Table of Contents

Section 3: 

Set theory
Rhythm/ form 
12- tone 
Polyrhythm
Metric modulation
Meter

Section 4: 

Basic Assumptions 
Motive, Phrase and Period
Cadence
Binary form
Ternary form
Rounded binary form
Sonata form
Rondo form
Theme and variation
Dance forms

Section 5: 

Basic assumptions 
and procedures
Harmony
Form and rhythm
Melody
Timbre

Section 6: Bibliography

home

 Contents     Journal     Index     First Aid     Instructional Papers     Forum 

Intervals

Basic Concepts:

1.  An interval is the distance between two notes, not in time, but in musical space. 

2.  Intervals are classified two ways:
    a.   the basic interval of the unison, second, third, fourth, fifth, sixth, seventh, and octave,
    b.  the type of basic interval (perfect, major, minor, augmented, diminished)

3.  Many theorists by default refer to an interval's notes in ascending order.  Therefore, an interval  between C and E usually means that C is the lower note of the interval. This usage will be employed here.

4.  An interval can be inverted by placing the upper note under the lower note and vice versa.  For example, the interval C-E can be inverted by placing the E below the C or the C above the E.

5.  Intervals beyond an octave are usually referred to as compound intervals.  This means that the interval of a ninth is equivalent to the interval of a second, displaced by an octave. 

6.  Intervals are measured according to the spelling of each pitch.  This means that C-D sharp is some kind of second, even though the interval may not sound like a second, while the interval between the same actual keys on the keyboard, respelled C-E flat, is considered a third.  

Key word: ENHARMONIC.  Enharmonic means the same pitch spelled differently.  Common usage: E flat is the enharmonic equivalent of D sharp.

Section I-Basic Intervals

The basic intervals may be thought of as the letters of the musical alphabet.  A unison is the interval between notes of the same letter. A second is the interval between adjacent letters like A-B (remember that by convention B-A would be a seventh because it is an ascending interval, B as the lower note).  A third skips a letter: E-G.  A fourth skips two letters: D-G and so forth. 

Another way of thinking about basic intervals is the layout of the keyboard.  On the white keys, adjacent notes comprise a second; a third has one note between.

The basic unit of measurement between notes is the half-step, which is the shortest possible distance between two notes in the diatonic system. On the keyboard, a half step is the distance between two adjacent keys, including the black keys.  Therefore, C-C sharp is a half step, C-D is a whole step. When measuring basic intervals, half steps do not come into play.

CAUTION: Basic intervals are counted from "one."  For example, C-D is counted one-two and the basic interval is a second. C-E is counted one-two-three (C-D-E) and the basic interval is a third.  The interval type (major, minor, augmented, diminished) is counted from zero by half step. Therefore, C-C sharp is counted zero-one, and the interval is one half step.  The difference in the counting is that basic intervals are counted from one pitch to another. Interval types (half step) measure the distance "between" two pitches.  The distance between a note and itself is zero.

Section 2-Interval type

Process: To determine the type of interval, (until one has enough experience) one must follow a two step process. First, determine the basic interval.  Remember, the options are unison, second, third, fourth, fifth, sixth, seventh, octave.  Then, to answer the question of what type of interval you have, count the half steps between the two notes. For example, C-E is a third. How many half steps between?  C-C sharp 1, C sharp-D 2, D-D sharp 3, D sharp-E 4.  Four half steps.  Therefore, you have a major third because a third that has four half steps is major (see the list below for the half steps in all the intervals).

The confusion comes in the fact that a diminished fourth also has four half steps between notes (C-F flat).  This is why one must determine the basic interval first, before counting half steps.

Types of intervals: The following information must be memorized.  The basic interval types are major, minor, augmented, diminished, and perfect. The only basic intervals that can be perfect are unisons, fourths, fifths, and octaves (which actually are compound unisons).  All intervals can be augmented. All intervals but the unison can be diminished. Only seconds, thirds, sixths, and sevenths can be major or minor.

Seconds, thirds, sixths, and sevenths: Let us deal with seconds, thirds, sixths, and sevenths first.  The section below will provide detail on the fact that seconds and sevenths are related by inversion, as are thirds and sixths.  These four interval types may be major, minor, augmented, or diminished. The sequence of type goes by half step: diminished-minor-major-augmented, meaning that diminished is a half step smaller (closer) than a minor interval, a major is a half step larger (wider) than a minor interval, and the augmented is a half step larger than the major interval.

Here is a basic list of interval types by half step:

*Major second-two half steps (E-F sharp)  *Augmented second-three half steps (E flat-F sharp)  *Minor second-one half step (G-A flat)  *Diminished second-0 half steps (G sharp-A flat).

*Major third-four half steps (E-G sharp)  *Augmented third-five half steps (E flat-G sharp)  *Minor third-three half steps (C-E flat)  *Diminished third-two half steps (C sharp-E flat).

For measuring the intervals of the sixth and seventh, please see the shortcut under the inversion section.

Unisons, fourths, fifths, and octaves: The perfect intervals, unison, fourth, fifth, and octave, may be augmented and diminished as well, but they are never major or minor.  Detail on the inversional relationship between the fourth and the fifth will be provided below.

The perfect unison is the same note.  C sharp to D flat is not a perfect unison because of the spelling.  It is a diminished second.  The perfect octave is the same note removed by an octave.  C-B sharp is not a perfect octave.  It is an augmented seventh.

The perfect fourth has five half steps between pitches, and the perfect fifth has seven.  The augmented intervals are one half step wider than the perfect, and the diminished are one half step narrower than the perfect.

ALWAYS REMEMBER TO DETERMINE THE BASIC INTERVAL FIRST, THEN FIGURE THE TYPE OF INTERVAL!

Section 3-Inversion

It will be useful to be aware that there are two types of inversion.  In this chapter, since we are dealing with intervals, we will use only one type, to which we may conveniently refer as Type I.  Type I inversion is the switching of the position of each note in an interval.  For example, D-A may be inverted by placing the A below the D, forming the A-D interval.  Notice the change in interval type: D-A is a perfect fifth, while A-D is a perfect fourth.  This is a fundamental principle that applies universally in music. All perfect fifths invert to perfect fourths.

Type II (called thus here only) inversion refers to the practice of turning a melodic line upside down, or creating a vertical mirror image of the melody.  In this case, all intervals invert to themselves (that is, the major third A flat-C inverts to the major third A flat-F flat or C-E).  The section on 20th century music theory treats this concept in detail.  In the example below, the second melody is a Type II inversion of the first.  Notice that that the intervals form a mirror image around the first pitch, G.

The following lists the inversional relationships (Type I inversion) of basic intervals and types:

2nd-7th
3rd-6th
4th-5th

All major intervals invert to minor intervals.  E.g. major second inverts to minor seventh.

All minor intervals invert to major intervals.

All perfect intervals invert to perfect intervals.

All augmented intervals invert to diminished intervals.  All diminished intervals invert to augmented intervals.

Shortcut for reckoning interval types: If you know the inversional relationships, you only have to memorize the interval types to the augmented fourth.  If you have an interval larger than an augmented fourth, simply invert it, figure the interval, then invert that. For example, the interval D-B flat is a sixth.  Instead of counting half steps to determine the type of sixth, invert it to B flat-D. Now you have a third, you can count the half steps, four, and determine that it is a major third. Therefore, your original interval is a minor sixth, the inversion of the major third.

Copyright ©2000 Music Theory Resources.  All rights reserved.