12 more that the previous one 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).</p>
<p><b>Note:</b> 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 <a href="calculator.html#note" class="t-db">Acoustic Calculator</a>. Finally, the table uses equal tempering with a base of A4 = 440Hz. Again, the calculator will let you change this base frequency.</p>
<table class="p-m-s">
<tr class="g-h-n">
<td>Note</td>
<td>0</td>
<td>1</td>
<td>2</td>
<td>3</td>
<td>4</td>
<td>5</td>
<td>6</td>
<td>7</td>
<td>8</td>
<td>9</td>
<td>10</td>
</tr>
<tr >
<td class="g-h-n">C</td>
<td>16</td>
<td>33</td>
<td>65</td>
<td>131</td>
<td>262</td>
<td>523</td>
<td>1047</td>
<td>2093</td>
<td>4186</td>
<td>8372</td>
<td>16744</td>
</tr>
<tr >
<td class="g-h-n">C#</td>
<td>17</td>
<td>35</td>
<td>69</td>
<td>139</td>
<td>277</td>
<td>554</td>
<td>1109</td>
<td>2217</td>
<td>4435</td>
<td>8870</td>
<td>17740</td>
</tr>
<tr >
<td class="g-h-n">D</td>
<td>18</td>
<td>37</td>
<td>73</td>
<td>147</td>
<td>294</td>
<td>587</td>
<td>1175</td>
<td>2349</td>
<td>4699</td>
<td>9397</td>
<td>18795</td>
</tr>
<tr >
<td class="g-h-n">D#</td>
<td>19</td>
<td>39</td>
<td>78</td>
<td>156</td>
<td>311</td>
<td>622</td>
<td>1245</td>
<td>2489</td>
<td>4978</td>
<td>9956</td>
<td>19912</td>
</tr>
<tr >
<td class="g-h-n">E</td>
<td>21</td>
<td>41</td>
<td>82</td>
<td>165</td>
<td>330</td>
<td>659</td>
<td>1319</td>
<td>2637</td>
<td>5274</td>
<td>10548</td>
<td>21096</td>
</tr>
<tr >
<td class="g-h-n">F</td>
<td>22</td>
<td>44</td>
<td>87</td>
<td>175</td>
<td>349</td>
<td>698</td>
<td>1397</td>
<td>2794</td>
<td>5588</td>
<td>11175</td>
<td>22351</td>
</tr>
<tr >
<td class="g-h-n">F#</td>
<td>23</td>
<td>46</td>
<td>93</td>
<td>185</td>
<td>370</td>
<td>740</td>
<td>1480</td>
<td>2960</td>
<td>5920</td>
<td>11840</td>
<td>23680</td>
</tr>
<tr >
<td class="g-h-n">G</td>
<td>25</td>
<td>49</td>
<td>98</td>
<td>196</td>
<td>392</td>
<td>784</td>
<td>1568</td>
<td>3136</td>
<td>6272</td>
<td>12544</td>
<td>25088</td>
</tr>
<tr >
<td class="g-h-n">G#</td>
<td>26</td>
<td>52</td>
<td>104</td>
<td>208</td>
<td>415</td>
<td>831</td>
<td>1661</td>
<td>3322</td>
<td>6645</td>
<td>13290</td>
<td>26579</td>
</tr>
<tr >
<td class="g-h-n w-10">A</td>
<td>28</td>
<td>55</td>
<td>110</td>
<td>220</td>
<td>440</td>
<td>880</td>
<td>1760</td>
<td>3520</td>
<td>7040</td>
<td>14080</td>
<td>28160</td>
</tr>
<tr >
<td class="g-h-n">A#</td>
<td>29</td>
<td>58</td>
<td>117</td>
<td>233</td>
<td>466</td>
<td>932</td>
<td>1865</td>
<td>3729</td>
<td>7459</td>
<td>14917</td>
<td>29834</td>
</tr>
<tr >
<td class="g-h-n">B</td>
<td>31</td>
<td>62</td>
<td>123</td>
<td>247</td>
<td>494</td>
<td>988</td>
<td>1976</td>
<td>3951</td>
<td>7902</td>
<td>15804</td>
<td>31608</td>
</tr>
</table>
<p><b>Notes:</b></p>
<ol>
<li><p>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.</p></li>
<li><p>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.</p></li>
<li><p>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). </p></li>
<li><p>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.</p></li>
<li><p>C# (C sharp) = D<sup>b</sup> (D flat), D# (D sharp) = E<sup>b</sup> (E flat), F# (F sharp) = G<sup>b</sup> (G flat), G# (G sharp) = A<sup>b</sup> (A flat) , A# (A sharp) = B<sup>b</sup> (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. </p></li>
</ol>
