Generating polyphonic music with coherent global structure is a major challenge for automatic composition algorithms. The primary difficulty arises due to the inefficiency of models to recognize underlying patterns beneath music notes across different levels of time scales and remain long-term consistency while composing. Hierarchical architectures can capture and represent learned patterns in different temporal scales and maintain consistency over long time spans, and this corresponds to the hierarchical structure in music. Motivated by this, focusing on leveraging the idea of hierarchical models and improve them to fit the sequence modeling problem, our paper proposes HAPPIER: a novel HierArchical PolyPhonic musIc gEnerative RNN. In HAPPIER, A higher 'measure level' learns correlations across measures and patterns for chord progressions, and a lower 'note level' learns a conditional distribution over the notes to generate within a measure. The two hierarchies operate at different clock rates: the higher one operates on a longer timescale and updates every measure, while the lower one operates on a shorter timescale and updates every unit duration. The two levels communicate with each other, and thus the entire architecture is trained jointly end-to-end by back-propagation. HAPPIER, profited from the strength of the hierarchical structure, generates polyphonic music with long-term dependencies compared to the state-of-the-art methods.
PRO's:
+good problem: generating polyphonic music with long-term structure
+reasonable approach: modification of SampleRNN: makes sense
CON's:
-doesn't work. 
My fundamental critique of this paper is that, while the authors claim that their system " generates polyphonic music which maintains long-term dependencies", in fact what it generates it is not really polyphonic, nor-- more importantly-- does it demonstrate the kind of long-term structure present in the training set.
1) Polyphony: The model predicts a combination of monophonic melody plus chords (i.e. chord names such as "A+", "C7" etc). This is different from polyphony, in which the model would predict the actual voicing used for those chords. However, this could be seen as an error in terminology; if the authors claimed that they were predicting a monophonic musical voice plus chords, and they did that well, that would be absolutely fine. Generating a coherent melodic line that continues, along with the chords underneath it, would be a great achievement. However, that is not what happens here. For examples, in the provided examples, e.g. Measure 19 of Fig 4, Measures 1,3,4,5, ... of Fig 6, contain stylistically unusual combinations of chords and melodic lines. By "stylistically unusual", I simply mean that those examples are not consistent with the Nottingham dataset.  Furthermore, in my subjective opinion, the examples that I listed above also just don't really musically work. There is no question that in the right context, any of those particular combinations of chords and melody notes *could* be made to work: for example, the first measure of Fig 6 would be perfectly fine as the beginning of a different song. (E.g. it could be taken as a slight reharmonization of the opening of "lullaby of birdland", but that would require a coherent continuation. )
2) Long-term structure: It seems to me that one of the key things that this paper sets out to do is to get strong long-term dependencies. The motivation for the SampleRNN-inspired approach is to have generation at multiple time scales, for example. However, there is no evidence in the presented examples of long-term structure. Consider Fig 6, for example. Where is the long-term structure? A D major chord is frequently repeated with occasional A7. That is reasonable but it does not necessarily demonstrate long-term structure, anymore than learning that "q" is often followed by "u" demonstrates long-term structure. There is no melodic motif, there is no sense of 4-bar phrasing (or any other recurring such pattern that I can tell). In fact, all of the samples shown (Fig 4, 6, 7, 8) all end up with the chord D major played most of the time, after what appears to be a bit more variation in the first few chords.
The results of the listening test are strange to me (beyond some of the apples-to-oranges comparisons). I cannot comment on those without hearing the pairs of examples that were actually played. How were those pairs selected?
At the moment, it does not seem worthwhile for this review to get into details about exactly how the system works, in light of the problematic output. If there is reason for me to do so, I would gladly oblige. The authors do make a variety of choices that appear to be fairly sensible. 
I would very much look forward to seeing a revised version of the system in future that produces the  kind of output that the system is intended to produce (and described as producing).