All the AI music I’ve heard so far has a really unpleasant resonant quality to it. Why is that? Can it be removed?
Audio spectrograms have two components: the magnitude and the phase. Most of the information and structure is in the magnitude spectrogram so neural nets generally only synthesize that. If you were to look at a phase spectrogram it looks completely random and neural nets have a very, very difficult time learning how to generate good phases.
When you go from a spectrogram to audio you need both the magnitudes and phases, but if the neural net only generates the magnitudes you have a problem. This is where the Griffin-Lim algorithm comes in. It tries to find a set of phases that works with the magnitudes so that you can generate the audio. It generally works pretty well, but tends to produce that sort of resonant artifact that you're noticing, especially when the magnitude spectrogram is synthesized (and therefore doesn't necessarily have a consistent set of phases).
There are other ways of using neural nets to synthesize the audio directly (Wavenet being the earliest big success), but they tend to be much more expensive than Griffin-Lim. Raw audio data is hard for neural nets to work with because the context size is so large.
The other place where phase is critical is in impulse sounds like drum beats. A short impulse is essentially just energy over a broad range of frequencies, but the phases have been chosen such that all the frequencies cancel each other out everywhere except for one short duration where they all add constructively. Without the right phases, these kinds of sounds get smeared out in time and sound sort of flat and muffled. The typing example on their demo page is actually a good example of this.
The simplest demonstration of it is the doppler shift. But it's not at all that simple because moving relative to the source the sound pressure and thus the perceived loudness also change, distorting the wave form, thereby introducing resonant frequencies. Now imagine that the transducer is always moving, eg. a plucked string.
The ideal harmonic pendulum swings periodically, only losing attenuation. But the resonant transducer picks up reflections of its own signal, like coupled pendulums, which are intractable according to the three body problem.
On top of that, our hearing is fine tuned to voices and qualities of noise.
When you take a window of samples of a signal, and run the FFT on it, for every frequency bin, the calculation determines what is the amplitude and phase of the signal. If you have a frequency bin whose center is 200 Hz, and there is a 200 Hz signal, then what you get for that frequency bin is a complex number. The complex number's magnitude ("modulus") is the amplitude of that signal, and its angle ("argument"d) is the phase.
If the signal is exactly 200 Hz, and if the successive FFT windows move by a multiple of 1/200th of a second, then the phase will be the same in succcessive FFT windows.
But suppose that the signal is actually 201 Hz: a little faster. Then with each successive FFT window, the phase will not line up any more with the previous window; it will advance a little bit. We will see a rotating complex value: same modulus, but the angle advancing.
From how fast the angle advances relative to the time step between FFT windows, we can deduce that we are capturing a 201 Hz signal in that bin (on the hypothesis that we have a pure, periodic signal in there).
How is the phase determined in the frequency bin? It's basically a vector correlation: a dot product. The samples are a vector which is dot-producted with a complex unit vector. The complex unit vector in the 200 Hz bin is essentially a 200 Hz sine and cosine wave, rolled into a single vector with the help of complex numbers. Sine and cosine are 90 degrees apart in phase, so they form a rectilinear basis (coordinate system). The calculation projects the signal, expressing it as a sum of the sine and cosine vectors. How much of one versus the other is the phase. A signal that is 100% correlated with the sine will have a phase angle of 0 degrees or possibly 180. If it correlates with the cosine component, it will be 90 or 270. Or some mixture thereof.
Because a complex number is two real numbers rolled into one, it simplifies the calculation: instead of doing a dot product with a sine and cosine vector to separately correlate the signal to the two coordinate bases, the complex numbers do it in one dot product operation. When we go around the unit circle, each position on the circle is cos(θ) + isin(θ). These complex values values give us samples of both functions. Exactly such values are stuffed into the rows of the DFT matrix: complex values from the unit circle divided into equal divisions.
