PC-assisted computation can serve useful application for counterpoint study. I can imagine a scenario where a program could calculate the correct specifics (intervals, etc) that different types of canon would require to function. There is evidence that such tables have circulated since the 16th century (William Blaithe, Pietro Aaron). More generic matrix-tables for music making are mentioned by Silverio Picerli and Athanasius Kircher (respectively the Golden table and the tabula mirifica omnia contrapunctisticae artis arcana revelans -the "magic table that reveals every secret about counterpoint").
Despite seeming tedious, it is possible that memorizing such long lists of possibilities might also have been at the core of the music training process, as we can see in the way rules are exposed in Vicente Lusitano's "Introduttione facilissima, et novissima, di canto fermo, figurato, contraponto semplice, et in concerto".
Also, I can envision scenarios where computers could succesfully assist the completion of a score when composing music. Actually, this was the main wish that brought David Cope to start working on EMI during the end of the 20th century.
It's not hard to hear speculation about parts of cantatas by J.S.Bach wich might not be entirely "original", being instead written or completed by other members of the family. Perhaps, once the main ideas are on paper or the outer voices are done, the remaining music can be done more or less automatically -assuming the composer agrees with the assistant.
At this point, some reader might slowly start to feel oppressed. Afterall, what holds magic in a vision of music where every process is seen as deterministic and somehow predictable?
One short answer is the Universe: viewing music as the manifestation of universal order. By transforming proportions into sound, music lets you contemplate the mysteries of the Chosmos and the laws of Nature.
An alternative answer for many seems to be "breaking the rules": the true Artist is the one who, tired of being contained, finally breaks the schemas and present a new vision. It does sounds exciting, at least on paper.
Yet the many "must" found throughout music treatieses make "breaking the rules" extremely tempting to attempt and easy to accomplish.
While aspects such as 4 part counterpoint see disputes between composers, mostly driven by personal taste or different necessities (melodic voice leading vs still position of the hand, etc.) the very fundamentals of harmony -preparation and resolution of dissonances, the use of parallels- are hardly ever touched. How so?
This should at least open the discussion on whether rules were truly to be regarded as "stylistic trends" -subject to change every few years- rather than something so objective that were able to transcend time and remain untouched for entire centuries, much like scientific laws.
I would argue a 7th resolving to 6th is not a boundary but rather a tool, a logical statement necessarily derived from simpler assumptions.
Studying counterpoint soon started showing me a new kind of beauty in music. Instead of purely relying on the beauty of the sound that my ears were receiving and the suggestions I was getting, I started appreciating more and more the "architectural" skillcraft, how the composer could tie the ideas together with such degree of perfection. For example, how the last note of a scale precisely matches the entrance of the Tutti right on the beginning of the bar and how such a condition could have been met etc.
On the same line, something really beautiful to contemplate which the 14 canons BWV 1087 convey really well, almost in a minimalistic fashion, is also the idea intricate works of art might be nothing else than the "unfold" of simpler ideas (what Gilles Deleuze describes in his The Fold: Leibniz and the Baroque, 1992). It's nothing new recursion can easily invoke the same beauty that can be found in fractals (here a 2 hours long zoom of the Mandelbrot set).
If the aim was to use recursiveness to convey a physical sensation of infinity, humans may not necessarily be more able than computers in achieving such task -although it's incredible to notice how sometimes they still are.
Consequently, amazement is felt as generated by the rule as it exists because of it. In other words, amazement is guaranteed by the rule.
But most importantly, like assumptions in science, rule guide us through chaos.
Without assumptions, no scientific truth could be drawn. It is only through assumptions we get the power to jump to conclusions we can't quite grasp just in our daily experience. When contemplating the Universe -something we did not stop doing since Counterpoint was born- it is only through assumptions if we can get any estimate about its age and size, etc. as we don't have the possibility to see it just with our naked eyes.
Alpha Centauri (our closest star) being photographed by New Horizons (a probe sent by NASA) and from Earth. Because of the great distance between the probe from us, we can see Alpha Centauri in 2 different places in the sky. The reason why it's the only "moving" dot in the picture is that the rest of the stars are so far they barely change their placement from our view. What you see is the same effect as if looking at a fly with the left and right eye on a very far background (like clouds in the sky). Knowing the distance the two photos were taken allows us to get an estimate on its relatively small distance from us (4.2 light years). Changing our assumptions changes the way we see things.
