Networks are currently popular in studies of music. However, they tend to be unrooted similarity networks, showing some form of alleged commonality among artists or their music, as shown in the first graph. This example displays phenotypic similarity among the named artists, although how the "similarity" is measured is not always clear (the post on The Music Genome Project is no such thing briefly discusses this).
[Note: For an alternative approach, Glenn McDonald's Every Noise at Once has a two-dimensional scatter-plot of 1,491 music genres.]
Of more interest to us is the use of a network to study the historical development of music genres, for which we need a rooted network. Clearly, music history will be reticulate rather than tree-like, given the obvious transfers of musical modes between and within cultures, and even the possible resurrection of earlier styles at a later time and even place. A similar argument applies to musical instruments, of course (see Cornets: from a tree to a network; Guitars and networks).
Music networks appear in a previous post, on Reconstructing ancestors in a splits network. That post discusses the paper by J. Miguel Díaz-Báñez, Giovanna Farigu, Francisco Gómez, David Rappaport & Godfried T. Toussaint (2004) El Compás flamenco: a phylogenetic analysis. Proceedings of BRIDGES Conference: Mathematical Connections in Art, Music and Science, pp. 61-70.
The authors provide an analysis of the hand-clapping patterns of the flamenco music of Andalucia, in southern Spain. There are four recognized patterns, plus the fandango pattern, and the authors use two different distance measures to assess their rhythmic similarities. They produce unrooted phylogenetic networks based on each of these distances, using NeighborNet, one of which is shown in the second graph.
The authors ignore the fact that "it is well established that the fountain of flamenco music is the fandango", which would make the fandango the outgroup for rooting if we did wish to treat the networks as rooted. Instead, they try to "reconstruct the 'ancestral' rhythms correspnding to the nodes" by using mid-point rooting. This is a tricky business for networks, because there are multiple paths through the graph, and so the mid-point is not necessarily unique.
A similar NeighborNet analysis had previously been provided by Godfried Toussaint (2003) Classification and phylogenetic analysis of African ternary rhythm timelines. Proceedings of BRIDGES Conference: Mathematical Connections in Art, Music and Science, pp. 25-36. This involved an analysis of the 12/8 time bell rhythms in African and Afro-American music. The distances were based on "measures of rhythmic oddity and off-beatness" (this is briefly discussed in Hunting for rhythm’s DNA).
Very few people seem to be interested in producing rooted phylogenetic diagrams directly, except when their model is a tree rather than a network. Perhaps the most ambitious of these is by Victor Grauer (2011) Sounding the Depths: Tradition and the Voices of History. This is available as a paperback or for kindle. The audio-visual examples are available as a blog page, as are the figures.
His tree is shown in the next graph, including the characters on which it is based. Note that group B3. "Social Unison" is associated with a historical bottleneck, so that the prior history appears to be uncertain.
Finally, not everyone agrees about the importance of the obvious reticulation patterns in music history, notably Sylvie Le Bomin, Guillaume Lecointre, Evelyne Heyer (2016) The evolution of musical diversity: the key role of vertical transmission. PLoS One 11: e0151570. These authors study the music of groups of farmer and hunter-gatherer Bantu and Ubanguian speakers from Gabon, in western Africa. Their music characters are from three groups: repertoire (set of pieces including circumstance and social or symbolic implicit information), performativ (polyphonic process, form, instruments and vocal techniques), and intrinsic (metrics, rhythm and melodic).
The authors present a rooted phylogenentic tree, but there is also a "filtered" NeighborNet tucked away in an appendix. It seems to contradict any claim for the data being particularly tree-like.
Finally, to return to where I started, you could take a look at Musicmap, which allegedly covers The Genealogy and History of Popular Music Genres from Origin till Present (1870-2016). To quote from the info:
Musicmap attempts to provide the ultimate genealogy of popular music genres, including their relations and history. It is the result of more than seven years of research with over 200 listed sources and cross examination of many other visual genealogies. Its aim is to focus on the delicate balance between comprehensibility, accuracy and accessibility.
You need to zoom in a long way to appreciate the complexity of the network, covering 230 music genres. There is nominally a timeline from top to bottom (starting in 1870), although the network connections are not strictly time-consistent. As the (mostly Belgian) creators (lead by Kwinten Crauwels) note:
The ideal genealogy is not only complete and correct, but also easy to understand despite its complexity. This is a utopian balance that can never be achieved but only approached. By choosing the right amount of genres, determining forms of hierarchy and analogy and ordering everything in a logical but authentic manner, a satisfactory balance can be obtained ... Musicmap is a platform in search for the perfect balance of popular music genres to provide a powerful tool for educational means or a complementary framework in the field of music metadata and automatic taxonomy.