<h2 id="frequencies">Audio Frequencies</h2>
<p>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 <a href="sound.html" class="t-db">harmonics and overtones</a> 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.</p>
<p><b>Note:</b> We are now crediting reader input. Apologies to all previous contributors for the grievous oversight. Table augmented by contributions from - Thomas Wildman - many thanks.</p>
<table class="p-m-s">
<tr>
<td class="w-120"></td>
<td class="w-200"></td>
<td class="w-100"></td>
<td class="w-80"></td>
<td></td>
</tr>
<tr class="g-h-n">
<td colspan="5">Keyboard Instruments</td>
</tr>
<tr class="g-h-n">
<td class="w-120">Instrument</td>
<td class="w-200">Fundamental</td>
<td class="w-100">Harmonics</td>
<td class="w-80">dB(SPL)</td>
<td>Notes</td>
<tr >
<td class="t-td1">Piano</td>
<td class="t-td2">A0 (28 Hz) to C8 (4,186 Hz or 4.1 kHz)</td>
<td class="t-td1"></td>
<td class="t-td2">60 - 100</td>
<td class="t-td1"></td>
</tr>
<tr >
<td class="t-td1">Organ</td>
<td class="t-td2">C0 (16 Hz) to A9 (7,040 kHz)</td>
<td class="t-td1"></td>
<td class="t-td2">35 - 110</td>
<td class="t-td1">some are said to be capable of C-1 (8 Hz)</td>
</tr>
<tr class="g-h-n">
<td colspan="5">Wind - without a reed</td>
</tr>
<tr class="g-h-n">
<td>Instrument</td>
<td>Fundamental</td>
<td>Harmonics</td>
<td>dB(SPL)</td>
<td>Notes</td>
</tr>
<tr >
<td class="t-td1">Concert Flute</td>
<td class="t-td2">C4 (262 Hz) to B6 (1,976 Hz)</td>
<td class="t-td1"></td>
<td class="t-td2"></td>
<td class="t-td1">Some start at B3 (247 Hz)</td>
</tr>
<tr >
<td class="t-td1">French Horn</td>
<td class="t-td2">A2 (110 Hz) to A5 (880 Hz)</td>
<td class="t-td1"></td>
<td class="t-td2"></td>
<td class="t-td1"></td>
</tr>
<tr >
<td class="t-td1">Picolo</td>
<td class="t-td2">C5 (523 Hz) to B7 (3,951 Hz)</td>
<td class="t-td1"></td>
<td class="t-td2"></td>
<td class="t-td1"></td>
</tr>
<tr>
<td class="t-td2" colspan="5">Trombone</td>
</tr>
<tr >
<td>Tenor</td>
<td class="t-td2">E2 (82 Hz) to D5 (587 Hz)</td>
<td class="t-td1"></td>
<td class="t-td2"></td>
<td class="t-td1">Exceptionally F5 (698 Hz). Bb fundamental, sometimes F.</td>
</tr>
<tr >
<td>Contrabass</td>
<td class="t-td2">E1 (41 Hz) to E4 (330 Hz)</td>
<td class="t-td1"></td>
<td class="t-td2"></td>
<td class="t-td1">F fundamental, sometimes Bb.</td>
</tr>
<tr >
<td>Bass</td>
<td class="t-td2">C1 (33 Hz) to C5 (523 Hz)</td>
<td class="t-td1"></td>
<td class="t-td2"></td>
<td class="t-td1">Can start around Bb0 (A#0 - 29Hz). Bb fundamental.</td>
</tr>
<tr >
<td class="t-td1">Trumpet</td>
<td class="t-td2">E3 (165 Hz) to B5 (988 Hz)</td>
<td class="t-td1"></td>
<td class="t-td2">55 - 95</td>
<td class="t-td1"></td>
</tr>
<tr >
<td class="t-td1">Tuba (Bass)</td>
<td class="t-td2">F1 (44 Hz) to F4 (349 Hz)</td>
<td class="t-td1"></td>
<td class="t-td2"></td>
<td class="t-td1">Many play around Bb0 (A#0 - 29Hz)</td>
</tr>
<tr class="g-h-n">
<td colspan="5">String Instruments</td>
</tr>
<tr class="g-h-n">
<td>Instrument</td>
<td>Fundamental</td>
<td>Harmonics</td>
<td>dB(SPL)</td>
<td>Notes</td>
</tr>
<tr >
<td class="t-td1">Violin</td>
<td class="t-td2">G3 (196 Hz) - G7 (3,136 Hz) (G-D-E-A) (or C8 (4,186 Hz?) </td>
<td class="t-td1">to 10 kHz</td>
<td class="t-td2">42 - 95</td>
<td class="t-td1"></td>
</tr>
<tr >
<td class="t-td1">Viola</td>
