Altered Intervals

If you look closely at the rainbow we’ve been building for the basic intervals, there is a color missing. Where is violet?

This means we’re ready for the altered intervals. Buckle up.

It’s not exactly true that perfect 4ths and 5ths are set in stone. Actually, there is a way to alter them : augmenting or diminishing them. Augmenting an interval adds a half step to it, diminishing it removes a half step from it.

Mainly we’ll be using this to access the tritone interval, which is located exactly in between the perfect 4th and the perfect 5th. It’s called the tritone because it’s made of 3 tones, or 6 half steps. It can be reached either by augmenting a perfect 4th, or diminishing a perfect 5th.

This is the diabolus in musica, symbolizing the devil in music since the Middle Ages, and home to various twisted and dissonant harmonies. Medieval theorists found its sound so unstable that it was often avoided in sacred chant, since it clashed with the smooth, stepwise motion favored in Gregorian melodies. Contrary to a popular myth, the Church never officially “banned” the interval; it was simply considered awkward to sing and difficult to fit into the modal system. Still, its eerie tension made it unforgettable. Centuries later, composers began using that very instability for expressive power: the tritone drives the harmonic drama of dominant seventh chords, which is a cornerstone of the tonal system. In other words, the interval once feared as “devilish” quietly became one of the most useful engines of tension in Western music.

A bit like the devil, the tritone is a sneaky little guy because when you invert a tritone, you get… a tritone.

So this guy will be the center of the rainbow with the violet color.

We know have access to every note inside the octave! Feel free to take a moment and take all of it in. Measure intervals, and look at their inversions in the other direction. The track below is showing the inversion of the interval in a different way, as what’s missing to complete the octave.

Let me cover 2 edge cases of altered intervals, that you might encounter in your musical journey. If you’re just starting out you don’t really need to know about these, I’m just putting them here for reference.

Sometimes, 5ths will be augmented. Now this is a bit confusing because when you do that, you get the same number of half steps as a minor 6th. Still, this is musically useful because sometimes you want to take a dominant chord, like E, and make it more weird and mysterious, using an augmented fifth. Now, this note is still your fifth, it hasn’t been transformed into a 6th all of a sudden, so you still want it to be written B with a sharp, and not C. But practically speaking, an augmented 5th is the same thing as a minor 6th.

Finally, we saw that 7ths are by default minor, and that they can be made major. Well, they also have a 3rd possible state: they can also be diminished. This is also very confusing because it essentially becomes a major 6th. But, it’s useful in the case of completely diminished chords, where you want to have this note, but you still want the notes to be named in leaps of thirds.

You now have access to the full tree of intervals (below the octave line).