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

If you found this post helpful, please feel welcome to like, share or leave a comment. If you have any questions, leave them as a comment and I’ll respond as soon as I can. To stay up to date wth new posts, please subscribe.

(Guitar) String Theory 2: Why Do Frets Get Closer Together? 

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.

All comments are welcome. If you enjoy my post, please give it a like and share it or subscribe to my blog.

Frets on a guitar are placed 1 semitone apart. The 12th fret produces a note one octave above the open (full-length) string.

The Relationship Between Pitch And Frequency

The frequency of a note is the speed at which a sound wave vibrates in order to produce a given pitch. The lower the frequency, the lower the pitch.

The common factor between the pitch of a note and its frequency is the octave. One octave equals 12 semitones, where each semitone sounds the same distance apart as the next, like centimetre or inch markings on a ruler. 

An octave is also the frequency ratio of 2:1. Every 12 semitones higher, the frequency doubles. We can look at the relationship between sound waves and what we hear by creating a graph with pitch on one axis and frequency on the other. It would look something like this:

The above frequencies are based on a guitar A string, A = 110Hz.

  • One octave higher = double the frequency.
  • Double the frequency = half the wavelength and thus half the string length.
  • One octave higher than the open (full-length) string is half the string length, half-way from the nut to the saddle.
  • The next octave higher is half of the remaining string length = 3/4 of the string away from the nut.

In other words, the first half of the string has 12 frets and the next quarter of the string also has 12 frets.

The effect of this relationship is that for every semitone higher in pitch, the frequency increases by a little bit more than the last semitone.

The Relationship Between Frequency And String Length

Frequency and wavelength are inversely related: as one goes up, the other goes down. As the frequency increases, the wavelength, and thus the string length, becomes smaller, a little less so for each semitone. 

Strings are effectively half a wave. Higher notes are produced by making the playing part of the string, and thus the wave length, shorter. For each semitone higher, the adjustment is a little less than the previous semitone. The frets mark these positions.

Why do we care? Maybe we don’t need to, but isn’t it nice to know why frets are laid out differently from piano keys?

(Guitar) String Theory 1: Strings and Octaves

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.

All comments are welcome. If you enjoy my post, please give it a like and share it or subscribe to my blog.

A plucked guitar string is a good physical representation of half a sound wave. 

Sound waves, like ripples in a pond, are wave shaped pulses that travel and spread away from the source. Single frequencies have an evenly-curved shape called a sine wave. A complete wave, from the start to where it begins to repeat, is called a cycle.

One Wave Cycle

Unlike ripples in a pond, a string on a guitar (or any string instrument) is fixed and doesn’t travel. A vibrating string produces half a sine wave at a time, moving gradually upward then downward for each wave cycle. (The full sine wave is twice the length of the string.)

A Guitar (or other stringed instrument) String Is Half A Sine Wave

When you lightly touch the string above the 12th fret (half-way along its length) and pluck the string, we hear a pure sound called a harmonic. By not pressing all the way down, both halves of the string are free to vibrate: only the middle is blocked, allowing a complete sine wave of half the string length.

Guitar String With Octave Harmonic

The sound we hear is exactly one octave above the sound of the open (whole) string.

  • One octave higher = half the string length.
  • In other words, one octave higher = half the wavelength.

By the way, you can check the accuracy of a guitar’s intonation by comparing just touching the string at the 12th fret to pressing all the way down at (behind) the 12th fret. The pitch should sound the same.

In Why Are Octaves Special? we saw that one octave higher = double the frequency, so:

  • double the frequency = half the wavelength. As the frequency goes higher, the sound wave becomes shorter.

You can also place a finger lightly over the 5th fret, 1/4 of the string length, and hear a note 2 octaves above the open string, at 4x the frequency.

This is just another way of demonstrating the close relationship that exists between notes one or more octaves apart. The octave is fundamental to how music behaves. It is a universal musical phenomenon, independent of genre or culture.

Even though we don’t think of sound waves when playing or listening, I suspect that we are innately aware of them. We tend to think of bass notes as big and piccolo or tin whistle notes as little…

Bear with me- there’s a little more in the next post, (Guitar) String Theory 2: Why Do Frets Get Closer Together? 

Welcome to Music Theory De-mystified!

