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The Covert Clock Theory posits a covert clock at a cross-rhythm to the tactus as an alternative reference which distorts tatum timing positions. If the covert clock theory is applied to a macroperiod comprising four beats of four tatums each, the microtiming deviations produced should fall within the range of microtiming deviations found in successive iterations of the Funky Drummer break.

A cross-rhythm of three against a four-tactus macroperiod is commonly found in African traditional music (Arom, 1991), and funk is one of the musics of the African

diaspora (Pressing, 2002).”For the Funky Drummer break, it was assumed a covert clock dividing the macroperiod into three equal durations was active. The 3/4 clock would fall on tatum 1-1, 345msec after the second tactus pulse at 2-1 (49msec after the nominal time of tatum 2-2), and 395msec after the third tactus pulse at 3-1 (99msec before tatum 3-4). One way of reconciling the tactus clock with the covert clock would be to generate a motor plan for the first five tatums in the bar which would spread them evenly between the macroperiod start and the covertclock pulse at 2-2 The five tatums would be payed a little more slowly than usual, and a positive deviation would progressively result. Tatum 2-2 itself would then be triggered by the covert clock pulse and the next motor program would fit the six tatum onsets from 2-2 to 3-3 evenly into the duration until the third covert clock pulse, with tatum 3-1

coinciding with the third (main) tactus pulse. Tatum 3-4 would be triggered early by the third covert clock pulse and the remaining the five remaining tatums beginning with 3-4 would be spread evenly over the remaining duration of the macroperiod. The result is shown graphically in Figure 5-3, with an absolute swing value of 12msec added to every even-numbered tatum deviation.

The ratio of mean squared error between the prediction of this application of the model – with 100% shift towards covert clock trigger times - and the actual deviations of the 8-bar Funky Drummer break, was calculated at 2.54. Despite the high error, visual inspection of the deviations produced by locking the motor program triggers directly to the covert clock (see Figure 5-3 shows that deviations produced do share some features with the actual deviations, most notably the peak at tatum 2-2, which is found in all iterations of the break.

However, the Covert Clock theory does not predict that motor program trigger times will be shifted to coincide exactly with covert clock onsets. Rather, the space between the tactus clock onset and the covert clock onset becomes a free temporal space in which the musician can flexibly choose to place the motor program trigger. If the model deviations are scaled by a factor of 0.5 – which corresponds to placing the trigger at the midway point between the tactus clock onset and the covert clock onset - the deviations show close agreement with the first 7 tatum deviations (up to and including the peak at 2-2). With the Covert Clock model scaled to 0.5, 13 of the 16 tatum deviations of the model fall within the range of actual deviations in successive iterations of the Funky Drummer break.

Deviations generated by 3/4 covert clock -0.080 -0.060 -0.040 -0.020 0.000 0.020 0.040 0.060 0.080 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 tatums seconds

Model Mean of actual deviations .5 Scaled model

Figure 5-3 Deviations generated by a covert 3/4 clock against a 4/4 tactus with 16th tatums (see text).

After the peak at 2-2, the two sets diverge. The actual deviations are grouped closely around this peak, within 12msec of each other. After 2-2, the data for the different bars show much less agreement with each other, as well as with the model, although they do have a general trend to the positive (as shown by the mean), in contrast to the model. The furthest the 0.5 model is from the range of actual deviations is at tatum 3- 4, where the 0.5 model give a deviation of –19msec, while the lowest actual deviation is +4msec.

The model also shows points of agreement within individual iterations of the performed break. Bars 1 and 6 both show a steep dive from 2-4 (+18msec and +36msec

respectively) to 3-1 (-16msec and –1msec, respectively) at 3-1, the same position that the 0.5 scaled model drops from 14msec to 0msec to coincide with the third pulse from the main tactus clock. Bars 2, 5, 7 and 8 of the actual deviations all have local minima at 3-3, for bar 2 it is a global minimum, and for bars 2 and 8 it is below zero. At this position the .5 scaled model falls to –16msec, although its global minimum comes two tatums later at –20msec. Overall, there seems to be a tendency for deviations in successive bars of the Funky Drummer to stabilise the mean deviation, usually at a positive level, towards the end of beat 3, sometimes after rebounding from a local – or global – minimum. From 3-3 in the actual deviations a pattern of oscillation gradually sets in and amplifies to some extent by 4-2.

The minimum for the whole data set at 4-1 in Bar 8 appears to be an anomaly, perhaps caused by Brown rushing the count as he cues the rest of the band to re- enter. The almost flat deviation curve for Bar 8 1-2 to 2-3 – but remarkably, topping the next-highest deviation at 2-2 by only 1msec – follows the oscillation in Bar 7 around a similar positive value, which is the positive boundary of the data set from Bar 7 2-4 to 4-4. Bar 8 is then the positive boundary for the whole set from 1-2 to 2-3, and contains the most extreme deviation of the set at 4-1, the last tactus beat before the band re- enters. The microtiming strategy from Bar 7 2-4 to the end of Bar 8 appears to be a mix of the previously-applied deviation pattern (Bar 7 follows the slope of the mean closely from 2-4 to 4-4) and a push to extremes, possibly as a structural marker for the close of the 8-bar antecedent-consequent group. Structural markers are also provided in the form of the snare drum stick-bounce effects in Bar 4 beat 3 and Bar 8 beat 3. Overall, the 3/4 covert clock model, scaled at 0.5, provides a good fit for the data from the 1-1 to the 2-3 positions, after which the data diverges widely within itself although still displaying similarity in some features, these necessarily located at the same tatum position in each iteration. The pattern of close fit to the model, up to the same point in

each bar, followed by variation, suggests a repeated strategy of utilising the covert 3/4 clock for each bar up tatum 2-3 and then allowing some freedom for the rest of the bar, with a tendency to be behind the beat rather than ahead. This characteristic is consistent with a strategy of stretching the first beat by reference to the covert clock or cross rhythm and following a trend back towards zero deviation afterwards – perhaps loosely referencing the underlying tactus but without constraining the beginning of motor programs until the start of the next macroperiod.

If the function of microtiming is at least in part to break down the clear sense of tactus in favour of both motor-level timed tatum groupings and the containing macroperiod, the strategy described in the preceding paragraph would be effective. The deviation timing pattern is combined with a corresponding kit rhythm pattern which could be designed to reinforce clear timing in the first half of the macroperiod and undermine it in the second half. Apart from constant 16ths on the hi hat, tatums 1-1 to 2-1 in every bar consist of two kick drum hits (on 1-1 and 1-3) and one snare drum hit (on 2-1); this very regular and clearly-marked pattern is immediately followed for the rest of the macroperiod in each iteration by a much busier, less regular and less distinct pattern of off-beat snare hits (played softer than the backbeat), plus variable kick drum placement.