Researched by Thomas DeMichelePublished - February 15, 2016 Last Updated - May 19, 2017
How to Understand Music Theory Through Intervals – An Introduction to the Art and Science of Music
Music theory and the basics of playing music (especially on the piano) can be understood through music intervals. All scales, chords, and most songs are based on intervals.[1]
The above is especially true in terms of harmony (from there it is just a matter of learning rhythm, voicings, and other aspects of music that add dynamics).[2]
Metaphorically speaking, we can think of the piano like a game board, and we can think of intervals like the jumps a player makes (each 1 or more spaces away).
Harmonically, all music is comprised of these jumps. Meanwhile, musical notation is little more than a language that tells one what jumps to play and when.
Below we explain how you can learn the basics of music by discussing music theory pertaining to intervals.
What are Intervals in Music?
In music theory, intervals are distances between two pitches (notes, half-steps, or semitones).
There are only 12 notes in western music (counting the root), and only 13 possible intervals (counting the root and the octave).
To illustrate this, we offer an example below using C as the “root note” (and therefore necessarily “the octave”). This “chromatic C” scale can be transposed to any key using the same logic.
A List of Possible Intervals (Basic)
The possible intervals (in a single octave), each a semitone apart, are:
Root – P1 – Tonic (no steps, 0 semitones). ex. C
Minor Second – m2 – Half step (1 semitone). ex. C#/Db (meaning C sharp or D flat depending on what scale you are in)
Major Second – M2 – Whole step (1 whole-tone or 2 semitones) AKA two half steps (semitones). ex. D
Minor Third – m3 – Whole step plus a half step (3 semitones). ex. D#/Eb
Major Third M3 – Two whole steps (4 semitones). ex. E
Perfect Fourth – P4 – Two and a half steps (5 semitones). ex. F
Perfect Fifth – P5 – Three steps and a half step (7 semitones). ex. G
Minor Sixth – m6 – Four whole steps (8 semitones). ex. G#/Ab
Major Sixth – M6 – Four steps and a half step (9 semitones). ex. A
Minor Seventh – m7 – Five whole steps (10 semitones). ex. A#/Bb
Major Seventh – M7 – Five whole steps plus a half step (11 semitones). ex. B
Perfect Octave – P8 – Six whole steps or 12 half steps (12 semitones). ex. C
TIP: Try counting on the keyboard below starting with C as the root to find each interval. They simply repeat in each octave up and down the keyboard. When you count, don’t count the note you start on and count semitones. So C is zero semitones from itself, C# is 1 semitone, D is 2 semitones, etc.
This image shows two octaves of the notes on a keyboard. The notes repeat from the first C to the next. The black keys can be described as sharps (#) or flats (b) depending on what scale you are in. The octaves are repeated in the graphic to display the black keys first as sharps and then as flats.
TIP: To be clear, on a piano the black keys each have two names, for example C# can be called C# or Db. The correct name of the note depends on what key you are in. On this page I’ll discuss the notes as sharps sometimes and flats other times, the name changes, but the note that is played doesn’t.
Interval Number and Quality
Above each interval can be described by its quality. That is it can be described as Perfect (P), Major (M), Minor (m), Augmented (A), or Diminished (d) where, in general terms: perfect denotes harmony, major denotes the note being referenced, minor and diminished denote “1 note down from the note being referenced,” and augmented means “1 note up from the note being referenced.”
Further, each interval gets a hand number, so we can quickly denote a jump in short form. So a P5 is a perfect fifth, and a capital M3 is a major third interval and lowercase m3 is a minor third interval. There are only some of the ways to express which jump one is referring to.
TIP: Perfect intervals are so-called because they were traditionally considered perfectly consonant in a traditional “diatonic scale” (a scale that includes five whole steps and two half steps in each octave; the traditional major and minor scales in western music). The root/octave, 4th, and 5th are are generally considered harmonic in these scales, where the other intervals add to the harmony or disharmony. The other intervals have other qualities, but for now we are less concerned with dissonance and harmony (dissonance and consonance) and more concerned with the gist (we’ll detail this more below). See Wikipedia on Interval number and quality.[3][4]
TIP: A C major “diatonic” scale denoted in the short-form above is, P1, M2, M3, P4, P5, M6, M7, P8. Any jump to a P will sound harmonic, any jump to a M will add flavor. In a minor scale, the M3 becomes a m3 and the M7 becomes a m7. This can be transposed to any key by changing the root note (by changing the note the scale starts on).
