The Man with the Horn

The Musically shapeshifting genius that is Miles Davis

Self Portrait by Miles Davis

For my corpus I have decided to investigate the jazz trumpet player Miles Davis. Davis is known within the jazz and global community as a constant innovator and key figure of jazz music. His method for innovation was to constantly attract upcoming talents and stars within the upcoming current in jazz. He then instructed these youngsters with his own vision of jazz and this was reciprocated by the youngsters how provided him with their own new views.

In my corpus I will try to analyse Davis’ music by answering the following questions:

How did Davis’ music change over time, what are the constants in his music and what are the variables?
Are these changes visible using only Spotify Data
Is the current selection of Miles’ phases justified? Or might there be a better way to classify his music?

For selecting the phases, I have looked at the bandmembers Miles had played with during these years and made playlists in Spotify to group these phases. The corpus consists of six phases:

Early bebop/Charlie Parker phase: 1945-1950
During his formative years, Miles played with the bebop greats like Charlie Parker and Dizzy Gillespie, still mostly as a sideman, only playing solo’s or accompanying the theme of the main player. Bebop is characterized by fast paced, harmonically nimble tunes that follow the standard jazz-structure of theme, solo and theme again

Hard Bop phase: 1950-1955
After the 40ies, most jazz musicians started to get tired of the musical acrobatics that bebop demanded and switched to a less complex style of jazz called hard bop. These are mostly mid-tempo, mellow tunes that follow clear structure and allowed for more space in songs. This is the period in which Miles would collaborate with a lot of different musicians and would be the birth of his “cool” sound.

Modal phase: 1955-1962
Pushing the limits of hard-bop, Miles wanted to winnow harmonic complexity even further, opting to reduce chord changes to as little as possible, in exchange for focussing on a certain mode (minor and major are the main categories, but come in a lot of variations). This is his most popular period, in which he released the most successful selling jazz album of all time: Kind of Blue.

Acoustic experimental phase: 1963-1968
After “dumbing down” the music, Miles wanted to experiment again with harmonies, this time eschewing traditional harmony and pushing for less structured, more atonal music (heavily influenced by the harmonic departures of John Coltrane and the Free Jazz Movement). This is the period of his second great quintet, involving amongst others the youngsters Wayne Shorter and Herbie Hancock.

Frantic Fusion Miles: 1969-1975
With electronic instruments bursting onto the scene, and with his bandmate Herbie Hancock being at the forefront of the revolution, Miles could not be left behind. He surrounded him with some of these frontrunners and went full electrical, except for his trumpet. This period is characterized by long jams in which multiple genres (mostly from the funk/soul and rock influence) were blended with his own sounds, to create a frantic melting pot.

The Lost Period (1975-1980)
Not included in this corpus, in 1975 Miles left music behind following mental issues, drug addiction and overall fatigue. Having arguments with record companies and collaborations that fell through, Miles went on a 5-year hiatus to recentre himself. Perhaps something in the data would provide clues to this sudden departure.

The Final Miles (1980-1991)
After returning, Miles continued his innovative crusade, this time trying to incorporate the hip-hop and R&B influences of the time into his music. The music itself remained frantic to his death, but Miles showed willingness to revisit his older phases during this time.

Miles transformations are visible in data from Spotify

The slope graph plot on the left shows Miles’ changes in the average Spotify features for each Time period. Clearly visible is the huge decline of acousticness during his lifetime. Other interesting elements are the general increase in energy, a maximum of liveness during his ’63 to ’68 phase and a decline in overall valence, which increased during his final years. Danceability stayed constant, with a big increase during his last years.

The acousticness drop is easily interpreted, since he mostly switched to electrical instruments later in life. A more difficult trend to interpret is the valence line. Valence is a measure of joyfulness in music, and as Miles became more erratic, his overall vibe became less joyful, after the hiatus it goes back to his original level, perhaps indicating that this hiatus motivated him to make more joyful music.

As valence dropped, energy rose, which is perhaps an odd combination, because you would assume that energetic music would be joyful music. The energy increase is perhaps best explained by the increase in Miles increasing franticness. Although he seems to have solved the balance of valence and energy in his final years. Even increasing danceability as well (perhaps hip-hop influences are responsible for this).

A limitation of the slope graph is that it currently shows no indication of the feature variances, which could provide more information on how broad the spectrum of the features were per time period, later on there will be more information on this.

