Evaluating Intervals
The definition of an interval is the distance between two notes. The rule for evaluating intervals is that you include the note you start on and the note you end on; in other words, both ends of the intervals are counted.
Perfect Unison
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Major Second
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Major Third
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Perfect Fourth
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Perfect Fifth
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Major Sixth
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Major Seventh
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Perfect Octave
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Sometimes students ask, why do you need an interval of a unison. Answer: the pitch may be sung and/or played by different instruments/voices.
Intervals of 1, 4, 5 and 8 are called Perfect (or diminished); intervals of 2, 3, 6 and 7 are called Major (or minor). Intervals may be made smaller (than Major or Perfect) by either raising the bottom or lowering the top. A minor third might be a C-E flat, or alternatively, a C#-E. An interval 1/2 step smaller than a Major is a minor: an interval 1/2 step smaller than a Perfect is a diminished (written with a °). Intervals larger than a Major or Perfect, are called Augmented.
Intervals may be Major (M), minor (m), diminished (dd) or Augmented (Aug.) To determine this, you must understand the keys as demonstrated in the Circle of Fifths. You look at the note on the bottom of the interval (whatever it may be) and ask is the top note in that key (of the bottom interval).
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Circle of Fifths
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Example: The interval C-E (see, above). It is a third because you count: C, D, E. Remember the rule, count both ends of the interval. Then you look at the bottom note, C. Is the E in C Major? If it is, then the interval is a Major 3rd.
Example: The interval C-E flat is minor because there is no E Flat in C Major; the interval is 1/2 step smaller than the minor, due to the lowered top pitch.
Example: The interval C-F# is an Augmented 4th (or diminished fifth). This is a special interval known as a Tritone or "Devil's interval," forbidden by the Church in the Middle Ages, and often used by modern composers to indicate fear, evil, and program music having to do with witches, etc.
See: Intervals, Wikipedia