ANDREW CHADWICK'S MUSIC ( more soon)
Future Music
Innovations
Here I will talk about some of my innovations and discoveries in 19-Equal Temperament and in extending the application of the Tonnetz of Euler, Kepler and Hugo Riemann
19-ET
Why stick to 12 notes to the octave?
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OK, 12 factorises by 2, 4 and 3 giving you a 6-note whole-tone scale, a diminished seventh with minor thirds that can continue indefinitely, and strings of major thirds that give you augmented sixth chords. You don't get any of these with a prime number of chromatic intervals in the octave.
On the other hand, the major third in 12-ET (12-note equal temperament) is so out of tune from just intervals (a 5/4 frequency ratio) that it was rejected as a discord for many centuries, And the minor third is not much better. 19-ET gives you an amazingly pure minor third. Suspend your disbelief and listen to some of the creations in 19-ET from composers such as Sevish, Gabriel Torre and others - or, at a time when keyboard design was in flux, Guillaume Costeley around the year 1570, as shown here by Roger Wibberley.
Even Gesualdo sounds richer in this temperament!
The Tonnetz
I have built a visualisation that works in both 12-ET and 19-ET and, among other features, helps turn arbitrary letter sequences into harmonic progressions. This applies the 'honeycomb' geometric visualisation invented by Euler and extends the letter coding of Hugo Riemann which helps explain the set of all possible triad transitions - in Brahms' and later composers' journey away from functional harmony. This user guide gives much more detail. Within the honeycomb are five video recordings of the tool in action (spot the 'Ode to Cheese!) .
Linked also is a recent, polished web-friendly parallel in 12-ET from University of Strasbourg. Their rectilinear layout does not however show the enharmonic 'folding' from right to left and top to bottom - the true geometry is a torus. A#=Bb in 12ET or Bbb in 19ET.
Tonnetz demos
Tonnetz videos
Bayesian Harmonisation
In an ambitious 2021 experiment for CoMA, which still has the legs for further development, I applied the Bayesian network tool Netica from Norsys to make a probabilistic harmoniser that can set up to five chords in sequence, optionally fitting a given melodic sequence and/or bass line. Opposite is the basic layout of one transition between chords, showing some of the options available - and the size of the whole network. You can set a 'target chord' or cadence and the network will infer - appling inverted probabilities - the best fit of chords to lead to it.
The CoMA composers' group was very interested in looking at the extent to which this could replicate, at the micro level, aspects of a given composer's style, for example a characteristic transition of Vaughan Williams. The tool, christened 'RoboCoMA', was able to satisfy a number of requests from members for examples [sound files to follow]
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The full network was as much as Netica could handle. As well as basic functional harmony (dominant, subdominant regions - Riemann again!) there is avaiable, for detailed tailoring, a table of transition probabilities from all chord variants to any other variant. No doubt this concept has been overtaken since!
More weird and wonderful games and animations
During lockdown, musicians trying to play together over Zoom were struggling to keep in time due to latency on the overloaded networks. This 'Entrain' prototype was an attempt to give them visual feedback on the overall rhythm within any particular pitch range. In the user window it creates bubbles stretching upwards according to the detected pitch, which change to a brighter colour and start to move at right angles once a rhythmic pattern is established. At first a fixed tempo is selected as the reference for rhythm detection, but there is the option smoothly to 'entrain' that tempo, pulling it toward the speed of the players. It has created quite quirky results, but is now (like me) retired....
