Just briefly... might just be me, but I've serious problems understanding your post! :) Guess I'll start from the top, why is the duration of a note relevant?

Because it tells us the frequency resolution of the signal. Sample length is just a other name for frequency resolution. The frequency resolution also means how closely the FFT bins are located on a spectrum analyzer (that's why it depends on the selected FFT size = sample size). Most FFT analyzers don't actually draw points though - just like waveform analyzers don't. But only points exist, no straight lines..

Very easy way to think about it, if you construct any signal out of sine waves, you can not have any waves in it that aren't complete sine waves (by definition). The lowest complete sine wave in a 1 second signal is obviously one second long (1hz) then the next one is half a second (2hz) and so on. So there is a limited frequency resolution that depends on the length of the signal.

I arbitrarily picked 1 second because it's hard to point out to a supersaw sound that is played for a longer duration than that.

You're confusing a lot of stuff. You're confusing everything, really.

Example: if you were to combine sine waves, you could produce nearly every timbre imaginable by simply combining them and changing their relative volumes. Actually, that's the theory behind Additive Synthesis.

With a standard (cd format) sample rate of 44.1 Khz, you have 44100 points within a second. A simple sine wave is made of several of these points, and they're not containers for wave cycles, they're just the audio equivalent of pixels if you will, the distance of them being so small that we humans can't pick the space between them, so it feels like a continuous stream instead of a vibrant fast tremolo of sorts - if you will, which is ultimately what it is.

FFT is a math algorithm to transform time and waveform into frequency, to help analyse a signal. The blocks you get to choose don't actually change anything relative to the audio, just the under-the-hood calculations involved in producing the analysis. You're not supposed to see points on a spectral analyser at all, you could expect to see them with an oscilloscope or an audio editor whose resolution allows you to zoom in to the actual points (and yes, they do exist for more then a decade now).

In case you're wondering, humans range of listening is said to be somewhere round 20Hz-20K, so what's the point of even mentioning a 1Hz sine wave? A second is nothing more then the scale we use to count cycles, that's all. How many times has it cycled within a second? That's the definition of Hertz.

How long you sustain a note bares absolutely no connection with any of the above. If I hold a 30Hz sine wave or a 200Hz one for one second, the only thing that's changing is that there's 30 cycles on the first example and 200 on the second.

If you're using detune, then it's natural - even desirable - that the harmonics of the various sawtooth waves get mashed together. That was intentional btw, since the whole point of doing this is to produce a much richer timbre. If you pick two sawtooth oscillators and detune the second one by a few cents, if there's no phase reset on note press and the oscillators are not hard synced, then you'll have beating, that's the perceivable difference between the cycling of the two waveforms - and in musical terms, it just sounds warmer and fatter. Same thing with a handful of saw waves on top of each other, thus the options you get: you get to detune them and pan them, producing larger then life sounds while you're at it.

I hardly doubt you could identify a difference of 1 cent on a blind test. most people would be delighted to pick semitones, that's even called perfect pitch ears - go figure!

Not really...

Exactly, that is the whole point of my analysis. But you are incorrect with the term "nearly". Any sample imaginable can be produced by combining sine waves, and that is exactly what the FFT does. Sine waves are synonymous with frequencies, as long as they are the length of the selected sample.

I didn't say the samples were containers for wave cycles - although if you think about it they actually are containers for the sinc function once put through the converters. This (the time domain) actually is a continuous wave in analog domain, not collection of fast points creating some illusion of continuous wave.

Anyway the sample points ARE containers for sine waves when the sample is converted into frequency domain via FFT, or other algo. The spectrum can't be continuous if the sample is not infinitely long, even in the analog domain. This is rather obvious if you read my last post.

I don't think I said that the block size that is chosen affects the audio, since FFT represents the signal exactly, that is absurd. The fact however is that it will affect the results of the FFT and you can't have, for example a 1.5hz frequency on a 1 second signal (that would be FFT size of 48000 with 48khz sample rate). The frequency domain can't be continuous unless the time of the sample is infinite, and this has nothing to do with digital resolution.


The point is that the 1hz is the frequency resolution, and from that a case can be made on how many saw waves are optimal. I don't understand where you are going with this...

Did I somewhere imply the above is not the case? You are wrong that this has nothing to do with what I said. It has everything to do with synthesizing waves which require long time (high frequency resolution) such as supersaws. By the way, try holding a 30.5hz sine wave for one second - you will win a nobel if you pull that off.

