(Colin Morris’ SongSim visualises lyrics, in fact, not notes, but wow don’t they look handsome ?)

Where my audio software frameworks page does more DSP, this is mostly about MIDI—choosing notes, not timbres. A cousin of generative art with machine learning, with less AI and more UX.

Sometime you don’t want to measure a chord, or hear a chord, you just want to *write* a chord.

See also machine listening, musical corpora, musical metrics, synchronisation. The discrete, symbolic cousin to analysis/resynthesis.

Related projects: How I would do generative art with neural networks and learning gamelan.

## Geometric approaches

Dmitri Tymozcko claims, music data is most naturally regarded as existing on an orbifold (“quotient manifold”), which I’m sure you could do some clever regression upon, but I can’t yet see how. Orbifolds are, AFAICT, something like what you get when you have a bag of regressors instead of a tuple, and evoke the string bag models of the natural language information retrieval people, except there is not as much hustle for music as there is for NLP. Nonetheless manifold regression is a thing, and regression on manifolds is also a thing, so there is surely some stuff to be done there. Various complications arise; For example: it’s not a single scalar (which note) we are predicting at each time step, but some kind of joint distribution over several notes and their articulations. Or it is even sane to do this one step at a time? Lengthy melodic figures and motifs dominate in real compositions; how do you represent those tractably?

Further, it’s the joint distribution of the evolution of the harmonics and the noise and all that other timbral content that our ear can resolve, not just the symbolic melody. And we know from psycho-acoustics that these will be coupled— dissonance of two tones depends on frequency and amplitude of the spectral components of each, to name one commonly-postulated factor.

In any case, these wrinkles aside, if I could predict the *conditional distribution* of the sequence in a way that produced recognisably musical sound, then simulate from it, I would be happy for a variety of reasons. So I guess if I cracked this problem in the apparently direct way it might be by “nonparametric vector regression on an orbifold”, but with possibly heroic computation-wrangling en route.

## Neural approaches

Musenet is a famous current one from OpenAI

We’ve created MuseNet, a deep neural network that can generate 4-minute musical compositions with 10 different instruments, and can combine styles from country to Mozart to the Beatles. MuseNet was not explicitly programmed with our understanding of music, but instead discovered patterns of harmony, rhythm, and style by learning to predict the next token in hundreds of thousands of MIDI files. MuseNet uses the same general-purpose unsupervised technology as GPT-2, a large-scale transformer model trained to predict the next token in a sequence, whether audio or text.

## Composition assistants

### J74

⭐⭐⭐⭐ (EUR12 + EUR15)

J74 progressive and J74 bassline by Fabrizio Poce’s apps are chord progression generators built with Ableton Live’s scripting engine, so if you are using Ableton they might be handy. I was using them myself, although I quit Ableton for bitwig, and although I enjoyed them I also don’t miss them. They *did* make Ableton crash on occasion, so not really suited for live performance, which is a pity because that would be a wonderful unique selling point. The real-time-oriented J74 HarmoTools from the same guy are less sophisticated but worth trying, especially since they are free, and he has lot of other clever hacks there too. Just go to this guy’s site and try his stuff out.

### Helio

⭐⭐⭐⭐ Free

Helio is free and cross platform and totally worth a shot. There is a chord model in there and version control (!) but you might not notice the chord thing if you aren’t careful, because the UI is idiosyncratic. Great for left-field inspiration, if not a universal composition tool.

### Orca

Free, open source. ⭐⭐⭐⭐

Orca is a bespoke, opinionated weird grid-based programmable sequencer. It doesn’t aspire to solve every composition problem, but it does guarantee weird, individual, quirky algorithmic mayhem. It’s made by two people who live on a boat.

