[Smt-talk] Doubling the tone of resolution

[Dmitri Tymoczko]

Dear List,

Some weeks ago, the list considered the question "when can you double the tone of resolution in a suspension?"  Since I was interested in this, I decided to have a look at Bach's practice.  I thought I'd report my results, as they provide a nice example of the potential interactions between corpus studies and pedagogy.

A few notes:

1) The rule I learned, and which teach, was "don't double the tone of resolution unless it is the root of a root position triad."  In other words, not just a 9-8 suspension, but a 9-8 where the 8 is the root of a root-position triad.

2) This is the rule you find in Gauldin's textbook (though it is not very clearly stated).  Kostka and Payne, and Aldwell and Schachter, at least in the editions I checked, both offer the more permissive rule "you can double the tone of resolution in ANY 9-8 suspension."

3) Out of about 1500 suspensions, we can actually list the doubling patterns that occur.  What follows are "figured bass normal forms" where the bass is always 0.  On each line I provide the chord of resolution, the actual suspension chord, and the number of times this pattern appears. 

So, for example, ('[0, 4, 7] [0, 0, 5, 7]', 498) means that there are 498 cases where you have a root position major triad (0 4 7), with a doubled root and a 4-3 suspension that delays the arrival of the third (0 0 4 7).  

Another example: ('[0, 3, 8] [0, 3, 3, 10]', 50) means that you have 50 cases where you have a first-inversion major triad (0 3 8) with a doubled fifth and a 7-6 suspension that delays the arrival of the root (0 3 3 10).

One more, just for clarity: ('[0, 3, 6, 8] [1, 3, 6, 8]', 7) means seven cases of a bass suspension that delays the arrival of the third of a first-inversion dominant seventh.

4) It turns out that my rule corresponds well with Bach's practice in the chorales.  Here are the suspension patterns that appear more than 5 times.  Note the very prominent 9-8 over a root position triad (434 cases, counting both major and minor).  The only exception to my rule here is (0, 4, 9) (0, 2, 4 11), which is a double suspension over a first inversion minor triad (starred below).  This occurs 7 times, which is not a lot (7/1547 = 0.5% of all suspensions, one out of 200 cases).

('[0, 4, 7] [0, 0, 5, 7]', 498)
('[0, 4, 7] [0, 2, 4, 7]', 223)
('[0, 3, 7] [0, 2, 3, 7]', 211)
('[0, 3, 7] [0, 0, 5, 7]', 56)
('[0, 4, 7] [0, 5, 7, 7]', 51)
('[0, 3, 8] [0, 3, 3, 10]', 50)
('[0, 4, 9] [0, 4, 4, 11]', 50)
('[0, 3, 9] [0, 3, 3, 10]', 48)
('[0, 4, 7, 10] [0, 5, 7, 10]', 43)
('[0, 3, 9] [0, 0, 3, 10]', 30)
('[0, 3, 8] [0, 0, 3, 10]', 25)
('[0, 3, 8] [1, 3, 3, 8]', 24)
('[0, 3, 8] [1, 3, 8, 8]', 21)
('[0, 3, 6, 8] [0, 3, 6, 10]', 11)
('[0, 3, 7] [0, 2, 3, 3]', 8)
('[0, 4, 7] [0, 2, 5, 7]', 7)
('[0, 3, 6, 8] [1, 3, 6, 8]', 7)
*** ('[0, 4, 9] [0, 2, 4, 11]', 7)
('[0, 3, 6, 9] [1, 3, 6, 9]', 7)
('[0, 3, 6, 8] [0, 3, 6, 9]', 7)
('[0, 4, 7] [0, 2, 4, 4]', 7)
('[0, 3, 7] [0, 2, 5, 7]', 6)
('[0, 3, 8] [0, 3, 3, 9]', 6)

If anyone cares, the full list is at: http://dmitri.tymoczko.com/suspensionpatterns.txt

5) Final comment: it is very likely that different composers have different tendencies in this regard.  It would be too much to hope that a single rule covered all the great classical and romantic composers.  As pedagogues this leaves us with a dilemma, either to (a) teach the practice of some worthy exemplar (like Bach); (b) teach many different composer-specific rules; or (c) concoct our own rules.  I favor (a).

DT

Dmitri Tymoczko
Professor of Music
310 Woolworth Center
Princeton, NJ 08544-1007
(609) 258-4255 (ph), (609) 258-6793 (fax)
http://dmitri.tymoczko.com