copyright © 1995 Rick Bellinger Last Modified: Oct 1, 1995
This lesson originally appeared on StickWire - the Official Chapman Stick Mailing List.
Reproduced here by permission. This article can be reprinted only in its entirety.

Theory On Tap
Lesson 1: Intervals

This lesson will cover the concept of intervals. It will contain much terminology that will probably bore the advanced player while confusing the beginning player. The important thing is to associate a sound with each term. If it doesn't make sense now, hold on to this page - after a few more lessons, it probably will.

Intervals within one octave

An interval is simply the distance between two notes. If we play one note after the other, the notes form a "melodic interval." When we play the notes together, they form a "harmonic interval." If the two notes are the same, we refer to the interval as a "unison." The smallest interval above a unison is a "half step" (which, as we shall see below, is also called a minor second). Any notes played on the stick on the same string separated by one fret are a half step apart. If they are separated by two frets, they are a whole step (or major second) apart. Notes separated by 12 half steps make up an Octave. On any one string of the stick, an octave is made up of two notes exactly twelve frets apart. The scale made by playing the notes on every fret between the octave notes is a "chromatic" scale.

There are twelve distinct notes on most western instruments. We refer to the intervals within one octave as seconds, thirds, fourths, fifths, sixths, and sevenths. Unisons, fourth, fifths, and octaves are called "perfect" intervals. Seconds, thirds, sixths and sevenths can be either "major" or "minor," with the "major" interval being a half step greater than the minor interval. Between the perfect fourth and the perfect fifth is an interval called the "tri-tone," which has the same distance as three whole steps.

Below is a chart of the different intervals within one octave and the amount of half and whole steps that make up that interval.

Table of Intervals
Name Width
Unison none
minor second one half step
major second one whole step
minor third one whole + one half steps
major third two whole steps
perfect fourth two whole steps + one half step
tritone three whole steps
perfect fifth three whole + one half step
minor sixth four whole steps
major sixth four whole and one half steps
minor seventh five whole steps
major seventh five whole and one half steps
octave six whole steps

Intervals on the melody strings

The diagram below shows how to play these intervals on the melody side of the stick. Note that the diagram shows two ways to play each interval.

R = Root
mi = minor
Ma = major
p = perfect
TT = tri-tone
Oct = octave

First play the root, and then the other note marked with the interval. The interval refers to the distance between the root ant the second note. Play the notes first as a melodic interval, both ascending and descending, and then (unless the notes are on the same string) as a harmonic interval. The point here is to demonstrate the sound of the interval. However, you should eventually find good fingerings to play each melodic and harmonic interval within one octave.

Intervals on the bass strings

Below is a diagram showing the intervals within one octave on the bass strings of the stick.

R = Root
mi = minor
Ma = major
p = perfect
TT = tri-tone
Oct = octave

Some intervals are difficult to play on the bass side unless you use two hands (although Bob Culbertson of San Jose often uses the thumb of his left hand to give him more reach to play these intervals.)

Diminished, Augmented, flat and sharp intervals

A "diminished" interval is always a half step lower than a minor or perfect interval. Thus, a diminished 7th is the same as a major 6th. A diminished fifth is the same as a tri-tone. An "augmented" interval is always one half step higher than a major or perfect interval. An augmented 5th is the same as a minor 6th, and an augmented 4th is the same as a tri-tone. Note that all diminished and augmented intervals will be equal to another interval. The terms augmented or diminished are usually used when the interval is different from one would expect from the type of chord or the key.

"Flat" (or "b") or "sharp" (or "#") intervals are other common terms used to denote intervals. A flat interval is either a minor or diminished interval; it is used to identify an interval a half step lower than one would expect from the chord type or key. A b7 will usually mean a minor 7th. Sharps are usually augmented intervals but sometimes can be major intervals, and are used to identify an interval one half step higher than one would expect. A #6 is often a major 6 interval in a minor chord or key, which ordinarily contains a minor 6. A tri-tone is often called a b5 or a #4.

Intervals greater than one octave.

The number sequence continues beyond the octave in a similar fashion. A 9th is the same as a 2nd but one octave higher. An 11th is the same as a 4th + one octave, and a 13th is the same as a 6th + one octave. These terms are mostly used for extended seventh chords. The terms 10th, 12th, and 14th are not usually used for reasons that will become clear when we discuss chords.


When you descend from the root to an interval of on fourth, the second note will be an octave below the fifth. Thus the "inversion" of a perfect fourth is a perfect fifth. The rules about inversions are:

  1. if you add up the interval numbers of an interval and it's inversion, the total is always 9
  2. the inversion of a major interval will always be a minor interval, and vice versa
  3. the inversion of an augmented interval is always a diminished interval, and vice versa
  4. the inversions of perfect intervals are always perfect

Ear training

It is important to be able to distinguish different intervals by ear. Practice the intervals all over the stick. Play intervals at random, and try to identify them. There are various books with cassette tapes for ear training (most notably those by David N. Baker). There are also various software tutorial programs available.

Lessons: Intro | 1 | 2 | 3 - Part I| 3 - Part II| 4 - Part I| 4 - Part II| 5| 6| 7| 8| 9| 10| 11| 12|
rick bellinger San Diego, CA

copyright © 1995 Rick Bellinger

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