### Hookpad

⭐⭐⭐ (Freemium/USD149)

Hookpad is a spin-off of cult pop analysis website Hook Theory. I ran into it later than Odesi, so I will frame my review in terms of Odesi, but it might be older. Compared to Odesi it has the same weakness by being a webapp. However, by being basically, *just* a webpage instead of a multi-gigabyte monster app with the restrictions of a web page, it is less aggravating than Odesi. It assumes a little (but not much) more music theory from the user. Also a plus, it is attached to an excellent library of pop song chord procession examples and analysis in the form of the (recommended) Hook Theory site.

### Odesi

⭐⭐ (USD49)

Odesi has been doing lots of advertising of their poptastic interface to generate pop music. It’s like Synfire-lite, with a library of top-40 melody tricks and rhythms. The desktop version tries to install gigabytes of synths of meagre merit on your machine, which is a giant waste of space and time if you are using a computer which already has synths on, which you *are* because this is not the 90s, and in any case you presumably have this app because you are already a music producer and therefore already *have* synths. However, unlike 90s apps, it requires you to be online, which is dissatisfying if you like to be offline in your studio so you can get shit done without distractions. So aggressive is it in its desire to be online, that any momentary interruption in your internet connection causes the interface to hang for 30 seconds, presenting you with a reassurance that none of your work is lost. Then it reloads, with some of your work nonetheless lost. A good idea marred by an irritating execution that somehow combines the worst of webapps and desktop apps.

### Intermorphic

USD25/USD40

Intermorphic’s Mixtikl and Noatikl are granddaddy esoteric composer apps, although the creators doubtless put much effort into their groundbreaking user interfaces, I nonetheless have not used them because of the marketing material, which is notable for a inability to explain their app or provide compelling demonstrations or use cases. I get the feeling they had high-art aspirations but have ended up doing ambient noodles in order to sell product. Maybe I’m not being fair. If I find spare cash at some point I will find out.

### Rozeta

Ruismaker’s Rozeta (iOS) has a series of apps producing every nifty fashionable sequencer algorithm in recent memory. I don’t have an ipad though, so I will not review them.

### Rapid compose

Rapid Compose (USD99/USD249) might make decent software, but can’t really explain why their app is nice or provide a demo version.

### Synfire

EUR996, so I won’t be buying it, but wow, what a demo video.

synfire explains how it uses music theory to do large-scale scoring etc. Get the string section to behave itself or you’ll replace them with MIDIbots.

### Harmony Builder

USD39-USD219 depending on heinously complex pricing schemes.

Harmony builder does classical music theory for you. Will pass your conservatorium finals.

### Roll your own

You can’t resist rolling your own?

sharp11 is a node.js music theory library for javascript with demo application to create jazz improv.

Supercollider of course does this like it does everything else, which is to say, quirkily-badly. Designing user interfaces for it will take years off your life. OTOH, if you are happy with text, this might be a goer.

## Arpeggiators

- Bluearp vst does 2-note chord extrapolation (free)
- Hypercyclic is an LFO-able arpeggiator (free)
- kirnu cream (EUR35) is a friendly VST for fancy chord wiggling
- Polyrhythmus (Max 4 live only)

## Constraint Composition

All of that too mainstream? Try a weird alternative formalism! How about constraint composition? That is, declarative musical composition by defining constraints on the relations which the notes must satisfy. Sounds fun in the abstract but the practice doesn’t grab me especially as a creative tool.

The reference here is strasheela built on an obscure, unpopular, and apparently discontinued Prolog-like language called “Oz” or “Mozart”, because using popular languages is not a grand a gesture as claiming none of them are quite Turing-complete enough, in the right way, for *your* special snowflake application. That language is a ghost town, which means headaches if you wish to use it in practice; If you wanted to *actually* do this, you’d probably use overtone + minikanren (prolog-for-lisp), as with the composing schemer, or to be even more mainstream, just use a conventional constraint solver in a popular language. I am fond of python and ncvx, but there are many choices.

Anyway, prolog fans can read on: see Anders and Miranda (AnMi10, AnMi11).

