\by: Francesco Elgorni, Master student in Harpsichord.
\supervisor: Santo Militello, Professor of Music Theory at KC, Den Haag.
How can counterpoint be computed? Instead of looking at counterpoint solely from a historical perspective and reducing it to "music trend of the past", the research contemplates counterpoint as generative technique while exploring its immense yet mechanical creative power through a small selection of case-studies.
Finally, a few thoughts are spent on the meaning of rules in music and the role of the computer in historically informed practice is briefly investigated.
Yes. Perhaps, that's the whole point of it. I was surprised to find -thanks to friends and, most importantly, my supervisor- so many sources from past centuries offering methods for doing so. Some have already been discussed, some less. What I hope I did here was to offer an informative yet engaging summary of some of our findings while trying to suggest how they might fit into the bigger picture that is the Galilean idea of a Universe which can be expressed through numbers and mathematical laws.
Throughout my life, I always perceived Art and Science being as being so far apart to the point of assuming they were exact opposites. Suits and lab's coats on one side and crazy, extravagant outfits on the other. Clean, rigorous logic proofs here and suggestive streams of consciousness there.
When looking at paintings from the 18th century or earlier, however, a clue such as a compass or a music instrument is often needed to correctly identify the subject's profession, almost as if those objects happened to be there when the portrait was being made.
Moreover, by turning my eyes to old music and science treatises, I noticed those two fields being even harder to tell apart.
Could it be that I was looking at both things at the same time?
Well aware a question such as "how can counterpoint be computed?" has infinite answers, what I really hope to achieve with \\Computing Counterpoint is to provide a point of view of music that -contrary to nowdays' ideals- favours efficiency over emotions.
Rather than choosing a mathematically formal and systematic approach -which I wish I could attempt, if only I were able to...- I fell back on a more playful one by walking through the examples and sharing my thoughts as counterpoint practitioner. I hope to provide information the reader might find useful -interesting, at least.
The more we deal with technology to assist us, the more we divide creativity -the fun part- from hard work -what can be automated. Is it possible the use of algorithms for music making is commonly despised because of a bias we have from living in the computer era? And do algorithms really always lead to the same -boring- outputs?
Already by the 16th century, tables can be found containing the few melodic intervals to use for quick and easy polyphonic composition (see Pietro Aron or William Bathe). Centuries later, Francesco Geminiani attempts a harmonic dictionary designed for complete beginners in music with over 2000 little harmonic cells to be combined together to create simple yet working harmony. The Art of Descant by Thomas Campion contains a deterministic technique for harmonizing 4-part polyphony that leaves room for freedom only in the choice of the starting position.
For many, the sheer prolific nature of some major composers can be interpreted as proof of a highly sophisticated yet 'mechanical' or 'automatic' musical craftsmanship, rooted more in Ars-Combinatoria rather than feelings. The smile we get while contemplating such ingenious systems -especially when all the outputs stick to the same form or style, like as in Mozart's dice music for generating minuets- easily makes us forget about both the generative power of algorithms as well as the huge effort devoted to their intricate design. However -especially in a time assisted computation was not available- were algorithms "just games"?
In some treatises on music theory, combinatorics is described as both the most primitive and the most divine way music is created. When authors guide the reader through astronomically large numbers resulting from complex permutations, it's easy to feel lost when contemplating those vast arrays of possibilities.
In such scenarios, we might feel the temptation to exploit the computational power of computers as an attempt to shine a brighter light towards the mysteries of harmony -as if trying to run faster towards infinity.
