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Printable PDF: Intervals explained

An interval is the distance between two notes, and it is indicated by ordinal numbers (2^nd, 5^th , 7^th) except when describing the unison (identity of pitch) and the octave (two notes 12 semitones apart).

Intervals of a 2^nd ,3^rd ,6^th ,7^th are called major.

Intervals of a 4^th ,5^th  and octave are called perfect.

If a major interval is raised by a half step it is called augmented. If a major interval is lowered by a half step it is called minor. If lowered by two half steps, diminished.

If a perfect interval is raised by a half step it is called augmented. If a perfect interval is lowered by a half step it is called diminished (note the difference).

There are two basic ways to calculate an interval,  that will lead to the same result.

1. Calculating by the number of half steps between the two notes:

where m=minor, M=major, P=perfect, dim=diminished, aug=augmented.

2. Finding  the interval from the major scale. All the intervals from the tonic of a major scale to any other note of that scale are major or perfect (i.e. between C and D=major2nd,  C e E=major3rd, C e F=perfect4rth, and so on…). Of course you need to know your major scales!!