## Random ideas

- How would you reconstruct a piece from its recurrence matrix? or at least constrain pieces by their recurrence matrix?

## Refs

- ReYE12: K. Reese, R. Yampolskiy, A. Elmaghraby (2012) A framework for interactive generation of music for games. In 2012 17th International Conference on Computer Games (CGAMES) (pp. 131–137). Washington, DC, USA: IEEE Computer Society DOI
- KoSW18: Filip Korzeniowski, David R. W. Sears, Gerhard Widmer (2018) A Large-Scale Study of Language Models for Chord Prediction.
*ArXiv:1804.01849 [Cs, Eess, Stat]*. - WiTH09: Daniela M. Witten, Robert Tibshirani, Trevor Hastie (2009) A penalized matrix decomposition, with applications to sparse principal components and canonical correlation analysis.
*Biostatistics*, kxp008. DOI - DiMS10: A Di Lillo, G. Motta, J.A Storer (2010) A rotation and scale invariant descriptor for shape recognition. In 2010 17th IEEE International Conference on Image Processing (ICIP) (pp. 257–260). DOI
- Bod02a: Rens Bod (2002a) A unified model of structural organization in language and music.
*Journal of Artificial Intelligence Research*, 17(2002), 289–308. - BCCZ14: Christian Borgs, Jennifer T. Chayes, Henry Cohn, Yufei Zhao (2014) An \(L^p\) theory of sparse graph convergence I: limits, sparse random graph models, and power law distributions.
*ArXiv:1401.2906 [Math]*. - BiGS11: Louis Bigo, Jean-Louis Giavitto, Antoine Spicher (2011) Building Topological Spaces for Musical Objects. In Proceedings of the Third International Conference on Mathematics and Computation in Music (pp. 13–28). Berlin, Heidelberg: Springer-Verlag DOI
- MaQW16: Sephora Madjiheurem, Lizhen Qu, Christian Walder (2016) Chord2Vec: Learning Musical Chord Embeddings.
- YaMu17: Anna K. Yanchenko, Sayan Mukherjee (2017) Classical Music Composition Using State Space Models.
*ArXiv:1708.03822 [Cs]*. - Mont15: Andrea Montanari (2015) Computational implications of reducing data to sufficient statistics.
*Electronic Journal of Statistics*, 9(2), 2370–2390. DOI - EiPa13: Arne Eigenfeldt, Philippe Pasquier (2013) Considering vertical and horizontal context in corpus-based generative electronic dance music. In Proceedings of the fourth international conference on computational creativity (Vol. 72).
- AnMi10: Torsten Anders, Eduardo R. Miranda (2010) Constraint Application with Higher-Order Programming for Modeling Music Theories.
*Computer Music Journal*, 34(2), 25–38. DOI - AnMi11: Torsten Anders, Eduardo R. Miranda (2011) Constraint programming systems for modeling music theories and composition.
*ACM Computing Surveys*, 43(4), 1–38. DOI - YeFW05: Jonathan S. Yedidia, W.T. Freeman, Y. Weiss (2005) Constructing free-energy approximations and generalized belief propagation algorithms.
*IEEE Transactions on Information Theory*, 51(7), 2282–2312. DOI - CoDu02: Michael Collins, Nigel Duffy (2002) Convolution Kernels for Natural Language. In Advances in Neural Information Processing Systems 14 (pp. 625–632). MIT Press
- Haus99: David Haussler (1999) Convolution kernels on discrete structures. Technical report, UC Santa Cruz
- BrHP17: Jean-Pierre Briot, Gaëtan Hadjeres, François Pachet (2017) Deep Learning Techniques for Music Generation – A Survey.
