This research could have been a more detailed study on counterpoint with the help of the computer, as I admitted at the beginning -although I'm still not very sure what the audience would have been like.
Furthermore, after my supervisor Santo Militello pointed me to the amazing work by Giorgio Pacchioni, I changed idea once seeing such an extremely detailed work on counterpoint theory.
I'm sorry for all the people who went through this research expecting to find more experimentation with coding. My initial wonder was if the computational power of a computer could extend our capabilities for complex counterpoint, just like wings attached to our arms could let us fly.
I did not know a canon for 36 voices was already made by Johannes Ockeghem.
(https://www.youtube.com/watch?v=1bYGmISF3ME)
I did not know the Agnus Dei by Josquin des Près (an Augmentation Canon for 3 voices) existed (https://www.youtube.com/watch?v=hbvJ17cL9a0)
Furthermore, I did not consider augmentation for 5 voices even remotely possible.
(https://www.youtube.com/watch?v=FCe7WGoJVLI)
Although I'm confident that -with a little bit of luck- if I devoted more time coding I might have reached some new curious results (mostly by adding implementations to the canonchecker), I felt like the "why" question on my shoulders started to get heavier as I spent my time typing codes on my laptop.
This is the scenario in my head that I had to freeze, unfinished. Of all the following questions, little clues are all I have about.
What was making Science like in the 17th and 18th century compared to what it is like now? Are both these two things substantially the same? Has Music really been closer to Science in the past and if yes how? Should we aim for a reconciliation of Science and Art, at least in the field of historically informed music practice? In such a scenario, how should we deal with the discrepancy in the standards of scientific rigor in our two distant eras? How to deal with the changing of beliefs when Art is built around them? Are we doomed to some kind of oblivion because of scientific progress? Is it better to ignore the inclusion of Science in the field of Music, at least today?
While working on the research I got asked several times if I had in plan to code a software for basso continuo realization or if I knew people who attempted such a task. At the time of release (early 2025) I could not find such tools online. Although the idea tempted me a couple of times, I eventually did not put my effort into it. To be honest I think my coding skills are way too insufficient. Major challenges would be OMR (Optical Music Recognition), still far from solved, and the ability to ornament. However, if limiting to simply chords on the bass my gut feeling suggests it should be possible to have something working within reasonably acceptable standards. There are sources showing continuo being made in quite a straight manner, too. Perhaps, users could later add extra plug-ins for imitations, arpeggio patterns etc.
The truth is that I don't want to make such a tool. Being a harpsichord player I am not in the position to encourage and support anything similar. Beware, I don't necessarily mean the risk of my profession being threathened. At least at the moment I am not envisioning such scenario to become reality anytime soon ...although I do like surprises. What I really mean is that studying partimento and basso continuo has probably been of the biggest revelation in my whole music study life and at the moment I feel I prefer to support that.
Although I can see myself enjoying working on a similar tool, I would not like my name to be associated with it. What I would also not like is people coming to me and saying their handmade realization is better than the software's, showing anyone how dumb it is. But this would be a problem about my ego.
Thinking it through, though, I often wonder about other potential kinds of software. Wouldn't it be great -I often tell myself- if there were more generic "counterpoint assistants"? For example, softwares that could help the user find imitations with their motifs, stretti, canons, etc. In such a tool, for example, we might decide what our consonances and dissonances should be and how should they be dealt with, etc. so that we could get a series of outputs depending on our parameters. E.g. Why is the seventh and ninth a dissonance in the first place if it also appears in the harmonic series, afterall? How would it sound if we included it in the consonances list? how does that affect the possible counterpoint I can make? and so on... all this, possibly with a friendly user-interface that favours a playful approach. It is incredible how by designing unique user-interfaces, apps such as Midinous really force you to build music from a different approach compared to with a linear staff. Sure, I'm now busy studying partimento and I don't know all music softwares invented which work by computing MIDI. My impression is that there are not so many, contrary to "audio manipulation" ones or DAWs in general. I know of some interesting extensions for Python, Max or Super Collider but let's be honest: they are likely not the most accessible for the average early music student -me included.
Sure, "you could also do it by hand", but the point of software is to serve as a tool for easily exploring new sonorities. Indeed, when looking at the computer as instrument for optimizing a mass production, together with a view of music as an art form that prioritize individualism -the uniqueness of each person- it doesn't become hard to see how such "assistants" have no artistic meaning -and therefore zero interest for an audience. We want to know what people (artists) think, do with their hand; not what a computer does for them. Not that I care about what a computer think, as I am just genuinely curious about what is possible to do. If there's anything we left behind. Anything we forgot.
