I am a researcher within the Performing Arts Medicine Association. I was interested in looking at Beethoven's use of range over time in his piano sonatas. Although several previous studies have looked at the question of how Beethoven's compositions were affected by his hearing loss, the results were far less than conclusive. A study in the British Medical Journal counted the notes in the first movements of the first violin parts of Beethoven's string quartet's by hand. For a number of reasons, I thought it might be better to look at the piano sonatas, including that Beethoven wrote more piano sonatas than he did string quartets and symphonies, so the statistical power would be greater. Counting all of the notes in Beethoven's piano sonatas by hand would be a Herculean task for sure, but fortunately with scores available from the Center for Computer Assisted Humanities and music21 sufficient coding skills would do the job.
In addition to the number of high notes, I was also interested in Beethoven's overall use of range, the average note, average frequency, number of measures with high notes, and in calculating values based on the number of notes, as well as weighting those measures by the duration of notes. The methods available in music21 allow the collection of this data very quickly. To collect the majority of the data I needed from all 103 movements of Beethoven's piano sonatas, count over a quarter million individual notes, and organize the data into sonatas, and separating the data by movement number, takes about 11 minutes.
Some Interesting Findings
Beethoven's use of high notes was lowest around 1800 (for all the graphs below, the colors within the dots represent the Sonata Numbers, going from red to purple from 1-32):
The average frequency of each sonata follows a similar trend:
In general, as there are more notes per measure, there are more high notes per measure. This trend does not hold many of the sonatas written before 1802.
Also, the relationship between the use of high notes, and the average frequency was different between the earlier and later sonatas:
Technology like music21 is an invaluable tool for the empirical study of musicology. Relatively quickly, data gathered can be used to analyze the possible relationships between Beethoven's use of high notes and his overall range, and compare that with what we understand about his hearing loss. These data suggest that Beethoven was significantly affected by his hearing loss, though it seems that sometime around 1802 he developed strategies to cope with his progressing disability.
The well known melody...occurs in the T[enor] range in the Tournai MS; the question therefore remains whether one or more voices would have accompanied it. For this reason we decided to include this purely monodic piece in the present edition.
With these adjustments, the piece is almost entirely consonant, with the following breakdown of sonorities (discounting triplets in the middle of a semibreve):
36% Perfect fifth
18 Major triad
12 Major third
12 Minor triad
9 Minor third
8 Minor triad as 6-3
3 Major sixth
2 Minor sixth
0.5 Perfect fourth
Cattin and Facchin note that piece seems to be on the chant cantus firmus of no. 58 of Margaretha Landwehr-Melnicki's catalogue. The first Kyrie is indeed similar to this chant, but as a look at Paris, BNF lat. 14819, f. 34v. or Paris, BNF lat. 17309, f. 27v will show, the rest of the work is unrelated to this chant.
Otherwise the style of the work is similar to many French works from around 1350 (and also Spanish and Italian works from this time or slightly later). Facchin's description of these pieces, largely homophonic but with decorations, as part of a Wandering Style, or Stile Vaganti! seems quite appropriate for this work that wandered around the foot of a more famous Mass, waiting to be rediscovered.
More about the Sanctus and a fuller realization of it to come soon, thanks to an idea from Jan Janovčik. Here's a preview of his great recording with his Cantores Sancti Gregorii
Thanks to Jan Janovčik, Rob C. Wegman, and Dominique Gatté for aid and suggesting the Tournai manuscript as a source worth returning to. And to Anna Grau and Jeremy Jennings for their work on the EMMSAP project that made this work quickly possible.
|The bottom rungs of the |
May 26, 2014 rankings
It always rankles me when my favorite teams appear lower than other teams with the worse records than my teams' own. Of course that's part of the point of these rankings: to show subjective impressions of who is actually better than someone else despite having the record not showing their "inner strength" or some mumbo-jumbo like that. Still, when week after week, it appears that your team is getting the shaft, you begin to wonder if perhaps the rankings aren't so much about power on the field as power to draw viewers to the Sunday Night featured game, which doesn't exactly showcase all thirty teams equally.
