The document discusses musical intervals. It defines two types of intervals - perfect and imperfect - and identifies specific classes of each type. Perfect intervals include unisons, octaves, 4ths and 5ths. Imperfect intervals are 2nds, 3rds, 6ths and 7ths, which can be major or minor. The numerical and qualitative measurements used to define intervals are also explained.

1. Harmony 1
Week 3

2. Learning Outcomes
• By the end of today’s session students will be able to:
• Understand the two aspects of interval measurement
• Identify 2 different classes of intervals
• Construct perfect, major, minor, augmented and diminished intervals

3. Intervals
• An interval is the distance between notes
• The distance between two notes sounded one after the other is called
a melodic interval
• The distance between two notes sounded at the same time is called a
harmonic interval
• Intervals are defined by two measurements: Numerical and
Qualitative

4. Numerical measurement
• Numerical measurement is a general description that simply counts
the number of staff line and space names (inclusive) from one note to
the other.
• Accidentals are not included in this measurement
• For example, the distance from C up to A is six letter names: C, D, E, F,
G, A
• Therefore, the interval between C and A is a sixth
• This is true for both ascending and descending intervals

5. Qualitative measurement
• Qualitative measurement defines the interval’s distance as an exact
number of half steps.
• For example, the sixth – C up to A – is the distance of nine half steps.
• It’s called a major 6th
• The sixth – C up to Ab – is the distance of only eight half steps
• It’s called a minor 6th because its smaller than a major 6th
• These two measurements; number and quality allow us to define the
distance between any two notes

6. Perfect Class intervals
• Intervals fall into two basic categories: perfect and imperfect.
• Perfect intervals have a ‘purer’, less complex sound.
• The perfect unison is the easiest to understand
• Numerical value: 1
• Quality: 0 half steps
• The interval sounds absolutely pure because we are repeating the
same note

7. • The perfect octave is the next most pure sound
• Number value: 8
• Quality: 12 half steps
• Repeating the same note at different pitchs
• There are four perfect class intervals:
• Perfect unison (P1)
• Perfect octave (P8)
• Perfect 5th (P5)
• Perfect 4th (P4)

8. Perfect 5th
• The perfect 5th spans 5 letter names, and comprises 7 half steps
• If we place each of the fifths on the white keys of the keyboard we
can hear the same perfect vibration in all of them except one: WHY?

9. Count the steps
• The distance is 6 half steps, not 7 – which is the required distance for
a perfect 5th.
• The 5th from B to F is called a diminished fifth because it is a half step
smaller than a perfect 5th.

10. Perfect 4th
• A perfect 4th is the distance of 4 letter names and 5 half steps
• I.e. C up to F
• Examine the white note fourths, they all sound perfect except one:
WHY?

11. Count the Steps:
• F up to B is four letter names – same as the other white note fourths,
but it is larger than the other perfect fourths by a half step
• Because F to B is a half step larger than a perfect fourth, it’s called an
augmented fourth

12. Imperfect Class Intervals
• Seconds, Thirds, Sixths and Sevenths are imperfect class intervals
• They do not sound as pure as perfect intervals

13. Seconds
• Seconds are the distances between scale steps
• They come in two sizes
• The minor second is the distance of one half step
• Minor seconds and augmented unisons are enharmonic (they sound
the same but are written differently)
• The major second is the distance of two half steps (one whole step)
• It’s quality is referred to as major because it has a greater distance
between the two pitches than the smaller minor second

14. White note seconds:
• We can see that the 2nds that stand out are
the ones that fall between B and C and E and
F – where the jump from white note to white
note is only a half step

15. Thirds
• Thirds are intervals that are 3 letter names inclusive
• The major 3rd is four half steps
• The minor 3rds is three half steps
• Look at the white note thirds: both major and minor thirds

16. Sixths
• Sixths are intervals that are six letter names inclusive
• A major 6th is nine half steps
• A minor 6th is eight half steps
• The white note sixths include both major and minor 6ths:

17. Altering Thirds
• Major thirds can be made minor by decreasing the size of the interval
by one half step.
• Major thirds can be made augmented by increasing the size of the
interval by one half step.
• Minor thirds can be made major by increasing the size of the interval
by one half step.
• Minor thirds can be made diminished by decreasing the size of the
interval by one half step.

18. Altering Sixths
• Major sixths can be made minor by decreasing the size of the interval
by one half step.
• Major sixths can be made augmented by increasing the size of the
interval by one half step.
• Minor sixths can be made major by increasing the size of the interval
by one half step.
• Minor sixth can be made diminished by decreasing the size of the
interval by one half step.

19. Summary
• There are two classes of intervals: perfect and imperfect
(major/minor)
• Perfect intervals include unisons, 4ths, 5ths and octaves
• A perfect interval made larger by a half step becomes augmented
• A perfect interval made smaller by a half step becomes diminished
• Except there is no such interval as a diminished unison

20. Summary
• Imperfect intervals are either major or minor. 2nds, 3rds, 6ths, and
7ths are imperfect intervals
• A major interval made larger by a half step becomes augmented
• A major interval made smaller by a half step becomes minor
• A minor interval made larger by a half step becomes major
• A minor interval made smaller by a half step becomes diminished