Hi, I’m Erik Kowarski. Welcome to my blog! At any time, please feel free to comment. If you find my posts useful, please like and share them. You can also subscribe so you’ll be notified of new posts. To go straight to the latest post, scroll down.

In this blog I try where possible to look at music, or at least Western music, as a whole, rather than in terms of a specific genre; to explore the underlying principles and learn by observation rather than by a set of rules.

The posts are grouped into categories. On the Posts page there is a list of individual posts within each category, oldest first. This is particularly useful for Basic Music Theory Lessons as they should be done in numerical order.

Categories

Basic Music Theory Lessons

Basic Music Theory Lessons is a 2-part course designed for beginners and self-taught musicians. Using clear explanations rather than rules it focuses on theory that applies broadly, across all genres. The emphasis is on learning by listening and observation.

The lessons can be done as a course, in small modules or as individual lessons.

If you’re a beginner, Basic Music Theory Lessons are the posts for you. Nothing is assumed, everything is explained from scratch. There are plenty of illustrations, audio clips and mini movies as well as practical tips and exercises. Every major point is backed by examples you can hear.

If you have a question, please post it as a comment and I will reply when I can.

Beginner’s Tips and Hacks

Beginner’s Tips offers some handy hacks and tips as well as lists for quick reference.

Music Theory De-mystified

Music Theory De-mystified, aka The De-mystified Files, is a series of brief investigations into what makes music theory tick. A very basic understanding of music theory is assumed, such as note names, key signatures and basic interval names. Although I still endeavour to explain related background information, the posts would get too long and with too many detours if I followed every back story. Instead, I try to look at one unusual aspect of music theory and provide some context.

Musicianship

A list of all posts which contain musicianship/ear training exercises. These include timing, rhythm, singing scales, pitching intervals, recognising notes in a triad and more.

Musings

Musings is a forum for discussion. The posts are my personal thoughts and observations- you might agree or disagree with my views. I would love to receive your comments.

The Interval-Singing Project

A survey looking for different intervals used at the start of popular songs in various genres. The aim is to build a database of familiar songs containing each interval, as a learning aid for singing intervals. The database will be available free to subscribers.

The Theory Of Practice

Tips on practice technique.

Please like and share my posts. If you have any questions, please leave them as a comment and I’ll reply as soon as I can.

Erik Kowarski 

Posts

Latest Posts

Introduction: Music Theory is my Friend

Welcome to my blog!

I’m Erik Kowarski and I’ve been a musician and music teacher in Perth, Western Australia for well over 40 years. Throughout my career I have benefited from my music theory knowledge and I believe there is a useful place in every musician’s toolkit for a basic understanding of music theory and notation.

My main instrument is violin. I was brought up with Classical training including music theory, which I studied to AMEB (Australian Music Examinations Board) Grade 6.

When my musical interests widened to include many popular music genres I was lucky enough to be invited to “play along” in a variety of local bands of different genres, largely because to many the violin was considered a novel instrument outside Classical music (and traditional folk music).

I found it relatively easy to adapt to these various styles because of my understanding of music theory. I could recognise chord structures, identify and play characteristic rhythms and recognise other qualities that define the genre or style, enabling me to sound plausible in the band even though the instrument wasn’t native to that genre. (In other words, I was good at faking it).

I’m not trying to claim that I’m a great player: far from it, but my knowledge of music theory gave me an edge in learning and adapting to what was for me, new territory, which in turn gave me more insight into the inner workings of music.

Why music theory?

I have met many musicians who believe that music theory is only valid for Classical music and is irrelevant to popular music genres. Even Classical students often struggle to see a point to music theory beyond learning to read music. Creative players, especially, are afraid that learning music theory will stifle their creativity.

I can see why they feel concerned: music theory is often portrayed as highly theoretical and in most cases it is taught as a complex series of rules and conditions.

Sure, there are some aspects of music theory that must be learned by heart to be effective. Basics such as the names of musical note pitches and the symbols indicating note length require this approach because note names, note values and staves are the written language of music. Just as we learn basic spelling and grammar in order to speak and write English, note names and note values, keys and time signatures provide the basic communication of musical language.

Classical players are taught basic theory and music notation as part of learning to play an instrument, much of it by rote.