To test whether there's something more happening, I looked at all of the power rankings from Week 15 of 2005, when ESPN started them or at least put them online in their current format, to the latest incarnation, Week 10 of 2014. (No, I didn't look at them all directly, I have computers for that.). For each team each week, I assigned a "bias point" for every rank that a team was above them with a worse win-loss record than them. For instance, if a the Jays at 25-20 were ranked 2 and the teams in ranks 3 and 5 had better records then them then the Jays would get 4 bias points, one for the team with rank 3 and three for the team in rank 5. Similarly teams would get negative bias points for teams ranked above them with worse records. In the illustration above, the Padres (my favorite, generally losing team) would get -1 points for being a position below the Red Sox (my next favorite, generally winning team). The Cubs and Diamondbacks would exchange no bias points even though percentage wise the Snakes are slightly ahead.
Over about ten years of Power Rankings, the teams most often ranked above their records were
1. Yankees (2052 points)
2. Red Sox (1101)
3. Tigers (968)
4. Angels (945)
5. Blue Jays (918)
The bottom five were
30. Pirates (-1141)
29. Astros (-1113)
28. Orioles (-977)
27. Rockies (-848)
26. Marlins (-805)
Since I started this to look at the Padres (-774), I'll just note that they ranked 24th. For the most part, these numbers make sense -- even though these bias rankings already take into the power ranks assigned on the basis of current records, the people at ESPN wouldn't be earning their keep if they didn't take into account historical trends. In fact, looking at weeks 8 and beyond, the amount of bias is less, and there's some shuffling throughout the ranks, though not at the very top:
1. Yankees (285)
2. Indians (241)
3. Phillies (210)
4. A's (178)
5. Angels (122)
30. Brewers (-380)
29. D'backs (-326)
28. Astros (-220)
27. Cardinals (-175)
26. Mariners (-153)
(Padres jump to 18th at -30 points, actually beating the Red Sox who drop all the way to 22nd at -70! Clearly those second half spurts and slumps, respectively, make a difference.)
A stronger showing of bias would be whether there's a long-term difference between the record of a team and its bias measure. The five most winning teams over the ten-year period were 1. Yankees, 2. Angels, 3. Red Sox, 4. Cardinals, and 5. Phillies and the most losing were 30. Royals, 29. Pirates, 28. Astros, 27. Mariners, and 26. Orioles (Cubs fans, be glad I didn't extend this list one more spot! oops.; Padres hit #21). Subtracting the win-loss rank from the Power Rankings bias rank gives a ranking of systematic difference that cannot be explained by records alone.
Most biased for:
1. Cubs (WL rank: 24.5; PR rank: 12; = difference: 12.5)
2. Blue Jays (17 - 5 = 12)
3. Royals (!! Rob Neyer?) (30 - 22 = 8)
4. Indians (19 - 13 = 6)
5. Tigers (7 - 3 = 4)
At the bottom:
30. Cardinals (4 - 16 = -12)
29. Brewers (11 - 20 = -9)
28. Rockies (22 - 27 = -5)
27. Reds (15 - 19 = 4)
26t. D'backs, Padres, Marlins (20 - 23 or 21 - 24 or 23 - 26 = -3)
In both of these lists there are good, average, and pretty bad teams. There are some adjustments that could be made. For instance, since the records only reflect the regular season we could adjust for World Series wins and pennant wins, subtracting a system bias point for each (i.e., 2 pts for winning the Series and one for losing). To keep the numbers exactly constant we'll add one point per team (I love it when the math works out: 3 pts per season and 10 years in the dataset = 30 points, or exactly one per team). At the top nothing changes, since none of the top four teams have done anything in late October, except that the Tigers disappear from the most overrated (two pennants will do that for you) to be replaced by the Nationals. At the very bottom, nothing changes -- in fact four World Series appearances for the Cardinals just makes the bias even worse. San Francisco and Philadelphia make their way into 27 and 26.
