Two notes separated from each other by 7 half-steps form an interval of a perfect 5th when, assigning the number name of '1' to the lower note, the letter name of the higher note corresponds to '5' in the number system. (E.g., G and D, with G being the lower of the two notes: D is 7 half-steps higher than G, and D is '5' when G is '1': G (1), A (2), B (3), C (4), D (5).)
Two notes separated from each other by 5 half-steps form an interval of a perfect 4th when, assigning the number name of '1' to the lower note, the letter name of the higher note corresponds to '4' in the number system. (E.g., D and G, with D being the lower of the two notes: G is 5 half-steps higher than D, and G is '4' when D is '1': D (1), E (2), F# (3), G (4).)
The 7 natural notes arranged in perfect 5ths are, in order: F, C, G, D, A, E, B, which can be remembered by:
Father Charles Goes Down And Ends Battle.
Reversing this order results in the 7 same notes being arranged in perfect 4ths: B, E, A, D, G, C, F:
Battle Ends And Down Goes Charles' Father.
Practical Application #1: In the alternating bass pattern used for playing bluegrass bass and rhythm guitar, the note that the root note of the chord is alternated with is to immediate right of the root note in the sequence of perfect 5ths: so for playing the alternating bass pattern for the C chord, one alternates between a C note (the root note of the chord) and a G note (the '5' of C), for a G chord, one alternates between a G note (the root note of the chord) and a D note (the '5' of G), etc.
Practical Application #2: In the sequence of perfect 5ths, the 5 chord is to the immediate right of the 1 chord, and the 4 chord is to the immediate left of the 1 chord: E.g., when 1 = G, then 5 = D and 4 = C.
The list of practical applications goes on and on, but these two applications make for a good start. Suffice it to say for now that the sequences of perfect 5ths and 4ths clump the notes and chords together that most frequently show up together in songs, whereas the chromatic scale (the sequences involving ascending and descending in half-steps) separates these from each other.
The sequences of perfect 5ths and 4ths can be expanded to include sharps and flats (this will be dealt with in a future teaching segment at the jam), and this is something we will need to do, for instance, to account for the '4' chord in the key of F, and for the '5' chord in the key of B and for the alternating bass pattern for a B chord. In preparation for this, a good thing to make it a point to remember is that F and B are at the two ends of the sequences of natural notes. (The reason why F and B are the two outermost natural notes of the sequences will be made clear when we expand the sequences to include sharps and flats.)