I. Intervals

II. Scale Degrees

III. Scales and Keys

IV. Modes

V. Intro to Modulations

VI. Modulations of Aeolian and Ionian

VII. Other Modulations and Ethnic Scales

VIII. 5, 6, 7, 8, 9, 10, and 12 Tone Scales

 

 

Part I: Intervals

There are two types of intervals. A harmonic interval is playing two tones simultaneously. A melodic interval is two tones played in succession.

 

 An interval in most basic terms is the distance between two notes. There are many types of intervals, and theoretically it extends indefinitely (since you can pick any two notes and theres really no limit to how high the second note it). However in practical usages, there is no application for anything past the second octave (some modern composer use chromatics to achieve chords made up of all twelve tones, which spans into the fourth octave).

 

One last term to know is a step. There are technically only two types of steps. A half step represents the difference between two successive notes. For example, going from C to C# is a half step. Going from E to F is also a half step. As long as no other note (including black keys as well as white keys on the piano) exists between the two compared notes, its a half step. In numerical format it is written as .

 

A whole step represents the difference between two notes on a piano with a note included in between. C to D is a whole step (C# is in between). E to F# is a whole step (F is in between). A half step is commonly represented by a 1.

 

 

Below is a chart listing the melodic interval name, the step difference, and an example using notes.

Octave One

Interval Name

Step Difference

Total Steps

Example

Perfect Unison (Perfect First/Diminished Second)

0

0

C and C

Minor Second

1

C and C#

Major Second (Diminished Third)

1

2

C and D

Minor Third (Augmented Second)

1

3

C and D#

Major Third

2

4

C and E

Perfect Fourth (Augmented Third)

2

5

C and F

Tritone (Augmented Fourth/Diminished Fifth))

3

6

C and F#

Perfect Fifth

3

7

C and G

Minor Sixth (Augmented Fifth)

4

8

C and G#

Major Sixth (Diminished Seventh)

4

9

C and A

Minor Seventh

5

10

C and A#

Major Seventh

5

11

C and B

Perfect Octave

6

12

C and C

 

Octave Two

Minor Ninth

6

13

C and C#

Major Ninth

7

14

C and D

Minor Tenth (Augmented Ninth)

7

15

C and D#

Major Tenth

8

16

C and E

Perfect Eleventh

8

17

C and F

Augmented Eleventh (Diminished Twelfth)

9

18

C and F#

Perfect Twelfth

9

19

C and G

Minor Thirteenth (Augmented Twelfth)

10

20

C and G#

Major Thirteenth

10

21

C and A

Minor Fourteenth

11

22

C and A#

Major Fourteenth

11

23

C and B

Perfect Fifteenth

12

24

C and C

*Note that in the second octave, the C to D for example isnt the same D as before. You are moving chromatically up the tones so its the D one or two octaves away.

 

There are many applications for each one of these intervals in all forms of music. Even the highly dissonant minor second is used in a variety of places. This concludes the lesson on intervals.