The Tritone: its Elemental Functions[1]
The tritone is one of the more important intervals in music. Theory text books barely mention it. The interval of a tritone is the distance of three steps, hence ‘tri’- tone. It is the characteristic interval of the dominant with and without a root. It also is made up of two possible enharmonic[2] intervals; the augmented 4thand diminished 5th. The tritone is the fulcrum upon which the dominant (x), with or without a root is identified with its characteristic intervals of a major 3rdand a minor 7th..
In the line below, the first measure starts with a perfect 4th, ‘F-Bb’. ‘Bb’ is raised to create an augmented 4th(#4). The second measure starts with a perfect 5th. ‘C’ is lowered creating a diminished 5th. The augmented 4thand diminished 5thare enharmonic, ergo[3]the same tritone, just spelled differently.
Tritones that are inverted remain the same tritone, but change their name; #4/o5. The third measure shows and augmented 4thinverted to another augmented 4th. They, again are the same tritone.
In the following line the dominant (x) contains a tritone from the major 3rd to the minor 7th. In the first measure the dominant (x) is spelled with an augmented sixth, ‘B-sharp’. The tritone is an augmented fourth, ‘F-sharp’ to ‘B-sharp’. In the second measure the dominant (x) is spelled with a minor seventh, ‘F-sharp’ to ‘C’. The two dominants and the two tritones are identical albeit spelled differently. The third measure shows a ‘D’ dominant (x) spelled with a minor 7th. The same dominant is then spelled with an augmented 6th, ‘B-sharp’. The tritone is ‘B-sharp’ to ‘F-sharp’. The two dominants and tritones are identical while spelled differently. ‘A rose is a rose by any other name’ (Gertrude Stein).
A tritone inverted remains the same tritone even if it’s spelled enharmonically. The first measure below shows identical tritones…all of them. The second measure shows a tritone that is the minor 7thand major 3rdof the dominant (x). The third measure shows the same tritone, but functions as the major 3rdand augmented 6thof the dominant on ‘C-flat’. (Please note that accidentals remain good within a measure).
The following two lines are taken from the Chopin Prelude nr 15. Measure 9 shows a dominant (x) on the dominant (V) on the 4thbeat. The tritone of this dominant is ‘C-flat’ to ‘F’. All well and good. But measure 13 shows the same tritone without its root (D-flat). Theory texts do not and cannot handle this since they do not subscribe to the tritone and the characteristic intervals of the dominant (x).
The following line is taken from the JS Bach Prelude nr 3 from the set of twelve. Measure 23 contains a dominant (x) on the sub-mediant (VI). The tritone of this dominant is ‘C-sharp’ to ‘G’, a diminished 5th. Theory texts will describe this chord as an ‘augmented-six’ chord since ‘C-sharp’ is the augmented sixth above the root, ‘E-flat’. And, augmented sixths are to resolve upward according to these texts. But here it resolved down to ‘C-natural’. Did Bach make a mistake? Or is the issue of enharmonic intervals meaningless, theoretically?
The following is taken from the Chopin Fantasy Op 49 in F minor. Measure 65 shows a passage based on the dominant (x) on the sub-mediant (VI), a ‘D-flat’ dominant harmony. This moves to a major triad on the dominant (V), a ‘C’ major harmony. But like the Bach example above there is a problem here. The tritone of the dominant (x) is ‘C-flat’ to ‘F’. The minor 7th, ‘C-flat’ resolves up to ‘C’. According to theory texts shouldn’t ‘C-flat’ be written as its enharmonic, ‘B’, an augmented-sixth of this dominant? Did Chopin also make a mistake? First off, there is no such thing as an ‘augmented-six’ chord. An augmented-six is an interval, not a chord. Secondly, the chord is a ‘D-flat’ dominant chord, and the scale is a ‘D-flat’ dominant scale employing the characteristic interval of a minor 7th, ‘C-flat’. If the chord should have been spelled with an augmented sixth (B-natural), shouldn’t the scale also have been called an ‘augmented-six’ scale? Mmmm, one wonders! The point is… it really doesn’t matter how you spell it because its identity does not change with either spelling. For example; Sue and Susan, Bob and Robert. Different spellings, same persons.
Music theory texts are full of nonsense that piano students neither understand, nor remember once they graduate. To quote Dr. Leopold Mannes, founder of the Mannes Music School in New York…
“To the gifted and experienced musician, music is a language—to be understood in sentences, paragraphs and chapters. The student who is still struggling with letters and words, so to speak, needs the guidance that will reveal to him the larger meanings of the musical language. Theory, as it is called, has always been upheld as the promised gateway to this broad understanding, but there are thousands upon thousands of eager young musicians as well as disappointed older ones who will testify to the seemingly unbridgeable gap between their theoretical studies and the living experience of music itself.” … from the Preface of Dr. Felix Salzer’s book, ‘Structural Hearing’.
Ralph Carroll Hedges B.Ed., B.M., M.M.
