Mix and oscillator amplitudes, more research

I just can't let this one go. The code appears to add a linear amount of the side oscillators to the sum, but Adam Szabo says differently - the center oscillator is attenuated and the outer ones follow a curved gain.

I just had a happy accident. I am trying to find the contribution of each oscillator to the total if one normalize the sum - saying the total should always be 1.

However, I only added one single outer oscillator - but the output was very interesting:

Here it is compared to the graph in the article:

 

Here, the value of oscillator 1 is 1 / (1 + mix), whereas the plot for the others is mix / (1 + mix). The plots are quite similar! It really makes me want to understand this even more!

But - if I assume that ALL 6 outer oscillators should be included in the normalization, everything breaks down, so clearly that's not correct.

Going back to the article, we have this graph (Figure 9):

Note that the amplitudes of 5, 6 and 7 are higher than 1, 2, 3.

In the text, Szabo says that 2, 3, 5, 6 and 7 are removed, leaving 1 and 4, as illustrated in the first graph.

I don't know if he DID measure those too, but there is a chance that they don't follow the exact same curve. We'll see if we can figure that one out.

Also, let's renumber the spikes in the plot to match the order in the detune_table:

[0, 318, -318, 1020, -1029, 1760, -1800], let's call them A-G to keep them separated

That gives us:

A = 4, B = 5, C = 3, D = 6, E = 2, F = 7, G = 1

In case it matters, what is called 1 here is actually the last element added in the summing in the ESP code. 

 

Now, I'm not entirely sure how to interpret Figure 9 in terms of "max wave amplitude". The spectrum has peaks of a certain width, not just a single frequency, and there are no units on the Y axis. If the scale is linear and one assumes that the amplitude of each wave in the result is actually propotional to the max value of the center oscillator, we get the numbers in the table (each pure frequency is a sine wave, so the highest peak would correspond to the root frequency of the saw waves, wouldn't it)?

It looks like that's what Szabo means that they are, so let's accept that.

If so, the sum of all amplitudes is definitely not 1. Could the perceived total "loudness" be equal if one uses dB instead of a linear scale? The total energy or something?  

And in any case, how does one go from the sum += saw[i] * mix to this thing?