Brizm
Intervals: the distance between notes
An interval is the distance between two notes, counted in semitones. Every chord, scale and melody is built from intervals, and each one has its own emotional color. Learn their names and their sounds and the rest of theory becomes easy.
An interval's name has two parts: a number (count the letter names, including both ends: C up to E is C-D-E, a 3rd) and a quality (major, minor, perfect, augmented or diminished) that pins down the exact number of semitones.
Compound intervals: where 9, 11 and 13 come from
Intervals larger than an octave are compound. Add 7 to the number (and 12 to the semitones) and you get the same note an octave higher: a 2nd becomes a 9th (14 semitones), a 4th becomes an 11th (17), a 6th becomes a 13th (21). Hold onto this; it's exactly how chord names like m9, m11 and 13 work in lesson 7.
Consonance and dissonance
Octaves, 5ths and 4ths sound stable and blend (consonant). 3rds and 6ths are sweet. 2nds, 7ths and the tritone rub and create tension (dissonant). Tension isn't bad: it's what makes music move. Cumbia builds tension with the tritone in its V7 chord and releases it on the I chord; dub techno leaves soft dissonance (the 7th and 9th) hanging forever.
Inversion
Flip an interval upside down and it becomes its complement; the two always add up to 12 semitones. A 5th inverts to a 4th, a major 3rd to a minor 6th, a minor 7th to a major 2nd. This is why a bass going up a 4th from A lands on the same note (D) as going down a 5th.