Intervals

Week 7

Learning Outcomes

• Know the basic rules for determining major, minor, perfect, augmented, diminished, double augmented and double diminished intervals

• Understand and recognize compound intervals• Be able to invert intervals and analyze interval

inversions

Harmony Worksheets

• 9• 10• 11a• 11b

Intervals

• We need a method of identifying the relationship between any two notes

• We can show the distance or interval from one note to another

• Count each possible staff degree between the two notes to find the number the top pitch represents

• See Ex. 1 p. 16

Intervals in a Major Scale

• The perfect intervals are unison, 4th, 5th, octave

• If a major interval is made smaller by a half step the major interval becomes minor

• The major/minor intervals are 2nds, 3rds, 6ths, and 7ths.

• Intervals may occur as harmonic or melodic intervals

• When a minor or perfect interval is made smaller by a half step, it becomes diminished

• Major and perfect intervals made larger by a half step are called augmented intervals

• Diminished intervals made smaller than an additional half step become double diminished.

• Augmented intervals made larger by additional half step become double augmented

Summary

• 2nds, 3rds, 6ths and 7ths are major intervals• Unisons, 4ths, 5ths and octaves are perfect

intervals• Major intervals made smaller by a half step

become minor• Major intervals made smaller by 2 half steps

become diminished

• Perfect intervals made smaller by a half step become diminished

• Perfect intervals made smaller by 2 half steps become double diminished

• Major or perfect intervals made larger by a half step are augmented

• Major or perfect intervals made larger by 2 half steps are double augmented

Worksheet Time!

• Complete Exercise 2 and 3 on Worksheet 9• Complete Exercise 9a on Worksheet 9• Complete Exercise 10a on Worksheet 9

Compound Intervals

• Intervals greater than an octave are compound intervals

• All compound intervals are a combination of a perfect octave plus an additional intervals

• They are often analyzed as the actual number of steps or as a simple interval.

Compound Intervals

Worksheet Time

• Complete the first part of Exercise 1a on Worksheet 10

• Complete Exercise 2a on Worksheet 10

Inversion of Intervals

• Intervals describe the distance between two notes.

• The notes involved can appear to sound two ways:

• When an interval is inverted, the note names involved are still the same

• The intervallic relationship follows a pattern• Here are some simple rules for inversion:

• 9 minus the number of the interval equals the inversion interval

• EG 9 – 2(nd) = 7(th) • 9 – 7(th) = 2(nd)

• Major intervals inverted become minor• See Ex.3 p.20

• Minor intervals inverted become major• See Ex. 4 p. 20

• Perfect intervals remain perfect• See Ex1 p.21

• Augmented intervals become diminished• See Ex 2 p.21

• Diminished intervals become augmented• See Ex. 3 p.21

• Double diminished intervals become double augmented

• See Ex. 4 p. 21

• Double augmented intervals become double diminished

• See Ex.5 p.21

• In order to produced an inversion of an intervals, the bottom pitch must be raised one octave or the top pitch must be lowered one octave

The Tritone interval

• The tritone interval is an interval of an augmented 4th (3 whole steps)

• Unlike any other interval, when a tritone is inverted, it becomes a diminished 5th, but remains a tritone (3 whole steps)

Compound Interval Inversion

• We can invert compound intervals in two ways:

• 1) move the lowest pitch up and octave, or the higher pitch down an octave

• 2) reverse the position of the high/low notes

Worksheet Time!

• Complete Exercise 1-4 on Worksheet 11