Considering other Aspects of Intervals
Although we can and do consider more than one octave when considering music intervals (see compound intervals), from a simple perspective that considers that (octaves aside) there are really only 12 notes, we can say all music can be thought of as the harmonic relationships between the aforementioned intervals.
Specifically, music is (harmonically speaking) the harmony and disharmony those intervals create when played in a certain order (either one at a time or in unison).
IMPORTANT: In music, like other fields, sometimes two different concepts get the same name, a single concept will get a variety of names, or short hand expressions are used. We won’t worry about that for now, but it is important to note that terms like “minor sixth” have more than one meaning. Specifically a “minor sixth” chord and a “minor sixth” interval are two separate concepts. Thus, until you get all the lingo down, when discussing intervals say “interval” and when discussing chords say “chord.” This is explained and clarified below.
TIP: We discuss each possible interval and the different relations between them below, but consider checking out the following video for a quick audio/visual example.
NOTE: Some non-western music types (Eastern music for example) use different pitches, intervals, and rhythms. These can be understood through the lens of western music, though, so let’s leave that discussion for later. The goal here is to introduce you to the logic behind music, once you get the logic there is a lifetime of things to learn.
A Basic Introduction to Music Theory Using Intervals as a Foundation
With the basics out of the way, let’s zero in more on other aspects of intervals.
Intervals are the foundation of all western music (harmonically speaking at least; I say this because rhythm, space in between notes, resonance, tempos, orchestration, and other such things are vital aspects of music).
Intervals can be put together and played at once to make musical chords, or they can be arpeggiated (played one at a time in order) to form scales and melodies.
The term interval is used in music theory to describe the next “jump” the music will make. Ex. Start on “the root” of the scale, then play the perfect 5th (so in C, start on C and then play the G), and then the perfect 4th below the root (which in C is F). (More on that below).
Each different jump has a unique harmonic quality, either adding or “resolving” tension.
Notice how the video below discusses shifting only between two chords. Notice how each shift has a different harmonic quality? That shifting of intervals to create and resolve tension is what makes music (harmonically).
TIP: Not every song starts on “the root note,” but most basic songs will. Likewise, not every song resolves to the root note, but it is the most common “resolution.” Play a G, then a C. Notice how our ear tells us the G wants to go to the C? It is more obvious with chords than single notes anyway. Consider checking out the following video below to better understand intervals, building tension, and resolving using two chord progressions (parts of songs comprised of only two chords).
TIP: We get back into the basics of intervals below, but while I have you here, let’s jump to some more complex theory to better understand the full picture of everything music theory has to offer.
Given this, not only can we hear harmonic qualities, but we can actually see them by looking at waveforms (using the right equipment; see the video below for examples).
If one plays two of the same notes, the wave forms will line up nicely, if one plays a root and 5th, the waves will be off but will line up often (making a nice pattern; and sounding “harmonic”), however when two notes right next to each other are played, it creates disharmony and a messy pattern.
Speaking very generally, disharmony creates tension, and harmony “resolves” tension.
FACT: Each note equates to a waveform that vibrates the molecules in the air (and other mediums around you) at a specific frequency. when vibrations are played in a specific sequence, or in unison, it results in either harmony or disharmony. One can hear this with their ears, but one can also see this using the right equipment. Music is largely a thing of mathematics and physics in this sense.
With the introduction covered, let’s return to the theory of intervals.
There are only 12 notes in western music, but we can think of the possible intervals in two different ways.
From on perspective there are only 12 possible intervals or “jumps” not counting the root note (but counting the octave).
From another perspective there are 13 possible intervals counting both the root note and octave (we can stay on the root and thus make zero jumps to the root).
Both the above sentences are describing the same thing, that is how many jumps one can logically make within the 12 notes of an octave.
