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Re: Loudness of complex tones

In reply to Bruno Repp's inquiry:

> > >         I am just completing a small experiment that demonstrates that
> > > lower-pitched piano tones are perceived as louder than higher-pitched
> > > matched for peak rms sound level. (The opposite would be true for pure
> > > in the same fundamental frequency range, below 1000 Hz.)
> > > I suspect that is so because of the larger number of harmonics and energy
> > > in a larger number of critical bands when the fundamental frequency is low
> > > rather than high.

Yes, this is probably the main effect. A possible additional effect is that
the spectral envelope of lower-frequency tones tends to be flatter (less
average falloff in dB/oct).

> > > I am not very up-to-date on the literature concerning
> > > loudness perception and have encountered hardly any papers on the loudness
> > > of complex tones, on realistic instrument tones in particular. Can anyone
> > > me in the right direction?

Miskiewicz, A., & Rakowski, A. (1992). Music vs noise: A comparison of
loudness estimates. Archives of Acoustics, 17, 2, 203-216.

M&R found that loudness of musical instruments depends on their spectral
distribution in much the same way as does loudness of noise. One can thus
apply Zwicker's concept of adding loudness across critical bands in much the
same way as you would do for a steady-state noise. However, the result is not
necessarily valid for sounds that change rapidly with time.

Miskiewicz has a more recent paper on a similar topic whose publication may
be imminent in JASA.

> > > Is my result obvious from what is known about
> > > the loudness of complex harmonic tones? Has anyone predicted or shown that
> > > such tones get louder as you lower their fundamental?

Predicted but not directly shown, to my knowledge. R&K asked musicians to
perform at given dynamic levels (pp, mf, ff) and the resultant loudnesses
were more or less independent of pitch, as might be expected if the
musicians were adjusting loudness by ear.

 Richard Parncutt
 Keele University