Technically by this method, the Red Sox tie Philadelphia, but as #2 on the PR positive bias, they're hardly being discriminated against by any measure, but they do have a legitimate beef against the way they've been treated in the last two-thirds of the season.
There are a lot of ways to slice the data; some of which make the Padres look exploited, and others the give them more credit than they deserve. However, any way you look at the numbers -- adjusting or not for postseason success, including or excluding the start of the season -- there are some teams that the ESPN staff are definitely fans of: the Cubs, Royals, Indians, Nationals, Rays, and Jays. And there are some that get no love: Rockies, White Sox, Reds, Rangers, Giants, Diamondbacks, and Brewers. But most of all its the St. Louis Cardinals who time and time again get the shaft on the Power Rankings. Maybe it's time for the crew to stop batting their eyelashes at the Friendly Confines and look for inner strength down I-55.
(attachments: Excel Spreadsheet and, in case anyone wants to look at NFL, NBA, or NHL Power Rankings, the Python program that generated the data)
Cuthbert received his A.B. summa cum laude, A.M. and Ph.D. degrees from Harvard University. He spent 2004-05 at the American Academy as a Rome Prize winner in Medieval Studies, 2009-10 as Fellow at Harvard's Villa I Tatti Center for Italian Renaissance Studies in Florence, and in 2012–13 was a Fellow at the Radcliffe Institute in 2012-13. Prior to coming to MIT, Cuthbert was Visiting Assistant Professor on the faculties of Smith and Mount Holyoke Colleges. His teaching includes early music, music since 1900, computational musicology, and music theory.
Cuthbert has worked extensively on computer-aided musical analysis, fourteenth-century music, and the music of the past forty years. He is creator and principal investigator of the music21 project. He has lectured and published on fragments and palimpsests of the late Middle Ages, set analysis of Sub-Saharan African Rhythm, Minimalism, and the music of John Zorn.
Cuthbert is writing a book on Italian sacred music from the arrival of the Black Death to the end of the Great Schism.
Download what is almost certainly an out-of-date C.V. here (last modified June 2012)
Bologna Q15: the making and remaking of a musical manuscript, review for Notes 66.3 (March), pp. 656-60.
"Palimpsests, Sketches, and Extracts: The Organization and Compositions of Seville 5-2-25," L’Ars Nova Italiana del Trecento 7, pp. 57–78.
Der Mensural Codex St. Emmeram: Faksimile der Handschift Clm 14274 der Bayerischen Staatsbibliothek München, review for Notes 65.4 (June), pp. 252–4.
"Generalized Set Analysis and Sub-Saharan African Rhythm? Evaluating and Expanding the Theories of Willie Anku," Journal of New Music Research (formerly Interface) 35.3, pp. 211–19. [.pdf]
Unless otherwise mentioned, the writings, compositions and recordings on this site are licensed under a Creative Commons Attribution-Noncommercial-No Derivative Works 3.0 United States License.
Copyright 2010-14, Michael Scott Cuthbert. Web design by M.S.C.
Fonts for musicology: Ciconia (14th/15th c.) and ClarFinger (clarinet music).
In my copious spare time as a junior faculty member on tenure track, I do web design and programming consulting for the National Bureau of Economic Research.
Lectures on the web
enChanting: Musical Artifacts in Unlikely Places, lecture March 3, 2009
Ambiguity, Process, and Information Content in Minimal Music, podcast of a lecture to Comparative Media Studies at M.I.T.
Just for fun...
Mondrian meets Finding Aids in a map of books in my former apartment.
Numeric Deathmatch, a game I coded that was taught to me by Jon Wild. More fun in person, but the web interface encourages trashtalking.
Musicology Buzzword Bingo, useful for AMS meetings (requires Bach and Futura fonts)
Automatic New Musicology Paper Generator based on the Dada engine