Intervals

Now we've already talked about intervals a whole bunch but up until now we've been expressing intervals in terms of whole tones or semitones. Now we move past that.

An interval is the space between two notes. We classify intervals as a quality and a number. The number represents the number of note names between the two notes. For example: C4 is a third above A3, Bb2 is a fifth below F2. There are 3 note names between A and C (A,B,C) and five between Bb and F (B, C, D, E, F). Notice that we include the notes on the perimeter of the interval. Unless otherwise stated, an interval is measured from the lower pitched note to the higher one.

The quality of an interval may be major, minor, diminished, or augmented.

Major intervals are intervals we would find on the major scale if we compared them to the tonic. We will abbreviate them with an M. These intervals are:

Major second: M2 (whole tone)
Major third: M3 (2 whole tones)
Major sixth: M6 (4 whole tones and a semitone)
Major seventh: M7 (5 whole tones and a semitone)

You'll notice that there is no major fourth or fifth. We use a different terminology for fourths, fifths, and octaves. We call a "major" fourth, fifth, or octave "perfect". So:

Perfect fourth: P4 (2 whole tones and a semitone)
Perfect fifth: P5 (3 whole tones and a semitone)
Perfect octave: 8ve (12 semitones)

Minor intervals are achieved by taking major intervals and inverting them, essentially flipping them so the top not is on the bottom and the bottom on top. If we do this to the above intervals they will become in order:

Minor seventh: m7 (5 whole tones)
Minor sixth: m6 (4 whole tones)
Minor third: m3 (1 whole tone and a semitone)
Minor second: m2 (a semitone)

Perfect fifth: P5 (3 whole tones and a semitone)
Perfect fourth: P4 (2 whole tones and a semitone)
Perfect unison: PU or P1 (in this case we are considering the inverted octave to be a unison, two of the same note)

Notice that the inverted perfect intervals are still perfect whereas the inverted major intervals became minor. If we inverted those minor intervals again we'd get our major intervals back.

Now augmented and diminished intervals are made by taking minor or perfect intervals and lowering them a semitone or taking major or perfect intervals and raising them a semitone. If we raise the pitch of a major or perfect interval a semitone we get an augmented interval, lowering a minor or perfect interval a semitone gives us a diminished interval.

It's important to remember that the note names here do not change. For example, A - C# is a major third, but A - Db is a diminished fourth. The notes C# and Db would sound the same but the intervals depend on how the notes are written and not necessarily what they sound like. We call notes that sound the same but are written differently "enharmonic".

Consonance and Dissonance

Now we get into the actual theory. We have a broader class of intervals that we haven't yet discussed. There are consonant intervals and dissonant intervals. To understand the distinction, we'll dip into a little history.

Early music was written largely for voice. In fact a whole chunk of theory was created to ease writing for choirs or duets. Now some intervals are easier to sing than others. To be brief and blunt we call intervals that are easy to sing consonant and intervals that are hard to sing dissonant. Music revolves around the idea of creating dissonance only to resolve it. The goal is to create some kind of tension and have it resolve only to move to some other tense harmonies. Dissonant intervals are these tense intervals because when we hear them we naturally want to resolve them into consonances.

The consonant intervals are:

All major and minor intervals except major seconds and sevenths
All perfect intervals

The dissonant intervals are:

Major and minor sevenths and seconds
All augmented and diminished intervals

Lastly, there are two types of intervals which has nothing to do with notes but entirely with rhythm.

Harmonic intervals are intervals between notes that sound at the same time (like in a chord).

Diatonic intervals are intervals between notes that don't sound together (like in a melody).