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...

Contents

Musical Notes by Frequency
Frequency Ranges of Things
Contributed Frequency, Harmonics and Under Tones Table
Loudness and Sound Power
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 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.

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) = 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 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.

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.

Problems, comments, suggestions, corrections (including broken links) or something to add? Please take the time from a busy life to 'mail us' (at top of screen), the webmaster (below) or info-support at zytrax. You will have a warm inner glow for the rest of the day.