That mathematics generally underscores most forms of music is not a new concept; what is interesting is the possibility that a precise mathematical structure can be proposed as a computationally tractable foundation for several quite disparate musical traditions. In this book, mathematical and statistical techniques are brought to bear on several aspects of the classical Indian tradition known as Hindustani music, and more specifically to characterize the sophisticated concept of a raga.

The mathematical foundation used in this book is provided with the use of RUBATO [1], a software platform that explores the deep connection between musical objects and category theory. Music representation goes beyond simple sequences and patterns of notes, but uses the idea of denotators in an abstract space. This foundation allows music to be explored through statistical methods, in particular as a time series that can be examined as any stochastic process. Two kinds of data are used in the analysis: published sequences of notes that are supposed to be within a raga and transcriptions of vocal performances by musicians, after signal processing to create mathematical representations.

The book is organized around several chapters of varying lengths. Some of the chapters are way too short: in some cases, they are only four pages long, which isn’t really enough space to even introduce concepts, let alone to explore the ideas coherently. The longest chapter is chapter 3 where the RUBATO package is introduced. It is a shame, however, that the software is discussed in terms of its software components and the signal processing aspects; I would have very much appreciated a description of the semantic representation. Words like category theory and denotators were simply thrown in but not explained at all. This is a standalone chapter and doesn’t refer to Hindustani music at all.

The preface makes the different contribution of each author quite explicit. However, such heterogeneous authorship needs to be controlled by strong editing, which this book lacks, resulting in poor integration and general lack of clarity. Definitions are repeated several times, in different chapters. A more serious problem is inconsistency: for example, the same raga name is spelled three different ways: as Bhimpalashi in chapter 1; Bhimpalashree in chapters 4, 5, and 9; and the widely used Bhimpalasi in chapter 10. This editorial sloppiness can be confusing to readers who are not familiar with ragas and Hindustani music.

Chapter 7, in particular, is very poorly presented, with more than half a dozen grammatical errors in the first paragraph itself. It also doesn’t seem to follow a sensible narrative: Section 7.8 talks about using a recording of raga Bhairav, but the next section discusses raga Bihag, without even mentioning anything about where the data came from. I am left wholly perplexed by the concluding section of that chapter. Chapter 8, too, feels very incomplete: sections 8.4 and 8.5 are simply displays of outputs from the RUBATO software with very cryptic headings, with absolutely no text explaining the figures or guidance to readers on what they should observe in the figures, followed by a concluding section consisting of three sentences. For me, it seemed that the authors ran completely out of steam or time to wrap up the volume properly.

Other important issues include reproducibility and access to data. The main source of raga data is a Bengali manuscript providing sequences of notes for various ragas, which seems impossible to get hold of. The authors cite a Bengali publisher called Brati Prakashani, not indexed by any search engine. But there is evidence of a publisher called Bharati Prakashani: could this be the intended one? No other reference to the manuscript by Dutta by either publisher could be found. Some of the results rely on live recordings of Hindustani vocalists; it would have been excellent if these could have been made available on the web and referred to explicitly. A web resource would have been invaluable. Chapter 9 is about composition, and it concludes with a sequence of notes with a directive: “Render it!” How much more useful it would have been if a musical rendering of this sequence were provided, allowing readers to appreciate the result more vividly.

Chapter 10 is the least technical and launches a completely new stream, as a first-person singular recollection of a traditional Hindustani concert where the narrator (the first author of the volume) gave a short talk about computational musicology and music therapy to the unprepared audience at a traditional Hindustani concert. Instead of introducing a new idea (music therapy), which was just skimmed over, it would have been great to use the last chapter of the book to weave together the many ideas and results presented in such a sketchy way over the rest of the text.

Despite these weaknesses, this book makes a huge contribution in providing an accessible account published by a mainstream and highly reputed publisher of the complex mathematical foundation of a historical and established musical tradition that has not been considered by many Western musicologists.