lesson 1 1305 revised

7/27/2019 Lesson 1 1305 Revised

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LESSON 1

INTERVALS

OVERVIEW

LESSON DESCRIPTION:

In this lesson, you will learn to name intervals, chromatically alter intervals, invert intervals, identify consonant and

dissonant intervals, and identify diatonic and chromatic intervals.

ENABLING LEARNING OBJECTIVE 1:

ACTION: Identify intervals.

CONDITION: Given the information provided in this lesson.

STANDARD: Demonstrated proficiency by accurately completing the Practical Exercises contained

in this lesson.

REFERENCES: The material contained in this lesson was derived from the following publication: TC

12-41, Basic Music.

INTRODUCTION

An interval is the distance in pitch between two notes. Knowledge of intervals assists musicians in accurate

intonation and sight singing.

PART A-NAMING INTERVALS

1. Intervals occur as eitherharmonic ormelodic intervals.

a. Two notes sounded simultaneously form a harmonic interval (Figure 1-1).

Figure 1-1: Harmonic Interval

b. Two notes sounded in succession form a melodic interval (Figure 1-2).

Figure 1-2: Melodic Interval

2. There are two types of intervals: simple and compound.


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a. Simple intervals encompass an octave or less (Figure 1-3).

Figure 1-3: Simple Intervals

b. Compound intervals are larger than (but NOT including) an octave (Figure 1-4).

Figure 1-4: Compound Intervals

3. Intervals consist of two components: the name or distance of the interval and the quality of the interval.

4. Interval Name. Intervals are named according to the number of letter names, or the number of successive staff

degrees encompassed by the interval. The intervals name is determined by measuring the distance from the

bottom note to the top note of the interval. Count the bottom note as one (NOT zero) and count the lines and

spaces of the staff up to and including the top note (Figure 1-5).

Figure 1-5: Determining Interval Name

a. Figure 1-5 indicates six lines and spaces included in the interval between the top and bottom notes.

b. The interval name may also be determined by counting the letter names encompassed in the interval. The

interval with the bottom note C and the top note A is a sixth since six letter names are encompassed.

c. The interval name is written as an Arabic numeral (1, 2, 3, etc.).

d. When both notes of an interval are on the same line or space (have the same letter name), the interval is

called a prime.

e. Adding an accidental to the top, bottom, or both notes DOES NOT change the name of the interval. Each

interval in Figure 1-6 is still a sixth.

f. In performance, melodic intervals are referred to as either ascending or descending; however, they are

measured from the bottom note to the top note.


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Figure 1-6: Intervals of a Sixth

SELF REVIEW EXERCISE 1. Write the name for each interval. The first one has been done for you. CLICK

HERE FOR PRINTABLE VERSION. When finished, hit the back button on your browser to return to this page.

Figure 1-7: Identify Interval Names

SELF REVIEW EXERCISE 2. Write a note above the given note to form the interval indicated. The first one has

been done for you. CLICK HERE FOR PRINTABLE VERSION. When finished, hit the back button on your

browser to return to this page.

Figure 1-8: Write the Top Note of an Interval

SELF REVIEW EXERCISE 3. Write a note below the bottom note to form the interval indicated. The first one

has been done for you. CLICK HERE FOR PRINTABLE VERSION. When finished, hit the back button on your



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Figure 1-9: Write the Bottom Note of an Interval

5. Interval Quality. The quality of an interval denotes the exact distance of the interval. There are five common

interval qualities: perfect, major, minor, augmented, and diminished. Quality designators are abbreviated-

Per - Perfect

Maj - Major

min - Minor

Aug - Augmented

dim - Diminished

a. The quality of the interval can be determined by the scale from which the interval is taken. A thorough

knowledge of scales and key signatures helps in identifying intervals.

b. In major scales, the intervals that occur between the tonic and subsequent scale degrees form perfect and

major intervals (Figure 1-10). The perfect intervals are prime, fourth, fifth and octave. The major intervals

are second, third, sixth, and seventh.

Figure 1-10: Interval Quality of Major Scale

c. In natural minor scales, the intervals that occur between the tonic and subsequent scale degrees form perfect,

major, and minor intervals (Figure 1-11). The perfect intervals are prime, fourth, fifth, and octave. The major

interval is the second. The minor intervals are third, sixth, and seventh.


