Interval Names

(This is the first of two slightly dry posts on naming conventions.)

The intervals of European Equal Temperament scales are defined by counting the number of semitones between the notes and applying the following names (see here https://en.wikipedia.org/wiki/Interval_(music) for a longer discussion, including diminished and augmented intervals)

0 Unison P1
1 Minor second m2
2 Major Second M2
3 Minor third m3
4 Major third M3
5 Perfect fourth P4
6 Augmented fourth A4 / Diminished fifth D5
7 Perfect fifth P5
8 Minor sixth m6 / Augmented 5 A5
9 Major sixth M6
10 Minor seventh m7
11 Major seventh M7
12 Octave P8

The numbers 1,2,3... in the names are given by the number of lines and spaces ("staff positions") between the notes on the familiar five-bar stave. That method of counting notes will work for any scale with any number of notes in it.

C-F is... Tone(D)-Tone(E)-Semitone(F) = 5 semitones = Perfect fourth.

D-F is three semitones = Minor Third (D-E-F - D is on a line, E is in a space, and F is on a line, so an m3)

B-G♯ is Semitone(C)-Tone(D)-Tone(E)-Semitone(F)-Tone(G)-Semitone(G♯) = 9 semitones = Major sixth (G♯ is the sixth note in B-Major).

A♭ - E is Semitone(A)-Tone(B)-Semitone( C)-Tone(D)-Tone(E) = 8 semitones = Minor sixth (E♭ is the fifth note in A♭ and F is the sixth)

(You can use any method you like to count the semitones. This is my method at the moment.)

Since the number of semitones between any two notes is independent of the scale or key, interval names are independent of the underlying key or scale, since it depends only on the number of semitones. The same holds for staff positions, so the names of the intervals are also independent of the key or scale.