• The Three Ts Of The Octave — The Tetrachord, Tritone, And The Tone Of Disjunction

There are theoretical concepts that are associated with the octave and we’re focusing on them in this lesson.

The octave is the eighth tone of the major scale and it’s considered important because it is a duplicate of the first tone of the scale. Using the C major scale as a reference:

…you can clearly see that the first and eight tones are C:

First tone (C):

Eighth tone (C):

…and the distance between these notes (C-C):

…or all the notes within its compass:

…are considered as an octave.

We’ll be covering the three Ts of the octave:

The tetrachord

The tritone

The tone of disjunction

…and at the end of this lesson, you’ll see the octave in a different light.

Concept #1 — “The Tetrachord”

The major scale encompasses an octave. Placing the C major scale side-by-side with the C octave:

C major scale:

C octave:

…proves this beyond every reasonable doubt.

The concept of the tetrachord divides the octave-long C major scale:

…into two parts:

The lower tetrachord:

The upper tetrachord:

Let’s throw more light on the tetrachord.

A Quick Breakdown Of The Tetrachord

The notes of the major scale can be divided into two sets; with each set consisting of four notes each. So, the first four notes of the C major scale (which are C, D, E, and F):

…make up the lower tetrachord, while the last four notes (which are G, A, B, and C):

…make up the upper tetrachord.

“Tetrachord + Tetrachord = Octave”

Every octave can be broken down two tetrachords and each of the tetrachords consists of 50% of the notes of the major scale.

For example, the Eb octave:

…consists of two tetrachords:

The lower tetrachord:

The upper tetrachord:

…and this is true for every other octave on the keyboard.

Concept #2 — “The Tritone”

Yes! There are so many definitions of the tritone out there; the simplest being this:

A tritone is a distance of three whole-steps (aka – “whole-tones”)

Three whole-steps from C is F#:

Here’s a breakdown:

C to D (first whole-step):

D to E (second whole-step):

E to F# (third whole-step):

So, the interval (melodic or harmonic) between C and F# is a tritone and it’s know as an augmented fourth interval.

The Relationship Between The Tritone And The Octave

The division of the octave into two equal parts produces the tritone.

There are twelve half-steps in the octave and the tritone is the interval between a given note and the sixth half-step. For example, the octave of C consists of twelve half-steps:

C to C:

Twelve half-steps:

From C to F# (which is a tritone):

…encompasses the first six half-steps, while from F# to C (an inverted tritone):

…consists of the remainder six half-steps.

The division of the octave:

…into two equal parts:

C-F#:

F#-C:

…produces the tritone.

Tritone + Tritone = Octave

Two tritones (a tritone and its inversion) add up to produce the octave.

For example, “E-Bb” and its inversion (which is “Bb-E”):

E-Bb:

Bb-E:

…produce the E octave (“E-E”) when added up:

…and this is true for every other tritone on the keyboard.

Concept #3 — “The Tone Of Disjunction”

Every octave is divided into two tetrachords like we covered earlier in this lesson.

In between the lower and upper tetrachords is a whole-step known as the tone of disjunction that links up both tetrachords. For example, the C major scale:

…consists of the following tetrachords:

The lower tetrachord:

The upper tetrachord:

…and they’re separated by the tone of disjunction, which is the whole-step distance between F and G:

Altogether, we have:

The lower tetrachord:

The tone of disjunction:

The upper tetrachord:

…and this is true for every octave of the major scale.

Final Words

In one octave (the C octave), you can go beyond seeing C and C:

…to see three theoretical concepts:

The tetrachords (lower and upper):

The tritone:

The tone of disjunction:

…and that’s the goal of this lesson.

If you have questions, suggestions, and contributions, please feel free to use the comment box .

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Chuku Onyemachi

Head of Education at HearandPlay Music Group
Hello, I'm Chuku Onyemachi (aka - "Dr. Pokey") - a musicologist, pianist, author, clinician and Nigerian. Inspired by my role model Jermaine Griggs, I started teaching musicians in my neighborhood in April 2005. Today, I'm privileged to work as the head of education, music consultant, and chief content creator with HearandPlay Music Group sharing my wealth of knowledge with hundreds of thousands of musicians across the world.