Hey everyone! Rodrigo here again!
This is the continuation of the article “Simple Intervals”, and it ideally shouldn’t be read until you have a good understanding and have explored the sounds of the previous topic. Many of the same concepts that I consider important will be repeated here, since many people might get to this blog through this article and could end up missing some important information.
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
First of all, something that I want you to keep in mind is that your goal for this article should be to understand the Table of Compound Intervals and apply it to your instrument. As you advance through the reading, you will notice that I have categorized each interval by their name, definition, and application, and if this is your first contact with music theory, most of the application part might not make sense yet. Everything will become clear once you understand the formation of chords (triads and 7h-chords) and the difference between chord-tones and tensions, which you will find in the following articles.
WHAT ARE COMPOUND INTERVALS?
Compound intervals are intervals larger than one octave. For the sake of this article, we’ll be exploring all the intervals within the range of one octave to two octaves, from the ninths to the fifteenths.
Compound intervals are actually the same as the simple intervals, but with the addition of an octave interval (6 whole-steps) to each one of them. So, it is correct to say that every simple interval has its own corresponding compound interval.
Student: So, what’s the importance of studying more intervals?
Rodrigo: As I mentioned at the end of the previous article, there’s many more applications to intervals than you could imagine. The more topics we learn about, the more ideas we have to use them and to be more creative as well. For now, I just want you to understand that in the formation of chords, given the limitations of our instrument, many times we’ll have to shift a note up or down an octave to make a given chord playable. Sometimes not all the notes fit in the same region, and a possible solution for that would be to play that note as a larger interval. You’ll clearly see this application when we get to the articles of Drop-2 and Drop-3 chords.
THE FRETBOARD
I’m also adding the fretboard’s images here one more time for reference.
[Fretboard with flats]
[Fretboard with sharps]
TABLE OF COMPOUND INTERVALS
COMPOUND INTERVALS
MINOR NINTH
Interval: Minor ninth.
Definition: The minor ninth interval is equivalent to 6 ½ steps (or 1 octave + ½ step).
Application: The minor ninth interval is usually used as a tension for the dominant 7th chords (i.e., C7(addb9)).
[Minor ninth interval skipping one string]
[Minor ninth interval skipping two strings]
MAJOR NINTH
Interval: Major ninth.
Definition: The major ninth interval is equivalent to 7 steps (or 1 octave + 1 step).
Application: The major ninth interval is usually used as a tension for many types of chords (i.e., C7(add9); Cmin7(add9); Cmaj7(add9); among others).
[Major ninth interval skipping one string]
[Major ninth interval skipping two strings]
AUGMENTED NINTH
Interval: Augmented ninth.
Definition: The augmented ninth interval is equivalent to 7 ½ steps (or 1 octave + 1 ½ step).
Application: Just like the minor ninth, the augmented ninth interval is usually used as a tension for dominant 7th chords (i.e., C7(#9)).
[Augmented ninth interval skipping one string]
[Augmented ninth interval skipping two strings]
MINOR TENTH
Interval: Minor tenth.
Definition: The minor tenth interval is equivalent to 7 ½ steps (or 1 octave + 1 ½ steps).
Application: The minor tenth is most of the time used as equivalent to the minor third interval one octave above when building chords (read the “Drop-2 chords” article) and is also used as a tension for 7sus4 chords.
[Minor tenth interval skipping one string]
[Minor tenth interval skipping two strings]
MAJOR TENTH
Interval: Major tenth.
Definition: The major tenth interval is equivalent to 8 steps (or 1 octave + 2 steps).
Application: Just like the minor tenth, the major tenth is most of the time used as equivalent to the major third interval one octave above when building chords (read the “Drop-2 chords” article) and is also used as a tension for 7sus4 chords.
[Major tenth interval skipping one string]
[Major tenth interval skipping two strings]
From now on, the interval leap skipping one string gets too large and not easily playable, so the following intervals will only be played by skipping two or more strings when needed.
PERFECT ELEVENTH
Interval: Perfect eleventh.
Definition: The perfect eleventh interval is equivalent to 8 ½ steps (or 1 octave + 2 ½ steps).
Application: The perfect eleventh is most of the time used as a tension for minor chords such as: Cmin7(add11); Cmin(add11), among others.
[Perfect eleventh interval skipping two strings]
[Perfect eleventh interval skipping three strings]
AUGMENTED ELEVENTH
Interval: Augmented eleventh.
Definition: The augmented eleventh interval is equivalent to 9 steps (or 1 octave + 3 steps).
Application: The perfect eleventh is most of the time used as a tension for major and dominant chords such as: Cmaj7(add#11); C7(add#11), among others.
[Augmented eleventh interval skipping two strings]
[Augmented eleventh interval skipping three strings]
DIMINISHED TWELFTH
Interval: Diminished twelfth.