In other words there are 13 possible jumps from one single note if we count a jump to itself (“staying on the root”), a jump to its octave (going up 12 steps), or a jump to another note (try counting for yourself using the keyboard above). It is important to differentiate between staying on the root and jumping an octave, so we will be considering 12 notes and 13 jumps on this page.
To illustrate this, starting in C and going up (ascending), we can go to the:
1. C (the root, zero jumps away), 2. C#, 3. D, 4. D#, 5. E, 6. F, 7. F#, 8. G, 9. G#, 10. A, 11. A#, 12. B, 13. C (the octave 12 jumps away). The same is true when descending to a lower note. If we count the “zero” jump, we get a total of 13 jumps for 12 notes.
This subtle distinction is important, because when we count distances between notes, we don’t count the note we are on (so C to C# is 1 semitone, or interval, away, not 2).
In other words,
We want to consider 12 notes, because there are 12 and only 12 notes in western music,
We want to consider 13 intervals (counting the root and octave), because this describes our possible jumps, and
We want to also think of an octave being 12 jumps away (because we don’t count the note we are on when we count intervals).
That might seem slightly confusing, but it is helpful to grasp when dealing with music intervals.
Considering Octaves
Each set of 12 notes can be called an octave, but also, somewhat confusingly, a jump from a note to its equivalent 12 notes away is also called an octave.
In both cases the name comes from the idea that there are 8 notes in a “major scale” counting the root and… octave (octave, meaning “8”).
TIP: The notes repeat in each octave (each set of 12 notes repeats up and down the keyboard), and thus, the choices of 12 notes and 13 jumps offered above are the only possible choices for notes in western music.
An Introduction to the Basics of Scales, Arpeggiation, Chords, Major/Minor, and Transposition
If we are on C4 (a C in the middle of the keyboard), we can go to C3 (the octave below) or C5 (the octave above).
If we play every note along our way, then we played a “C chromatic scale.”
If we just play C, D, E, F, G, A, B, C, then we played a “C major scale.”
Each scale has a different harmonic quality (minor scales are darker, major scales are brighter), and within each scale different sequences of jumps will have different harmonic effects.
Likewise, if we play any set of two or more notes in a scale in unison, it is technically “a chord.”
The simplest and most common chords are based off the diatonic major and minor scales.
An example of a simple two note chord is one that uses the root and the perfect fifth (on a guitar it is called a “power chord”; the P1 and P5 or in C, the C and G).
However, the more common versions are the “major triad”: Ex. In C: C, E, and G (or generally P1, M3, and P5), and the “minor triad”: Ex. In C: C, D#/Eb, and G (or generally P1, m3, and P5).
When we use the major third as the third in a triad, it is a major chord, and we can arpeggiate the major scale on-top of it to create uplifting major-key harmony (arpeggiation is playing one note in a chord or scale at a time).
When we use the minor third in a triad, it is a minor chord, and we can play the minor scale on-top of it to create somber minor-key harmony.
The order in which we arpeggiate and which notes we arpeggiate will determine the harmonic quality. Or rather, it will create many sound-waves that will either line up nicely (creating harmony and resolving tension) or will create sound-waves that don’t line up as nicely (creating disharmony and tension).
This push and pull between harmony and tension is at the heart of music.
Building on the Basics of Chords
The table below shows some common chords. By adding extra notes to a chord, it changes its flavor and changes its harmonic relationship with the other chords. A C triad and a G triad will sound very harmonic together, with the G wanting to resolve into a C. However, adding a note can open up new harmonic possibilities. There is more we can add to this, like the concept of passing chords, but for now it is enough to just get the basics of the concept.[5]
TIP: There are other ways to denote major and minors as you’ll see below.
TIP: The two most important scales in music, and the two most important chords are the major and minor chords.
TRANSPOSING: The scale that includes every note and starts in C is called a “C chromatic scale,” if we started on D it would be a “D chromatic scale (it would be the same notes, but a different starting point). The same is true for C major, or C minor, or any other scale. Almost everything you learn about music can be transposed to any key, so to learn the basics of music one only needs to learn a single scale.
