Greetings everyone!
This is Rodrigo Moreira, guitarist and music instructor based in the NYC area, and this is the first of many articles I’ll be publishing on my website in order to spread all my knowledge with my students and whoever might be interested in learning more about music theory and its application to their instrument.
I’ve decided to start with what I consider to be the most important topic of all, and one that is often ignored by beginners and sometimes not taught well by music teachers. Getting a good grasp on Intervals is a breakthrough in every musician’s journey, and given its importance, it must be practiced every single day you touch your instrument.
Student: Every day?
Rodrigo: Yes.
Student: For how long?
Rodrigo: For good.
Some people like to define intervals as being “the building blocks of all polyphonic music”, but I personally like to call it the alphabet. It’s through combining different intervals that we build more complex structures like chords, arpeggios, scales, and finally make music.
By the end of this article, you should be able to find any intervals on your instrument, be able to name them, and through a lot of practice, recognize them by ear.
Student: I’ve practiced these intervals for the past two years and now I can easily visualize them on the fretboard, but I still can’t recognize them by ear. What should I do?
Rodrigo: Keep practicing.
In case you need to jump to any other article, you can just click on any of them:
Simples Intervals -> Compound Intervals -> Triads -> Drop-2 Chords -> Drop-3 Chords -> Shell Chords & Extensions -> Triads & Extensions -> Arranging with Drop-2 Chords -> Guitar Arpeggios
WHAT ARE INTERVALS?
By definition, Intervals are the gap or the distance between two given notes, and these notes can be played either simultaneously [harmonic interval] or successively [melodic interval].
[Harmonic interval]
[Melodic interval]
SEMITONE vs. WHOLE TONE (Half-step, whole step)
Semitone is the smallest interval or space that you can find between two given notes. If you’re a guitarist or bassist, a semitone corresponds literally to the distance between one fret and the one right next to it (in any direction and on the same string.)
[Semitone on the same string]
As the name itself suggests, a whole tone is the double of a semitone’s size. In other words, 1 whole tone = 2 semitones. Then, a whole tone will always have an empty fret between the two notes (at least when played on the same string.)
[whole tone on the same string]
[whole tone on two adjacent strings]
These two intervals are the most important of those that I will post about, since every other upcoming interval is going to be measured based on the number of semitones (ST) or whole tones (WT) there are within the distance between the two given notes.
Semitones (ST) can also be called half-steps (HS) while the whole-tones (WT) can also be called whole-steps (WS.)
Make sure you understand what semitones and whole tones are before continuing.
Natural notes vs Accidentals
Natural notes are the seven first notes we learn as kids:
C D E F G A B…C*
*The C is repeated in the end to indicate that after the seventh note, the sequence starts repeating itself.
All the natural notes are separated by a whole-step, except from E to F (half-step) and from B to C (half-step.) Therefore:
“C (WS) D (WS) E (HS) F (WS) G (WS) A (WS) B (HS)...C”
As we discussed previously, all the notes separated by a whole-step (or whole-tone) interval have an empty fret between them (if played on the same string.) Each one of those empty spaces are notes as well and they can have two different names. i.e., the space between C and D might be called either C# (sharp) or Db (flat); the space between D and E might be called either D# (sharp) or Eb (flat); the space between F and G might be called either F# (sharp) or Gb (flat); the space between A and B might be called either A# (sharp) or Bb (flat).
Notice that I didn’t name anything between E and F and also between B and C. The reason is because there is no physical space between them.
Flats (b) shift one note’s pitch down a half-step while sharps (#) shifts one note’s pitch up a half-step.**
**All sharp and flat notes are considered accidentals.
Student: How do I know what to call them then?
Rodrigo: It depends on the key we are in and the type of chord. We’ll see that in the future.
THE FRETBOARD
Before we continue, it’s very important that you know how to find any note on your instrument first. It doesn’t matter how long it takes for you to find it as long as you are able to do so. To do this, we’ll use the concept of semitones and whole tones applied to a guitar’s fretboard.
I’m assuming that you already know the name of every string on your guitar, but in case you don’t, from the thinnest to the thickest string we have the following: e B G D A E.
[Strings order]
Notice that one of the “E” strings is written with a capital letter while the other “e” is not. This is just to demonstrate that the first and last strings are both “Es”, one of them being the thickest and the other one the thinnest. They are often referred to as “high e” and “low E” as well.
Something very important to point out is the fact that many people don’t realize that from the open string (let’s call it “fret zero” for now) to the first fret, there is one semitone interval. i.e., on the E string, the “fret zero” would be the string’s name itself, E, and on the first fret there will be an F, since between these two notes there’s no other note or an empty space. The same exact thing happens to the B string, where B is the open string (fret zero), and the first fret is a C.