<td class="t-td2">C3 (315 Hz) - D6 (1,175 Hz)</td>
<td class="t-td1"></td>
<td class="t-td2"></td>
<td class="t-td1"></td>
</tr>
<tr >
<td class="t-td1">Cello</td>
<td class="t-td2">C2 (65 Hz) - B5 (988 Hz (C5))</td>
<td class="t-td1">to 8kHz</td>
<td class="t-td2"></td>
<td class="t-td1"></td>
</tr>
<tr >
<td class="t-td1">Double Bass</td>
<td class="t-td2">E1 (41 Hz) to B3 (247 Hz) </td>
<td class="t-td1"> 7kHz</td>
<td class="t-td2"></td>
<td class="t-td1"></td>
</tr>
<tr >
<td class="t-td1">Guitar (Acoustic)</td>
<td class="t-td2">E2 (82 Hz) to F6 (1,397 Hz)</td>
<td class="t-td1"></td>
<td class="t-td2"></td>
<td class="t-td1">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)</td>
</tr>
<tr >
<td class="t-td1">Guitar (Bass)</td>
<td class="t-td2">4 string E1 (41 Hz) to C4 (262 Hz).</td>
<td class="t-td1"> 15kHz.</td>
<td class="t-td2"></td>
<td class="t-td1">5 string Bass normally starts at B0 (31 Hz) but tops out at the same C4 value.</td>
</tr>
<tr >
<td class="t-td1">Guitar (Electric)</td>
<td class="t-td2">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)</td>
<td class="t-td1"></td>
<td class="t-td2">Unlimited!</td>
<td class="t-td1">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.</td>
</tr>
<tr>
<td colspan="5"><b>Note:</b> 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 <a href="sound.html#notes" class="t-db">timbre</a> 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.
</tr>
<tr class="g-h-n">
<td colspan="5">Percussion Instruments (things you hit)</td>
</tr>
<tr class="g-h-n">
<td>Instrument</td>
<td>Fundamental</td>
<td>Harmonics</td>
<td>dB(SPL)</td>
<td>Notes</td>
</tr>
<tr >
<td class="t-td1">Drums (Timpani)</td>
<td class="t-td2">90Hz - 180Hz</td>
<td class="t-td1"></td>
<td class="t-td2"></td>
<td class="t-td1"></td>
</tr>
<tr >
<td class="t-td1">Bass (Kick) Drum</td>
<td class="t-td2">60Hz - 100Hz</td>
<td class="t-td1"></td>
<td class="t-td2">35 - 115</td>
<td class="t-td1"></td>
</tr>
<tr >
<td class="t-td1">Snare Drum</td>
<td class="t-td2">120 Hz - 250 Hz</td>
<td class="t-td1"></td>
<td class="t-td2"></td>
<td class="t-td1"></td>
</tr>
<tr >
<td class="t-td1">Toms</td>
<td class="t-td2">60 Hz - 210 Hz</td>
<td class="t-td1"></td>
<td class="t-td2"></td>
<td class="t-td1"></td>
</tr>
<tr >
<td class="t-td1">Cymbal - Hi-hat</td>
<td class="t-td2">3 kHz - 5 kHz</td>
<td class="t-td1"></td>
<td class="t-td2">4 - 110</td>
<td class="t-td1"></td>
</tr>
<tr >
<td class="t-td1">Xylophone</td>
<td class="t-td2">700 Hz - 3.5 kHz</td>
<td class="t-td1"></td>
<td class="t-td2"></td>
<td class="t-td1"></td>
</tr>
<tr class="g-h-n">
<td colspan="5">Wind (Reed or Woodwind) Instruments</td>
</tr>
<tr class="g-h-n">
<td>Instrument</td>
<td>Fundamental</td>
<td>Harmonics</td>
<td>dB(SPL)</td>
<td>Notes</td>
</tr>
<tr >
<td class="t-td1">Bandoneon</td>
<td class="t-td2">Descant (right) side G3 (196 Hz) to A6 (1,750 Hz). Bass (left) side C3 (131 Hz) to A5# (932 Hz) </td>
<td class="t-td1"></td>
<td class="t-td2"></td>
<td class="t-td1"></td>
</tr>
<tr >
<td class="t-td1 w-120">Clarinet</td>
<td class="t-td2">E3 (165 Hz) to G6 (1,568 Hz)</td>
<td class="t-td1"></td>
<td class="t-td2"></td>
<td class="t-td1">C7 sometimes possible (2,093 Hz)</td>
</tr>
<tr>
<td class="t-td2" colspan="5">Saxophone</td>
</tr>
<tr >
<td>Tenor</td>
<td class="t-td2">G#2 (104 Hz) to E5 (659 Hz)</td>