More on harmonics

[AK]

Can anybody tell me the formula for working out the harmonics above the initial frequency for various waveforms?

If we work from A/440:

Sawtooth

Square

I'm not interested in a Pulse waveform as I'd imagine the pulse width may vary the complexities of the overtones?

So just those 2.

Also, I have been looking around and can't really find anything other than mathematical sums which I don't really want to be looking at. Simple mathematics I can cope with, laymens terms basically.

Am I right in thinking with an A/440hz sawtooth, the next harmonic would be 220hz above and half the amplitude? Ad infinitum? If so, how does this translate to say other notes, ie: a formula. Say my lowest note was E1 for example?

Also, just to complicate matters more, is there any relationship between any diatonic scale and the harmonic series of a sawtooth waveform? For example, say I created a sine wave for each of the harmonics in a sawtooth, would the frequencies of these start to go outside of 12tet?

Obviously I don't wish to create an infinite amount of sines but enough to give me an amount of playable frequencies.

So a formula for saw's and squares would be cool.

Thanks.

[Roqqert]

stop thinking and start making music

[AK]

I see you stopped thinking, right at the point where you posted that silly post.

[s.k.]

saw - fundamental frequency + itself ad infinitum
square - funamental frequency + 2times itself ad infinitum

if F - fundamental frequency,

SAW - F | 2xF | 3xF | 4xF ....

so if you have a 440Hz saw, first harmonic would be 880, not 660.


SQUARE - F | 3xF | 5xF | 7xF .... repeat with all odd numbers ad infinitum

[hydrogen]

I see you stopped thinking, right at the point where you posted that silly post.

touche'

[steevio]

saw - fundamental frequency + itself ad infinitum
square - funamental frequency + 2times itself ad infinitum

if F - fundamental frequency,

SAW - F | 2xF | 3xF | 4xF ....

so if you have a 440Hz saw, first harmonic would be 880, not 660.


SQUARE - F | 3xF | 5xF | 7xF .... repeat with all odd numbers ad infinitum

this sums it up perfectly.

in answer to your question about 12 tet, the only harmonics which conform to 12 tet, will be the octaves, the rest are all sharp or flat to some extent, the closest ones will be the perfect fifths (3rd, 6th, 12th, harmonic)
the ones which are along way off are the 7th, 11th, 13th and 14th harmonics, (as much as 49 cents out)

wiki 'harmonic series' for the details bro

[AK]

Many thanks s.k and steevio.

[simonb]

saw - fundamental frequency + itself ad infinitum
square - funamental frequency + 2times itself ad infinitum

if F - fundamental frequency,

SAW - F | 2xF | 3xF | 4xF ....

so if you have a 440Hz saw, first harmonic would be 880, not 660.


SQUARE - F | 3xF | 5xF | 7xF .... repeat with all odd numbers ad infinitum

This. Also the amplitudes of the harmonics are the original amplitude divided by the harmonic number.

i.e. amplitude of the fundamental is A, amplitude of the second harmonic is A/2, the third is A/3, and so on....