To me, though, music theory is more than that. Music theory allows us to understand the fundamental principles of music. These principles are natural phenomena: forces which are always present. Understanding these forces helps us in listening to, playing and creating music.

Mode and Time signature

When we play or listen to music we can feel that the piece has a certain overall character. In part this is due to the mode the piece is based on, such as major or minor, and the piece’s time signature and tempo. The mode and time signature/tempo provide a basic setting within which the piece is written.

Phrases

Within this setting, individual pieces can vary hugely in the emotions they invoke and how direct or complex they are. Just like a spoken language, music is based on phrases. Musical phrases, like sentences, have a beginning, middle and end. One phrase leads to another, forming a melody, the musical equivalent of a sentence.

Just like sentences, there are open phrases, equivalent to questions, and closed phrases, which are like answers. Often a melody is made up of one or more open phrases followed by a closed phase. We can feel the music lead from one phrase to the next, often arriving at a conclusion; a place where the melody feels that it has arrived.

A sense of home

One of the key concepts of music theory is the idea of home. Home is a note: the root note or tonic. Every piece that sounds like music in the conventional sense has a root note. Without an obvious root note, we can’t make sense of what we hear.

When we combine a root note and a mode we have a key, such as C major or A minor. Knowing the key of a piece tells us what the overall character is and which note it’s based on.

Often a piece starts and finishes at home and visits various neighbouring keys along the way. The most prominent chords that accompany the melody indicate these keys by pointing to their respective root notes.

Knowledge is power

It is my belief that music theory would be easier to accept as valid and useful if based on an understanding of the principles: how music actually works. Too often students are expected to take on faith a large number of rules and conditions without knowing why they exist. By understanding the musical principles at work we can see that these are not actually rules: merely ways in which to achieve a certain musical character or effect.

I have touched on just a few of the most significant musical principles to illustrate that an understanding of these principles greatly enhances our understanding of the music we listen to, play and create. I believe that knowledge, if presented clearly, is power that can only add to our musical skill set, not take away from it.

Music theory is especially useful for creative music, be it composition/ songwriting or improvisation. Every note we play has an effect – a consequence. An understanding of music theory allows the composer or player to choose which note produces the effect that they are after. This greatly speeds up processes like finding a nice solo to play or writing a melody that captures a certain emotion or character.

Music theory for working musicians

That said, I realise that such an in-depth approach doesn’t appeal to everyone.

There are many competent working musicians who have achieved their skills without the benefit of music theory. Over time they have developed a sense of the musical principles through listening and playing by ear. For many such players, the idea of delving into the theory behind the music may seem redundant.

Even so, I would like to recommend at least a basic grasp of music notation, if only for the communication benefits. I believe that it’s much quicker to learn a piece of music by reading it than by having to play an audio file 1 or 2 bars at a time, several times over.

Most musicians are familiar with the natural note names, A to G, and possibly sharp and flat. As letters on a page we can’t tell whether a note is in a high or low octave without some made-up symbols to help. I believe that it’s actually easier to learn to read these notes on a stave: the music is much more graphic in terms of high and low notes. Key signatures may look strange at first but they make sense once you can associate a key signature with a root note and a scale.

Musicians who play by ear are also familiar with beats and bars and the use of strong and weak notes. Note values and time signatures provide the rhythmic information of a piece in a way that makes it easy to teach yourself the rhythm. If the rhythm isn’t one that’s familiar to the player, I believe it’s both quicker and clearer to read as notation than to learn by ear.

Music notation has evolved by and for musicians. Notation exists because it makes musical sense.

One other useful aspect of musical language is being able to name intervals. An understanding of interval names is the gateway to understanding chords and chord symbols. It’s quite easy to learn the basics of interval names as they are based on counting notes in the major scale, something quite familiar to most musicians.

Please feel welcome to make comments or ask questions.

In the coming months I intend to put up posts in two categories:

  • Music notation and basic theory tips.
  • A holistic approach to understanding the principles of music theory.

If you can’t wait and would like to get started straight away with a quick course in basic notation and music theory, you can purchase my e-book, The Tiny Music Theory Book: How to Read and Talk Music in 16 Tiny Chapters, either as an EPUB or PDF, from my Shop page.

NOTE: my blog is entirely based on Western music theory. Many other cultures use different modes or even different tuning systems and are beyond the scope of this blog.

Erik Kowarski