If you look here at the definition of the ω (omega) parameter:
https://en.wikipedia.org/wiki/DFT_matrix
It is the N-th complex root of unity. But what that really means is that it is a 1/Nth step of the way around the unit cicrcle. For instance if N happened to be 360, then ω is the complex number whose |ω| = 1 (unit vector), and whose modulus is 1 degree: one degree around the circle. The second row of the DFT matrix has 1, ω, ω², ω³, ... the second row represents the lowest frequency (after zero, which is the first row). It captures a single cycle of a sine and cosine waveform, in N samples. The values in that row step around the unit circle in the smallest increment, so they go around the circle exactly once. The subsequent rows go around the circle in skipped steps, yielding higher frequencies: 1, ω², ω⁴ for twice around the circle; 1, ω³, ω⁶ for three times, ... we get all the harmonics up to our N resolution.
That pure sine wouldn't generate any artefacts. It would result in a 200Hz output from the AI if it throws the phase information out. You wouldn't hear a difference unless its an (aptly so called) complex signal. Eg. 200 and 201 Hz layered is an impure signal with a period below 1Hz, far outside the scope. Eventually the signals will cancel out completely. [1]
The important point is, I think, that FFT doesn't simply look at the offset aka phase. Rather, 201 Hz looks like a 200 Hz that is moving. So it encodes phase-shift in the delta of the offset between two windows. For a sum of 200 and 201 Hz it has to assume that the magnitude is also changing, which I find entirely counterintuitive.
From the mathematical perspective, this seems like a borring homework, far detached from accoustics. So, I don't know. The funny thing is that rotation is very real in the movement of strings. If the orbit in one point is elliptic, that's like two sinusoids at different magnitudes offset by some 90 degree, in a simplified model. But it has nearly infinite coupled points along its axis. As they exite each other, and each point has a different distance to the receiver, that's where phase shift happens.
> If you look here at the definition of the ω (omega) parameter
I wasn't going to make drone, but I will take a look.
1: https://graphtoy.com/?f1(x,t)=100*sin(x)&v1=true&f2(x,t)=100...
But the same thing could be done as a post-processing step, finding points where the spectrum is changing fast and resetting the phases to make a sharper transient.
Models which operate directly on the time domain have generally had a lot more success than models that operate on spectrograms. But because time-domain models essentially have to learn their own filterbank, they end up being larger and more expensive to train.
A neural vocoder such as Hifi-Gan [1] can convert spectra to audio - not just for voices. Spectral inversion works well for any audio domain signal. It's faster and produces much higher quality results.
It's definitely a useful approach as an early stage in a project since Griffin-Lim is so easy to implement. But I agree that these days there are other techniques that are as fast or faster and produce higher quality audio. They're just a lot more complicated to run than Griffin-Lim.
But the issue is not that the spectrogram is low quality.
The issue is that the spectrogram only contains the amplitude information. You also need phase information for generating audio from the spectogram
Looking back at image generation just a year or two ago and people would have said similar things.
Not hard to imagine the trajectory of synthesized audio taking a similar path.
> For every stunning example that gets passed around the internet, thousands of others sucked.
From personal experience this is simply untrue. I don't want to debate it because you seem to have strong feelings about the topic.
I don't feel strongly about this topic at all.
This iteration does, but that's an artifact of how it's being generated: small spectograms that mutate without emotional direction (by which I mean we expect things like chord changes and intervals in melodies that we associate with emotional expressions - elevator music also stays in the neutral zone by design).
I expect with some further work, someone could add a layer on top of this that could translate emotional expressions into harmonic and melodic direction for the spectrogram generator. But maybe that would also require more training to get the spectrogram generator to reliably produce results that followed those directions?
Prompting is an art and a science in its own right, not to speak of all the ways these tools can be strung together.
In any case, everything is a remix.
I don’t get the objection.
…implying there may be an art to AI art. Hmm.
Meanwhile, the degree to which it is off-puttingly hideous in general can be seen in the popularity of Midjourney — which is to observe millions of folks (of perhaps dubious aesthetic taste) find the results quite pleasing.