A perfect prime is also called a unison . It is two notes that are the same pitch . A perfect octave is the "same" note an octave - 12 half-steps - higher or lower. A perfect 5th is 7 half-steps. A perfect fourth is 5 half-steps.
Listen to the octave , perfect fourth , and perfect fifth .
Major and minor intervals
Seconds, thirds, sixths, and sevenths can be major intervals or minor intervals . The minor interval is always a half-step smaller than the major interval.
- 1 half-step = minor second (m2)
- 2 half-steps = major second (M2)
- 3 half-steps = minor third (m3)
- 4 half-steps = major third (M3)
- 8 half-steps = minor sixth (m6)
- 9 half-steps = major sixth (M6)
- 10 half-steps = minor seventh (m7)
- 11 half-steps = major seventh (M7)
Major and minor intervals
Listen to the minor second , major second , minor third , major third , minor sixth , major sixth , minor seventh , and major seventh .
Augmented and diminished intervals
If an interval is a half-step larger than a perfect or a major interval, it is called augmented . An interval that is a half-step smaller than a perfect or a minor interval is called diminished . A double sharp or double flat is sometimes needed to write an augmented or diminished interval correctly. Always remember, though, that it is the actual distance in half steps between the notes that determines the type of interval, not whether the notes are written as natural, sharp, or double-sharp.
Listen to the augmented prime , diminished second , augmented third , diminished sixth , augmented seventh , diminished octave , augmented fourth , and diminished fifth . Are you surprised that the augmented fourth and diminished fifth sound the same?
As mentioned above, the diminished fifth and augmented fourth sound the same. Both are six half-steps, or three whole tones , so another term for this interval is a tritone . In Western Music , this unique interval, which cannot be spelled as a major, minor, or perfect interval, is considered unusually dissonant and unstable (tending to want to resolve to another interval).
You have probably noticed by now that the tritone is not the only interval that can be "spelled" in more than one way. In fact, because of enharmonic spellings , the interval for any two pitches can be written in various ways. A major third could be written as a diminished fourth, for example, or a minor second as an augmented prime. Always classify the interval as it is written; the composer had a reason for writing it that way. That reason sometimes has to do with subtle differences in the way different written notes will be interpreted by performers, but it is mostly a matter of placing the notes correctly in the context of the key , the chord , and the evolving harmony . (Please see Beginning Harmonic Analysis for more on that subject.)
Inverting intervals
To invert any interval, simply imagine that one of the notes has moved one octave, so that the higher note has become the lower and vice-versa. Because inverting an interval only involves moving one note by an octave (it is still essentially the "same" note in the tonal system), intervals that are inversions of each other have a very close relationship in the tonal system.
- To name the new interval, subtract the name of the old interval from 9.
- The inversion of a perfect interval is still perfect.
- The inversion of a major interval is minor, and of a minor interval is major.
- The inversion of an augmented interval is diminished and of a diminished interval is augmented.
To find the inversion of an interval
What are the inversions of the following intervals?
- Augmented third
- Perfect fifth
- Diminished fifth
- Major seventh
- Minor sixth
- Diminished sixth
- Perfect fourth
- Augmented fourth
- Minor second
- Major third
Summary
Here is a quick summary of the above information, for reference.
Number of half steps | Common Spelling | Example, from C | Alternate Spelling | Example, from C | Inversion |
0 | Perfect Unison (P1) | C | Diminished Second | D double flat | Octave (P8) |
1 | Minor Second (m2) | D flat | Augmented Unison | C sharp | Major Seventh (M7) |
2 | Major Second (M2) | D | Diminished Third | E double flat | Minor Seventh (m7) |
3 | Minor Third (m3) | E flat | Augmented Second | D sharp | Major Sixth (M6) |
4 | Major Third (M3) | E | Diminished Fourth | F flat | Minor Sixth (m6) |
5 | Perfect Fourth (P4) | F | Augmented Third | E sharp | Perfect Fifth (P5) |
6 | Tritone (TT) | F sharp or G flat | Augmented Fourth or Diminished Fifth | F sharp or G flat | Tritone (TT) |
7 | Perfect Fifth (P5) | G | Diminished Sixth | A double flat | Perfect Fourth (P4) |
8 | Minor Sixth (m6) | A flat | Augmented Fifth | G sharp | Major Third (M3) |
9 | Major Sixth (M6) | A | Diminished Seventh | B double flat | Minor Third (m3) |
10 | Minor Seventh (m7) | B flat | Augmented Sixth | A sharp | Major Second (M2) |
11 | Major Seventh (M7) | B | Diminished Octave | C' flat | Minor Second (m2) |
12 | Perfect Octave (P8) | C' | Augmented Seventh | B sharp | Perfect Unison (P1) |
- A perfect prime is often called a unison. It is two notes of the same pitch.
- A perfect octave is often simply called an octave. It is the next "note with the same name".
- Perfect intervals - unison, fourth, fifth, and octave - are never called major or minor
Summary notes: perfect intervals
- An augmented interval is one half step larger than the perfect or major interval.
- A diminished interval is one half step smaller than the perfect or minor interval.
Summary notes: augmented and diminished intervals
- To find the inversion's number name, subtract the interval number name from 9.
- Inversions of perfect intervals are perfect.
- Inversions of major intervals are minor, and inversions of minor intervals are major.
- Inversions of augmented intervals are diminished, and inversions of diminished intervals are augmented.