Music Intervals

Interval Quality & Number

To name an interval, we need to determine the quality and number of the interval, e.g., a minor third (m3) is the name of the interval. The m (minor) describes the quality of the interval, while the third (3) describes the number of the interval.

• Minor Interval - contains 1 semitone less than a major interval.
• Major Interval - contains 1 semitone more than a minor interval.
• Augmented Interval - contains 1 semitone more than a Perfect or Major Interval.
• Diminished Interval - contains 1 semitone less than a Perfect or Minor Interval.
• Perfect Interval - raised by one semitone becomes an Augmented Interval.
• Perfect Interval - lowered by 1 semitone becomes a Diminished interval.
• Intervals are always counted upwards unless stated to the contrary, with the lower note counted as 1.
• The lower note of a music interval is always classed as the keynote or root of the interval in question, even when inverted.
• A major third is equal to 4 half steps or 4 semitones (2 tones)
• A minor third is equal to 3 half steps or 3 semitones (1+1/2 tones)
• A major second is equal to 2 half steps or 2 semitones (1 whole tone)
• A minor second is equal to 1 half step or 1 semitone (1/2 tone)
• 1sts, 4ths, 5ths and 8ths can be made Perfect, Augmented and Diminished.
• 2nds, 3rds, 6ths and 7ths can be made Major, Minor, Augmented and Diminished.

Classes of Intervals

Harmonic or Melodic Intervals

• Harmonic - are formed when 2 notes are played together
• Melodic - are formed when 2 notes are played in succession—one after the other.

Consonant or Dissonant Intervals

• Consonant - Satisfactory to the ear and do not need resolution. They are divided into 2 classes:
  1. Perfect Intervals: 1sts, 4ths, 5ths & 8ths
  2. Imperfect Intervals: Major Thirds, Minor Thirds, Major Sixths and Minor Sixths.
• Dissonant: Unsatisfactory to the ear and generally require resolution. These include 2nds, 7ths, 9ths and all Augmented and Diminished Intervals

• When a 2nd is an octave higher, it is called a 9th.
• When a 3rd is an octave higher, it is called a 10th.
• When a 4th is an octave higher, it is called an 11th.
• When a 5th is an octave higher, it is called an 12th.
• When a 6th is an octave higher, it is called a 13th...

Interval Inversions

A simple interval can be inverted by raising the lower pitch an octave, or lowering the upper pitch an octave. To invert, place the lower note above the upper note or vice versa.
Example: The interval C → E upon inversion becomes E → C.

There are 2 rules to remember in determining the number and quality of any simple interval inversion:

• The number of the interval and the interval inversion always add up to 9
• Subtract the interval number from 9. The remainder is the numerical value of the Inversion.
• Example:
  • C → E is a third interval.
  • Upon inversion E → C becomes a sixth interval.
  • If you add the 3rd interval and 6th interval, you reach 9.
  • Alternatively, if you subtract the interval number (3rd) from 9, you get the interval inversion (6th).

Now we need to calculate the quality of the interval, i.e. minor, major, diminished, augmented, perfect, etc.

• Major ↔ Minor
• Perfect ↔ Perfect
• Diminished ↔ Augmented

When an interval is inverted, the number and quality both change.
Here are some examples:

• Major becomes a Minor:
  Example: a major 3rd becomes a minor 6th (9 - 3 = 6)
  C → E is a major 3rd. Upon inversion, E → C becomes a minor 6th.
  
  
• Major becomes a Minor:
  Example: a major 7th becomes a minor 2nd (9 - 7 = 2)
  C → B is a major 7th. Upon inversion, B → C becomes a minor 2nd.
  
  
• Minor becomes a Major:
  Example: a minor 3rd becomes a major 6th (9 - 3 = 6)
  C → E♭ is a minor 3rd. Upon inversion, E♭ → C becomes a major 6th.
  
  
• Minor becomes a Major:
  Example: a minor 7th becomes a major 2nd (9 - 7 = 2)
  C → B♭ is a minor 7th. Upon inversion, B♭ → C becomes a major 2nd
  
  
• Augmented becomes Diminished:
  Example: an augmented 5th becomes a diminished 4th (9 - 5 = 4)
  C → G# is an augmented 5th. Upon inversion, G# → C becomes a diminished 4th.
  
  
• Diminished becomes Augmented:
  Example: a diminished 7th becomes an augmented 2nd (9 - 7 = 2)
  C → B♭♭ is a diminished 7th. Upon inversion, B♭♭ → C becomes an augmented 2nd.
  
  
• Perfect intervals always remain perfect when inverted.
  This is because the intervals involved (1st, 4th, 5th, 8th) are perfect in both keys.
  When you invert an interval, the two interval numbers always add up to 9.
  So a perfect 4th becomes a perfect 5th (4 + 5 = 9), and a perfect 5th becomes a perfect 4th.
  Example: C → F is a perfect 4th.
  Inversion gives F → C, which is a perfect 5th.
  The quality stays perfect in both directions.

• Diatonic - occurs in an unaltered Diatonic Scale.
• Chromatic- occurs in an unaltered Chromatic Scale.
• Harmonic - sounds are heard simultaneously or together.
• Melodic - sounds are heard in succession or one after the other.
• Simple - contained within the range of an octave.
• Compound - beyond the range of an octave.

Tritones

A Tritone is a Music Interval which contains 3 full tones (diatonic) or 6 semitones(chromatic)

In a Major Key, there is one example of a tritone between the subdominant (4th degree of a scale) and the leading tone (7th degree of the scale)
Example: In the C Major Scale C D E F G A B there are 3 full tones from F (4th degree) to B (7th degree)

1. Between the subdominant (4th degree) and the leading tone(7th degree)

   Example: D Harmonic Minor: D - E - F - G - A - B♭ - C# (3 whole tones between G and C#)

2. Between the subdominant (6th degree) and the upper supertonic (2nd degree)

   Example: D Harmonic Minor: D - E - F - G - A - B♭ - C# - D - E (3 whole tones between Bb and E)