By accepting rules as "axioms" (term Fedele Fenaroli actually uses in the partimenti) what happens is that we shift our attention from the rule itslef to its application. How is the rule being used? What's the conclusion the composer guides us to? How is the same piece of evidence (of consonances and dissonances, etc.) being investigated by composers? what theorem are they demonstrating?
Afterall, a major chord stays major no matter how many centuries pass by. Its fullness, resonance can and will most likely be felt by any human who will ever live. Likewise, a seventh will feel resolved when followed by a sixth. In parallel octaves, voices cancel out -or sum- as a matter of fact. A diminished fifth wants to resolve inwards, an augmented fourth outward etc. This is what allows a dramatic non mesuré prelude to still feel a "dramatic non mesuré prelude" centuries later.
When composers really need to turn a blind eye, they don't hesitate doing so. Still, with its rules often being presented rigorously and by coldly exhausting scenarios with interminable bruteforcing, Counterpoint and historical Music Theory easily conveys the idea that music is a purely rational process, a "science". Criterias are often expressed in terms of DOs and DON'Ts and it's not rare to stumble across systematic treatises that span for pages without wasting a single word neither on the why nor on the emotional features of music, contribuing therefore to an ideal of mechanicism or "mechanical sublime" (Annette Richards, Automatic Genius: Mozart and the Mechanical Sublime), almost suggesting the idea that every note could potentially be "justified", explained and traced back to rules in turn founded on simpler statements, etc. E.g. in a 2 voice context, the rule "Don't double the leading tone" is a direct consequence of more fundamental rules "Avoid parallel octaves" and "the leading tone should always resolve". Like Aleksander Mocek points out in one of his video essays, it's easy to imagine how the study of law might have played a crucial role for such forma mentis.
From Geminiani, The Art of Accompaniment, Op. 11:
Not that the book is small, but neither it is complete. If one really wanted to reach further modulation there would be absolutely no way to do that with his book.
I'm always puzzled when reading "It would have swelled this Book too much". Does he mean it's theoretically doable? He does not say "impossible" afterall... what if the composer wasn't getting the right compensation for the job or what if he was hoping to keep the rest for further volumes eventually never published?
Rules are not just stylistic or social boundaries to accept. They can be an easy shortcut to the result, too. This explains the leading role of the "Maestri" going through the hassle of computing counterpoint for the ones not so willing to dive into the complex realm of music -or for the less gifted pupils- by designing them systems they can move within, freely and without harm.
Also, rules not necessarily make everything sound the same and stick to the same output. By walking the composer through the harsh path of a good voice leading, rules can -paradoxically- end up revealing unique, new solutions. By forcing the composer find the "best possible counterpoint", rules can shuffle the plans built in our mind and lead to results we would have not reached otherwise. They shake us from our habits, clichés, our biases. In short, they get us out of the comfort zone.
In one of his YouTube videos, Aleksander Mocek gives a fantastic overview on the importance of rules under many more aspects.
In one of her conferences, professor of History and Philosophy of Science Paula Findlen makes an interesting distinction between the machines of G.Galilei and A.Kircher. While for Galileo -or Da Vinci for that matter- the machine is a tool that lets you achieve tasks impossible to be done without it (the telescope to see planets, wings and other flying devices, etc) almost becoming an extension of the human body, for Kircher the machines serves a "metaphysical purpose". Kircher's utility of most of his machines is questionable to say the least (the "vomiting lobster", the "sunflower clock", etc...) because they instead serve the purpose of stimulating the imagination around the mechanism, often intentionally hidden from your sight.
Acknowledging the large historical offset of almost three centuries, to a post XX-century reader this might remind of the concept of black box in system theory.
In the study of functions, we might benefit from reducing complex systems to a box whose processes are hidden and unknown. Perhaps we might want to try studying the inner components or decide to voluntarily ignore them and focus on some other aspect.