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Figure 1-11: Interval Quality of Natural Minor

d. Adding accidentals to the notes of an interval changes the intervals quality. These changes are explained in

the section on chromatic alterations.

6. Identifying Intervals.

a. Think of the bottom note of an interval as the tonic of a major scale. If the top note of the interval is a

member of that major scale, the interval is either perfect or major. If the top note is NOT a member of that

major scale, the following intervals result.

(1) Minor intervals are one half step smaller than major intervals.

(2) Diminished intervals are one half step smaller than minor and perfect intervals.

(3) Augmented intervals are one half step larger than major and perfect intervals.

b. Intervals can also be identified by the number of half steps they contain.

(1) The number of half steps in an interval can be directly related to a keyboard or a chromatic scale. Start

on the bottom note of the interval and count up the number of half steps (keys) to the top note (Figure

1-12).

Figure 1-12: Half Steps


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(2) Each interval contains a specific number of half steps. The chart below indicates the number of half

steps of common intervals (Figure 1-13).

Figure 1-13: Half Steps in Intervals

PART B - CHROMATIC ALTERATION

7. Chromatic Alteration is the process of raising or lowering the pitch of a note by adding accidentals (sharp, flat,

natural, etc).

8. Perfect Intervals. Chromatically altering perfect intervals (prime, fourth, fifth, and octave) by half step makes

them either augmented (Aug) or diminished (dim) intervals (Figure 1-14).

Figure 1-14: Altered Perfect Intervals

a. Raising the top note one half step or lowering the bottom note one half step of a perfect interval creates an

augmented interval (Figure 1-15).


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Figure 1-15: Augmented Intervals from Perfect Intervals

b. Lowering the top note one half step or raising the bottom note one half step of a perfect interval creates a

diminished interval (Figure 1-16).

Figure 1-16: Diminished Intervals from Perfect Intervals

NOTE: A perfect prime cannot be altered to make a diminished prime.

c. The augmented fourth (Aug 4) and the diminished fifth (dim 5) are also called the tritone. This interval

contains six half steps (Figure 1-17).

Figure 1-17: Tritone

SELF REVIEW EXERCISE 4. Write the bottom note to form the interval indicated (Figure 1-18). The first one

has been done for you. CLICK HERE FOR PRINTABLE VERSION. When finished, hit the back button on your



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Figure 1-18: Chromatic Alterations

SELF REVIEW EXERCISE 5. Write the top note to form the interval indicated (Figure 1-19). The first one has

been done for you. CLICK HERE FOR PRINTABLE VERSION. When finished, hit the back button on yourbrowser to return to this page.


SELF REVIEW EXERCISE 6. Identify and label the intervals (Figure 1-20). The first one has been done for you.

CLICK HERE FOR PRINTABLE VERSION. When finished, hit the back button on your browser to return to this

page.


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Figure 1-20: Identify Intervals

9. Major Intervals. Chromatically altering major intervals (second, third, sixth, and seventh) by a half step

creates augmented (Aug) or minor (min) intervals (Figure 1-21).

Figure 1-21: Altered Major Intervals

a. Raising the top note one half step or lowering the bottom note one half step of a major interval creates an

augmented interval (Figure 1-22).

Figure 1-22: Augmented Intervals from Major Intervals

b. Lowering the top note one half step or raising the bottom note one half step of a major interval creates a

minor interval (Figure 1-23).


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Figure 1-23: Minor Intervals from Major Intervals

10. Minor Intervals. Chromatically altering minor intervals (second, third, sixth, and seventh) creates major (Maj)

or diminished (dim) intervals (Figure 1-24).

Figure 1-24: Altered Minor Intervals

a. Lowering the top note one half step or raising the bottom note one half step of a minor interval creates a

diminished interval (Figure 1-25).

Figure 1-25: Diminished Intervals from Minor Intervals

b. Raising the top note one half step or lowering the bottom note one half step of a minor interval creates a

major interval (Figure 1-26).