I think you completely missed my point. By mashing harmonics together I meant that they are located on top of each other, meaning that when the phase is random they are going to vary in amplitude and sometimes disappear. Just try playing two hypersaws or whatever in unison with exactly the same detune parameters - it will sound subjectively bad - this is what I am talking about.

You are correct, but even a monkey could tell the difference when there are other waves involved, try detuning an osc against a other by 1 cent. We are not talking about an isolated wave here.

That's 30 entire cycles and a half. What else would you expect? Besides an audible audio click 'cause the audio cuts on a non zero cross point, right?

So I guess I'm entitled for the Nobel Prize now.

You are indeed confusing a lot of stuff m8. 30.5Hz means exactly that, just that and nothing but that.

I may have come across as being excessively rude with you. But there's no nice way of saying this: you've overloaded your mind with theory that you don't fully understand and you've managed to loose perspective while at it.

Sample rate is to audio what pixels are to image. Think of it this way: there's a threshold to human perception that kind of defines how far we need to go in terms of resolution. That's how we arrived at the standards. That's why some recent Apple equipment is claiming to have hit that threshold with their "retina" monitors - they're claiming that the human eye can't possibly perceive a point with such resolutions.

With audio it's not much different. A point is just a point. It only carries volume information and phase position (time). That's it. Even if you were to create a sine wave with the same exact frequency of your sample rate, that cycle would fall between the points and there's nothing there to hold the information. So if you were to double the sample rate and keep that frequency, then you'd have something akin to an extreme bit crushed sine wave, which would look more like a square wave due to technical limitations.

But one of them is band limits. You can't even produce such wave on the digital realm (and you'd have a hard time producing it anywhere else...). And if you could, it wouldn't even matter, at least for humans, due to the limits of our perception as I explained above.

But I still fail to grasp why you'd think of all this things when confronted with a fairly simple sound design endeavour such as a super saw kind of oscillator. I think they came to be with the Roland JP series (not sure, but think that's correct) and it was precisely the detuned mess (if you will) that gave this sound its famous thickness and the power to cut through any mix you through it at. Right? So if you were to not use detune, the saws would just be tuned together and hard synced, so only volume would rise, the moment you start detuning them, you'll get a much richer tone, filled with beating - again due to different phases, due to different wave cycle lengths - and some phase cancelation as well.

Again, I fail to see where the problem is with any of this.

This post is completely wrong. A 30.5hz sine wave in a 1 second window is an impossibility because it can't be a complete sine wave, it is cut off. This means it is composed of many different sine waves. Read about spectral leakage.

Further, ALL sine waves are going to have a click at the start, because it is actually impossible for us to hear a real sine wave, since our hearing does not function like a FFT.

Hey, no problem, I don't have any problems with criticism. That's what figuring out the best configuration is all about. Also, I would like to point out that nowhere did I say that my approach to this is the only usable one.

No, the sample rates defines the audio bandwidth and how much aliasing there is going to be, I am not sure if that's what you are trying to say. However, it sure sounds like you actually think that those points are what is coming out of the converters. Picture reproduction works very differently than audio. Our eyes work completely differently than our ears.

I don't understand what this has to do with anything I said. Doubling the sample rate, if done properly would not create a square wave, but estimate the position of the actual analog waveform by low pass filtering and computing the results. When those points enter the analog domain they are convolved with a sinc function which will produce a continuous bandwidth limited analog waveform.

I have no idea what you are talking about here. There is nothing impossible about creating 30.5hz sine waves in digital domain, or wave of any frequency that is not above the sample rate (although that is possible as well actually), or very tightly detuned supersaws. However, it's impossible for a 30.5hz sine wave to exist in a one second time frame.

There is no complete phase cancellation if the saw waves are tuned to different frequencies. Further, you are assuming an oscillator that magically hard syncs when many waves are on top of each other. Try it without the hard syncing and you will definitely hear the extremely weak sound.

You are correct, however about the JP8000s supersaw sounding excellent.

https://www.youtube.com/watch?v=bI2URDbI9I0

check this out! ;)

I think Access has done a wonderful job at recreating this oscillator, but you be the judge now. As far as I can tell, you don't even need hardware these days to recreate similar sounds, like Diva for instance.

You misunderstood big chunks of my earlier post, but it doesn't really matter much. Amidst all this, I still don't know what you're looking for or having trouble doing or if you're just a technical oriented person obsessed with technology's limitations (?)... So, what is it you're trying to do?