Measuring the Coherence Threshold
Metronome designers have done what most good engineers do when specifying systems for human use. They have built in a little slack. If the exit ramp states that 25 mph is a safe speed, you can probably do it at 35 mph without losing control. 40 bpm is safe but it is a little conservative. The actual note spacing is a little wider than 1.5 seconds for music to lose its coherence. The following experiment illustrates how I measured the coherence threshold using a straightforward method of adjustment.
The web is full of midi files that can be imported into a sequencer such as Cubase. My lab assistant picked out 24 songs that would be highly familiar to University of Texas undergraduates. Dancing Queen, Sweet Dreams, and Money for Nothing gives an idea of the songs we used – familiar top 40 tunes. Sections of each song were imported into Cubase and the participants listened to them while they adjusted the tempo. Their instructions were to pick a tempo at which the song began to become difficult to recognize – where the notes started to separate into islands. If you have used Cubase, you will recall that the tempo can be controlled by the mouse. This is what the participants did. They just moved the mouse until the music stopped sounding like music to them. The experimenter then wrote down the tempo they selected. Each participant judged each of the 24 songs 4 times. Their averaged data is shown in the adjacent graph.
On the x-axis I have plotted the average number of notes per beat. Most of the songs have a few eight notes and some have passages with sixteenths. From the graph you can see that the average top-40 pop song has about 1.5 notes per beat being largely comprised of quarter and eight notes. The y-axis is tempo and is the variable that the participants adjusted. Tempo here is measured as seconds per beat rather than as beats per minute. The principal finding from this experiment is that all of the songs scatter around a common line. The slope of this line is 1.9 seconds per note and it gives the overall spacing at which songs lose their musical coherence. For music made up of quarter notes this corresponds to a tempo of roughly 30 bpm.
