Intervals and Scales

Intervals are the building block of music. If we look at the chromatic scale there are 12 possible pitches each a semitone or half-step apart. Lets say the chromatic scale starts on C a semitone or half-step away would be C# or Db. Lets take a look at the scale going up and down.

C# and Db are enharmonic equivalent as they have the same pitch but are notated differently. The basis for notation depends on alteration and direction of resolution. There are 5 different qualities of intervals: Major, Minor, Perfect, Diminished, or Augmented as shown below.

Intervals can be inverted to and from:

Unison (1) to Octave (8)

Second (2) to Seventh (7)

Third (3) to Sixth (6)

Fourth (4) to Fifth (5)

Interval qualities can be inverted as well to and from:

Major to Minor

Perfect to Perfect

Augmented to Diminished

For example, a major second inverted becomes a minor seventh. The letter names of pitches determine the interval. So, a C to a D is a major second. A C to an F# is an augmented 4th, whereas a C to a Gb is a diminished 5th, though the notes are enharmonic.

Intervals can be consonant or dissonant as well. Consonant suggest resolve and generate a pleasing sound; whereas, dissonance suggest conflict and generate tension. A consonant interval would be a major 3rd whereas a dissonant interval would be a minor 2nd.

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We use intervals as the building blocks of scales. There are numerous amounts of scales. Western diatonic music is built on a 7-note scale and repeats at the octave. The notes in the major scale are C, D, E, F, G, A, B. The intervals in a scale can be related in two different ways.

1.     They can relate to the Tonic pitch. Below are the notes as they relate to C, the tonic pitch denoted by M for major, m for minor, and P for perfect. Tonic means the first scale degree and is the tonal center. In the key of C the tonic or 1st degree of the scale is C, if you were in G the tonic or 1st degree of the scale would be G.

2.     They can relate to the adjacent pitch. Below are the notes moving diatonically through the scale and their relation to one another in minor and major seconds and whole and half steps.

So, in mathematical terms, we can say the construction of the major scale in whole and half steps or major and minor 2nds. This is also known as the Ionian scale or Ionian Mode. You can start on any note in the chromatic scale and follow this pattern to get a specific key in the Ionian Mode. You can build different modes starting on the different notes in the C Major scale; to learn more see here. Because the scale moves in seconds, we always move from one note to the next. So if you are in the key of F and follow this pattern, when you get to A, you have to move to B something, and in that case, it is a Bb a minor second away.

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Each note in the scale derives its name based on its relationship to the tonic as shown below:

The subdominant is called the subdominant because it is the same distance, a 5th below the tonic as the dominant is above the tonic, a 5th. This is the same for the submediant, which is a 3rd below the tonic as the mediant is a 3rd above the tonic.