Whips

Usage examples of beats.

Regular Beat Assumption: that the occurrence of regular beat in music relates to the importance of regular beats from some other source or sources.

I found that the hierarchical nature of musical time is a consequence of the constraint that musical rhythm should contain multiple regular beats, so there is no need to make specific assumptions about the existence and perception of hierarchy just to explain this feature of musical time.

Each of the 4 beats in a bar has an implicit intensity: beat 1 is the strongest, beat 3 is the next strongest and beats 2 and 4 are the weakest and similar to each other.

The time within beats can be further divided up into smaller portions.

The smallest duration of time such that all notes in a tune can be placed on regular beats separated by that duration defines the finest division of time that occurs within that tune, and in most cases is equal to the shortest note length occurring in the tune.

That famous dance the waltz requires music that is 3 beats to the bar.

Music can also be found that is 6, 9 or 12 beats to the bar, in which the beats on the bars are interpreted as 2 groups of 3 beats, 3 groups of 3 beats or 2 groups of 2 groups of 3 beats respectively.

In these cases the groups of beats may be grouped into uneven halves, e.

Normally the unit of time is minutes, so tempo is given as beats per minute.

For example, if we program a drum machine to emit beats at a particular regular interval, we can detect the regularity of the beat, and are sensitive to any errors or changes in the timing.

If we further program the machine to randomly omit a certain portion of the beats, we can still detect changes or errors in the underlying regular beat.

However, given that the frequency of regular beats is much lower than the frequency that neurons can fire at, it may not be absolutely necessary for neurons representing beats to fire at the exact millisecond the beat occurs: it may, for example, be sufficient to represent a beat by a short burst of firings, in which case the number of firings in the burst represents the perceived intensity of the beat.

A slower version of the same rhythm might consist of beats at times 0, 1.

If three beats occur, say X, Y and Z, with Y occurring halfway between X and Z, and one neuron A responds to the durations X to Y and Y to Z, and another neuron B responds to the duration from X to Z, then we can determine that the ratio between the duration periods of neurons A and B is 1:2.

That there should be an identifiable chord for each bar, and the notes in the bar should relate to this identifiable chord: the notes on the main beats should almost always be members of the chord.