My last hope is that by forcing the computer into our early-21st-century view of art, I invited a reflection on the role of technology and -perhaps- better stimulated the sensation of what a true absence from digitalization really feels like.
Thank you for reading,
Francesco Elgorni
I want to say thank you to my family for the enourmous support, especially to my brother Filippo for his sharp scientific eye and guidance.
Thanks to Nicola Ariutti, Tomio Shota and Jan whose contribution and insights have also been really eye-opening, like the ones from my school teachers Enrico Barbagli, Giovanni Amico and current music professors Patrick Ayrton, Fabio Bonizzoni, Carole Cerasi and Edoardo Valorz, as well as Giancarlo Vighi and Tullia Pedersoli.
Thanks to Aleksander Mocek for the amazing informative content posted online on early music Theory.
A thanks also goes to the classmates who got involved into this Research in one way or another: Irene Luraschi, Elza Heinsberga, Zosia Piasecka, Antonio Pellegrino and Agata Sorotokin, Lukasz Moroz, Eriko Nagayama, Matteo Fiorina And Tomio Shota, Menghan Wu, Daniele Pisano, Marcel Jorquera Vinyals, Laura Mingo Perez, Daan Soare for sending their canon contribution.
Thanks to Eva Valentini for letting me perform my electronic debut (although remote) of AAAAAAAA in Milan during her installation "Iperbolica" during Milan Arch Week.
I would like to express my deepest gratitude to Santo Militello, for allowing me the privilege of having him as my supervisor. His expertise, extensive knowledge of sources and thoughtful insights through constructive critiques have been instrumental in the successful completion of this Artistic Research.
It has been a privilege to learn from him, and I will always be grateful for his mentorship and encouragement.
Old sources:
-Ornithoparchus, Andreas. De arte cantandi micrologus. Cologne: Joannem Gymnicum, 1535.
-Lampadius, Auctor. Compendium musices, tam figurati quam plani cantus ad formam dialogi, in usum ingenuae pubis ex eruditis Musicorum scriptis accurate congestum, quale ante hac nunquam uisum, et iam recens publicatum. Adiectis etiam regulis de concordantiarum et componendi cantus artificio, summatim omnia musices praecepta pulcherrimis exemplis illustrata, succincte et simpliciter complectens. Bern: Mathias Apiarius, 1537.
-Aron, Pietro. Il Toscanello in musica. Italia: Marchio Sessa, 1539.
-Coclico, Adrianus Petit. Compendium Musices descriptivum in quo tractantur de modo ornate canendi, de regula contrapuncti et de compositione. Nuremberg: Joannis Montani & Ulrici Neuberi, 1552.
-Lusitano, Vicente. Introduttione facilissima et novissima di canto fermo, figurato, contraponto semplice, et in concerto. N.p.: Marcolini, 1558.
-Virgiliano, Aurelio. Il Dolcimelo d’Aurelio Virgiliano dove si contengono variati, passaggi, e diminutioni cosi per voce, come per tutte sorte d’instrumenti musicali; con loro accordi, e modi de sonare. 1600 ca.
-Campion, Thomas. The Art of Descant or A New Way of Making Fowre Parts in Counterpoint By a Most Familiar and Infallible Rule. 1615
-Picerli, Silverio. Specchio ... di musica. Nel quale si vede chiaro il vero (etc.). N.p.: Nucci et Peltraud, 1631.
-Mersenne, Marin. Harmonie universelle: contenant la théorie et la pratique de la musique. Paris, 1636. Édition facsimilé de l'exemplaire conservé à la Bibliothèque des arts et métiers et annoté par l'auteur. Francia: Centre national de la recherche scientifique, 1965.
-Artusi, Giovanni Maria., Zarlino, Gioseffo. Impresa del molto R. M. Gioseffo Zarlino ... dichiarata dal R. D. G. M. Artusi. Italia: G. B. Bellagamba, 1604.
-Kepler, Johannes. Ioannis Kepler [...] Strena seu De nive sexangula. N.p.: n.p., 1611.
-Mersenne, Marin. Harmonie universelle, contenant la théorie et la pratique de la musique: ... Par F. Marin Mersenne, .... Francia: S. Cramoisy, 1636.
-Kircher, Athanasius. Musurgia universalis sive Ars magna consoni et dissoni. Italia: n.p., 1650.
-Kircher, Athanasius. Ars Magna Sciendi. Paesi Bassi: n.p., 1669.
