Timothy Summers

harmonypartition works simply and cleanly with MIDI files.

Using the music21 package, harmonypartition is able to analyze a MIDI file in exactly the same way it analyzes an audio file.

Results from MIDI are cleaner than those from audio – though not necessarily better, since resonance and continuity play such a key role in analysis, performance, and understanding. But MIDI is an important and stable reference in music notation, and provides invaluable information on many levels.

analysing a MIDI file

Below is an analysis of the same progression as on the previous pages: vi-ii-V-I in C Major, from a MIDI file:

bin_a, kpdve_a = pt_analyzeMIDI.analyze_notation_file("vi_ii_V_I.mid", beats_per_slice=2)

This analysis (like all analyses in harmonypartition yields two crucial pieces of information. The first is a binary ‘punch card’ of pitches. The second is an analysis of probable function. These can be seen below. First, in binary (with analysis given below):

Second, coded by proximity and most probable (or, more to the point, laziest possible) harmonic function:

This analysis is very close to what derives from the Fourier analysis of a live performance of the same music, here played on a lightly out-of-tune piano:

further examples: MAESTRO dataset

Then, to take a leap away from the vi-ii-V-I, here is a somewhat more sophisticated examples: Prelude and Fugue in A Minor, WTC II, BWV 889 (Johann Sebastian Bach), from the MAESTRO dataset. First an analysis of the audio recording:

And here an analysis of the MIDI version of the same performance:

These analyses could use some smoothing and statistical comparison, but all in all, it’s not bad for pure binary logic – which seems like a good, rooted place to have a meeting point.

I’ve built the harmonypartition system to generate harmonic sequences with just a few small numbers. Here is a simple one, built from simple piles of sine waves. Later they can of course expand to MIDI and DAW systems.

harmony as a sequence

So to begin: the following sequence:

base_seq = [4,3,2,1]

…can generate this chord sequence:

This is not such a big deal, but it is already interesting that a harmonic parametrization can be rendered as simply as a melodic contour.

What is interesting is that the system underneath is much more than usually flexible. Change one parameter:

p = 5

… and you get this:

This means, for example, that you could change the entire harmonic atmosphere of music (e.g in a game or film) according to easily structured parameters.

Intuitive relationships among these parameters would allow harmonic atmospheres to change meaningfully based on the motion of a joystick, a changing of levels, or other measurable conditions.

minimal encoding

And the encoding is very small, but non-trivial: it gives not only the notes but the function of each chord, which allows for improvisation. Here, for example is the encoding for the chords of ‘Blue in Green’:

b6e3/b6e3/b763/b763/bd22/9da2/a8e3/a8a3/b023/b023/b763/b763/b123/b123/925/925/b364/b364/b123/b123

…which sounds like this (with its bass line calculated from the encoding):

…and like this with a field of (mathematically extrapolated, and slightly hysterical) notes above it:

I also use these small generated files (looped, and longer) to help violin students play over chords. Also, the encoding of a chord is small enough (32 bits) that the sharing of harmonic sequences over software (and IoT) could be rigorous on the one hand (for systems), and flexible (for people) on the other.

flexible decompression

What’s curious is that the system employs a type of compression which can be flexibly decompressed – delivering a world of sensible possibilities rather than a single unambiguous solution. This ambiguity derives from the fundamental ternary treatment of the byte.

harmonypartition can harmonically analyze audio files by dynamically seeking and organizing tonal continuities.

In a great many musical cases, these continuities take the form of familiar keys and chords.

example: vi-ii-V-I

Here, for example, is a vi-ii-V-I progression in C major, generated from fourier analysis of a .wav file:

Here is the same progression, analyzed from my own lightly out-of-tune piano, with a different voicing:

Although the underpinnings and overtones (shown below and atop the central graphs) are shaken by the realities of live sound, the central analysis holds equally.

generating graphs

We can generate graphs with the following python code from the harmonypartition modules:

audio_kpdve_graph.graph_audio_file("C_6251_live.wav", chroma_threshold=0.3)

A firm, unchanging mathematical system undergirds the analysis, working within the idea of number, group, and ternary rather than with statistical operations. In the course of this method, the harmonic system functions as a hybrid, highly efficient form of neural network, using a miniature backpropagation to find meaningful (and maximally lazy) tonal centers.

It is possible in this manner to analyze any audio file for music-harmonic content, exposing large-scale structures in the musical works. Examples of this type of analysis can be seen in the “Audio and Insights” pages at the Charlottesville Chamber Music Festival.

Beethoven: Sonata No. 1 for Violin and Piano in D Major, Op. 12, No. 1, Mvt. 3 with Jennifer Frautschi, violin, and Max Levinson, piano

Schubert: Fantasie for Violin and Piano, D934, excerpts with James Ehnes, violin, and Inon Barnatan, piano

Beethoven: Sonata No. 10 for Violin and Piano in G Major, Op. 96, mvt. 4, with Timothy Summers, violin, and Benjamin Hochman, piano

The same process can be applied to MIDI and to live-streamed audio. The next post will address the process in MIDI.

Please send along any files for analysis — I would be happy to experiment with them in the course of further development, and discuss results.

The fourier analyses use the librosa package for pitch detection.