Intervals are Useless

Musicians learn three to four fundamental concepts separately in their early training: letter names, scale degrees, solfege, and intervals. They look wildly different on the page, yet they are in fact structurally the same.

Let’s compare notes (ha).

Letter namesCC#DEbEF#GbG
Inflected solfegedodirememifiseso
Scale degree namestonicsharp
Scale degree

That means you are learning the same thing four times because we have such a convoluted, patchwork music theory. If I were to put this in a more positive light, I’d say they weave a complex tapestry of history, an the rich variety of language gives us perspectives on yadda yadda. That is actually true for a history of theory class, but not fundamentals pedagogy. This is not the first time people found music theory confusing; 17th-c. musicians in Europe had it worse, and there’s a good reason we don’t pair 7 letters with 6 solfege names anymore.

In fact, the different names reflect the different reference points of each system. Letter names anchor to frequency (A = 440Hz), and the interval P1 anchors to the lowest sounding note. For scale degrees and do-minor solfege, do/^1/tonic anchor to tonal stability; for la-minor solfege, ti anchors to the leftmost sharp in a key signature, and fa anchors to the leftmost flat.

For students, if you understand one system–most likely letter names, you understand all others with a conversion chart. For teachers, this is a opportunity to streamline your teaching to make space for (gasp) actual music. For music theorists, we need to get our shit together.

Let’s look at how the assortment of concepts might conceal a straightforward calculation.

First, understand that we can add intervals.

P1 + M3 + m3 = P5

The addition above traverses a major triad. The numbers look wonky, but the math checks out (story for another time).

Second, to show that they are only different symbolically, we can replace the intervals above with letter names or scale degrees.

C + E + Eb = G
1 + 3 + b3 = 5

Weird. But OK.

Now try this question.

A flute player is trying to match the trumpet player’s pitch (and, OK, for whatever reason they can’t hear each other).
– The flute player is playing an alto flute in G, and in fact, doing so quite in tune.
– The trumpet player is playing a Bb trumpet that is a minor 2nd too sharp.
– The trumpet player is playing an arrangement of “Maria” from West Side Story, and in their score, they just reached scale-degree #4 in G major.
What note should the flute player play?

One could solve this step by step:
– scale-degree #4 in G major is C#;
– written C# on a Bb instrument is actually B (natural);
– B tuned up a minor 2nd is C;
– concert C on a G instrument is G.

Or, because they are structurally the same, we could
– add all of them up: G + Bb + m2 + #4 + G = G
– or write them as intervals: P5 + m7 + m2 + A4 + P5 = P5 = G
– or write the intervals as successive notes from C: G, F, Gb, C, G

The flute player plays a G.

Realistically, the question might look like this: “what’s the Bb clarinet’s G in concert pitch if I were to play it on my Eb saxophone,” which I’ve done countless times in a school band setting. But this goes to show that intervals are useless …not! Intervals in fact underlie all fundamental pitch concepts. But if you know letter names already, then you can already work out a lot more than you think.