To write intervals, memorize the following: Music Fundamentals   William Wieland
Augmented (A)
Major (M)
minor (mi)
diminished (d)
( 2, 3, 6, 7 )
Augmented (A)
Perfect (P)
diminished (d)
( 1, 4, 5, 8 )
P8 — same name
M7 — almost an octave (mi2 smaller) — Sevenths Diagram
mi7 — close to an octave (M2 smaller) — Sevenths Diagram
M6 — M2 larger than a P5 — Sixths Diagram
mi6 — mi2 larger than a P5 — Sixths Diagram
P5 — root to 5th of any major triad or minor triad — FCGDAEB — Circle of 5ths
A4 or d5 — a.k.a. tritone — without accidentals, only F/B or B/F
P4 — BEADGCF — The Circle of 5ths is also the circle of 4ths.
M3 — 4 half steps — root to 3rd of any major triad — 1 to 3 of any major scale or major key
mi3 — 3 half steps — root to 3rd of any minor triad — 1 to 3 of ANY minor scale or minor key
M2 — 2 half steps, i.e. 1 whole step
mi2 — half step
P1 — identical pitch
 
do
ti
la
sol
fa
mi
re
do do do do do do do
    The major scale method:     M2         M3         P4         P5         M6         M7         P8