*ArXiv:1709.01620 [Cs]*. - HaPa16: Gaëtan Hadjeres, François Pachet (2016) DeepBach: a Steerable Model for Bach chorales generation.
*ArXiv:1612.01010 [Cs]*. - LeGK06: Su-In Lee, Varun Ganapathi, Daphne Koller (2006) Efficient Structure Learning of Markov Networks using \(L_1\)-Regularization. In Advances in neural Information processing systems (pp. 817–824). MIT Press
- WaKR13: Larry Wasserman, Mladen Kolar, Alessandro Rinaldo (2013) Estimating Undirected Graphs Under Weak Assumptions.
*ArXiv:1309.6933 [Cs, Math, Stat]*. - Poss86: Antonio Possolo (1986) Estimation of binary Markov random fields
- Rath96: Stephen L. Rathbun (1996) Estimation of Poisson intensity using partially observed concomitant variables.
*Biometrics*, 226–242. - PPRS15: Alexandre Papadopoulos, François Pachet, Pierre Roy, Jason Sakellariou (2015) Exact Sampling for Regular and Markov Constraints with Belief Propagation. In Principles and Practice of Constraint Programming (pp. 341–350). Switzerland: Springer, Cham DOI
- WiTi09: Daniela M Witten, Robert J. Tibshirani (2009) Extensions of sparse canonical correlation analysis with applications to genomic data.
*Statistical Applications in Genetics and Molecular Biology*, 8(1), 1–27. DOI - Tymo09: Dmitri Tymoczko (2009) Generalizing Musical Intervals.
*Journal of Music Theory*, 53(2), 227–254. DOI - Grav13: Alex Graves (2013) Generating Sequences With Recurrent Neural Networks.
*ArXiv:1308.0850 [Cs]*. - ElWA17: Andrew J. Elmsley, Tillman Weyde, Newton Armstrong (2017) Generating Time: Rhythmic Perception, Prediction and Production with Recurrent Neural Networks.
*Journal of Creative Music Systems*, 1(2). - Bret08: Romain Brette (2008) Generation of Correlated Spike Trains.
*Neural Computation*, 0(0), 080804143617793–28. DOI - KrSh09: Michael Krumin, Shy Shoham (2009) Generation of Spike Trains with Controlled Auto- and Cross-Correlation Functions.
*Neural Computation*, 21(6), 1642–1664. DOI - Dean17: Roger Dean (2017) Generative Live Music-making Using Autoregressive Time Series Models: Melodies and Beats.
*Journal of Creative Music Systems*, 1(2). - TNIY17: Hiroaki Tsushima, Eita Nakamura, Katsutoshi Itoyama, Kazuyoshi Yoshii (2017) Generative Statistical Models with Self-Emergent Grammar of Chord Sequences.
*ArXiv:1708.02255 [Cs]*. - Hall08: Rachel Wells Hall (2008) Geometrical Music Theory.
*Science*, 320(5874), 328–329. DOI - LCWL10: Han Liu, Xi Chen, Larry Wasserman, John D. Lafferty (2010) Graph-Valued Regression. In Advances in Neural Information Processing Systems 23 (pp. 1423–1431). Curran Associates, Inc.
- Poll04: Dave Pollard (2004) Hammersley-Clifford theorem for Markov random fields
- MeBü06: Nicolai Meinshausen, Peter Bühlmann (2006) High-dimensional graphs and variable selection with the lasso.
*The Annals of Statistics*, 34(3), 1436–1462. DOI - RaWL10: Pradeep Ravikumar, Martin J. Wainwright, John D. Lafferty (2010) High-dimensional Ising model selection using ℓ1-regularized logistic regression.
*The Annals of Statistics*, 38(3), 1287–1319. DOI - TiBB00: Barbara Tillmann, Jamshed J. Bharucha, Emmanuel Bigand (2000) Implicit learning of tonality: a self-organizing approach.