From this point, you should be able to name all the natural notes on your fretboard just by following the semitones and whole-tones sequence previously explained. Remember that we only have semitones between E to F and B to C.
Try to locate all the notes by yourself and compare them to the image below:
[fretboard with only natural notes]
The image contains only the notes from the open string to the twelfth fret. This is because from the twelfth fret on, the notes start repeating themselves. That happens because the twelfth fret marks exactly the middle of the string's size from the headstock to the bridge.
Now that you have located all the natural notes, we can fill in the empty spaces with their respective accidentals. As I mentioned before, each one of these spaces can have two different names depending on the context, so I’m adding two different images. One with only flats and another with only sharps.
[fretboard with flats]
[fretboard with sharps]
At this point you should be able to name every single note on your guitar’s fretboard. if you’re not feeling comfortable with that yet, don’t go any further. Try to make your own exercises: Play any random note and try to name it. You should get the same results from the images above.
Student: I’m feeling confident.
Rodrigo: Good. Because there’s a lot more coming up.
As you advance through the reading, you will notice that I have categorized each interval by their name, definition, and application. If this is your first contact with music theory, the application part might not make sense yet. Everything will make sense once you understand the formation of chords (triads and 7h-chords) and the difference between chord-tones and tensions, which we will be working on in the following articles. All you have to do for now is to understand the Table of Simple Intervals and memorize it.
TABLE OF SIMPLE INTERVALS
SIMPLE INTERVALS
UNISON
Interval: Unison.
Definition: The unison interval consists of two notes of the same pitch. It can also be described as the same note being played twice.
Application: Given its distance, the unison interval is quite challenging to be played harmonically (in two adjacent strings). Most of the time this interval is found as the same note played twice on the same string, usually as part of a melody. Although the two adjacent string-shapes might not look very useful now, it will be very helpful to visualize where the same note can be found on different strings.
[Unison interval on the same string]
[Unison interval on two adjacent strings]
MINOR SECOND
Interval: Minor second.
Definition: The minor second interval is also known as semitone or half-step, and it is the smallest interval we have in Western music. This interval is the distance between two adjacent frets.
Application: As mentioned previously, the concept of steps and tones are used to measure the distance between all the following intervals and also to find any scale, chord, and arpeggio formula.
[Minor second interval on the same string]
[Minor second interval on two adjacent strings]
MAJOR SECOND
Interval: Major second.
Definition: The major second interval is also known as whole-tone or whole-step and it is equivalent to two half-steps, two semitones, or even two minor seconds.
Application: Just like the minor seconds, the concept of steps and tones are used to measure the distance between all the following intervals and also to find any scale, chord, and arpeggio formula.
[Major second on the same string]
[Major second on two adjacent strings]
AUGMENTED SECOND
Interval: Augmented second.
Definition: The augmented second interval is equivalent to 1 ½ step.
Application: The augmented second interval is a bit rarer to be seen than the other second intervals and it is usually used as a tension (the augmented ninth, or #9 - read the “Compound Intervals” article). But as a scale degree, this interval is originated from the sixth degree of the Harmonic Minor scale, and it generates the Lydian #2 mode.
[Augmented second interval on the same string]
[Augmented second interval on two adjacent strings]
MINOR THIRD
Interval: Minor third.
Definition: The minor third interval is equivalent to 1 ½ step. The minor third and the augmented second intervals have exactly the same “length”, and what will differentiate them is the context (read “Important things” at the bottom of this article).
Application: While second intervals are used to describe scale formulas, the third intervals are used to describe chords. At least when speaking of tertial-harmony, all chords (triads and 7th-chords) are built of stacked triads.
[Minor third interval on the same string]
[Minor third interval on two adjacent strings]
MAJOR THIRD
Interval: Major third.
Definition: The major third interval is equivalent to 2 steps (or 2 whole-steps).
Application: Same application of the minor thirds. While second intervals are used to describe scale formulas, the third intervals are used to describe chords. At least when speaking of tertial-harmony, all chords (triads and 7th-chords) are built of stacked triads.
[Major third interval on the same string]
[Major third interval on two adjacent strings]
From now on, the interval leap on the same string gets too large and not easily playable, so the following intervals will only be played on two adjacent strings or by skipping strings when needed.
PERFECT FOURTH
Interval: Perfect fourth.
Definition: The Perfect fourth interval is equivalent to 2 ½ steps.
Application: The perfect fourth interval has a wide variety of applications. It is part of the sus4 chord, 7sus4 chord, many double-stop lines/licks are based on fourth intervals too, and in quartal-harmony, chords are built through stacked fourths instead of the usual thirds.
[Perfect fourth interval on two adjacent strings]
[Perfect fourth interval skipping one string]
AUGMENTED FOURTH
Interval: Augmented fourth.
