Test your theory chops with the weekly challenge from Breaking Barlines! You’ll find a new question here every Monday. Please comment to post your reply.
This Week’s Challenge:
Sound is a funny thing. Matter doesn’t just vibrate at one fundamental frequency. It also vibrates at a series of fractional frequencies called overtones. In pitched instruments, these are usually much weaker than the fundamental, but in double basses they can be unusually strong, and therefore audible. At left below is an A minor chord orchestrated for strings (all notes are at concert pitch). At right are the overtones generated by the double basses’ low A. What problem does this cause, and how can it be solved?
Post your reply and come back Friday, July 22nd for the answer!
ANSWER for 7/18/22
In this root-position A minor chord, the basses’ 4th overtone introduces an unwanted C sharp, which clashes with the chord’s C natural. Fortunately, the solution is an easy one: simply make sure that at least one other instrument has the correcting pitch. In this example, the first violins will actually do the job, provided they are playing louder than the basses. Their C will be more than adequate to drown out the offending bass overtone. A less ideal voicing would be this, in which the 4th overtone would be audible:
The reality of overtones often directs the choices made by composers. Until the late 18th Century, keyboard composers avoided anything other than octaves in the low bass, and for good reason. Try playing an A minor triad in close position way down at the left end of the piano keyboard, and you’ll get mush! That’s because the low bass strings have audible overtones, and with small intervals like thirds, each pitch’s overtone series will clash with the others:
Mozart and Haydn often wrote only octaves this far down. Beethoven was one of the first keyboard composers to actually prefer the muddy, gritty sound of low-bass triads, and you’ll hear them in works as early as the Piano Sonata No. 8 in C minor, Op. 13 (the Pathètique).
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John Trotta says
Here’s another thought.
I was trying to harmonize an antiphonal church song. We were in the key of D, and at one point the given accompaniment shows a melody note of F# with a fifth (F# and C#) in the bass.
I remembered your example and harmonized that chord with an A#, making the chord an F# major chord resolving to a B minor.
Other occurrences in the hymn added an A natural to the given accompaniment, so I called that chord an F# minor.
The difference between the major sound and the minor sound fit the lyrics.