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Re: maximum tatum (one tatum, two tata)

At 12:52 10/04/02 -0700, Bruno Repp wrote:
>A variety of phenomena have been mentioned in connection with the
>"tatum", but has anyone given a clear definition of the tatum? Who
>coined that term in the first place? I have encountered it only once
>previously, in Vijay Iyer's dissertation. Is he the inventor of the
>Brian Whitman, in the original message leading to this discussion,
>referred to "the maximum amount of discrete musical events a person
>can identify in a second". One needs to ask: What kinds of musical
>events? Identify in what way?
>I would like to argue that the minimal tatum be defined as the
>inter-onset interval between successive identical sounds in an
>isochronous sequence at which it becomes impossible to reliably
>synchronize an action (such as a finger tap) with any single event or
>with periodically recurring events in the sequence (e.g., every
>fourth event). This is the limit that was investigated by Bartlett &
>Bartlett (1959) and more recently by me, and which seems to be around
>100 ms for musically trained (but not highly expert) participants.
>This limit may be different in realistic musical sequences, where
>higher-order periodicities, auditory streaming, pitch contours, and
>other factors may play a role. Also, experts such as professional
>percussionists perhaps could go a tiny bit faster.
>If there are other, better definitions of the tatum, I'd be
>interested to learn about them.

I think it was Jeff Bilmes in his Masters Dissertation, Vijay gives this
impression in his at least:

"Bilmes (1993) has developed a tripartite model for expressive timing in
performance of groove-based music. In addition to the salient
moderate-tempo pulse or tactus, another important pulse cycle is defined at
the finest temporal resolution relevant to a given piece of music. It is
called the temporal atom or tatum (in homage to the great African-American
improvising pianist, Art Tatum), the smallest cognitively meaningful
subdivision of the main beat. Multiple tatum rates may be active
simultaneously, particularly in ensemble performance. In Western notation,
tatums may correspond typically to sixteenth-notes or triplets, though they
may vary over the course of a performance. As noted above, groove-based
music is characterized in part by focused attentiveness to events at this
fine level. The tactus and the tatum provide at least two distinct clocks
for rhythmic synchronization and communication among musicians. "

This definition is consistent with yours above (as well as the period -
Tactus range as 300 - 800ms and the Tatum 80 - 150ms) although these
definitions primarily reflect expressive rhytyhm perception not event
perception/gap detection, which seeems more relevant to some of the
previous posts on the topic.


>Bruno H. Repp
>Senior Research Scientist
>Haskins Laboratories
>270 Crown Street
>New Haven, CT 06511-6695
>Tel. (203) 865-6163, ext. 236
>FAX (203) 865-8963
>e-mail: repp@haskins.yale.edu