CHROMATIC SCALES AND ROOT NOTES: The root note, or tonic (in C, the C), is the note we start a scale on (when naming a “chromatic scale,” but not always when playing it), the octave is that same note a full 12 steps (or semitones) away not counting the root (i.e. the root is “a full octave,” or 12 notes, away from the next iteration of itself in a higher or lower pitch).
THE MAJOR AND MINOR SCALES: In each octave there are 11 common intervals counting the root and octave (the ones that relate to a major scale and sounds good with major chords, in C that is: C, D, E, F, G, A, B, C; and the one that relates to the minor scale and sounds good with minor chords, in C that is: C, D, Eb, F, G, A, Bb, C) and then 2 others (the minor second, which in C is Db, minor sixth, which in C is Gb).
Generally when one plays a major scale they play all the perfects and majors (but not the minor second, minor sixth) for a total of 8 notes.
Likewise, when one plays a minor scale, they switch the major third to a minor third and the major seventh to a minor seventh for a total of 8 notes (i.e. only two notes are different between a major and minor scale).
If you learn how to play a major and minor scale (and then learn how to transpose it to each “key”), then you’ll know most of what you need to know about the basics of playing music (harmonically at least).
Diatonic Functions (How Chord Sequences Resolve and Create Tension)
We can then expand on this further with “Diatonic function” (that is, how notes in a non-chromatic, and especially diatonic major or minor, notes or chords in a scale resolve into each other).
In tonal music theory, a function is a term denoting the relationship of a chord to the “tonal center” (root note).
What that means in English is that each “chord” (set of notes played at once) can be said to resolve to other specific chords with varying degrees of harmony and disharmony (either actually resolving tension or building tension; there are a few music terms that are used loosely and mean more than one thing, “resolve” is one of them).
To understand the relationships between functions (in music), we can (like we did with intervals and scales) consider this all in one scale (for example C) and then transpose it.
In the United States, Germany, and other places the diatonic functions are:[6]
Note that the ii, iii, vi, and vii are lowercase; this is because in relation to the key, they are minor chords. Without accidentals, the vii is a diminished viio. The “o” denotes a diminished chord (although dim is used much more often. Likewise, the dash “-” is another way to denote a minor chord (so you don’t have to write “m” or “min” all the time).
TIP: Remember, as noted above, chords and intervals sometimes share names. Notably a Minor 6th interval and a vi (or minor sixth chord) have almost nothing in common. If we are discussing chords the terms minor and major describe whether or not we are playing in a major or minor scale. If we are discussing intervals, the terms minor and major relate to how many jumps we make. They aren’t directly related concepts. In C a minor 6th chord is A minor… which is a chord that starts on the major 6th (in terms of intervals). To avoid confusion, terms like raised 5th are used to describe a “minor 6th” interval. When we discussing functions, we are discussing chords. Here we are still conceptually discussing intervals (the jumps between chords), but we are using a different set of lingo.Below we’ll offer other names for each interval.
Each of the above functions resolves to other functions. For example, here are 3 essential functions (notice the “minor 6th” here is a minor sixth chord, start on the M6 in a scale, not on the m6… it is a minor version of the 6th note in a major diatonic scale. It is played as a minor using only the notes in the major scale):
We can consider the above chart to offer a simple example of how chords resolve. Here we should note that there is no “correct” choice, rather there are common choices that we hear often in music.
A simple move is to start on the Tonic (the I or Root), go to the Dominant (the V or 5th), and then resolve back to the Tonic. An even simpler move it to start on the 5th and then resolve back to the root.
Generally speaking, the Predominant resolves to the Dominant, and Dominant resolves back to the Tonic (the Root).
The tonic can create tension by going to any dominate and then resolve back to the root (and can do so harmonically), or the tonic can create tension by going to the predominate and then to the dominate and then resolve back to the root.
These are just a few of many possible examples.
The reality is any major chord and minor chord will have a harmonic relationship, the trick is learning how each function resolves or creates tension when strung together as a song.
