[Note: the most recent postings appear at the top of the blog; to get to the beginning of the “greatest composers” series, start reading with “The Top Ten Greatest Composers,” further down.]
One advantage of my data-driven approach to identifying the greatest composers is that, having named the top 10, I have the statistics available to identify the “second ten” top composers. Here’s my list of composers 11 – 20, arranged alphabetically, with some explanation of how I arrived at this grouping:
Chopin
Copland
Dvorak
Mahler
Puccini
Schoenberg
Schumann
Shostakovich
Richard Strauss
Vivaldi
Wagner
There are 11 names here; I have included two composers at the bottom of the list numerically (Shostakovich and Vivaldi) who had identical scores.
A reminder, again, about my criteria; in brief, they were: 1) inherent quality of works; 2) scope of influence; 3) whether they wrote some widely recognized timeless classics; and 4) diversity of composing activity (diverse genres, forms, instruments). Composers were rated according to these criteria on a 1 – 5 scale.
The top of this second grouping is occupied by Dvorak, Schumann and Wagner (each had scores of 13). Parsing that out a bit, to show how the methodology works: I gave Dvorak a 4 for quality of works, a 2 for influence (he is a giant of the Romantic tradition, but influenced few after him), a 3 for recognized classics (after you get beyond the New World Symphony, there is little that has captured the popular imagination), and a 4 for diversity of works.
Schumann, by contrast, gets a 4 for quality, a 3 for influence (Mahler, for one, learned a lot from him), a 2 for the number of classics (most people probably couldn’t name a Schumann work) and a 4 for diversity of works (he wrote in almost all genres, and although he wrote only one opera, he has numerous choral and opera-like works, e.g., Scenes from Goethe’s Faust, Paradies und die Peri).
Wagner got a 4 for quality, a 4 for influence (his harmonic innovations and use of the leitmotiv were especially influential for later composers), 4 for recognized classics (numerous operas) but only a 1 for diversity of works (he has very few non-operatic works, including a symphony and the Siegfried Idyll).
Surprisingly (to me, anyway) Copland and Chopin ended up with the same numerical score (12); Chopin’s total was brought down by the lack of diversity of works, in terms of instrumentation.
People can quibble with my ratings—and I’m sure they will—but if so, I invite them to use my framework, or devise one of their own, and make their own ratings.
Hunter's Window 
This has some surprises in it! I’m surprised but pleased that Copland made it–a sentimental favorite for someone from Appalachia who appreciates the intense mythology of Appalachian Spring. But tied with Chopin! That’s amazing. But your criteria force us to re-think assumptions and popularity contests.
Both lists of ten composers are certainly among the best ever. Often when you are dealing with talent such as Beethoven or Wagner or Copland you almost have to split hairs to see who truly would be a better composer. The work you have done on these lists is respectable. I might have liked to see Gustav Holst (mostly because of ‘The Planets’) and Edward Elgar (mostly for ‘Enigma Variations’) in your initial considerations- though I can’t say it would have changed much. Every composer that appears on your lists is a musical juggernaut.
Yes, I struggled with the initial consideration list, and Holst and Elgar certainly were candidates. I think you’re right, though: the result would have been the same.
Very interesting topic, appreciate it for putting up.