Bistate Reduction and Comparison of Drum Patterns

BISTATE REDUCTION AND COMPARISON OF DRUM PATTERNS Olivier Lartillot Fred Bruford RITMO Centre for Interdisciplinary Studies in Centre for Digital Music Rhythm, Time and Motion, University of Oslo Queen Mary University, United Kingdom [email protected] [email protected] ABSTRACT patterns specifically, rhythmic interaction and instrumental configuration has been shown to have a significant affect This paper develops the hypothesis that symbolic drum on the perception of syncopation, a fundamental rhythmic patterns can be represented in a reduced form as a sim- property [3]. However, in much existing work on drum pat- ple oscillation between two states, a Low state (commonly tern similarity modelling, similarity is modelled as a linear associated with kick drum events) and a High state (often combination of monophonic rhythm similarity models cal- associated with either snare drum or high hat). Both an culated on each instrument part, without consideration to onset time and an accent time is associated to each state. rhythmic interactions or integration. The systematic inference of the reduced form is formal- Our aim is to design new models of similarity for drum ized. This enables the specification of a rhythmic struc- patterns that take into account both rhythmic interaction tural similarity measure on drum patterns, where reduced and rhythmic integration. The bistate reduction algorithm patterns are compared through alignment. The two-state proposed in this paper attempts to extract the core struc- representation allows a low computational cost alignment, ture of drum pattern as an interaction between two states, once the complex topological formalization is fully taken ‘Low’ and ‘High’, and to use this reduced representation into account. A comparison with the Hamming distance, as to compare drum patterns through alignment. well as similarity ratings collected from listeners on a drum The drum patterns used in this paper are part of a varied loop dataset, indicates that the bistate reduction enables to set of 160 stylistically accurate symbolic patterns recorded convey subtle aspects that goes beyond surface-level com- by human drummers on an electronic drum kit, taken from parison of rhythmic textures. the Groove library of BFD3 [4], a commercially available virtual drum kit plugin. Originally collected by [5], the pat- 1. INTRODUCTION tern dataset is drawn from a wide range of genres and sub- One of the most fundamental areas of both Music Infor- genres, with 8 genre groups used: Hiphop/Dance, Funk, mation Retrieval (MIR) and music cognition research con- Blues/Country, Pop, Reggae/Latin, Rock, Metal and Jazz. cerns the modelling of musical similarity, due to the es- In addition to multiple genres, they are of varied complex- sential importance of similarity in music perception and ity and function, with some containing fills. the practical utility of similarity models in music retrieval In Section 2, we discuss in greater detail approaches applications such as recommendation systems. Modelling to modelling monophonic rhythm similarity and assess the similarity for drum patterns is a particular challenging vari- state-of-the-art in drum pattern similarity modelling and its ant of this research, though one with potential applica- limitations. In Section 3 and Section 4, we begin discus- tion in a wide range of intelligent music production tools sion of the bistate reduction algorithm and bistate sequence such as drum pattern recommendation systems or auto- alignment technique respectively as a novel means of rep- matic drum pattern generation systems. resenting complex drum patterns and estimating the per- The challenges of drum pattern similarity modelling ceived similarity between them. In Section 5, the sequence lies in the complex nature of polyphonic rhythm percep- alignment algorithm is evaluated in its ability to predict tion. The integration of coincident rhythms into a resultant human similarity ratings for pairs on drum patterns in our ‘multirhythm’ has been argued to be an essential feature of dataset. polyphonic rhythm perception, especially in the context of drumming music [1]. Rhythmic interactions may also be 2. RELATED WORK a significant aspect of polyphonic rhythm perception, with complex rhythmic structures said to emerge from the inter- Models of rhythmic similarity are significant in both music action between rhythmic levels [2]. In the context of drum perception and music informatics research due to rhythm’s fundamental importance in music. For drum patterns in particular, models of rhythmic similarity have various c Olivier Lartillot, Fred Bruford. Licensed under a Cre- practical applications such as automatic generation of vari- ative Commons Attribution 4.0 International License (CC BY 4.0). At- tribution: Olivier Lartillot, Fred Bruford, “Bistate reduction and com- ations on drum patterns [6,7], or in visually mapping drum parison of drum patterns”, in Proc. of the 21st Int. Society for Music patterns by similarity to facilitate exploration of drum pat- Information Retrieval Conf., Montréal, Canada, 2020. tern libraries [8, 9]. 