Harmonics

Fundamental Pitch and Accompanying Harmonies

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When you hear a note on the piano or a string on the guitar, you are actually taking in many notes layered over one another.

The image reveals what happens when you hit a C3 on a piano. You can see there are subsequent "noise spikes" at C4, G4, C5, E5, and so on- these are all harmonic overtones of the C3 fundamental note.*

(If you want to count the notes to double check, the octaves in this graph have 11 lines in between them, with each line representing a half-step on the piano)*More technical explanation at bottom of this page

Harmonics have really interesting applications in the world of vocal music. Above is a linked YouTube video of someone performing overtone singing, utilizing harmonic overtones while maintaining a fundamental note.

(See 0:27 to 0:51 for the example)

The Subharmonic Register

Subharmonic bass, sometimes called throat singing, is a vocal technique that lets you sing really, really low. To the right is a guy who has mastered this technique.

Chest A2 Spectrogram

See the video explanation below

Subharmonic A1 Spectrogram

See the video explanation below

From a Hertz perspective, going up an octave means doubling a note's frequency. (A3 = 220 Hz, A4 = 440 Hz)

As such, these harmonic overtones are really just the fundamental pitch being multiplied by 2, 3, 4, etc.

Spectrogram Analysis.mp4

Link to video

Pictured: A fundamental pitch with harmonic overtones. The second harmonic/first overtone is double the fundamental, the third harmonic/second overtone is triple
the fundamental, and so on.

Harmonic Overtones (cont.)

The technical distinction between harmonic overtones and non-harmonic overtones lies within what multiple the overtone wave is of the fundamental pitch. Any overtone vibrating at an integer multiple of the fundamental is harmonic, while all other overtones are non-harmonic.

A wave vibrating at a multiple simply has a shorter wave-length than the original fundamental pitch. For example, The first harmonic overtone has half the wavelength of the fundamental pitch, and thus has double the frequency of the fundamental pitch (i.e. one octave higher).

Non-harmonic overtones

Things like instruments, human vocal chords, and cylindrical containers naturally create harmonic overtones when they resonate. However, sound travelling through mediums besides air or oddly shaped containers also creates sound waves with non-integer multiples. Cymbals, with their 3-D disc shape, produce non-harmonic overtones.

Overtones and

Harmonic Interference

When a fundamental pitch interferes with a harmonic overtone (i.e. a wave with an integer multiple amplitude), the resultant wave still has the same pitch as the fundamental. As shown in the image above, adding the harmonic overtone to the fundamental pitch doesn't change its overall frequency (i.e. wavelength), but it does change the wave shape. This change in wave shape is responsible for the different tone qualities in different instruments, among other things.

Fundamental Pitch

Non-harmonic Interference

When a fundamental pitch interacts with a non-harmonic overtone, it is wildly distorted. The crests and troughs of the non-harmonic don't line up with the fundamental wave at all, which completely modifies both the wave shape and frequency. Pictured above, the fundamental (black) and non-harmonic (red) create a resultant pitch (green) with no clear wavelength or amplitude.

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