To work out the numerical interval between two notes:
Counting the bottom note as "1", count up to the top note.
eg. from C to A (C, D, E, F, G, A) is a 6th.
Similarly, on the stave:
Count all lines and spaces.
Important: There are no exceptions to this rule. Sharps, flats, double sharps and double flats make no difference to the number of the interval.
Major, Minor, Perfect,
Imagine the bottom note of the interval is the first degree of a Major scale.
If the upper note belongs to the scale, it will be:
Major 2nd
Major 3rd
Perfect 4th
Perfect 5th
Major 6th
Major 7th
Perfect 8ve
If you flatten the top note of a major interval it becomes minor.
Diminished, Augmented?
If you sharpen the top note of a major or perfect interval, it becomes augmented.
If you flatten the top note of a minor or perfect interval, it becomes diminished.
Spelling / Enharmonic Equivalent
It is possible for 2 different intervals to sound the same (and be played the same on a keyboard).
eg. From D to G sharp is an augmented 4th
From D to A flat is a diminished 5th
G sharp and A flat are enharmonically equivalent (ie. sound the same and occupy the same space on a keyboards) so these two different intervals sound the same.
The augmented 4th / diminished 5th is also called the tritone for, I hope, obvious reasons.
RESOURCES:
There are excellent online tutorials on numerical intervals, specific intervals and how to write intervals.
You can test how well you recognise written intervals here.
(If you are confident and want to test yourself on more difficult intervals, try this.)
Guitarists and bassists:You may find this useful
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