Miles in terms of tempo, key and mode

Miles’ Modes
From the graph in the top left corner, it becomes apparent that Miles had a slight preference for the major key most of his life, although this effect is not substantive and could be due to errors in assigning modes in Spotify. The only clear difference is during his erratic period, in which Major keys seem to dominate his songs, although valence in this time dropped, showing that the major key is not always the happy key.

Miles’ Tempos
Overall, the tempos seem to be quite constant during Miles’ lifetime. Interesting is that the spread of the first phase is sloped towards the higher tempo’s (indicating the influence of bebop) and is slowing down during the cool and hard-bop phases. Another interesting outlier is the black dot at the zero mark during his 1969-1975 phase, this is an introduction track of a live album so should be omitted.

Miles’ Keys
In the early years there is a clear preference for the F-key in Miles’ oeuvre. This makes sense, as a trumpet is generally tuned in Bb, with the most comfortable keys being F, Eb and Bb. The 1969-1975 years were mostly comprised of long jams, and the bandleader (Miles) would usually determine the key, which coincides with this comfort key being Bb in those years.

The keys E, Eb and Gb seem to be less favoured by Miles, which is interesting because a lot of jazz is written in Eb. With musicians there is however a common tendency that if one favours a specific key (F in Miles’ case), the keys surrounding that key are less favoured, because they differ the most from the favourite key. It turns out that Miles follows this trend to avoid the keys near to his favourite key.

In conclusion of this page: Miles transformations are very clearly visible in terms of valence, danceability, acousticness and energy. The tempo’s remained mostly the same, but Miles had a specific preference for the key F during his lifetime. Since we now have a global overview of his oeuvre, it is time to check out the most typical songs of each phase. Click on the tab “Typical Miles” in the navigation bar to continue.

Typical Miles

Selecting Miles’ most typical tracks

The reason for selecting Miles’ most typical tracks, is that they allow me to zoom in on lower level audio features and get a better sense of the difference between time periods. These typical songs need to be representative of that time period, so later in this section I will check whether that was the case. The following questions are treated in this section:

What were the differences in timbre?
What were the differences in tempo?

I have decided to exclude Chord and Key-estimation, since jazz-music has a tendency to modulate a lot and use a lot of extended, ambiguous chords, which made interpreting these results very difficult.

To select Miles’ most typical tracks, I have made composite standardized z-scores based on acousticness, danceability, valence, energy and tempo. This allows me to filter out the most typical and atypical songs of each time period. The following is a list of typical songs (z < 0.1)

Most typical songs per time (based on tempo, valence, danceability, acousticness and energy)

1945-1949: Half Nelson

1950-1955: Boplicity

1956-1962: ‘Round Midnight

1963-1968: So What

1969-1975: Willie Nelson

1980-1991: Backyard Ritual

I’ve compiled these songs in a spotify playlist, and plotted their general characteristics. Check it out!

Analysing typical song structures shows both similarites and differences between phases

The self-similarity matrices (SSMs) shown here are based on timbre, with ‘Cosine’ distance and ‘mean’ summary statistic. The x and y axes are the songs duration in seconds (the song is being compared with itself), with brighter areas showing bigger timbre changes.

In the first three phases (1945-1962) the timbres remain mostly similar throughout the songs, with the squares of the checkerboard-pattern not showing major changes (green colours) and being mostly dark compared to other squares. For Half Nelson, there is one big change around the 120 second mark, which is the point where Miles starts to play his solo (prior to that Charlie Parker and Miles were playing together, with Charlie taking the first solo). Boplicity shows a similar pattern, in which solo’s are highlighted. Dolores also follows this pattern.

“So What” is an interesting SSM because it has big green lines instead of the clear square pattern. “So What” is a track categorized by a lot of call & response, in which first one instrument plays and the others respond afterwards. This could be the reason for the lines appearing as they do. Furthermore, Miles plays sparsely, not stringing melodies together, but rather making short statements with a lot of space between them, this is also a reason why the matrix shows these sharp lines of timbre-change instead of square-patterns.

Willie Nelson shows the largest amount of big timbre changes in the song, but is still quite structured in timbre-organization, indicating clear solo-preferences. The squares surrounding that show a lot of difference though, indicating that this song is more complex then the other ones. This is in contrast with Backyard Ritual, in which a bassline repeats over and over with a baseline by Marcus Miller. The only real differences are the intro, outro and when the Saxophone takes a short solo around the 180 mark.

