Timetables and music: An attempt at synthesis

Planning timed transfer public transport networks, composing music and designing piston-based engines are very different fields. However they are all based on repetition, based on pulses, beats or cycles.

At least in the cases of transport and music, where I think the parallels are strongest, it is quite possible for a system to have multiple beats.

Music for instance may have a series of regular pulses to form a beat (possibly played by percussion). Superimposed on these may be contributions from string or wind instruments that together form the music. Two similar instruments add a ‘body’ not discernible with one, but they must be tuned and played in time with one another and the conductor’s beat.

Good playing on its own is no guarantee of a tuneful result if the music was badly composed. An occasional bar may sound musical, mostly by accident, but most others are cacophany.

It’s the same with transport. Trains and buses are the instruments. Their drivers are the players. The timetable is the sheet music they play to. Their writer are the composers. The Department of Transport is the conductor, albeit perhaps less sensitive to harmony, rhythm and music selection than its orchestral counterparts.

Buses and trains

Trains set the pulse to pull the whole network together, while buses play the more intricate pieces to provide coverage. Removing the buses, much like withdrawing the string and wind, leaves only a sparse beat and an incomplete network or composition. And the best playing will not guarantee connectivity if buses and trains play to different rhythms composed to different specifications.

If the beat of trains is based on a service every 15 minutes, while buses come every 20 minutes, the result is an unconnected network. There is still a pulse where optimum connection times repeat, but it’s a weak and infrequent one. The pulse is the lowest common integer multiple, in this case every 60 minutes, and so is longer than either the train or the bus on its own, lowering effective frequency. Multiples are even higher with incompatible non-clockface headways such as 23 or 35 minutes, making connections more random than repetitive.

The drone machine

One of my other interests is electronics. Last week I built a drone machine. This is a bank of audio oscillators that when used together creates all sorts of interesting sounds and beat notes. It also has a feature where a low frequency oscillator can trigger a higher pitched note. This creates a beeping whose interval and note can be varied. The combined sound when several such tones are generated can be quite unusual. It is similar to the early synthesisers of the 1970s.

You can hear a demonstration below

A synthesis

Using this machine raised the possibility of creating music from bus and train timetables, possibly based on arrivals and departures at a particular interchange.

The sound produced would vary according to whether buses and trains were part of a timed transfer pulse network or random arrivals at varying times and frequencies. The difference would be so marked that a brief listen by a trained ear (especially if accompanied by a spectrogram displayed on an oscilloscope) could tell almost as much about network connectivity as poring through numerous timetables.

There is no doubt that the concept is feasible. However it would need a synthesiser more advanced than the basic model demonstrated.

As with the synthesiser above, this concept requires a low frequency oscillator beating triggering a higher frequency tone for each route to be compared. The frequency of the low frequency oscillator would be proportional to the service frequency for that route. In other words a 30 minute route might beat twice a second, while a 60 minute headway route might beat once a second. This isn’t that critical; all that matters is that the relationship between the two is exact. But you need flexibility to program this to accommodate any clockface headway, and preferably non-clockface headways as well.

This would activate a higher frequency oscillator. For musical effect I would recommend its pitch be some sort of note, eg based on a certain piano keyboard key. But again not critical.

That is a single channel. Add more identical channels for each extra route. In all cases the low frequency oscillator needs to be set to be proportionate to the service frequency, while the oscillator it triggers can be a note different from the others.

All outputs are fed to a speaker via an amplifier.

A simple interchange might have one oscillator set to a 15 minute frequency (eg a train) while another is set to 30 minutes (for a bus). The train might be assigned a lower frequency note than the bus. The sound would be four low (train) beats per second, with every second one of those accompanied by a higher (bus) beat. The overall results would be an even beat. However moving the bus to a 20 or 40 minute frequency would change the relationships between the beats. The output would still be a rhythm but be uneven, repeating every second (20 min bus frequency) or two (40 min bus frequency). Probably easier to demonstrate than describe.

The limitation of this approach is that it is based on frequency only. Hence it can only measure frequency harmonisation; it will not detect if services are harmonised but their arrival provides a constant bad connection. To overcome this the starting time of pulses needs to be variable by introducing a delay that can be user adjusted. Once this is done two 30 minute frequency bus routes, one at h:05 and the other at h:20 will be evenly spaced and not on top of one another. Having to shift the onset of certain pulses by an accurate but adjustable amount requires additional circuitry. This is complex but feasible.

However the overall result should be worth it as it is true to life. And it would truly be music composed by timetablers, or more accurately the interaction of the work of several at interchange points.