Last week we discussed some of the inherent problems with sub-bass frequencies and how to deal with them.  One of the major issues is how sounds in that bandwidth lack specificity.  One instrument’s rumble, boom, and thud sound pretty similar to any other instrument’s.  For the frequency bands above the sub, we have to start talking about fundamentals, overtones, harmonics, and formants in order to properly appreciate some of the roles each portion of the audible spectrum plays in our interpretation of sound.

Since most of our clients and readers deal at least some of the time in the digital domain, chances are you’ve seen a complex waveform that looks something like this:

In simple terms, waveforms of this type are the summation of various component frequencies.  In the illustration below, you see how a simple sine wave becomes more complex by the addition of harmonics:

The waveform starts with the fundamental frequency.  This is the lowest frequency present in the waveform that falls within the harmonic series.  When you play the 440 Hz A on the piano, 440 is really just the frequency of the fundamental, not the only frequency present.  Other frequencies are created when you play notes on almost any instrument in any environment—these additional frequencies beyond the fundamental are what help us distinguish one instrument from another.  Those that are above the fundamental are called overtones or upper partials.  Overtones that are integer multiples of the fundamental are called harmonics.

There can also be lower partials or undertones, though these are slightly less common.  And there are also sub-harmonics which follow the pattern of (1/x)(fundamental).  That is to say ½(440 Hz), ¼(440 Hz), etc.

Existing both above and below the fundamental are things called formants, which are acoustical resonances that, on an instrument, will sound no matter what.  For a violin, one formant of the instrument is a frequency whose nodes lie on opposite ends of the length of the violin.  Any vibration from any note stimulates the violin body itself to resonate and the aforementioned frequency sounds as well.

Formants and overtones are some of the things that allow us to distinguish a 440 A on the piano from a 440 A on a synthesizer, a singer, a violin, or a drum.  The also help us separate a Yamaha from a Stradivarius.

So if I were to hit that 440 Hz A on a piano, I would generate several frequencies:  the fundamental at 440 Hz; harmonics at 880, 1320, 1760, etc.; as well as whatever formants are present in that specific instrument.

The ratio of these frequencies relative to each other is what makes a characteristic sound.  So for instance, a guitar with nickel wound strings might sound that very same 440 Hz A and but have more emphasis on odd numbered harmonics whereas a guitar with nylon strings might hit that same 440 Hz A and have more emphasis on the even numbered harmonics.  Similarly, the nickel-stringed guitar might have a formant at 900 Hz and the nylon might have a formant at 4200 Hz.

You can see that when dealing with overtones and formants, you can very quickly span the entire audio spectrum.  That’s why if you get yourself a spectrum analyzer or even some of the nice plugin digital EQs out there, you’ll see that hitting any note on any instrument produces many more frequencies than that of the fundamental note you hit. 

When we talk about treating the bass, mid, and upper frequency bands over the next few weeks, you’ll see how important overtones and formants are to audio perception.

More from Phil’s Audible Spectrum series:

• The Audible Spectrum, Part 1: Introduction
• The Audible Spectrum, Part 2: Capture and Reproduction Limitations
• The Audible Spectrum, Part 3: Components
• The Audible Spectrum, Part 4: Sub-Bass Issues