Definition: The augmented fourth interval is equivalent to 3 steps (or 3 whole-steps).
Application: The augmented fourth interval, also known as tritone, is most of the time used as part of dominant 7th chords (i.e., C7, the tritone is located between the 3rd and the 7th degree) and as a tension (the augmented fourth, or #11 - read the “Compound Intervals” article).
[Augmented fourth interval on two adjacent strings]
[Augmented fourth interval skipping one string]
DIMINISHED FIFTH
Interval: Diminished fifth.
Definition: The diminished fifth interval is equivalent to 3 steps (or 3 whole-steps).
Application: The diminished fifth interval, also known as tritone too, since its distance is the same as the augmented fourth, is most of the time used as part of diminished triads, and certain types of 7th-chords (i.e., Cdim7, Cmin7(b5), Cmaj7(b5), C7(b5)).
[Diminished fifth interval on two adjacent strings]
[Diminished fifth interval skipping one string]
PERFECT FIFTH
Interval: Perfect fifth.
Definition: The perfect fifth interval is equivalent to 3 ½ steps.
Application: The perfect fifth interval is commonly used in the formation of the majority of the triads and 7th-chords.
[Perfect fifth interval on two adjacent strings]
[Perfect fifth interval skipping one string]
AUGMENTED FIFTH
Interval: Augmented fifth.
Definition: The augmented fifth interval is equivalent to 4 steps (or 4 whole-steps).
Application: The augmented fifth interval is most of the time used in the formation of “augmented chords” such as: C(#5), C7(#5), Cmaj7(#5).
[Augmented fifth interval on two adjacent strings]
[Augmented fifth interval skipping one string]
MINOR SIXTH
Interval: Minor sixth.
Definition: The minor sixth interval is equivalent to 4 steps (or 4 whole-steps).
Application: The minor sixth interval is most of the time used as a tension (the minor thirteenth, or b13 - read the “Compound Intervals” article).
[Minor sixth interval on two adjacent strings]
[Minor sixth interval skipping one string]
MAJOR SIXTH
Interval: Major sixth.
Definition: The major sixth interval is equivalent to 4 ½ steps.
Application: The major sixth interval is most of the time used in the formation of 6th-chords (i.e., C6, Cmin6) or as a tension (the major thirteenth, or 13 - read the “Compound Intervals” article).
[Major sixth interval on two adjacent strings]
[Major sixth interval skipping one string]
DIMINISHED SEVENTH
Interval: Diminished seventh.
Definition: The diminished seventh interval is equivalent to 4 ½ steps.
Application: The diminished seventh is almost exclusively used in the formation of diminished 7th-chords (i.e., Cdim7 AKA Co7).
[Diminished seventh interval on two adjacent strings]
[Diminished seventh interval skipping one string]
From now on, the interval leap on two adjacent strings gets too large and not easily playable, so the following intervals will only be played by skipping one or two strings.
MINOR SEVENTH
Interval: Minor seventh.
Definition: The minor seventh interval is equivalent to 5 steps (or 5 whole-steps).
Application: The minor seventh is used in the formation of min7th chords (i.e., Cmin7); half-diminished chords (i.e., Cmin7(b5)); Dominant 7th chords (i.e., C7); Altered chords (i.e., C7alt), among others.
[Minor seventh interval skipping one string]
[Minor seventh interval skipping two strings]
MAJOR SEVENTH
Interval: Major seventh.
Definition: The major seventh interval is equivalent to 5 ½ steps.
Application: The major seventh is used in the formation of different types of maj7th chords (i.e., Cmaj7, Cmaj7(b5), Cmaj7(#5)).
[Major seventh interval skipping one string]
[Major seventh interval skipping two strings]
PERFECT OCTAVE
Interval: Perfect Octave.
Definition: The perfect octave interval is equivalent to 6 steps (or 6 whole-steps).
Application: The perfect octave interval demarcates where the notes of a given scale, arpeggio, or chord start repeating themselves.
[Perfect octave interval skipping one string]
[Perfect octave interval skipping two strings]
IMPORTANT THINGS
If you have read the whole article up to this point, you should know that there are a few terms that I haven’t explained yet, and that’s because I needed you to take a good look at all the intervals first, just so it will make more sense. Here are some of the them:
Student: What are simple intervals?
Rodrigo: Simple intervals are all the intervals within the range of one octave. Anything beyond that will be called a “compound interval” and that’s exactly what we are going to explore in the next article.
Student: All the examples shown demonstrate all the intervals starting from the low E string (6th string.) Will the shape of those intervals be the same for all the other strings?