Definition: The diminished twelfth interval is equivalent to 9 steps (or 1 octave + 3 steps).
Application: The diminished twelfth is most of the time used as equivalent to the diminished fifth one octave above when building diminished and half-diminished chords (read the “Drop-2 chords” article).
[Diminished twelfth interval skipping two strings]
[Diminished twelfth interval skipping three strings]
PERFECT TWELFTH
Interval: Perfect twelfth.
Definition: The perfect twelfth interval is equivalent to 9 ½ steps (or 1 octave + 3 ½ steps).
Application: The perfect twelfth is most of the time used as equivalent to the perfect fifth one octave above when building a huge variety of major and minor chords (read the “Drop-2 chords” article).
[Perfect twelfth interval skipping two strings]
[Perfect twelfth interval skipping three strings]
AUGMENTED TWELFTH
Interval: Augmented twelfth.
Definition: The augmented twelfth interval is equivalent to 10 steps (or 1 octave + 4 steps).
Application: The augmented twelfth is most of the time used as equivalent to the augmented fifth one octave above when building augmented chords such as: Cmaj7(#5); C7(#5).
[Augmented twelfth interval skipping two strings]
[Augmented twelfth interval skipping three strings]
MINOR THIRTEENTH
Interval: Minor thirteenth.
Definition: The minor thirteenth interval is equivalent to 10 steps (or 1 octave + 4 steps).
Application: The minor thirteenth is most of the time used as a tension for dominant 7th chords (i.e., C7(addb13)).
[Minor thirteenth interval skipping two strings]
[Minor thirteenth interval skipping three strings]
From now on, the interval leap skipping two strings gets too large and not easily playable, so the following intervals will only be played by skipping three or more strings when needed.
MAJOR THIRTEENTH
Interval: Major thirteenth.
Definition: The major thirteenth interval is equivalent to 10 ½ steps (or 1 octave + 4 ½ steps).
Application: The major thirteenth is most of the time used as a tension for dominant 7th, minor, and major chords in (i.e., C7(add13); Cmin7(add13); Cmaj7(add13)).
[Major thirteenth interval skipping three strings]
[Major thirteenth interval skipping four strings]
DIMINISHED FOURTEENTH
Interval: Diminished fourteenth.
Definition: The diminished fourteenth interval is equivalent to 10 ½ steps (or 1 octave + 4 ½ steps).
Application: The diminished fourteenth interval is most of the time used as equivalent to a diminished seventh interval one octave above in the formation of diminished and half-diminished chords (i.e., Cdim7; Cmin7(b5)).
[Diminished fourteenth interval skipping three strings]
[Diminished fourteenth interval skipping four strings]
MINOR FOURTEENTH
Interval: Minor fourteenth.
Definition: The minor fourteenth interval is equivalent to 11 steps (or 1 octave + 5 steps).
Application: The minor fourteenth interval is most of the time used as equivalent to a minor seventh interval one octave above in the formation of a huge variety of chords (i.e., C7, Cmin7; C7alt; Cdim7; Cmin7(b5)).
[Minor fourteenth interval skipping three strings]
[Minor fourteenth interval skipping four strings]
MAJOR FOURTEENTH
Interval: Major fourteenth.
Definition: The major fourteenth interval is equivalent to 11 ½ steps (or 1 octave + 5 ½ step).
Application: The major fourteenth interval is most of the time used as equivalent to a major seventh interval one octave above mostly in the formation of major chords (i.e., Cmaj7; Cmin(maj7)).
[Major fourteenth interval skipping three strings]
[Major fourteenth interval skipping four strings]
PERFECT FIFTEENTH
Interval: Perfect fifteenth.
Definition: The perfect fifteenth interval is equivalent to 12 steps (or 1 octave + 6 steps).
Application: The perfect fifteenth interval, also known as two octaves, demarcates where the notes of a given scale, arpeggio, or chord start repeating themselves one more time. Both the perfect octave and the perfect fifteenth are very important for us to have more freedom when soloing using the whole fretboard and to avoid getting stuck in a specific region.
[Perfect fifteenth interval skipping three strings]
[Perfect fifteenth interval skipping four strings]
IMPORTANT THINGS
If you have read the whole article on “Simple Intervals'', you already know what this whole section is about. You should have noticed 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 them:
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 ninth intervals:
[Major ninth interval on the E and G strings]
[Major ninth interval on the A and B strings]
[Major ninth interval on the D 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 (as you can see in the last two images).
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 (read the "Simple Intervals" article) 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’re going to look at two random notes and be able to name the interval between them right away.
2) Another great exercise is to play two random notes and name the interval. No matter how long it takes you to name it, the more you try it the easier and faster it gets. 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 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 your fingers will 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 fifth intervals on the high e and B strings]
[Example of C major scale harmonized in sixth intervals on the B 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,