An Alternate Way of Calculating the Influences Ranks

A common complaint concerning efforts to establish a meaning for ranks describing influence is that one should, or shouldn't, take into account sequential, cumulative influences. For example, is it meaningful to say that because Mozart influenced Beethoven, and Beethoven influenced Brahms, that Mozart influenced Brahms? This, regardless of whether Brahms might have admitted direct influence of Mozart, or observers have seen any such influence in Brahms's compositions. Obviously, it *is* meaningful in one sense or another, but it is less obvious how one should *measure* this. Early composers in fact have had their influence on all later figures, but any comparative assessment of import among all composers should neither overemphasize historical order, nor ignore it.

The CMN originally dealt with this matter in the simplest fashion, by accumulating data on *direct* evidence of influence; that is, by looking for commonalities identified by observers in the music of composers, or acknowledgments of influence by the composers themselves. This is perhaps to some extent satisfactory, as we can always give primacy to what we are currently most interested in listening to. Still, it somewhat ignores how *relatively* important this or that composer was as a mover and shaker. In particular, it leaves both deep-history figures and recent ones at a disadvantage: the former, because of the swamping effect of the appropriations by later figures, and the latter because we have not yet seen how influential they may be over the longer term.

To get around this problem to a certain degree I have come up with a new statistic of influence which employs "second-order" thinking. Starting with the overall influence weights described in the previous sections, I connected these back to the periods their respective composers were alive, and produced new lists (decennially) within which new rankings could be established. One can then calculate a new average ranking for each composer which may legitimately be compared to others' over the whole of music history.

This can be more easily seen by bringing up the pdf below, but let us consider an example first. Claudio Monteverdi (1567 - 1643) ranks only no. 53 in the main list, but in the influences list comes in at no. 39. Through the new calculation, however, he advances to no. 13 because he was the dominant figure for five decades in his own time. Other composers whose rankings benefit significantly from this new way of looking at the matter include Lasso, Marenzio, Josquin Desprez, and Lully, and to a certain extent some recent figures. Interestingly, the top five in the earlier list remain the same (though not in the same exact order).

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