*Psychological Review*, 107(4), 885. - Huro94: David Huron (1994) Interval-Class Content in Equally Tempered Pitch-Class Sets: Common Scales Exhibit Optimum Tonal Consonance.
*Music Perception: An Interdisciplinary Journal*, 11(3), 289–305. DOI - KoCM08: Leonid (Aryeh) Kontorovich, Corinna Cortes, Mehryar Mohri (2008) Kernel methods for learning languages.
*Theoretical Computer Science*, 405(3), 223–236. DOI - MoSF13: Karim Abou- Moustafa, Dale Schuurmans, Frank Ferrie (2013) Learning a Metric Space for Neighbourhood Topology Estimation: Application to Manifold Learning. In Journal of Machine Learning Research (pp. 341–356).
- HiOB05: Geoffrey E. Hinton, Simon Osindero, Kejie Bao (2005) Learning causally linked markov random fields. In Proceedings of the 10th International Workshop on Artificial Intelligence and Statistics (pp. 128–135). Citeseer
- GiTK10: Jon Gillick, Kevin Tang, Robert M. Keller (2010) Machine Learning of Jazz Grammars.
*Computer Music Journal*, 34(3), 56–66. DOI - RiKe77: B. D. Ripley, F. P. Kelly (1977) Markov Point Processes.
*Journal of the London Mathematical Society*, s2-15(1), 188–192. DOI - BaVM96: A. J. Baddeley, Marie-Colette NM Van Lieshout, J. Møller (1996) Markov Properties of Cluster Processes.
*Advances in Applied Probability*, 28(2), 346–355. DOI - Bod02b: Rens Bod (2002b) Memory-based models of melodic analysis: Challenging the Gestalt principles.
*Journal of New Music Research*, 31(1), 27–36. DOI - HeCh17: Dorien Herremans, Ching-Hua Chuan (2017) Modeling Musical Context with Word2vec. In Proceedings of the First International Conference on Deep Learning and Music, Anchorage, US, May, 2017.
- BoBV12: Nicolas Boulanger-Lewandowski, Yoshua Bengio, Pascal Vincent (2012) Modeling Temporal Dependencies in High-Dimensional Sequences: Application to Polyphonic Music Generation and Transcription. In 29th International Conference on Machine Learning.
- MøWa07: Jesper Møller, Rasmus P. Waagepetersen (2007) Modern Statistics for Spatial Point Processes.
*Scandinavian Journal of Statistics*, 34(4), 643–684. DOI - GoKa04: V. Gontis, B. Kaulakys (2004) Multiplicative point process as a model of trading activity.
*Physica A: Statistical Mechanics and Its Applications*, 343, 505–514. DOI - BaMW00: A. J. Baddeley, J. Møller, R. Waagepetersen (2000) Non- and semi-parametric estimation of interaction in inhomogeneous point patterns.
*Statistica Neerlandica*, 54(3), 329–350. DOI - BTCC18: Tijn Borghuis, Alessandro Tibo, Simone Conforti, Luca Canciello, Lorenzo Brusci, Paolo Frasconi (2018) Off the Beaten Track: Using Deep Learning to Interpolate Between Music Genres.
*ArXiv:1804.09808 [Cs, Eess]*. - Lies96: Marie-Colette N. M. van Lieshout (1996) On likelihoods for Markov random sets and Boolean models. In Proceedings of the International Symposium.
- BoRo90: Paul T. Boggs, Janet E. Rogers (1990) Orthogonal distance regression.
*Contemporary Mathematics*, 112, 183–194. - HaDr13: Naftali Harris, Mathias Drton (2013) PC Algorithm for Nonparanormal Graphical Models.
*Journal of Machine Learning Research*, 14(1), 3365–3383. - KaGA05: B. Kaulakys, V. Gontis, M. Alaburda (2005) Point process model of \(1∕f\) noise vs a sum of Lorentzians.