Overall, the songs are quite differently structured from each other, showing differences in Miles approach during his phases. These are of course not fully representative of his phases but provide a good summary and indication.

Over the Barline and Beyond: the rhythmic differences of Miles compared to his brass Sidemen

Tempograms provide insight in how tempo evolves during a musical piece, once again the x-axis contains the song duration and the y-axis contains the measured bpm (this tempogram is based on energy), with brighter areas indicating larger amounts of energy. Here is a list of self-measured tempos and Spotify tempos of all the pieces:

Half Nelson: 192 bpm, Spotify: 94,5 bpm
Boplicity: 135 bpm, Spotify: 135.6 bpm
So What: 130 bpm, Spotify: 136.3 bpm
Dolores: 280 bpm, Spotify: 138.442 bpm
Willie Nelson: 112 bpm (but speeds up rapidly)
Backyard Ritual: 100 bpm, Spotify: 100 bpm

Judging by the tempograms, it seems like only Half Nelson was dead on, this was probably because of the walking bass and the fact that the drums also stayed fairly constant. This kept the novelty of energy constant which made it easier to determine tempo. For Boplicity the line around 135 bpm is also quite discernible, once again due to the drums being repetitive and the walking bass.

For So What the intro is all over the place, which makes sense as this was played rubato (without clear tempo). After that it settles in around 130 bpm, which is also a visible line in the tempogram, with triple time also being very clear (390 bpm). It gets a bit off track during John Coltrane’s saxophone solo however, which is quite funny when listening to the song, because it is very clear Coltrane moves around the rhythm a lot, whereas Miles stays a lot closer to the pulse. These influences are seen in Dolores as well, in which the best discernible line is around 560 bpm, this makes a lot of sense since Miles solos almost exclusively consist of 8th notes and Wayne Shorter’s solo does this as well. On top of that the drums are a lot less repetitive during these years.

Willie Nelson and Backyard Ritual are most clear in their tempograms, with Willie Nelson having a clear line around 410 bpm. This is weird, since the song speeds up and slows down a lot (the line does have some upward curve to it). I would’ve expected the lines to be less pronounced but did not expect the quadruple bpm mark to be this strong. The drums do subdivide the piece into 16th notes and emphasize this a lot, so perhaps that is the reason why that line is so prominent. Backyard Ritual has the straightest line of all tempograms, which is logical since it is using a drum computer as backing track. Once again, the subdivision of the drums is in 16th notes, which makes the 400 bpm mark the logical winner in the tempogram.

The takeaway from all this is that Miles is not as rhythmically adventurous a soloist as Coltrane was. It would’ve been interesting to check out the novelty functions as well to get confirmation on my hypotheses about subdivisions of beats, but I feel like that would make the corpus too long.

When comparing tempograms with Spotify’s decisions, it appears that Spotify got close to the right bpm most of time (which means their algorithm can detect differences between beats and subdivisions), except for Dolores and Half Nelson, which Spotify measured to be around half-time, whereas the bass clearly walks twice as fast in that piece.

Zooming out: Summarizing low level phase features

After analysing the typical tracks, it is time to check out if they hold any validity when analysing more songs per time period. Before interpreting the graph, here is a table with summaries on loudness, tempo and duration. I’ve tried to compare timbres across time periods, but this yielded no big differences between time-periods. For the graph I have looked at only the first 50 songs of each phase, since computing otherwise provided errors and took very long.

Time Period	Feature	Mean	SD
1940-1949	Tempo	121 bpm	37.4 bpm
	Duration	177 s	17.6 s
	Loudness	-11.45	2.0
1950-1955	Tempo	119 bpm	31.7 bpm
	Duration	273 s	111.4 s
	Loudness	-12.82	3.0
1956-1962	Tempo	113 bpm	30.0 bpm
	Duration	420 s	220 s
	Loudness	-15.1	4.35
1963-1968	Tempo	121 bpm	37.4 bpm
	Duration	471 s	213 s
	Loudness	-13.2	2.6
1969-1975	Tempo	121 bpm	31.7 bpm
	Duration	850 s	497.9 s
	Loudness	-11.2	3.9
1980-1991	Tempo	111 bpm	26.1 bpm
	Duration	261 s	90 s
	Loudness	-12.6	5.40

For the graph I have looked at only the first 50 songs of each phase, since computing otherwise provided errors and took very long.