-Bontempi, Giovanni Andrea. Nova quatuor vocibus componendi methodus, quâ musicae artis plane nescius ad compositionem accedere potest, authore Johanne Andreâ Bontempô perusinô .... Germania: typis Seyffertinis, 1660.
-Leibniz, Gottfried Wilhelm. Dissertatio de arte combinatoria, in qua ex arithmeticae fundamentis complicationum ac transpositionum doctrina novis praeceptis exstruitur ... . Praefixa est ... demonstratio existentiae Dei ... exacta autore Gottfredo Guilielmo Leibnüzio .... Germania: apud Joh. Simon. Fickium et Joh. Polycarp. Seuboldum, literis Spörelianis, 1666.
-Graupner, Cristoph.,Vierstimmiger Kanon mit 5626 schematischen Umkehrungen und Umstellungen, manuscript, 1730-1735
-Geminiani, Francesco., Guida Armonica, O Dizionario Armonico: Being a Sure Guide to Harmony and Modulation, in which are Exhibited, the Various Combinations of Sounds, Consonant, and Dissonant, Progressions of Harmony, Ligatures and Cadences, Real and Deceptive. Regno Unito: author, 1742.
-Geminiani, Francesco., The Art of Accompaniment, Op.11, London: John Johnson, n.d.
-Kirnberger, Johann Philipp., Decker, Georg Jakob. Die Kunst des reinen Satzes in der Musik: aus sicheren Grundsätzen hergeleitet und mit deutlichen Beyspielen erläutert. Austria: bey G.J. Decker und G.L. Hartung, 1774.
-Mozart, Wolfgang Amadeus, Musikalisce Wurfelspiele, K.Anh.C.30.01
Recent sources:
-Hofstadter, Douglas R.. Godel, Escher, Bach: An Eternal Golden Braid. New York: Basic Books, 1989.
-Goehr, Lydia. The Imaginary Museum of Musical Works: An Essay in the Philosophy of Music. Regno Unito: Clarendon Press, 1992.
-Zweit Janeg, Ars Combinatoria, Mystical System, Procedural Art and the Computer, 1997
-Richards, Annette., Automatic Genius: Mozart and the Mechanical Sublime, Music & Letters, 1999.
-Deleuze, Gilles., Tarizzo, Davide. La piega. Leibniz e il barocco. Italia: Einaudi, 2004.
-Gaines, James. Evening in the palace of reason : Bach meets Frederick the Great in the Age of Enlightenment. Londra: Fourth Estate, 2005.
-Schubert, Peter., Neidhöfer, Christoph. Baroque Counterpoint. Regno Unito: Pearson Prentice Hall, 2006.
-Schubert, Peter. Modal Counterpoint, Renaissance Style. Regno Unito: Oxford University Press, 2008.
-Cope, David., Intelligence, Experiments in. Fifteen Two-Part Inventions: After Bach. N.p.: CreateSpace Independent Publishing Platform, 2015.
-Agustín-Aquino, Octavio Alberto., Junod, Julien., Mazzola, Guerino. Computational Counterpoint Worlds: Mathematical Theory, Software, and Experiments. Germania: Springer International Publishing, 2015.
-Gjerdingen, Robert O.. La musica nello stile galante. Italia: Astrolabio Ubaldini, 2017.
-Harari, Yuval N.. Homo Deus: A Brief History of Tomorrow. Regno Unito: HarperCollins, 2018.
-Midinous. By Nornec / Nornec, 2021
-Nicolella, Marco., Celletti, Davide. I segreti dell'Harmonia. Comporre canoni musicali con la Tabula mirifica. Italia: Libreria Editrice Vaticana, 2021.
Online resources:
-https://imslp.org/wiki/Main_Page
-http://www.giorgiopacchioni.com/index.html
-https://www.bach-leipzig.de/en/bach-archiv
-https://www.instagram.com/large_deviations/
-https://www.arca1650.info/compose.html
-https://kircher.chierotti.it/tesi/
-https://www.earlymusicsources.com/
-https://doodles.google/doodle/celebrating-johann-sebastian-bach/
-https://magenta.tensorflow.org/
-https://www.bach-chorales.com/ConsecutivesInChorales.htm
Youtube videos:
-Leonard Schick- on Fugue Improvisation
-Paula Findlen- on Kircher's Machines
-Elam Rotem- a "magic" table for canon making
-Tim Braithwaite- interview on "Nikhil Hogan Show"
-Aleksander Mocek- on Ars Combinatoria (translated with AI)
-The Best Way to Pack Spheres - Numberphile
My links:
-https://francescoelgorni.com/