TIP: Many songs are “I – IV – V”. So in C, it is C chord (I), F chord (IV), G chord (V). Louie, Louie is I – IV – V – IV for example. When it comes to song writing, there are also tricks like this. For example, a simple song structure is ABABA (Where A is the verse, one set of chords often starting on the root, and B is the chorus, another set of chords often starting on the fifth). This is called “song structure.”
By knowing which chords resolve to which chords one can string together complex melodies and passing chords to create harmony… based on theory alone, without ever actually hearing the music being played.
Beethoven being a great example of this (see the video below).
Although I’m sure the above is overwhelming, once you get it, you have the science of everything Mozart or Bach knew.
We can thus say the foundation of all musical theory, and all western music, is the study of the 12 intervals and their relations (there is no 13th note… unless you count an octave).
From Bach to Mozart, to Beethoven, to the Beatles all western music demonstrates quantifiable patterns based on the 12 intervals and rhythm/timing (ok, so rhythm/timing is also a core property of music not yet discussed, but if you get the above you at least get the harmony part).
On this page, we focus on intervals, and we will leave rhythm and….. timing… for another page.
It’s helpful if you imagine a keyboard, so feel free to reference the keyboard below as we talk about each interval.
TIP: Counterpoint is a type of songwriting where melodies are played over each other and chords are essentially created from this. Bach’s style was counterpoint. It is an excellent exercise in music theory and intervals.[7]
What are the Different Music Intervals? – More Details
Above we covered the basics of intervals and some theory beyond that, let’s return to the intervals now below.
Below we cover each of the 12 possible intervals in western music. All intervals are “relative” to the starting note, called a “root note” or “tonic.”
We will learn the intervals in a “Chromatic C scale.” All that means is that we are starting on the C note and doing all 12 possible intervals or steps on a chromatic scale. These are also known as the black and white keys on a piano. We will move up the scale, but know you can move down to intervals as well. Also, know that you can start on any note and apply the same methods (all scales, chords, and intervals are relative).
Below we explain the most significant intervals, from there you should be able to glean everything else you need for our discussion from the handy Wikipedia-sourced chart.
NOTE: We will talk about scales and chords below. First, let’s cover the intervals.
The common music intervals are (I’ll offer alternative names for all the minors… because where all “major” intervals line up perfectly with major chords, minor intervals do not):
Root – Tonic (no steps). The note you start a scale on is “the root note” or more traditionally “the tonic”. A basic song will always resolve to the “root” of the scale. When two notes play the same pitch in the same octave they are in “perfect unison”.
Minor Second or Diminished Second – Half step (semitone). If I start at the C and go to C# I go one-half step (AKA semi-tone). This is a half step interval. If I’m forming a chord or referring to a scale I’d call it a “minor second” (it’s the second note a minor scale).
Major Second – Whole step (whole-tone). If I start at the C and go to D, I go one whole step (AKA whole-tone). This is a whole step interval. If I am forming a chord or referring to a scale, I’d call it a “major second” as it is the second note in a major scale.
Minor Third or Augmented Second – Whole step plus a half step. If I start at the C and go to D#, I go one whole step and one half step. This is a minor third interval, and is one of three notes used for forming “minor chords”.
Major Third – Two whole steps. If I start at the C and go to E, I go two whole steps. This is a major third interval and is one of three notes used for forming “major chords”.
Perfect Fourth – Two and a half steps. If I start at the C and go to F, I go two whole steps and one half step. This is a perfect fourth interval and one of the most common intervals.
Diminished Fifth or Tritone – Three whole steps.
Perfect Fifth – Three steps and a half step. If I start at the C and go to G, I go three whole steps and one half step. This is a perfect fifth interval. This is the third note along with the third and root note that forms all basic triads (the basic chords). The song Louie Louie is 1, 4, 5. In C, it’s C, F, G (then back to F again).
Minor Sixth or Augmented Fifth – Four whole steps.
Major Sixth – Four Steps and a half steps.
Minor Seventh – Five whole steps. The Minor Seventh, like the major seventh, is used to create tension before resolving back to the root. Traditionally, the minor 7th is used in minor scales and the major 7th in major scales.
Major Sevenths – Five steps and a half step. See above (this the major scale chord used to build tension).
