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Re: maximum tatum (one tatum, two tata)

I think that there should be an agreement between the tatumites as to what
we are talking about. I presume the point of interest is perception, rather
than production. Sticking to piano, one further note (no pun intended) is
the enormous difficulty of achieving ensemble playing for two pianists,
whether on one piano or two, mainly because the slightest inattention will
result in "broken chords", i.e., in places when the two "were not
together". The glissando example was an easy metric for demonstrating just
how little successiveness between two temporally adjacent piano notes
sounds like two piani.

Psychoacoustically speaking, the spectral commonalities between successive
notes, due to onset spectral splatter, can be regarded as an insurance
that, when judging simultaneity or succession, the listener can use
envelope analysis within similar spectral bands and thereby gain maximum
precision (see Divenyi and Danner, P&P 1977, Divenyi and Sachs, P&P 1978).
That is, the same game works even for random-frequency notes, because there
is substantial energy in a given spectral band (there are several in piano
notes) for the listener to perform effective envelope judgments. If one
disregards the spectral splatter (say, by using sinusoidal tones with
gradual onsets and offsets), then the perceived time interval between
adjacent tones will be affected by the musical interval between them
(again, see the above references) and who knows at what time separations
the listener will hear two tones as successive. Thank heaven, there is
spectral splatter in the output of most musical instruments -- hence the
need for an orchestra conductor who is paid (mostly overpaid) to ensure
that entries are successive only when the score calls for such.


At 08:01 PM 4/9/2002 -0400, mercuri@GRADIENT.CIS.UPENN.EDU wrote:

I beg to differ with Pierre but there should be a difference
between predictive sounds (such as a glissando, or even Morse code)
and totally random onsets. One of your contributors mentioned multiple
sounds, and there too, there is a matter of attention (cocktail party
effect) and illusion (alternating octaves) where there has been some
research, although not terribly much in the way of discrete event
counting. Diana Deutsch's work is of note.

Rebecca Mercuri.