music theory

Music Theory Formulas

Music theory formulas are a way to describe the tonal mix of a given chord, scale, or arpeggio. What follows is one type of formulaic system. We will talk about chords (arpeggios) in this lesson.
The basic premise is this: the major chord provides template or blueprint for a point of comparison. Major = normal. For chords, what is normal means what is true for the I chord in a Major key.
The formula for the Major chord is R, 3, 5, where R = Root, 3 = third (4 half steps away from root), and 5 = fifth (3 half steps away from 3rd, 7 half steps away from root).
These relationships need to be true for the chord or arpeggio to be Major. Once we establish this, we can now parallel or compare other types of chords to it.
We use sharp (#) and flat (b) symbols for the comparisons (independent of tonal names - even though flats or sharps can be in the names of the tones).
Examples: C Major is C E G. C minor is C Eb G. Eb is the flat 3rd and has a flat in the name. A Major is A C# E, while Am is A C E (C# has been lowered to C, is a flat 3rd - yet there is no flat in the name).

Chord & Arpeggio Formulas

These numbers represent distances from the root, where the root = 1.
Note: there is a system where the root = 0 called Numerical Chromaticism.
The first group above represents the 4 types of Triads:

• Major - R 3 5
• minor - R b3 5
• diminished - R b3 b5
• augmented - R 3 #5

The 7th chords listed above are the main 5 types, where the first 3, Major7, Dom7, and m7 are the primary. The min7b5 is a modified minor, and the dim7 (fully diminished 7) is a type of altered dominant.
There are endless other types (above), we listed these particular other types above because they are very common ones found in early playing.
Music theory formulas provide a basic way to relate chords to one another.

Multiple chord symbols for the same quality of chord

Depending on the source, chords can have different symbols. It is important to become acquainted with the symbols in use by any given source. Some are very consistent, others have variability.

Symbol 'Rules'

• little m = minor
• 7 = flat 7 (10 half steps away from root)
• Major 7 (Maj7) = normal 7 (selected by Major scale pattern - 11 half steps away from root)
• add = no 7 present, simply add the tone to triad. Sometimes replacing another chord tone (situational).

E, A, & D forms with MODS
More on music theory formulas - how chords are built