In such system most of the known information -if not all- would be the in the Input and Output, respectively: what comes in the blackbox (in our analogy the motifs in a piece, etc.) and what's generated as output (the whole piece). The more complex the blackbox is (the smarter the composer), the harder it is for the listener to really decifer what happend "under the hood" and understand how the input is transformed into output, thus creating a sense of wonder about the functioning.
Rather of claiming the computer kills art by forcing cold numbers on it, I wonder wether computers actually kill the beauty of numbers in the first place by depriving them of their hidden meanings, secrets, stories, connective power etc.
On top of that, computers kill the complexity of intricate systems.
From Wikipedia, the Free Encyclopedia
Combinatorics is an area of mathematics primarily concerned with counting, both as a means and as an end to obtaining results, and certain properties of finite structures. It is closely related to many other areas of mathematics and has many applications ranging from logic to statistical physics and from evolutionary biology to computer science.
In conclusion: the wonder behind huge permutations and the countless links between things is easily broken by a device (the computer) that can exhaust all possibilities in a matter of seconds -or less- and solve calculations faster than any human can do.
Perhaps, when we think of Ars Combinatoria we shouldn't think of computers and viceversa.
It's clear machines and automatas played a role in music during the time between the 17th and 19th century. From here, it's still hard to picture what the general opinion of machines might have been from the 17th century onwards. It is inaccurate to suggest that only Romanticism brought the soul and individualism to the forefront. Already in the 18th century Quantz showed his skepticism regarding an automata playing the flute, basically saying that it would never have the "warmth" of a human soul, even if it played with a much cleaner technique.
Impossible is also knowing what a composer from the past might have thought of the modern computer. It should be remembered that most of the complex machines (such as the Salzburg Bull, one of the biggest carillon of that time, or Vaucanson's automatas: the writer, harpsichordist, etc.) only served demonstrative purposes and were mostly showcased in exhibitions contexts. At times they were massive in size and very often extremely task-specific, meaning they only executed one or a very few set of tasks. Jacquard's mechanical loom, for example, required a huge amount of space to store its data, written in binary format (in series of 1s and 0s) with holes being made on physical tablets.
01001100 01101111 01101111 01101011 01101001 01101110 01100111 00100000 01100110 01101111 01110010 00100000 01100010 01101001 01100111 00100000 01110011 01100101 01100011 01110010 01100101 01110100 01110011 00100000 01101000 01110101 01101000 00111111 00001010 01001100 01101111 01101111 01101011 00100000 01100100 01100101 01100101 01110000 01100101 01110010 00001010
Although Sci-Fi contributed to solidify the stereotypical association of the binary language with computers, the origin of binary computation is actually quite old. During the 17th century, Leibniz was busy exploring its properties and possible uses. But because we are so familiar with the concept of binary data storage, we can hardly understand the excitement such discovery must have certainly generated around the intellectuals of that time. For people like us used to complain about limited memory storage on their smartphones, the loom data storage system not necessarily induces much amazement or a sense of progress. There is nothing cool, new or powerful about it. It's just a dusty, obsolete tool. Could such a machine potentially "contain ideas", or concepts? Could people foresee possible new applications of binary data processing outside the textile environment or people only associated such technology with this very specific machine?
By turning my eyes to all the science problems still open for debate, sometimes I do feel intrigued, amazed. I do wonder about what's behind the things we can't see. Distant galaxies, a virus silently killing me or how did your device download the text you are reading.
Every once in a while, some quantum computer prototype (now big strange bronze-looking machines) gets assembled somewhere around the world. Sometimes, new prototypes surpass older models' performances and we read it on the news. Although still extremely expensive and limited in their use-applications, there is a deep aura of mistery around them: some people don't even know what they are and what they do -I'd now put myself in this category- others wonder wether "this might be the new big thing", "we may soon get a new understandings of how the Universe really works" and "humanity might be just behind the corner of a revolutionary discovery". Binary computation likely turned out to be one of them.
The Arca Musaritmica was a wooden music box where by lifting little wooden rods containing various data, one was able to put together piece of music. Andrew A. Cashner created a copy that runs on browser and can be accessed on https://www.arca1650.info/compose.html .
Would you say the experience of playing with these two distinct music machines (the one on the right being a digital copy of the one on the left by A.Kircher) is the exact same?