Perfect Octave – Twelve semi-tones or six whole tones or whole steps. If I start on C and go to the next C, up it’s an octave. I’m playing the same note but 12 semi-tones higher.
Adding Complexity, Considering Compound intervals, and Putting the Above Together
Below is a “big ol table” that shows the many different names and aspects of each note.
Here we can consider a number of alternative names for chords and the related concept of “compound intervals” (A compound interval is an interval spanning more than one octave).
If we don’t stop at the octave and keep counting, then what we were previously calling a Major Second interval and a Minor Second interval now can be called a Minor Ninth and Major Ninth. It is the exact same note being played, but the term (speaking loosely) offers more detail.
Given this, we can use a term like “Nine” to describe a “Second.”
If no other information is given, the terms nine and second both imply a “major” interval (as a major second/nine is in a major scale, and a minor second/nine is only in uncommon scales and in chord progressions).
There is a lot of lingo and odd rules to consider, and we won’t get into all that here, instead this table is meant to help illustrate how everything fits together. When in doubt, count the notes and use the “widely used alternative names.”
NOTE: In the chart below, augmented means raised by a half step and diminished means lowered by one half-step.
If the information above is familiar, you should have no problem with musical scales. There are two basic types of scales, major scales and minor scales. A scale can have up to 12 notes counting an octave; that’s called a chromatic scale. Beyond this, any combination of notes, and even notes in specific octaves can technically be a scale.
Chromatic Scale. All twelve notes.
Major Scale. 8 Notes alternating whole steps (W) and half steps (H). Root, W, W, H, W, W, W, H. So In C it’s C, D, E, F, G, A, B, C. In other words these are “the white keys”.
Minor Scale. Same as major scale but starts on the first H. So E minor is E, F, G, A, B, C, D, E.
Other scales. Pentatonic is a five note scale starting on the tonic and is the foundation of rhythm and blues. A diminished scale uses only minor third intervals. Etc. Every combination of intervals is a scale. We can get heady but this is beyond an introduction to music theory.
TIP: Each chord has inversions equal to the number of intervals in it. There are 3 ways to play all triads on a piano using different ways to invert chords.
Music Intervals and The Circle of 5ths
We won’t go into it too deeply now, but it is useful to know that if you start on any root note and move through all the 5th or 4th intervals, you will come right back to the note you started on. This is handy for changing “keys” (which means switching scales).
This video explains the circle of 5ths, we will be doing more music centered page, and I want to cover this and all the theory above in more detail.
Music theory is straightforward compared to some of the concepts out there. This ruleset gets deep quickly, but the core is basic.
TIP: Mathematically there is a theoretically infinite amount of distance between notes. In a practical sense, though, there is a finite amount of “steps” between notes. In music, we move up and down by “cents” (the smallest frequency distance we track in-between notes). Typically each half-step is divided into 100 cents. So there are 100 cents (divisions) between a perfect C and a perfect C#. If you use an accurate tuner when tuning a stringed instrument, you can hear this. Restricting something to values is called quantization and quantization is crucial in music. It’s almost as though music is vibrating strings that quantize on a very small level. This occurs quite literal on a fretless stringed instrument. Learn more about quantization. Also see a discussion on 440Hz (the starting pitch of western music).
We can boil all this down to a few core statements, they are:
There are 12 notes in Western music (the core of all this).
There are 12 related intervals (or 13 jumps counting the root and octave).
There are scales that can be made from this (any combination of notes is a scale, but only some of the more harmonic combinations are generally used).
There are the chords that can be made from this (any combination of notes is a chord, but only some of the more harmonic combinations are generally used).
This is all based not only on the harmony we hear, but the harmony we can see by looking at waveforms (assuming we have the right equipment).
We can understand song writing based on how sequences of chords and notes create tension and resolve tension.
In other words, the foundation of music (in terms of harmony) can be understood by understanding intervals.
Thomas DeMichele is the content creator behind ObamaCareFacts.com, FactMyth.com, CryptocurrencyFacts.com, and other DogMediaSolutions.com and Massive Dog properties. He also contributes to MakerDAO and other cryptocurrency-based projects. Tom's focus in all...