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Figure 1-26: Major Intervals from Minor Intervals

11. Effects of Chromatic Intervals.

a. Perfect intervals NEVERbecome major or minor.

b. Perfect intervals made larger by one half step become augmented.

c. Perfect intervals made smaller by one half step become diminished-except for a perfect prime.

d. Major and minor intervals NEVERbecome perfect.

e. Major intervals made larger by one half step become augmented.

f. Major intervals made smaller by one half step become minor.

g. Minor intervals made larger by one half step become major.

h. Minor intervals made smaller by one half step become diminished.

i. Figure 1-27 is a graphic representation of how intervals are altered. Each level of the graph represents one

half step.

Figure 1-27: Half Step Movement

j. The most commonly occurring diminished intervals are the intervals of a fourth, fifth, and seventh

(occasionally the third).


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k. The most commonly occurring augmented intervals are the intervals of a second, fourth, and fifth

(occasionally the sixth).

SELF REVIEW EXERCISE 7. Write the top note of the interval indicated (Figure 1-28). The first has been done

for you. CLICK HERE FOR PRINTABLE VERSION. When finished, hit the back button on your browser to

return to this page.

Figure 1-28: Writing Intervals

SELF REVIEW EXERCISE 8. Write the bottom note of the interval indicated (Figure 1-29). The first note has

been done for you. CLICK HERE FOR PRINTABLE VERSION. When finished, hit the back button on your



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12. Enharmonic Intervals. Enharmonic intervals produce the same sound but are written differently.

a. The intervals of the augmented sixth and minor seventh in Figure 1-30 CANNOT be distinguished by

sound alone because D sharp and E flat are enharmonic notes (notes that sound the same).

Figure 1-30: Enharmonic Intervals

b. Although enharmonic intervals sound the same, use the correct numeric and quality designators when

writing them. The interval F to D sharp (Figure 1-30) is NOT a minor seventh. D is the sixth scale degree

of the F Major scale; therefore, the interval F to D is a Major sixth. The top note of the interval has been

raised one half step to D sharp; therefore, the interval F to D sharp is an Augmented sixth. The interval F to

E flat CANNOT be an Augmented sixth. E is the seventh scale degree of the F Major scale; therefore, F to


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E is a Major seventh. The top note of the interval has been lowered one half step to E flat. F to E flat is a

minor seventh.

SELF REVIEW EXERCISE 9. Write the accidentals needed to form the enharmonic interval indicated (Figure 1-

31). Label the enharmonic interval. The first one has been done for you. CLICK HERE FOR PRINTABLE

VERSION. When finished, hit the back button on your browser to return to this page.

Figure 1-31: Writing Enharmonic Intervals

PART C - INVERTING INTERVALS

13. Inverting intervals. Inverting intervals is the process of reversing the position of the top and bottom notes of a

simple interval. The letter names remain the same, only the octave is changed for one of the notes. There are

two ways to invert an interval.

a. Raise the bottom note one octave (Figure 1-32). This note becomes the new top note. The original top note

DOES NOT move, but it is now the new bottom note of the interval.

Figure 1-32: Raising the Bottom Note One Octave

b. Lower the top note one octave (Figure 1-33). This note now becomes the new bottom note. The original

bottom note DOES NOT move, but it is now the new top note of the interval.


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Figure 1-33: Lowering the Top Note One Octave

NOTE: Because compound intervals are larger than an octave, they CANNOT be inverted.

14. Three simple intervals that DO NOT invert:

a. The perfect prime (Per 1) DOES NOT invert.

b. The perfect octave (Per 8) DOES NOT invert because the resulting interval is a Perfect prime (Per 1).

c. The augmented octave (Aug 8) DOES NOT invert. Although the augmented octave is a simple interval, it

is larger than an octave.

15. The names of inverted simple intervals are predictable. The sum of a simple interval and its inversion is always

NINE. The following chart shows the inversion of common simple intervals (Figure 1-34).


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Figure 1-34: Inversion of Simple Intervals

NOTE: The sum of both intervals equals nine.

16. Inverting an interval also changes its quality.

a. Major intervals become minor intervals.

b. Minor intervals become major intervals.

c. Augmented intervals become diminished intervals.

d. Diminished intervals become augmented intervals.


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e. Perfect intervals remain perfect intervals.

Major - minor

Augmented - diminished

Perfect Perfect

NOTE: Perfect intervals are the only intervals that DO NOT change quality when inverted.

