Saxophone Lesson #29: Types of Intervals


Simple intervals
An interval is usually defined as the distance between two pitches, that is, how many semitones lie between them. When the two pitches are the same, they are said to be in unison. When they are twelve semitones apart, they are an octave apart. Simple intervals are defined as those intervals that are one octave or less apart.

Intervals are usually named according to the relationship of the higher note to the lower note in the major scale, though they also have alternate names depending upon the spelling of the particular notes on the page of music.

Semitones Common Name Alternate Names
0 perfect unison diminished second
1 minor second augmented unison
2 major second diminished third
3 minor third augmented second
4 major third diminished fourth
5 perfect fourth augmented third
6 tritone augmented fourth, diminished fifth
7 perfect fifth diminished sixth
8 minor sixth augmented fifth
9 major sixth diminished seventh
10 minor seventh augmented sixth
11 major seventh diminished octave
12 perfect octave augmented seventh

This table gives the most common nomenclature for each interval according to its relation to the major scale. For example, the interval of four semitones occurs as the third note of the major scale, and thus it is called a major third. The interval of seven semitones occurs as the fifth note of the major scale, and so it is called a perfect fifth.

Whether an interval is "perfect" or "major" depends on mathematical ratios of frequencies as determined by the Greeks. Other possible names are given under "alternate names," and the most common of these are emboldened. One may draw several inferences from this table:
If any perfect interval is raised by one semitone, the interval becomes augmented

If any perfect interval is lowered by one semitone, the interval becomes diminished

If any major interval is raised by one semitone, the interval becomes augmented

If any major interval is lowered by one semitone, the interval become minor

If any major interval is lowered by two semitones, the interval becomes diminished


Compound intervals
Compound intervals are defined as those intervals greater than one octave apart. These intervals may be considered by exactly the same rules as their simple counterparts.

Semitones Name(s) Simple Counterpart
13 minor ninth minor second
14 major ninth major second
15 minor tenth minor third
16 major tenth major third
17 perfect eleventh perfect fourth
18 augmented eleventh tritone
19 perfect twelfth perfect fifth
20 minor thirteenth minor sixth
21 major thirteenth major sixth


The compound intervals work by following the same five rules as the simple intervals above (so the augmented eleventh might also be called a diminished twelfth).


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