These 11 stimuli are the sum of 15 sine-wave overtones, with two peaks created by convolving a hamming window with a sawtooth whose baseline is always 120 Hz, and whose first peoak is always 169.34 Hz. The second peaks are at
[153.06 156.19 159.38 162.63 165.96 169.34 172.80 176.33 179.93 183.61 187.36] Hz,
so that in stimulus #6 the two points are actually equal:

There are four spectral-balance conditions:

1. (A) Overtone amplitude decreases as 1/N, to a point 15 dB down from the fundamental (See figure below).
2. (B) Overtone amplitude is constant.
3. (C) The first part is from condition (A), and the second part is from condition (B), with a 200-msec transition region in the middle.
4. (D) The first part is from condition (B), and the second part is from condition (A), with a 200-msec transitional region in the middle.

You can listen to results here:

 Parameters Stimulus (A) Stimulus (B) Stimulus (C) Stimulus (D) 1: 169.34 120 153.06 2: 169.34 120 156.19 3: 169.34 120 159.38 4: 169.34 120 162.63 5: 169.34 120 165.96 6: 169.34 120 169.34 7: 169.34 120 172.80 8: 169.34 120 176.33 9: 169.34 120 179.93 10: 169.34 120 183.61 11: 169.34 120 187.36

Prediction: If we do a forced-choice "Second peak is higher/lower" task, the identification function will be shifted in case (C) relative to case (A) (and maybe relative to case (B), I'm not sure), so that the peak with more high-frequency energy sounds higher.

Similarly, the case (D)( where the first peak has more high-frequency energy) should shift the ID function in the opposite direction.

Update: And it does! (Mean of ~50 subjects)

Except that the spectral quality of the second peak seems to have a really strong effect in and of itself -- perhaps listeners expect a sort of "final lowering" of spectral balance?

Post hoc analysis divided the subjects into 7 who attended exclusively to fundanmental frequency:

8 subjects who attended almost completely to timbre:

And 40 subjects whose responses were a mixture of both: