# Intervals

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An interval is the distance between pitches. Intervals have a number and a prefix. The number represents the number of pitch names (A,B,C,D,E,F,G) from the first to the second pitch. For example, the whole step F to G contains two pitch names, F and G. This interval is called a second. The interval from F to A contains F, G and A; three pitches. This interval is therefore called a third. The trend continues through to the interval containing eight pitch names. An interval containing eight pitch positions (from A to A or from G to G) is called an octave. An interval from one pitch to the exact same pitch is called a unison. The diagram below shows a C major scale. The intervals are marked.

The second part of an interval name is based on the quality of the interval. It is referred to as the prefix.

**Perfect** intervals include the unison and the octave. Perfect intervals also include fourths and fifths. Perfect intervals are labeled with a capital "P."

The **Major** prefix is only used for seconds, thirds, sixths and sevenths. Major intervals are labeled with a large "M."

**Minor** intervals occur when a major interval is made one half step smaller. This can be done by raising the bottom note or lowering the top note. Minor intervals are labeled with a small "m."

**Augmented **intervals are when a major or perfect interval is made one half step larger, and the interval number does not change. Augmented intervals are labeled with an "A," the abbreviation "Aug.," or a "+." For example, above, if the P5 from C to G were changed to a C to G#, it would become an augmented fifth, or +5.

**Diminished** intervals are created when a perfect or minor interval is made one half step smaller and the interval number is not changed. Diminished intervals are labeled with a "d," the abbreviations "dim" or "deg," or a "°." For example, if the perfect fifth from C to G above were changed to a C to Gb, the interval would become a diminished fifth, or °5.

Thus unisons, fourths, fifths, and octaves can be diminished, perfect, or augmented. Seconds, thirds, sixths, and sevenths can be diminished (only if the interval is decreased by two half steps, such as with a double flat), minor, major, or augmented.

Here are some examples of how this system works:

- P1- This is perfect unison.
- M7- This is a major seventh.
- m2- This is a minor second.
- A6, Aug. 6, +6 - These are all augmented sixths.
- d3, deg.5, dim. 5, °5 - These are all diminished fifths.

## Consonance and Dissonance

Consonant intervals are intervals that are stable. These intervals require no resolution. The consonant intervals are P1, m3, M3, P5, M6, and P8. All other intervals within the octave are said to be dissonant. Dissonant intervals are tense, and require resolution.

## Enharmonic Intervals

Enharmonic intervals are intervals that sound the same but are "spelled" differently. These intervals result from the inclusion of enharmonic equivalents.

The most common enharmonic intervals are the diminished fifth and the augmented fourth, shown below. These two intervals divide the octave into two equal parts. These intervals contain three whole steps, for this reason these intervals are referred to as the tritone.

## Inverting Intervals

When an interval is inverted, the lower tone is raised one octave. The table below shows some intervals and their inversions.

The Interval | When Inverted becomes |
---|---|

Unisons | Octaves |

2nds | 7ths |

3rds | 6ths |

4ths | 5ths |

5ths | 4ths |

6ths | 3rds |

7ths | 2nds |

Octaves | Unisons |

Perfect | Perfect |

Major | Minor |

Minor | Major |

Diminished | Augmented |

Augmented | Diminished |

## Compound Intervals

Compound intervals are intervals that span distances greater than an octave. These intervals are often labeled as their simple equivalents, as if an octave had been removed from the interval. The actual, or compound, interval name is only used if it is very important to stress the actual interval size.

## Identifying Intervals

The easiest way to find an interval's name is to first, count all the pitch names present, including the notes themselves (ignore sharps and flats at this point). Then, find out (had it been missing a flat or sharp) what type of interval it would be, depending on whether it is perfect (a 1,4,5,8) or major (2,6,7). If there are no sharps or flats, you are done. If there are, figure out if the flat or sharp decreases or increases the distance between the two pitches. If it increases the distance, the interval is augmented. If it decreases the distance, and the interval would otherwise be perfect, it is diminished. If it decreases the distance and the interval would otherwise be major, it is minor.

## Ear Training

Go to the Big Ears interval ear training Java applet to help learn what different intervals sound like, and quiz your recognition of different intervals.

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