I'm interested in learning more of the Devil's interval: how it originated, some of its uses and what exactly about the interval of a diminished fifth makes it sound ominous?
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2It might be worth adding the word 'tritone' (or similar) to the title. It'll help with searchability.– endorphCommented Dec 30, 2016 at 12:51
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2 Answers
From fouth to sixteeth centuries is a long time. But that's how long the tritone was a banned interval. Who banned it, I haven't found out yet, but obviously someone with some clout. It was deemed to be an ugly interval, and one that early singers apparently found difficult to sing.
Every major scale has the Devil's interval of three tones - hence tritone - between the 4th and 7th notes.Often labelled an augmented 4th, sometimes as a diminished 5th - both taboo. Early music had its 7th note a tone below root, but when that changed to being a semitone below - leading note/tone - it produced this seemingly diabolical sound when played with the 4th. It's the interval sounded by the two white keys when playing 'Chopsticks', mainly on black keys on piano.
Take out those two notes, and we're left with the pentatonic - which has always been a favourite, due to the fact that all those notes don't clash with each other. Interestingly, when a circle is drawn, and notes are arranged chromatically round it, diametrically opposite to any note (call it I) is the tritone, flanked on either side by the IV and V - the two other pivotal notes/chords in the I key. Maybe that's one reason: it's so close to a 'good' note on each side, that it just falls short!
There are just too many examples of its use in so many well-known pieces, some particularly to proke the Devil - Danse Macabre - some in t.v. themes. However, the tritone appears in just about every pop type song, hidden within the dominant 7th chord make up. The V chord , in C, comprises G,B,D and F. There's the B-F again, trying hard to resolve to C and E respectively. It's the usual one semitone pull to resolution, but here there are two notes, resolving in different directions. Same two notes also work (as B and E#) to resolve to F# major. Oh yes, that's tritone substitution. Works well!
Doubtless there are physical reasons, like maybe, clashing harmonics, which it's hoped someone else will explain.
EDIT: strange, but at his last lesson, a student was playing phrases diatonically, in a sort of follow my leader game we play. He played a tritone - in key, stopped and said 'sorry, I just played some wrong notes', which actually, he hadn't...
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The "ban" most likely goes back to the use of plainsong in church music, where the tritone interval was "eliminated" by introducing an extra note into the original Pythagorean scale - in modern notation, B natural and B flat. Plainsong melodies are mostly stepwise and with no regular rhythm, and therefore they have minimal harmonic implications. A progression like F G A B(natural) A G F audibly sticks out a mile compared with F G A Bb A G F, and the "solution" of using the B as a leading-note before C, (i.e. F G A B C) doesn't work when C is not a well-defined "key note of a scale".– user19146Commented Dec 30, 2016 at 11:21
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@alephzero - yes, followed soon after by modifying F to make F#. That also 'eliminated' the tritone as F#>B is P4. Also, at that point, keys of F and G became available, along with C/Am– TimCommented Dec 30, 2016 at 12:02
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Having the 7th a tone below the root means C major becomes C Mixolydian (Bb instead of B) which has the same key signature as F major. You still get a tritone between Bb and E, so I don't see much difference there. I guess this may play into the German notation "B"=Bb, Soft B and "H"=B natural, Hard B. Commented Dec 30, 2016 at 17:09
One amusing property of the tritone is that is "should" split an octave into two equal parts; it's half of an octave. As an octave has a 2:1 frequency ratio, the tritone should have a Sqrt(2):1 frequency ration. However, the value of Sqrt(2) is particularly hard to represent as ratios of whole numbers. (It's actually the second-hardest number to so represent. The Golden Section is the hardest.)
In just intonation one gets a ratio of 45/32 for the tritone. Similarly for Pythagorean intonation one gets 729/512 for this ratio. For theorists who use the size of numbers in a ration to suggest consonance or dissonance, this interval is rather dissonant. (On the other hand, most music theory considers the fourth, ratio 4/3, to be dissonant in many instances, consonant in others.)
In practice, the tritone is a bit difficult to sing. Some care is needed in resolution of harmonic tritones (augmented fourths resolve to minor sixths and diminished fifths to major thirds, following the general rule that augmented intervals expand and diminished intervals contract.) In practical music, the tritone does tend to create a sound that musicians usually wish to resolve, V7 to I or V7 to i or V7 to vi or V7 to VI, rather than hanging. This is not necessary; blues harmony often just has a tritone in each chord. It's a matter of style. In the common practice style, tritones are dissonant and should resolve. (In Renaissance style, tritones not only must resolve but must be approached carefully.)
In jazz harmony, tritones resolve, but chords containing the same tritone may be substituted for each other.
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"In just intonation one gets a ratio of 45/32 for the tritone": or 64/45, or 25/18, or 36/25, or ...– phoogCommented Mar 24, 2021 at 19:11