Interval (1) Counting ABC

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1. What is Interval?

A melody is a succession of notes and a chord is a stack of notes.

Whether horizontal or vertical, it is clear that the secret of music lies in the distance between tones, more specifically, the differential between pitches.

Now here’s C–E and C–G. It is clear that the gap between C–G is wider than the other. But how do you express it numerically? It is the main subject in this article.

Count on Fingers

What numeral unit for musical pitch do we have so far? — Frequency (Hz) may be one of them but it’s too scientific for daily use.

Or we have learned semitone but…

Actually this is not much convenient or practical when you’re in major/minor key system. In major/minor key music, you basically use only 7 out of the 12 notes. So, in measuring the distances between notes, it often becomes more practical to use only these 7 notes as measures.

Therefore, let’s just simply count the number of alphabets you pass through.

And we say like : C and E are 3^rd. E is 3^rd above C. C is 5^th below G.

Ordinal numbers are used to measure the distance between notes. And this measure is termed Interval. C and E are in the interval of a 3^rd.

When measuring intervals, beware NOT to calculate the numbers as subtraction like E–C = 3-1 = 2^nd. This is wrong. Just count on your fingers like 1,2,3,4,5!
This applies to addition as well. C–E is a 3rd, and E–G is also a 3rd, but the combined distance C–G is not 3+3=6th! How unfortunate is that? C–G spans five notes, so it’s a 5th.

Intervals are similar to the sense of counting dates. For example, if you have time off from work from August 1^st to August 3^rd, how many days are you free from work?? It’s not 2 consecutive days; it’s 3 days. Including both the beginning and the end is the concept of an interval.

August 3^rd to 5^th is also 3 days off. And August 1^st to 5^th, though it’s a combined version of 1^st-3^rd and 3^rd-5^th, is 5 days. So when you think of intervals, it’s easier to understand that they represent the “relationship” between two notes rather than pure “distance”.

Why oh Why?

However, given that intervals are the “distance” between notes, you might wish for a more straightforward calculation system. Why did it turn out this way? —It is said that this system was established even before the concept of “zero” was introduced to Europe. It’s inconvenient, but there’s no helping it. In reality, there are very few situations where you need to perform calculation with intervals, so you’ll seldom be troubled by this.

Intervals Wider Than Octave

However distant two notes are, you just count the alphabets to measure its interval.

C and D octave higher is 9^th interval, while C and D right next to it is 2^nd. Now you notice that going octave up takes 7 steps so the formula works that “widening the gap by octave = increasing the interval by 7“.

Interval of a 1st?

If you measure the gap between the same notes like C and C, strange as it may sound to measure the gap where there’s no gap, it is called Prime instead of 1^st.

Or it’s also called a Unison.

2. Use in Practice

For singers intervals are common vocabulary. When the main melody line is C–D–E, overdubbing the second line A–B–C results in harmony in 3^rd.

More specifically, this is a harmony 3^rd below. Harmonizing melodies by 3^rd below or above is the most common way of constructing harmony btw.

Relative

In earlier chapter I introduced the relationship called relative scales.

C major scale and A minor scale are relative. And I explained it with the sentence below:

Any major scale has its relative, which you can easily find by just re-setting its center to 2 notes below.

But in theoretical manner it’s much more appropriate to say “3^rd below” than “2 notes below”.

3. “Full Names” for Intervals

Pitches on black Keys are spelled with sharp/flat. But you can ignore those ♯♭, just count ABC. For example, Interval between E^♭–A is 4^th, just as E–A is 4^th.

But you know E^♭ is spelled D^♯ according to situations, which is termed enharmonic. It turns 5^th if E^♭ is spelled D^♯ because then you count 5 alphabets—D, E, F, G, A.

Now it’s going a bit confusing, but you don’t have to care about enharmonic for the time being, so don’t worry. Just counting ABC will be fine.

Simple or Full

But you may find a problem in this measure—How can you tell the difference between C–E and C–E^♭?

They’re both called 3^rd although their gaps are different (4 semitones vs 3 semitones). In fact, they have a bit longer name to tell from each other.

But to remember a “full name” is hard labor. Kopernik, Darwin, Nightingale, Gandhi…You should know these names but do you know their first names? ……😌
For theories of melody it basically works without identifying “full name”s so I’m gonna stick with this simplified interval system for a while, and the sequel will be explained in the chord chapter.

Summary

Interval is the distance between two notes, measured by steps (the number of ABC counted).
Intervals are expressed with ordinal numbers.
Sharps/Flats don’t affect intervals.

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