1. Pitch Intervals
Chapter 6

2. Pitch Intervals
Key Concept – page 95 An interval measures the musical space between two pitches or pitch classes. The intervals between pitches are called pitch intervals. The intervals between pitch classes are called pitch-class intervals.

3. Generic Intervals Labeled with a number, not a specific quality.
Numbers include: 1 2 3 4 5 6 7 8
Etc.

4. Labeling Generic Intervals
Starting with the bottom pitch, count it as 1
Count the lines and spaces to the next pitch
The number you count is the generic interval

5. Labeling Generic intervals
You can also use scales for intervals
For example:
In the Key of C
C-C = 1 (Unison – same pitches)
C-D = 2
C-E = 3
C-F = 4
C-G = 5
C-A = 6
C-B = 7
C-C = 8

6. Assignment – Try It #2 – page 96
Name the generic interval spanned by each pair of pitches.

7. Melodic Versus Harmonic Intervals
A melodic interval is the distance between to successive pitches
A harmonic interval is the distance played simultaneously

8. Simple Generic Intervals
Intervals that span within an octave.

9. Compound Intervals
A compound interval is an interval larger than one octave
When labeling compound intervals be careful to get correct intervals
Two options:
Count the distance between the pitches
Formula of:
7 + s (7 + the simple interval number)
Example:
C4 – D5 = (M)9
7 + 2 = 9
(This is because the unison is 1 and not 0.)

10. Interval Quality
Key Concept – page 99 When two generic pitch intervals share the same interval number but are not the exact same size, the difference in size is called the interval quality.

11. Types of Interval Quality
Major (based on the major scale)
Perfect (based on the major scale)
Minor (half step smaller than major intervals)
Diminished (half step smaller than perfect and minor intervals)
Augmented (half step larger than major and perfect intervals)
Key Concept – page 100
Major intervals are a half step larger than minor intervals.

12. Types of Interval Quality
HANDOUT

13. Examples

14. Using Major Scales to Spell Pitch Intervals
To get a major 3rd above the scale tonic, think about the major scale.
For example:
Major third above G is B
The same goes for minor scales.

15. Using Major Scales to Spell Pitch Intervals
Key Concept – page 102
One quick way to spell a pitch interval is to imagine that the interval is in a key, where the bottom note is the tonic and the upper note lies somewhere in the scale.
Always begin by writing the generic interval first (by counting lines and spaces.)
If the interval you want is perfect (unison, 4th, 5th, or octave) or major (2nd, 3rd, 6th, or 7th), add an accidental to the upper note so that it conforms to the major key signature of the bottom note.
If the interval you want is a minor 3rd, 6th, or 7th, add an accidental to the upper note that conforms to the minor key signature of the bottom note.
If the interval you want is a minor second, follow step #1, then add an accidental to the upper note if needed to make the interval a half step.

16. Using Major Scales to Spell Pitch Intervals
1. Always begin by writing the generic interval first (by counting lines and spaces.)

17. Using Major Scales to Spell Pitch Intervals
2. If the interval you want is perfect (unison, 4th, 5th, or octave) or major (2nd, 3rd, 6th, or 7th), add an accidental to the upper note so that it conforms to the major key signature of the bottom note.

18. 3. If the interval you want is a minor 3rd, 6th, or 7th, add an accidental to the upper note that conforms to the minor key signature of the bottom note.

19. Using Major Scales to Spell Pitch Intervals
4. If the interval you want is a minor second, follow step #1, then add an accidental to the upper note if needed to make the interval a half step.

20. Assignment – Try It #5 - page 102
Name the following notes.

21. Using Major Scales to Identify Pitch Intervals
Think of the scale of the tonic to help identify an interval that has been spelled for you.
For example:
F is the top pitch.
C is the bottom pitch.
Identify the generic interval.
Use scales to determine the quality.

22. Assignment – Try it #6 - page 103
Name the following intervals.

23. Spelling Pitch Intervals Beneath a Given Note
If we want to spell a major 6th below C:
Write the generic interval by counting down 6. (This pitch is now the tonic.)
Ask, “Does the C fit the the E-Major scale?”
What has to be done so the C fits a scale in which a form of E is the tonic? We can NOT change the given pitch.
Add an accidental to the E so we have a major 6th.

24. Assignment – try it #7 on page 103
Name the following notes:

25. Another Way to Spell Pitch Intervals
Label the generic interval.
Count the number of semitone (half-steps).

26. The Tritone
A tritone is the interval between P4 and P5. (Tri stands for the 3 whole steps (6 half steps) of the interval.) This interval may be spelled as an A4 or a d5. (If the generic interval is 4, it will be an A4. If the generic interval is 5, it will be a P5.) A4 d5

27. Spelling Diminished and Augmented Intervals
Key Concept - page 105
When a major or perfect interval is made one chromatic help step larger, we call it augmented. When a minor or perfect interval is made one chromatic half step smaller, we call it diminished.
When a major or perfect interval is made one whole step larger (without changing the letter names of the pitches), we call it doubly augmented. When a minor or a perfect interval is made one whole step smaller (without changing the letter names of the pitches) we call it doubly diminished.

28. Enharmonic Equivalent Intervals
Enharmonic Equivalent Intervals are intervals that span the same number of semitones but have different interval names.
For example a minor 3rd from F to Ab and an augmented second from F to G# both span three semitones.

29. The Relative Consonance and Dissonance of Intervals
Consonant intervals sound pleasing to the ear or are tonally stable. (Unison, 3rd, 5th, 6th, and Octave - perfect/major and minor)
Dissonant intervals sound tonally active, there is a need to resolves, and unpleasant. (2nd, (4th,) and 7th - major and minor; any augmented or diminished intervals)
Perfect consonances are unisons, fifths, and octaves due to their pure acoustic properties.
(Unison, 5th, Octave)
Imperfect consonances are not considered to be acoustically pure. (3rd and 6th)

30. Summary - page 108 Consonant intervals: unison, third, fifth, octave
Dissonant intervals: second, seventh, any augmented or diminished interval
Special case: fourth (acoustically consonant; melodic interval is usually a consonance, harmonic interval is usually a dissonance)

31. The Inversion of Intervals
Inversionally related intervals are intervals that are spelled with the same pitches but in a different ordered.

32. The Inversion of Intervals
Key Concept - page 109
Things to keep in mind when determining the quality and size of an interval inversion.
Quality:
Perfect intervals remain perfect;
Major intervals invert to minor, and vice versa;
Diminished intervals invert to augmented, and vice versa
Size:
The two numbers always sum to 9; for example 1 inverts to 8, 3 inverts to 6, 4 inverts to 5, etc.

33. The Inversion of Intervals

34. Assignment - Try it #9 - page 109
For each pair of pitches below, name the interval. Then write the inversion, and name the new interval. The first has been completed for you.