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Lesson 1 - Intervals and triads

Introduction

The basis of the music theory lessons you will find here is an old stenciled manuscript in English named "The jazz guitar theory and techniques". It was the first manuscript I read about jazz guitar theory. The author is unknown to me. I also used other material that I found on the internet, in other good books, and material that I invented myself by combining ideas from other sources. Valuable sources are:

In the lessons lower case letters refer to single notes. Capital letters refer to the root of a scale or chord. For example, a-c-e refers to the single notes which, collectively, make an A minor chord. The cryptic symbol bb refers to the single note B flat.

Intervals

An interval is the relationship between two tones or pitches. The relationship is determined by how far apart the two tones are in the vertical dimension of musical space or staff. If the two pitches are played one after the other, we have a melodic interval; if they are played at the same time, we have a harmonic interval. We measure intervals simply by counting the scale steps, that is, the lines and spaces from one note to the next:

intervals numbered

A good way to learn recognize intervals is by dividing them in odd-numbered intervals and even-numbered intervals. Odd-numbered intervals look symmetrical and the notes are on either a line or a space:

intervals numbered

For even-numbered intervals one note is on a line and one on a space:

intervals numbered

It is a good exercise to take any music sheet and say to yourself loudly the intervals that you see in the song.

Interval quality

Intervals can have five possible qualities. They are listed in the table below, along with their abbreviations, the intervals to which they apply, and some examples of ascending intervals (within the octave) in the key of C major.

quality abbreviation intervals examples of ascending intervals
perfect P unisons, octaves, 4ths, 5ths c→c, c→f, c→g, f→c
maior M 2nds, 3rds, 6ths, 7ths c→d, c→e, c→a, d→e, f→g, g→a, a→b, c→b
minor m 2nds, 3rds, 6ths, 7ths e→f, b→c, a→c, e→c
augmented + or A all intervals f→b
diminished ° or d all intervals b→f

Perfect intervals apply only to unisons, 4ths, 5ths, and octaves. Major and minor intervals apply only to 2nds, 3rds, 6ths, 7ths. So we’ll divide learning interval qualities into two groups: group one, the perfect intervals and group two, the major/minor Intervals.

The next table shows all intervals from the unison up to the octave in the key of C. All intervals are determined by the number of half steps between the two notes (#hs). They come with ascending and descending interval examples of tunes from the standard jazz repertoire. Unless otherwise noted, the interval in question is the first two melody notes of the song.

Table of possible intervals within the octave with song examples
name abbr #hs tones asc ascending song example tones desc descending song example
unison P1 0 c→c   c→c  
minor 2nd m2 1 c→db Thelonious Monk´s "Blue Monk" c→b Cedar Walton's "Bolivia"
major 2nd M2 2 c→d Miles Davis' "Four" c→bb Miles Davis' "Tune-Up"
minor 3rd m3 3 c→eb Charlie Parker´s "Confirmation" c→a Dizzy Gillespie's "Groovin' High"
major 3rd M3 4 c→e Thelonious Monk's "Monk's Dream" c→ab John Coltrane's "Giant Steps"
perfect 4th P4 5 c→f Duke Jordan's "Jordu" c→g Wayne Shorter's "ESP"
tritone, augmented 4th, diminished 5th tt, +4, -5 6 c→f#, c→gb Joe Henderson's "Isotope" c→gb, c→f# Third bar of bridge of Duke Ellington's "Sophisticated Lady"
perfect 5th P5 7 c→g Milt Jackson's "Bag's Groove" c→f Woody Shaw's "Katrina Ballerina"
minor 6th m6 8 c→ab Woody Shaw's "In A Capricornian Way" c→e Second bar of Joe Henderson's "Serenity"
major 6th M6 9 c→a Thelonious Monk's "Misterioso" c→eb Miles Davis' "All Blues"
minor 7th m7 10 c→bb Last bar of bridge of McCoy Tyner's "Aisha" c→d Fourth bar of bridge of Billy Strayhorn's "Chelsea Bridge"
major 7th M7 11 c→b Second and thirds notes of Joe Henderson's "Serenity" c→db Wayne Shorter's "Lady Day"
perfect octave P8 12 c→c Sam Jones' "Del Sasser" c→c Freddy Hubbard's "Philly Mignon"

Triads

If three or more pitches are played at the same time, we have a chord. The most simple chords are triads. They are the basic chordal units of traditional harmony. They consist of three different tones: root, 3rd, and 5th. The triad occurs in four basic forms: major (1-3-5), minor (1-b3-5), diminished (1-b3-b5), and augmented (1-3-#5). To get a profound knowledge of the fretboard it's important to study triads on the guitar. Every guitarist knows the next basic major and minor barre chords that are thaught in the beginning:

maior and minor barre chords

These chords consist of 5 or 6 tones, so they contain doubled tones. They are good for playing solo guitar at the campfire. Next triads consist of just 3 tones: root, 3rd, and 5th. So there are no doubled tones. Studying these triads will increase your knowledge of the guitar fretboard, serve as a basis for learning jazz chords, as a basis for slash chords like C/Db, Eb/C, etc, and for playing funk rhythm guitar in a band. And three note chords can be used in your guitarsolo when there's no other chord player in the band: if you want to make clear the harmony, just play a three note chord with your pick, middle finger, and ring finger. While studying these triads be aware of what tone is the root, what tone is the 3rd, and what the 5th.

Major triads
Strings 4, 5, and 6

major triads on strings 456

Strings 3, 4, and 5

major triads on strings 345

Strings 2, 3, and 4

major triads on strings 234

Strings 1, 2, and 3

major triads on strings 123

Minor triads
Strings 4, 5, and 6

minor triads on strings 456

Strings 3, 4, and 5

minor triads on strings 345

Strings 2, 3, and 4

minor triads on strings 234

Strings 1, 2, and 3

minor triads on strings 123

Augmented triads
Strings 4, 5, and 6

augmented triads on strings 456

Strings 3, 4, and 5

augmented triads on strings 345

Strings 2, 3, and 4

augmented triads on strings 234

Strings 1, 2, and 3

augmented triads on strings 123

Diminished triads
Strings 4, 5, and 6

diminished triads on strings 456

Strings 3, 4, and 5

diminished triads on strings 345

Strings 2, 3, and 4

diminished triads on strings 234

Strings 1, 2, and 3

diminished triads on strings 123

Diatonic is the term we use to describe music that uses only the pitches of a particular major or minor scale. Every note in the following excerpt is from the G major scale, therefore it is diatonic:

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