*Physical Review E*, 71(5), 051105. DOI - JoWe02: Michael I. Jordan, Yair Weiss (2002) Probabilistic inference in graphical models.
*Handbook of Neural Networks and Brain Theory*. - GaMa12: Mike Gashler, Tony Martinez (2012) Robust manifold learning with CycleCut.
*Connection Science*, 24(1), 57–69. DOI - LaWa08: John Lafferty, Larry Wasserman (2008) Rodeo: Sparse, greedy nonparametric regression.
*The Annals of Statistics*, 36(1), 28–63. DOI - RLLW07: Pradeep D. Ravikumar, Han Liu, John D. Lafferty, Larry A. Wasserman (2007) SpAM: Sparse Additive Models. In NIPS.
- KrBo13: Dirk P. Kroese, Zdravko I. Botev (2013) Spatial process generation.
*ArXiv:1308.0399 [Stat]*. - Seth97: William A. Sethares (1997) Specifying spectra for musical scales.
*The Journal of the Acoustical Society of America*, 102(4), 2422–2431. DOI - SMTP09: William A. Sethares, Andrew J. Milne, Stefan Tiedje, Anthony Prechtl, James Plamondon (2009) Spectral Tools for Dynamic Tonality and Audio Morphing.
*Computer Music Journal*, 33(2), 71–84. DOI - LiRW10: Han Liu, Kathryn Roeder, Larry Wasserman (2010) Stability Approach to Regularization Selection (StARS) for High Dimensional Graphical Models. In Advances in Neural Information Processing Systems 23 (pp. 1432–1440). Curran Associates, Inc.
- MeBü10: Nicolai Meinshausen, Peter Bühlmann (2010) Stability selection.
*Journal of the Royal Statistical Society: Series B (Statistical Methodology)*, 72(4), 417–473. DOI - HaSP16: Gaëtan Hadjeres, Jason Sakellariou, François Pachet (2016) Style Imitation and Chord Invention in Polyphonic Music with Exponential Families.
*ArXiv:1609.05152 [Cs]*. - Hutc17: P. Hutchings (2017) Talking Drums: Generating drum grooves with neural networks. In arXiv:1706.09558 [cs].
- GaMa11: Mike Gashler, Tony Martinez (2011) Tangent space guided intelligent neighbor finding. (pp. 2617–2624). IEEE DOI
- LSSC02: Huma Lodhi, Craig Saunders, John Shawe-Taylor, Nello Cristianini, Chris Watkins (2002) Text Classification Using String Kernels.
*Journal of Machine Learning Research*, 2, 419–444. - VeRo15: Victor Veitch, Daniel M. Roy (2015) The Class of Random Graphs Arising from Exchangeable Random Measures.
*ArXiv:1512.03099 [Cs, Math, Stat]*. - Tymo06: Dmitri Tymoczko (2006) The Geometry of Musical Chords.
*Science*, 313(5783), 72–74. DOI - LiLW09: Han Liu, John Lafferty, Larry Wasserman (2009) The Nonparanormal: Semiparametric Estimation of High Dimensional Undirected Graphs.
*Journal of Machine Learning Research*, 10, 2295–2328. - LHYL12: Han Liu, Fang Han, Ming Yuan, John Lafferty, Larry Wasserman (2012) The Nonparanormal SKEPTIC.
*ArXiv:1206.6488 [Cs, Stat]*. - BuSe14: Ryan Budney, William Sethares (2014) Topology of Musical Data.
*Journal of Mathematics and Music*, 8(1), 73–92. DOI - GBTE14: Ross Goroshin, Joan Bruna, Jonathan Tompson, David Eigen, Yann LeCun (2014) Unsupervised Learning of Spatiotemporally Coherent Metrics.
*ArXiv:1412.6056 [Cs]*. - Bod01: Rens Bod (2001) What is the Minimal Set of Fragments That Achieves Maximal Parse Accuracy? In Proceedings of the 39th Annual Meeting on Association for Computational Linguistics (pp. 66–73). Stroudsburg, PA, USA: Association for Computational Linguistics DOI