Rodrigo: That’s actually a good question! And the answer is: most of the time. The exception is, when we play an interval using two different strings and the second string of this interval is the B string. The interval will look “shorter” and even "longer" sometimes, just like the following major third intervals:
[Major third interval on the E and A strings]
[Major third interval on the A and D strings]
[Major third interval on the D and G strings]
[Major third interval on the G and B strings]
[Major third interval on the B and e strings]
Student: Why does this happen?
Rodrigo: Because the B string follows a different tuning pattern. All the guitar strings from the low E to the high e are tuned in perfect fourth intervals. E to A is a perfect fourth, A to D is a perfect fourth, D to G is a perfect fourth. The B string breaks the pattern, from G to B we actually have a major third interval, and right after that we have a perfect fourth interval from B to high e again. Intervals that skip the B string are also included in this concept.
Student: Why is that?
Rodrigo: Well, let’s say that most of the chords we know wouldn’t be playable whatsoever if there wasn’t such a difference. Mainly barre chords.
Student: Why are some of the intervals equal in distance but have different names?
Rodrigo: I’m going to use your question to mention a concept we have in music called “enharmony.” To sum up, enharmony means that the same pitch might have two different names. We spoke about it previously when explaining about the difference between natural notes and accidentals and we’re going to get deeper in this concept when we get to discussing the difference between chord-tones and tensions. For now, just keep in mind that if a note has two different names, the interval might also have a different name depending on the note it was named after.
Student: What does the key center column from the table of intervals mean?
Rodrigo: Well, that’s one more of those concepts that will become more clear as you explore the following articles. What you need to understand now is that, so far, we have been studying all the intervals isolated from any context. For example, you might have heard from someone else, another website, or YouTube video, etc., that there is a “major scale formula”, which is a sequence of intervals that will help you find all the notes belonging to a given major scale. The formula goes:
“whole step; whole step; half-step; whole step; whole step; whole step; half-step”
If we were looking for the, let’s say, G major scale, all we had to do is to start applying that sequence of intervals starting from G, and then we would have the following notes as a result:
G whole step; A whole step; B half-step; C whole step; D whole step; E whole step; F# half-step G.
This major scale formula could be also represented by the numbers 1 2 3 4 5 6 7 8. The “1” represents the root of a chord or scale (the main note of a chord or a scale, the note that gives the chord its name, which in this case is G). All the other numbers represent an interval or the distance from the root. So, 1 is root, 2 is major second, 3 is major third, 4 is perfect fourth, 5 is perfect fifth, 6 is major sixth, 7 is major seventh, and 8 is finally the octave. Try it! You'll get the same results.
HOW TO PRACTICE INTERVALS?
1) If you are a beginner and this is your first time learning about intervals/music theory, the best exercise you can practice is to choose a random note on your guitar’s fretboard and try to play all the possible intervals using that note as the starting point. If you were to do that, make it a routine, play it every single day as soon as you get your guitar on your lap, and I promise you that as time goes by, you’ll be able to look at two random notes and name the interval right away.
2) Another great exercise is to play two random notes and name the interval between them. No matter how long it takes you to name it, the more you try it the easier and faster it will get. The reason is because your eyes and fingers will get used to the physical distance between those notes. Don’t put a lot of pressure on yourself, if you do a little bit every day, it will work.
3) In case you already have some knowledge on scales and major and minor keys, the most effective exercise I suggest for you to practice is to choose a different key or scale every day, map it in two different strings, and harmonize them with different intervals. One at a time! Start with thirds, fourths, and fifths since they are the easiest intervals to play. Once you have done that, try to improvise solos and melodies all over the fretboard. Not only will your fingers get used to the intervals' shape but also your aural skills will develop faster. It'd be very helpful too if you solo over backing tracks in the respective key of the scale you're working on.
[Example of C major scale harmonized in third intervals on the high e and B strings]
[Example of C major scale harmonized in fourth intervals on the G and D strings]
4) If you don't want to spend your time trying to figure out how to harmonize scales with the different intervals, I have written a whole eBook with more than 300 hundred pages where I harmonized all natural major and natural minor scales, with all the simple and compound intervals, on every single string, and in every single key! You can find this eBook by either clicking on the link below or going to the "STORE" section.
This interval topic is not over yet! In fact, the more you advance through the material the more ideas you’ll have to practice and apply to the intervals. All these concepts will be available here on my blog for free to everybody who is interested in learning more about music. As you could imagine, producing all this content is very time-consuming, and if you found this article helpful, please consider buying the material to support the blog or join our membership plan (available in April 2023) where I'll be teaching different applications for all this material through weekly videos, and you'll have all your questions answered as well!
You can also follow me on Instagram @_rodrigodmoreira for weekly quizzes to test your comprehension on these topics and suggest more ideas for future articles!
All my best,