SELF REVIEW EXERCISE 10. Write the missing note of the inversion of each interval (Figure 1-35). Label the

new interval. The first one has been done for you. CLICK HERE FOR PRINTABLE VERSION. When finished,

hit the back button on your browser to return to this page.

Figure 1-35: Inverting Intervals

17. Compounding Intervals.

a. Compounding a simple interval is accomplished by moving the upper note up one octave or the lower note

down one octave. The top note remains the top note and the bottom remains the bottom note.

NOTE: The simple interval retains its identity regardless of how many octaves are between the two notes. For

example, the interval of an 11 is a compound 4. A compound interval sounds like the simple interval from which it

is derived, the difference being the added octave.

b. When compounding intervals, the name of the interval changes but the quality remains the same.


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c. When compounding a simple or compound interval, add the number seven (7) to the name of the interval

for each octave of displacement. A major third expands to a major tenth (3+7=10). Either note of the

interval can be moved (Figure 1-36).

Figure 1-36: Compounding Intervals

e. Compounding the perfect prime DOES NOT make it a compound interval. The perfect prime (Per 1)

expands to a Perfect octave (Per 8) (1+7=8). The perfect octave is still a simple interval.

18. Reducing Intervals.

a. A compound interval can be reduced to its corresponding simple interval. When reducing a compound

interval, subtract the number seven (7) from the name of the compound interval for each octave of reduction(Figure 1-37).

Figure 1-37: Reducing One Octave

b. Reducing the interval DOES NOT change the quality of the interval.

c. Additionally, two simple intervals can be reduced.

(1) The augmented octave reduces to an augmented prime (Figure 1-38).

Figure 1-38: Reducing an Augmented Octave

(2) A perfect octave reduces to a perfect prime (Figure 1-39).


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Figure 1-39: Reducing the Perfect Octave

SELF REVIEW EXERCISE 11. Identify and label the given interval. Expand or reduce each interval as

indicated. Label the resulting interval (Figure 1-40). The first one has been done for you. CLICK HERE FOR

PRINTABLE VERSION. When finished, hit the back button on your browser to return to this page.

Figure 1-40: Expanding and Reducing Intervals

PART D- CONSONANT AND DISSONANT INTERVALS

19. The basic sound of an interval may be generally described as consonant or dissonant. Consonant intervals tend

to remain stable. Dissonant intervals tend to be unstable.

20. Consonant intervals. Perfect primes, thirds, perfect fifths, sixths, and perfect octaves are generally consonant

intervals (Figure 1-41).


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Figure 1-41: Examples of Consonant Intervals

21. Dissonant Intervals. Seconds, perfect fourths, sevenths, augmented and diminished intervals are generally

dissonant intervals (Figure 1-42).

Figure 1-42: Examples of Dissonant Intervals

PART E-DIATONIC AND CHROMATIC INTERVALS

22. Diatonic intervals. Intervals are diatonic when both lower and upper notes of the interval are found in the key.

The simple interval of B flat to D is diatonic in the key of B flat major (Figure 1-43).

Figure 1-43: Diatonic Intervals

23. Chromatic intervals. Intervals are chromatic when one or both notes of the interval are foreign to the key. The

simple interval B flat to D flat is chromatic in the key of B flat major (Figure 1-44).

Figure 1-44: Chromatic Intervals

SELF REVIEW EXERCISE 12. Label each interval as either diatonic or chromatic (Figure 1-45). The first one

has been completed for you. CLICK HERE FOR PRINTABLE VERSION. When finished, hit the back button on

your browser to return to this page.


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Figure 1-45: Diatonic and Chromatic Intervals


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LESSON 1

ANSWERS TO SELF REVIEW EXERCISES

SELF REVIEW EXERCISE 1 (SOLUTION).

Figure 1-7: Naming Intervals


Figure 1-8: Top Note of the Interval



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Figure 1-9: Bottom Note of the Interval






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Figure 1-20: Identifying Intervals



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Figure 1-31: Writing Enharmonic Intervals



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Figure 1-35: Inverting Intervals



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Figure 1-40: Expanding and Reducing Intervals


Figure 1-45: Diatonic and Chromatic Intervals

lesson 1 1305 revised

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