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How is a motor program modified to better match goals? In Schmidt’s (Schmidt, 1975) account, as a motor program is run, information relating to instances of the action are stored:

• initial conditions (state of the body and its environment)

• parameters for the motor program, including force and timing information • sensory and kinaesthetic feedback

• the error between the feedback and the planned goal

The motor program is assumed to be a greater or lesser variation of an action which has already been learnt. A schema is the abstraction of a pattern of rules to generate a prototype. As a number of instances of the action have been

completed, a schema relating the four different elements given above begins to be abstracted from the stored sets of information. As enough sets of information are stored, and the motor response schema relating the different elements is refined, it becomes possible to successfully generalise the action to slightly changed initial conditions and goals, through the interpolation between parameter specifications. (Schmidt, 1975)

If we confine ourselves to specifying timing information – such as a pattern of temporal intervals which fills the tactus duration – the application of a schema becomes plausible. Assume that the goal is to fill the tactus duration with four evenly-spaced onsets, beginning on the beat, and ending with a fifth onset on the next beat. If entrainment to the current tempo has only recently been achieved and this is perhaps the first time we have played a note in this session (and perhaps we are not very expert), it may be that the motor program we call up is a little too fast. To repeat it correctly, we modify a parameter controlling overall speed, and play it again. Clearly, if we repeat that process many times (as people do when they practice a musical instrument) the speed of that particular program will become finely-tuned to the tempo of the tactus. A similar process would be applied if the intervals were perceived to be uneven when the motor program was executed. Changes are made offline and the program executed again.

Accurate feedback about the success of the executed program is essential for updating the schema. If the motor program is carried out without careful referencing of sensory feedback, the relations between the items of internally- stored information will begin to drift, and no longer specify achievement of the goal. This is a well-known phenomenon of music practice: careless practice is worse than no practice, and can led to deterioration of performance which it takes double the effort to correct. Conversely, precise knowledge of results can be used to refine the schema. The use of a MIDI sequencer to display the timing errors of a passage just played, for instance, leads to quick improvement.

2.4.3

Evidence for a different mechanism for timing below the

tactus level

A comparison of timing at the beat level with timing at the tatum level has been made by Shaffer et al (Shaffer et al., 1985) in timing data from performance by a concert pianist of Erik Satie’s Gnossienne No. 5. While the beat level is very slow (>1000msec), it is marked in the piece clearly and invariably by a bass note, alternating with a chord. The right hand plays a fluid melody, with groupings which (in notation) subdivide the beat evenly at different times into 4, 6, 7 and 8. At other times the RH has no onsets at all for two beats, or plays a variety of uneven rhythms. It was found that groups notated as comprising equal notes, were not in fact played evenly. If the duration of the beats depends on the sum of the durations of RH small notes, then the ratio of the variance of the sum of the intervals making up the beat to the sum of the variance of the intervals will be ≥1. It was found that the ratio was <1, indicating beat independently time from their sub-intervals, and sub-intervals constrained within the beats. The particular piano texture – a steady, even LH with fluidly-timed faster notes in the RH, is

characteristic of Chopin – whose instruction to keep the LH steady and vary the RH is well known to piano students. Examples of similar freedom in the RH and clock-controlled rhythm in the LH, were also found in performances of Chopin and Bach. (Shaffer, 1981) Shaffer (Shaffer, 1985) distinguishes between biological clocks and a less-precise temporal pattern generator which is triggered by a clock external to it.

An experiment in judgement and production of beat fractions, relative to an isochronous pulse shows a marked deterioration in accuracy for intervals <200msec. (Sternberg & Knoll, 1994) The poor judgement and production of single intervals in this region seems to reflect a lack of an interval timer, and compared to the ability of musicians at least to produce reasonably even intervals at that level if they are permitted to play all subdivision onsets seems to indicate that motor expression assists relative timing at this level.

While runs of small subdivisions of intervals below 200Hz are achieved eg. by many pianists, dividing the intervals in the tatum region into uneven parts appears to be more difficult, with mutual assimilation of longer intervals in rhythms, and the - sometimes unintentional - production of non-harmonic subdivisions of the clock period. (Repp, Windsor, & Desain, 2002) Friberg’s (Friberg & Sundström, 2002) analysis of jazz drummer’s swing ratios show that complex ratios (involving in this

case only two durations) can be reproduced consistently and accurately. Friberg (Friberg & Sundström, 2002) gives the range of ratios of the long note to the short note in jazz swing, at different tempi, as 1:1 to 3.5:1, while analysis of data for ten of the 16 different drummers given in Cholakis (Cholakis, 2003c) shows a variation between 1.5:1 to 2.7:1.

If concatenated, production of even intervals would be produced by an

(unconscious) revision of the motor program following a cognitive review of its evenness. The perception of evenness at this level of timing would relate to a direct comparison of the pattern’s component intervals to each other, rather than on asynchronies to a temporal grid produced by nested clocks.

Wright (Wright, 2002) notes that skilled drummers can control timing down to a single millisecond – when two drums are played together, such a small timing difference is heard as a timbre change, due to phase interference between the soundwaves produced by each drum. Such a level of control, combined with the non-simple ratios produced at sub-tactus timing levels, suggests a fast clock at ~1000Hz, with a counter mechanism.