Looking at the graph and the table, it becomes apparent that the song duration steadily increases over the phases, eventually dropping back in his last phase. A big increase is in his 1969-1975 years, with a whopping 850 second average duration (although standard deviation is substantial).

The standard deviations of the graph in tempo (indicating tempo consistency) in the first five phases are evenly dispersed between 2 and 5 bpm. Miles’ music was all played live during this time and bands tend to deviate between tempo’s compared to drum computers and such. This becomes visible in his last phase, in which most of the tempo SDs are concentrated between 0 and 1.

Concluding this section, it can be seen that Miles’ typical tracks are somewhat representative of their time periods. Firstly: Miles only favoured slower tempos in his last time period, before that the tempos were more distributed. The MFCCs showed a lot of activity in his earlier years, indicating a bigger presence of musical instruments, as in later life he preferred smaller ensembles. The constant in this time was that even in the frantic fusion period, Miles still preferred the traditional jazz song structure.

This was the analysis of Miles’ most typical pieces according to Spotify and my own selection of phases. Are these phases justified however? Click on the tab Predicting Miles.

Predicting Miles

How predictable are Miles’ Phases?

In the beginning of my corpus I decided to split Miles’ entire oeuvre into 6 distinct categories, based on the kind of music he was making at the time and the sidemen he surrounded him with, but I never checked whether the division into these categories was valid. It might be that another division of Miles’ periods based on Spotify data would fit better, thereby threatening the content validity of my corpus. Through prediction, I now have the tools to check if an algorithm can tell these different time periods apart from each other as well as I can. If that is the case, it provides proof that my current subset of phases is justified. Cluster analysis can provide further alternatives in splitting up the data, so perhaps that could either confirm or refute my hypothesis. Let’s start with the predictive models:

After fiddling around with the KNN-means method and the random forest method, I saw that the random forest model performed slightly better overall, so that became the model of choice, the tables on the left represent the unstandardized results and the standardized results in the form of percentages. The overall predictive success of the model was 78%, which is promising.

First, there is a very clear distinction between early Miles (1945-1962), transition Miles (1963-1968) and late Miles (1969-1991), as virtually none of the earlier songs get wrongfully assigned to later periods and vice versa. The Fusion (69-75) and the Modal (1956-1962) periods are the most distinct of all periods in this table, with very high accuracy. But what were the strongest predictors in this model?

Song duration saw the biggest changes over Miles’ career

This graphs shows the importance of each predictor when building the model, all predictors are currently visible and can be roughly divided into three groups: - Spotify general features (Acousticness, Valence, Danceability etc.) - Timbre features (c01 - c12) - Key features (C to B)

The predictors are ordered from low to high on their importance for predicting the time periods by their MeanDecreaseGini values, which is an indicator of predictor importance when using Random Forest Model. A higher score on MeanDecreaseGini translates to a higher importance for that predictor.

The predictor duration comes out as the most important predictor of this model, which makes a lot of sense given the last section of my corpus, which showed a lot of differences in duration per time period. The reasons for this are as follows: recording techniques in the 40ies were not suited for long pieces. So apart from Miles’ his own preferences for duration, he was also very heavily limited by the techniques at that time. The duration of his songs gradually increased and culminated during his fusion period (1969-1975), as can be seen in the table from the previous section.

The second most important predictor is acousticness, which already was apparent from the slope graph in the intro section. The acousticness heavily declined over the Miles’ lifespan, which makes it a prime predictor for the model. After 1969, most of his bandmates played electrical instruments. He himself however, never strayed far from his iconic muted trumpet sound.

Coming in third/fourth are the timbre features c06/c10,I will provide an interlude dedicated to this part in the next paragraph.

At the bottom are tempo and the keys, which makes sense as well. Jazz-culture is jam-culture, each musician is brought up on jam-sessions, in which any musician could call on any tune in any key (and at any tempo). Miles showed a consistent preference or aversion for specific keys, as shown earlier, although he did play a lot in F during his earlier years.