318 Proceedings of the 21st ISMIR Conference, Montreal,´ Canada, October 11-16, 2020 closed open high hat high hat closed snare high hat snare kick 12345678 kick 12345678 Figure 1. Drum pattern Early RnB 33. Velocity is represented in grey level, from 0 in white to maximum value in Figure 3. Drum pattern Reggae Grooves Fill 3. black. high high low low 12345678 12345678 Figure 4. Reduction of Reggae Grooves Fill 3. Figure 2. Reduction of Early RnB 33. State accents are shown in black and state onsets (if different from accents) in grey. ‘Low’ corresponds to and ‘high’ to . sultant ‘multirhythms’ due to the perceptual integration of # " simultaneous rhythmic streams. Additionally, while fixed weighting schemes have been used to weight more percep- Many models of rhythmic similarity for drum patterns tually important kit instruments [6], these may not be flexi- are based on monophonic rhythm similarity models. These ble enough to account for the possibly changing contextual methods are based on multiple possible representations of importance of different instruments in a drum pattern. rhythms. The most common method is as a vector consist- ing of either an onset or silence at each metrical position of the rhythm. The Hamming distance, a simple and popular 3. BISTATE REDUCTION model, works by counting the number of metrical positions Basic drum patterns are usually defined by the alterna- in two rhythm vectors that differ in value (one onset, the tion of, typically, bass (or “kick”) drum and snare drum other rest) [10]. The swap or directed-swap distance can strokes, with a further subdivision on the ride cymbal or also be calculated between rhythm vectors by counting the hi-hat 1 . The ordering in this definition implicitly indicates number of swap operations (exchanges between adjacent that the bass and snare drums alternation is of higher level metrical positions) that need to be performed to turn one of salience, while the cymbal or hi-hat subdivision is of rhythm into the other [11]. Other possible rhythm similar- lesser importance. ity measures use inter-onset intervals (IOIs), vectors of the distance between each successive onset as a multiple of the 3.1 Dominant Drum Selection smallest possible metrical position. An example of this is the chronotonic distance [10]. A thorough overview of nu- The first hypothesis guiding the approach presented in this merous approaches to rhythm similarity modelling can be paper is that drum patterns can be reduced by only focusing found in [10]. on these two most dominant classes of drum strokes. In the Typically, drum pattern similarity is modelled by stack- definition of basic drum patterns above, the two dominant ing these monophonic rhythm similarity models calculated drums are said to be bass and snare drums. But sometimes on each part separately. This has been found to be success- the snare drums can be replaced by, for instance, closed ful in a few cases; [7] found that the Hamming distance hi-hat. and directed-swap distance correlated strongly with human For a given drum pattern, we propose a simple method ratings of similarity for drum patterns, with the Hamming for selecting the two dominant drums. It consists in or- distance outperforming the directed-swap. In [8], the au- dering the drums in a decreasing hierarchical order, and thors found a 2D projection of the Hamming distance could selecting the two first drums, in this ordered list, that are partially cluster drum patterns in a way that matched their active in the given drum pattern. The first selected drum genre tags for a small dataset of patterns. In a pilot study, will be called the Low drum, as it often relates to the bass a model similar to the Hamming distance was also found drum and to the use of lower frequencies, while the second to correlate to listeners’ similarity ratings for drum pat- selected drum will be called the High drum. terns [12]. This model counts whether the number of met- For the drum patterns discussed throughout the paper, rical positions where rhythms differ, but adds a weighting the reduction was performed by using the following hier- metric based on metrical awareness. archical ordering: 1. kick drum, 2. snare drum, 3. closed The limitation of these models is that by stacking mono- hi-hat. It was not necessary to consider other drums, since phonic rhythm similarity measures calculated on each part at least two of these three drums were active in each drum separately, they fail to account for effects of rhythmic in- 1 Cf. for instance https://en.wikipedia.org/wiki/Drum_ teraction between instrument parts, or the perception of re- beat 319 up down 12345678 up 12345678 down Figure 4. Reduction of Reggae Grooves Fill 3. When 12345678 . Drum pattern N Country Intro with kick drum a state is repeated twice successively, the first square Figure 5 12345678(lower row), closed hi-hat (middle row).

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