By “3rd” I mean the sesquiquarta interval between the 4th and 5th harmonics, a proportion of 5/4, and most of what I say about 3rds goes for their 8ve inversion, 6ths, as well.
What is the special idiosyncratic personality of the 3rd, how different from the characters of the 8ve and 5th, and how might it be presented in music?
The Greeks knew of the 3rd, but didn’t mix it into the Pythagorean tuning derived from 8ves and 5ths. Introducing 3rds is a horror of complexity, and surpasses the limits of our notation, based on Pythagorean, which can be termed a “2-dimensional” tuning. Equal temperament is 1-dimensional, every interval a multiple of any other, and our notation is superfluous, with different symbols for the same note. Mean-tone is also 2-dimensional, combinations of 8ves and 3rds for 1/4-comma, and 8ves and tritones for 1/6-comma, so our notation fits. But with 3rds, 5ths, and 8ves all together, it’s 3-dimensional, and our notation is insufficient; especially in small ensembles, players will augment it with arrows showing which notes need to be lower or higher. The sad fact is that much of our music cannot have all simultaneous chordal and all consecutive melodic intervals “pure”, with simple ratios. 3rds, 5ths, and 8ves together do not make a concise tuning “system”, but more of an ever-branching tangle. Interestingly, a Pythagorean g-flat is an acceptable 3rd above d.
8ves and 5ths seem morally pure, inspiring, and their harmonies can feel spiritually uplifting. But 3rds just sound good; instead of ennobling justness, they only offer sensual pleasure. The sentimental interval. Very many of them render music cheap and schmaltzy, as in the stereotype of Bavarian music, or “How much is that doggie in the window?”. Chains of them have a recognizably sweet texture, cloying, saccharine.
Did renaissance musicians share this impression of the 3rd? Was the new “contenance angloise” music of a different affective temperament, as well as a possibly different tuning? Were 3rds performed with a special softness and sweetness? Studies suggest that about this time, life became softer and sweeter for many; was music a parallel? Sentimentality progressed through the baroque, and the new recorder, with its in-tune 5th resonance, was perhaps the specialist (“The 3rd Man”?), il flauto dolce in character as well as volume.
Without any firm conclusions, there might be enough possibility of special consideration for 3rds in the renaissance to deserve some attention and experimentation in performance.
Bob Marvin, XII 2014