During the building of my model, I culled several predictors, of which almost all keys, the tempo and speechiness variable (since most of the music is instrumental). Furthermore, I incorporated interactions in the model based on the slope graph of the first sections. I created interactions between energy/acousticness and instrumentalness/energy. All modifications added about 7% to the prediction accuracy, and a random forest performed about 10% better on average than a Knn-means model.

Interlude: MFCC 06 and 10 are great predictors, but why?

In the panel I have plotted the values of Mel-frequency Cepstral Coefficients (MFCC) c06 and c10. MFCCs range from c01 to c12. C01 can be interpreted as loudness and from there on upwards, the “importance” of each MFCC decreases.

As far as interpreting MFCCs goes, it can get quite tricky. In general they represent components of the overall timbre of a piece, but it by no means translates to a specific instrument. The biggest transition during Miles’ switch from acoustic to electrical (starting in 1969), might be the cause of the aforementioned pattern. During this time, only the drums and trumpet sound remained constant. The first four phases were mostly acoustic and the last two phases were mostly electrical instruments. The final phase also had a lot of samples and drum-computers. The overall changes in timbre seen here, might relate to the overall drop in acousticness (also a big predictor), but as mentioned before this is not easily derived from MFCCs.

Clusters analysis provides some evidence for the phases

To end my corpus, I’ve used cluster analysis to check if my hypothesis about Miles’ time periods were justified. I started out by using all predictors, but this yielded inconclusive results, so I used to first 8 predictors of the predictor panel (up until Valence) to cluster the songs. After scaling and centring, I used the K-means method to determine clusters.

The top left panel shows a scree plot in which the Within Sum of Squares (WSS) was calculated for each possible cluster amount k. The WSS provides a summary statistic of the distance of each datapoint to the centroid of their respective cluster. The scree plot is also known as an elbow plot, because to find the best cluster-amount you must look at “elbow” or clearest pivot point of the plot. In this case the plot shows a clear drop-off after class 6, with class 5 as an optional second choice. This provides some proof that my own time-period based clustering is justified but does not tell the entire story.

Below the scree plot is a Silhouette plot. The average silhouette widths on the y-axis provide a measure about how well the datapoints fit to their respective cluster, based on how near they are to other datapoints sharing that cluster and how far away they are of datapoints of neighbouring clusters. The range of the silhouette width per data point is from -1 to 1, with a positive value indicating a better fit to its own cluster and a negative value indicating better fit for other clusters. Overall, the average silhouette width is quite low for all classes, indicating that the clusters overall are not that well defined. This is also visible in the histograms and the scatterplot on the right. The centroids (marked by diamonds) show the centre of each cluster for the two strongest predictors. As you can see, cluster 6 is the farthest away, but also has a large average distance of the datapoints to their centroids. The clusters 3,4 and 5 are close together.

Finally, the barplots in the bottom left. It appears that cluster 1 quite accurately belongs to the final phase and cluster 6 and cluster 2 belong mostly to the fusion phase. What is interesting is that there are no clusters clearly favouring the first bebop phase or the 1963-1968 phase, as the 1945-1950 phase is mostly grouped with the first three phases in cluster 3. The 1963-1968 phase mostly gets grouped with the 1969-1975 phase, indicating that the switch from acoustic to electric was slower and the phases are somewhat similar.

The last panel of my corpus will try to integrate all the findings of the previous sections and summarize the insights to conclude on what really changed and stayed the same over the course of Miles’ career.

Conclusion

Miles throughout the years

When starting out this corpus, I wanted to check how Miles Davis’ music changed over time, and whether this was visible through Spotify data. What stayed constant and what was different during each time period according to Spotify:

The constants: - Average Tempo - Key preference - Song structure

The differences: - Acousticness - Song duration - Timbres (electrical or acoustic) - Tempo standard deviation (especially in his last years)

Through clustering it became apparent that 6 clusters best represent the data, although the clusters do not exactly follow the time periods I formulated. Especially the earlier bebop phase and the second quintet phase were hard to properly identify, but the later phases were all very easily discernable.

The corpus eventually only covered a limited amount of features to be explored, with chord-examination, key-examination and even melody examination through spectrograms still to be evaluated. Furthermore I would’ve liked to spend more time evaluating Timbres, as these consistently came up as important predictors. Another shortcoming is that I could’ve spend more time looking at standard deviations when means did not provide valuable information. Hopefully, you’ve enjoyed this corpus and have gotten some information on the enigma that is Miles Davis.