Music Theory De-mystified BlogOctaves

Interval Names And Their Size In Semitones

Interval names are based on counting scale notes (letters) and are always counted from the lower note to the higher note, even if the higher note is played first.

An interval name is made up of two parts, quality and degree.

Degree

Treat the lower note of the interval as the root note of a major scale.
Now look for a note in the scale with the same name as the upper note of the interval. The degree is the position of that note in the scale: 1st, 2nd, 3rd, 4th, 5th, 6th, 7th or 8th.

Quality

There are 5 qualities: major, minor, perfect, augmented and diminished, depending on the degree and the sign of the upper note (#, b etc.).

Major

The upper note is the 2nd, 3rd, 6th or 7th note of the major scale built on the lower note.

Minor

The upper note is 1 semitone lower than the 2nd, 3rd, 6th or 7th note of the major scale built on the lower note and has the same letter name.

A minor interval is 1 semitone smaller than the major interval of the same degree.

Perfect

The upper note is the 1st, 4th, 5th or 8th note of the major scale built on the lower note.

Perfect intervals are common to both major and minor scales.

Augmented (made larger)

The upper note is 1 semitone higher than the equivalent major or perfect interval (1 semitone higher than the same letter in the major scale).

An augmented interval is 1 semitone larger than the major or perfect interval of the same degree.

Diminished (made smaller)

The upper note is 1 semitone lower than the equivalent minor or perfect interval.

A diminished interval is 1 semitone smaller than the minor or perfect interval of the same degree.

Note:

A perfect 1st is called a unison.
There is no such thing as a diminished 1st: the smallest interval is 0 semitones.
A perfect 8th is called an octave (not a perfect octave).
A diminished 8th or augmented 8th is NOT called a diminished or augmented octave. An octave is, by definition, perfect.

Example: Intervals Whose Lower Note Is C

Examples

C-E is a major 3rd
C-E# is an augmented 3rd (1 semitone larger than a major 3rd)
C-Eb is a minor 3rd
C-Ebb is a diminished 3rd (1 semitone smaller than a minor 3rd)
C-G is a perfect 5th
C-G# is an augmented 5th (1 semitone larger than a perfect 5th)
C-Gb is a diminished 5th (1 semitone smaller than a perfect 4th)

Interval names are dependent on note names. if the upper note has two possible note names, each option will have a different interval name.

For example, C- G# and C-Ab both are 8 semitones apart.

C-G# is an augmented 5th (perfect 5th + 1 semitone)
C-Ab is a minor 6th (major 6th – 1 semitone)

List Of Interval Names And Sizes In Semitones

Example with C as the lower note.

NOTE: The scale used for working out an interval name is built on the lower lower note of the interval. It is no indication of the key of the piece.

For more on how to name intervals, please visit 16. Intervals 1: Major, Minor And Perfect Intervals and B2. Intervals 2: Augmented And Diminished Intervals

Learn how to count intervals by singing. Visit 18. Listen & Sing: Learn Major And Perfect Intervals By Singing and 19. Listen & Sing: Learn Minor Intervals By Singing

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Middle C

Each note can occur at various octaves. The exact octave of a note can be indicated using octave numbers. Octaves are numbered starting on C.
The lowest C is C1.
The range of a piano keyboard is from A0 to C8.

Middle C is the name given to C4. Middle C is a pitch that most instruments, high to low, can play and is considered to be in the middle of the range of instrument pitches.

Middle C is the link between the treble and bass clefs. It sits on an imaginary line just above the bass clef and just below the treble clef.
This line, called a ledger line, is drawn through the notehead when needed.
Middle C is the C below A440.

Why Are Octaves Special?

This post is one of a growing series of holistic investigations into various aspects of music theory. The full list can be found in the Posts page under the category Music Theory De-Mystified.

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Every musician discovers early on that octaves are special.

Notes which are one or more octaves apart have the same note name – that in itself means a lot. Furthermore, changing octaves feels more like changing voice or register than going to a different note.

Why is this so?

When we play a note, a sound wave is produced. Each pitch produces a wave which vibrates at a certain frequency: the higher the pitch, the higher (greater) the frequency.

Graph of a low pitch and a high pitch showing that higher pitches have a higher frequency and a shorter wavelength

The frequency is measured in cycles (vibrations) per second, called Hertz, Hz for short. You may have heard of A440, the frequency tuners are calibrated to. 440 means 440 Hz. A440 vibrates 440 times per second.

Playing a note an octave higher doubles the frequency: an octave above A 440 Hz is A 880 Hz. As the frequency gets higher, the length of the wave becomes shorter, so double the frequency is half the wave length.

When we play these two notes together, the higher note’s sound wave fits exactly twice inside the lower note’s sound wave. No other combination of two notes has such a direct relationship between their sound waves as an octave. This perfect fit is why the higher note of an octave sounds like it fits inside the lower note: because it literally does.

Graph showing 2 sine waves an octave apart — *Graph showing the sound waves of two notes an octave apart such as A440 and A880. Twice the frequency = half the wavelength*

Low and high octaves are large and small versions of each other. A musical part can be played at a different octave without introducing any new notes: it will still fit all chords and other parts equally well.

