Scale Math for to Build Your Knowledge

This page is a quick reference to build scales with the math formulas. 

Types of Scales

There are several types of music scales they are:

  • Chromatic Scale

  • Major Scale
  • Minor Scales (harmonic, natural or relative, and melodic)

  • Diminished and Polytonal Scale

  • Whole tone and Pentatonic
  • Blues and Gospel Scale

  • There are others as you build your advanced theory.

Music scales are the structures that make up which notes are used and how chords are constructed within all the key signatures. They are also the main basis for being able to improvise music.

Constructing Music Theory Scales with Scale Formulas

The 12 notes with their corresponding sharps and flats are used to build a music scale.

The music theory scales are developed mathematically using whole, half and minor third steps.

If we assign a numeric value to each note, this provides an interval to each note. with in the math pattern producing the scale formulas.

Notation for exploring scales.

W = whole step: such as C to D
H = Half Step: as in C to D#
m3 = minor 3rd which is a whole and a half step together: C to Eb


Major Scale:

Mathematically the major scale is produced using the following formula.

1 - 2 - 3 - 4 - 5 - 6 - 7 - 8
S - W - W - H - W - W - W - H
C - D - E - F - G - A - B - C

Very similar construction is used to develop the other scales mentioned above.

There is a specific way that the Music Learning Workshop uses to teach scales. You can’t just look at the text provided above and quickly learn them. You need to use a series of events and actions in a set way to learn them. Check out the workshops to learn them completely. Read more about the Keys and Scales workshop.

Learning Resources