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Re: maximum tatum (one tatum, two tata)
> If there are other, better definitions of the tatum, I'd be
> interested to learn about them.
I ran into the Tatum concept in Jarno Seppanen's recent paper "Tatum
Grid Analysis of Musical Signals" (2001 IEEE WASPAA, pp. 131-134).
Seppanen says that "The term tatum grid refers to the train of pulses
on the lowest meterical level, and the term tatum refers to the period
of the lowest-level pulse, i.e., the shortest notes present." In this
regard, he references a paper by Jeff A. Bilmes ("Techniques to foster
drum machine expressivity", Proc. 1993 Int. Comp. Music. Conf., ICMA,
San Francisco, pp. 276- 283). He doesn't reference Vijay Iyer.
I happen to have a copy of that proceedings, so I looked up Bilmes's
paper. Interesting that he references your 1990 JASA paper, among
others. He also references his 1992 ICMC paper ("A Model for Musical
Rhythm", pp. 207-210), but it is clear that he coined the term "tatum"
in the 1993 paper. In it he says
"When we listen to or perform music, we often perceive a high
frequency pulse, frequently a binary, trinary, or quaternary
subdivision of the musical tactus [i.e., beat]. What does it mean to
perceive this pulse, or, as I will call it, *tatum*."
Then, in a footnote, upon the suggestion of Barry Vercoe to call it
"temporal atom" or "tatom", Bilmes says "in honor of Art Tatum [the
jazz drummer], whose tatum was faster than all others, I chose the
PS The  are my inserts.