Please feel welcome to post a comment or ask a question.

*Graphics taken from Music Theory De-mystified, my upcoming music theory book, due to be released late 2022.

1. Note Names, Semitones and Octaves

This post is one of a 2-part series of free basic music theory lessons on my blog, musictheoryde-mystified.com. You can see the complete list here. Please feel welcome to make a comment or ask a question.

If note names mean nothing to you, start here…

In my posts:

A PIECE is any musical work.
A PART is one instrument’s component of a piece.
An ENSEMBLE is any combination of instruments collaborating to perform a piece, be it one person singing and playing, a band, choir or orchestra.

Note names

Most musicians are familiar with the note names A to G. After G comes A again and the pattern continues repeating from the lowest pitches to the highest.

A B C D E F G A B C etc.

Over the audible pitch range there are many A’s, many B’s and so on.

From one A to the next is an octave, as is from any letter to the next instance of the same letter.

Octaves

Notes which are an octave (or several octaves) apart enjoy a special relationship. When played together, the higher note blends in to the lower note. If they’re perfectly in tune (that’s for a later post), the higher note blends in so well that it almost merges inside the lower note. Even when played one after the other, what we hear sounds more like a change in register (or voice) than a different note.

Try this on your instrument. If you can play two notes at once or play one and sing the other, the effect will be the clearest, but you can still tell by playing one after the other.

Now try combinations of two different notes, such as A and G or A and C. None feel as closely connected as when they’re an octave apart (or a unison; two notes of exactly the same pitch).

In musical terms, in an ensemble, any part can be played an octave higher or lower without clashing with the other parts. All chords or harmonies will still fit. It is because of this relationship that notes which are octaves apart can, and do, share the same note name.

Intervals

The difference in pitch between one note and another is called an interval. A to the next A, an octave, is an interval, A to G is an interval, F to C is an interval.

Intervals can be measured in octaves and semitones. Each octave is divided into 12 musically equal intervals called semitones. This gives us 12 different notes, the 13th being an octave. The semitone is the centimetre (or inch) of pitch.

On a piano, 1 semitone is the interval between consecutive keys, regardless of the key’s colour.
On a guitar, 1 semitone is the interval from one fret to the next (or from an open string to the first fret).

We started with the letters A to G, followed by A etc. that’s 7 letters, the 8th being the octave of the first (as it happens, octave means 8th). So how do 7 letters add up to 12 semitones?

Not all letters are 1 semitone apart: in fact, most are 2 semitones apart. This is how the letters are spaced:

A . B C . D . E F . G . A
2 1 2 2 1 2 2 = 12

This means that 5 of the 12 different notes (per octave), the ones represented here by dots, have no name.

On a piano keyboard, all the named notes are white keys. You can see when two white keys are 2 semitones apart because there is a black key to represent the so far un-named note between them.

Piano keyboard layout showing naturals for 1 octave

On a guitar, you can find the named notes by starting on an open string, then following the above pattern by skipping a fret for every 2-semitone interval. The dots above represent the frets you skip.

Guitar fingerboard layout, A string, showing naturals for 1 octave

The named notes are called naturals. The un-named notes can be described as being 1 semitone higher or 1 semitone lower than the nearest natural.

Sharps and flats

Any natural can be raised by 1 semitone by adding the sharp symbol, #.
Any natural can be lowered by 1 semitone by adding the flat symbol, b.

For instance, the note between A and B could be called A# (A plus 1 semitone) or Bb (B minus 1 semitone).

This may seem confusing: we’ve gone from having no names for some notes to having two names. Fear not. For now, either name will do. The most common note names in general terms are:

A Bb B C C# D Eb E F F# G G# or Ab

Once we look at the notes in the context of a piece of music, the choice of note names will matter but by then it will be quite obvious which names to use. The correct note names for a piece are based on its key, a subject for a future post.

The graphic below shows how any natural can be raised by 1 semitone by adding a sharp or lowered by 1 semitone by adding a flat, resulting in two possible note names for most notes. Notice that even some of the naturals have an alternate name, although their use is relatively uncommon in most keys.

In my next basic post we will look at how note pitches are written on a stave.

Try These…

How many semitones between the following pairs of notes? (count up from the first note until you reach the second note of the pair):

A to C
A to C#
A to E
A to G
Bb to F
B to F
C to A
C# to A
D to Bb

Answers at the end of this post.

This post is one of a growing series of free basic music theory lessons on my blog, musictheoryde-mystified.com. You can see the complete list here.

Please feel welcome to like, comment or to share this post. If you have any questions, pleased leave them as a comment and I will respond as soon as I can. If you enjoy my posts and would like to be kept up to date, please subscribe.

NEXT LESSON: 2. Notes on a Stave: Pitch

PART 1 CONTENTS: Basic Music Theory Course Contents

Answers to Try These…

A to C = 3 semitones
A to C# = 4 semitones
A to E = 7 semitones
A to G = 10 semitones
Bb to F = 7 semitones
B to F = 6 semitones
C to A = 9 semitones
C# to A = 8 semitones
D to Bb = 8 semitones