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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.

Perfect intervals

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.

    Major and minor intervals

  • 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 .

Give the complete name for each interval.

Fill in the second note of the interval given.

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.

Some diminished and augmented intervals

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?

Write a note that will give the named interval.

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.)

Enharmonic intervals

Any interval can be written in a variety of ways using enharmonic spelling. Always classify the interval as it is written.

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.

Inverting intervals

    To find the inversion of an interval

  1. To name the new interval, subtract the name of the old interval from 9.
  2. The inversion of a perfect interval is still perfect.
  3. The inversion of a major interval is minor, and of a minor interval is major.
  4. The inversion of an augmented interval is diminished and of a diminished interval is augmented.

What are the inversions of the following intervals?

  1. Augmented third
  2. Perfect fifth
  3. Diminished fifth
  4. Major seventh
  5. Minor sixth
  1. Diminished sixth
  2. Perfect fourth
  3. Augmented fourth
  4. Minor second
  5. Major third

Summary

Here is a quick summary of the above information, for reference.

The examples given name the note reached if one starts on C, and goes up the named interval.
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)

    Summary notes: perfect intervals

  • 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: augmented and diminished 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: inversions of 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.

Questions & Answers

An investment account was opened with an initial deposit of $9,600 and earns 7.4% interest, compounded continuously. How much will the account be worth after 15 years?
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Source:  OpenStax, Music fundamentals 4: intervals. OpenStax CNX. Jul 13, 2009 Download for free at http://cnx.org/content/col10730/1.1
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