(1982). 10‘Mid-piece’ is significant because of the relatively common practice of ending minor key pieces with a major triad (with the so-called ‘Picardie’ third).

Tymoczko (2011), for instance, takes a suitably expansive view of this broad spectrum of tonality, identifying five features that draw this diverse set of musics together: These features are indeed descriptive of the Western repertoires mentioned: their melodies tend to move in conjunct steps (i.e. In the last decade, several corpora of human harmonic analyses have been published, spanning classical, jazz and pop/rock repertoires. In Figure 4 below a Remote Point has been created and automatically positioned at the centroid of the end face on the plate. arXiv:1609.03499. Like those musics themselves, most such descriptive systems share a great deal of common ground but diverge considerably in their details. The Bach example begins to show that more complex contexts can run these rules into self-contradiction. The RN annotations and these tools are available at https://gitlab.com/algomus.fr/functional-harmony, with links to the corresponding scores. For this constraint, we need to look at the chord labels.

As this discussion of overall accuracy metrics would seem to indicate, there is more to the task of evaluating the results of an RN analysis. In the best-performing of these models, convolutional layers gather the local information needed to analyse the chord at a given moment while a recurrent part learns longer-range harmonic progressions. Not All Roads Lead to Rome: Pitch Representation and Model Architecture for Automatic Harmonic Analysis. Machine Intelligence, 6. A Geometry of Music: Harmony and Counterpoint in the Extended Common Practice. (2008) implement a system called ‘Rameau’ which combines four different algorithms for RN prediction (but which does not offer precise comparisons between them).

Neural Computing and Applications. As such, we continue here to take a closer look at the ‘errors’ made by the models.

Unlike most systems, RNs also specify an analytical view of the local and global keys to which those chords belong and so also their harmonic functions (hence the term ‘functional analysis’). Befitting the fact that there have been formalisations of harmony throughout the history of music theory, there have likewise been attempts at computer-based modelling of this problem for as long as that has been practically possible. Not All Roads Lead to Rome: Pitch Representation and Model Architecture for Automatic Harmonic Analysis. The authors have no competing interests to declare. Oettingen, A. Measure 34 marks the completion of an uncontroversial B minor cadence. Rameau: a system for automatic harmonic analysis. As a possible, partial solution, one could transpose segments of the score separately. (2019). Finally, we divide all scores in segments of equal quarter-note duration and pad with zeroes to the right when needed. What’s key for key? Multi-scale context aggregation by dilated convolutions. The contents of our meta-corpus, drawing together existing harmonic analysis datasets. The pivot to (and pre-dominant of) the B minor cadence at the end of m.32 (not shown) was a clear German 6th and in the ‘correct’ inversion, thus putting the chord ‘in the listener’s ear’ and proving further precedent for this reading (rule 2 again). A modal analysis is often performed prior to another dynamic analysis in order to characterize the system of interest. Depending on the model, the total training time ranges from 20 minutes to 3 hours, when run on a CPU-only high-performance-computing server. Music Transformer. DOI: https://doi.org/10.1145/3144749.3144753. A Generative Theory of Tonal Music. Holtzman, S. R. (1977). Audacious Euphony: Chromatic Harmony and the Triad’s Second Nature. [6] Golson's early version was on his 1957 album Benny Golson's New York Scene.

Duinker, B. We hope that this will enable and encourage the community to share ideas about harmonic analysis in general, and on how to improve this model in particular. He's also the host of the music entrepreneurship podcast "Passive Income Musician.". As the chromatic and key range of each segment is necessarily less than (or occasionally equal to) that of the overall work, these sections would be transposed more times.

Finally, we found some cases we consider unacceptable readings, where the most compelling musical reading diverges from the statistically normative case. Such a test can be implied by fixing a base in ANSYS, and applying an acceleration load to the whole model with an ACEL command. Popular Music, 30(1), 47–70. Alternatively (Analysis A2), we could take the leaps in the melodic line to indicate chord membership (rule 3). We use a non-causal dilated convolution, meaning that we allow the system to use both past and future events when determining each chord.