A theoretical question

[Alphacodex]

There is something about fundamentals, harmonics, and non-tonal / formant part I dont understand.

As I understand it, when the fundamental plays different base frequencies the even and odd harmonics of the particular sound move together with the fundamental while the relation between the harmonics and the fundamental always stays constant (so when the fundamental frequency is doubled all harmonic frequencies are doubled as well).

Then there are frequencies that are important for the sound of an instrument but the dont move with the fundamental, they always stay at the same frequency. Those are the atonal part or in case of a voice the formants, right?

Well then I assume there must be a third category of harmonic parts, that do move with the fundamental, but do not keep their relation, e.g. when the fundamental plays the double frequency that particular harmonic plays like 3-times the frequency of before, or any othe formula (e.g. new freq = (oldfreq * fundamental-factor * x) + y*fundamental-factor, or whatever)

Does this 3rd category even exist and is is relevant, for example for tonal / noise separation or pitch-shifting, or formant-manipulations??

Sorry it's very theoretical... I even don't know if anyone here can answer it at all...

Cheers,
Codex

[dmbaer]

I'll take a stab at answering at least part of what you're asking.

First, with respect to formants, it's basically just EQ. The mouth is somewhat of a resonant chamber that will amplify certain frequency ranges and attenuate others. If you send an audio tone through it (fundamental and overtones), those frequencies are in the signal, to be sure, but the formant resonance (EQ-ing essentially) will cause the ratios between fundamental and overtone levels to be altered.

As to the third question, think of ideal vs. real-life. Ideally (as in a Melda oscillator), the frequencies of overtones are exact multiples of the fundamental. For real-life sound sources, this is not necessarily so, and the same source (be it a saxophone or vocal chords) can have different pitch ranges that may exhibit differing "impurities". Furthermore, in real-life sounds, the phase of an overtone might change during the course of a "held" note. When an overtone changes phase, it actually (at least for a short time) changes frequency during the transition.

If you ever looked at the spectral playback mechanisms in Alchemy (boo!!! hiss!!!), you'd see this in spades. Furthermore, Alchemy used two different additive synthesis methods, one with sine waves (usually close to but not exactly at a precise multiple of the fundamental frequency) and noise with finely differentiated frequency ranges, to construct the total sound. Any mechanical sound component (e.g., the "thunk" of a piano key being struck) would mostly be produced with the noise synthesis component.

[werzel]

It sounds to me like you are describing three distinct things.

1. Source sound - Waveform. Constant frequencies / relationships (otherwise you change the waveform)
2. Cavities - Mouth or instrument shape, material, thickness, etc. (formants / tonal qualities of source)
3. Environment - Reverb. (spaces with / without buffers allow overtones to take over a sound sometimes)

I don't know if I oversimplified it, it is just how I pictured it.

[Alphacodex]

Ok, I I'll try to give it a second shot, to deconstruct what a sounds consists of:

1) Fundamental and Harmonics (both perfect and imperfect harmonics)
When I got you right in real life the harmonics are not always fixed multiples of the fundamental (due to phase shifts or other impurities over the frequency range). However they are still harmonics of the sound

2) Formants / Tones
So the formants are just harmonics that have been eq'd by the "vocal chamber" or by the body of the instrument (like the body of a guitar). I think I got that one.

3) Atonal / Noise parts
Then there are atonal parts, special noises that that particular instrument makes when being played. I assume those noises are (mostly?) independent of the movement of the fundamental. Regarding the human voise those noises might be air streaming over the teeth resulting in a "white-noise-ish" sound. (Sibilants for example)

To keep things as simple as possible, let's just talk about an absolutely dry signal, so only the direct sound and no reflections whatsoever. That rules out any form of echo or reverb.

That leads to two thoughts for me:
1) When the harmonics are not always perfect multiples of the fundamental, it must be very hard to split tonal and non-tonal parts of a waveform.
2) I wonder how a synth would sound that produces harmonics as a function of the fundamental, like

h(n) = (f * 2 * n) - (100Hz * n)

f = fundamental frequency
h(n) = harmonic frequency of number n
n = number of the harmonic (1 for the first harmonic, 2 for the second ...)



Is there any way in MXXX or other plugin to try such things?

[dmbaer]

Top part (1 thru 3) is a pretty accurate statement of the way things work, as far as I understand things, at least.

As to the bottom part, this gets into how things work "under the hood". Almost all kinds of processing of this nature is going to be done using FFTs. The resolution of frequency bins is dependent upon how many bins there are (resulting from how many digital sample points are in the data used to construct a single FFT mapping). The bins are not spaced logarithmically, like most frequency plots you see are on the X axis. Instead, the first bin is at fs/2 (fs is the sampling frequency) and higher frequency bins are centered at multiples of that number. Except at low frequencies, there are enough bins that frequency drift is essentially not lost. So, even for non-integral multiples of the fundamental frequency, the presence of that frequency shows up in the FFT.

I saw a video lecture on how a sound can be split into tonal (reconstructed with sine waves) and non-tonal (reconstructed from noise at various frequencies). I don't recall the precise details, but it went something like this: Capture a pure FFT at some resolution. Capture one at a different resolution. Subtract one from the other and what's left is what's used in the non-tonal part. To reconstruct the non-tonal part, construct the FFT but set the phase components to random values, which somehow results in noise. I don't claim to be able to sit down and write the code that could do this, but I'm trying to supply a very general response to the first question.

As to the other question, you probably want to put some kind of per-n scaling factor in the equation. With or without it, though, I don't believe there's currently anything in the Melda catalog that could do this for any value of n that's not trivially small.

Edit:

>the first bin is at fs/2 (fs is the sampling frequency)

Ahem ... make that fs/2*n

Edit:

OK, third times a charm ... lowest bin frequency is fs / N where N is the number of samples and fs is the sampling frequency. Actually, the lowest bin is bin 0 and that is the DC component. What we're talking about here is the lowest frequency of which all the other bin frequencies is an integral multiple.

[MeldaProduction]

Ok, so most have been said, just a new notes:

1) Fundamental + harmonics - these are often refered as "tonal" part, since they belong together anyways. Since their period is a multiply of the fundamental, they are always "in sync". Once you shift something, a "beating" may start happening. Generally these together just represent a signal - like all the sines, triangles, saws etc...

2) Formants are not really an EQ as people commented here. More like dynamic EQ. Imagine a guitar - hit a string, the string itself will resonate - you have the fundamental and harmonics. Then the formants are like a resonating modes - if you play the guitar in a tilled bathroom, some of the strings will just sound really amplified and vice versa. This is sort of like formants, but formants are inside the instrument - inside a guitar, drum, or vocal chord. Ever wonder why the guitar is so weirdly shaped? Well, there you have it, it creates many modes, which sort of defines the formants of the guitar. By changing the guitar size you'd in a way shift the formants up or down. Similar to vocals.

3) Transient / noisy stuff - again with the guitar - whenever you touch the string, various physical things happen for a short time, which you may call a transient. Then if you have say snare drum - the snares are again completely atonal stuff, but this time it is produced continually. Classic with drums is also various ringing caused by all the moving things that sort of better shouldn't be there, but you just need to connect all the parts of the drum somehow .


Alphacodex: Sure, just use multiple Oscillator FX control them by MIDI, transpose and shift each. I think it will generally sound dirtier.