Our chordal intervals are like melodic intervals, they are numerical labels that measure the distance between pitches. So why the breakdown into separate pages? To simply make things easier for the new learner. We can base harmonic intervals on the arpeggio which we create from any musical scale. Lets create an arpeggio from the pitches of the C major scale and compare the two. Cool with the numbers? Example 1.
| scale degree | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
| C major scale | C | D | E | F | G | A | B | C |
| C major arpeggio | C | E | G | B | D | F | A | C |
| chord degree | 1 | 3 | 5 | 7 | 9 | 11 | 13 | 15 |
Lets compare the sound of these two regroupings of the same pitches. Example 2.
In the above examples, the arpeggio in bars 3 and 4 were created by respelling the major scale of bars 1 and 2 by using musical intervals of the major and minor third. This is where the chords come from, by simply respelling the scale in thirds, which oddly enough is simply achieved by skipping every other note of a scale, then tacking on what got skipped on the end. Lets create one giant chord from simply "stacking" the entire arpeggio. Example 3.
Giant chords! Not the most common of chords I must say, but giant non the less no? Are there other ways to use this major 3rd / minor 3rd sequence? Lets examine each of the diatonic harmonic or chordal intervals created from the arpeggio above. Example 4.
| major 3rd | perfect 5th | maj 7th | maj 9th | perfect 11th | maj 13th | perfect 15th |
Can you sing these intervals? Quite a task for sure! Lets put these colors into chords to get an idea of what the theory creates. Example 5.
C / maj 3 |
C triad | C maj 7 | C maj 9 | C 7 / 11 | C maj 9/13 | C maj 6/9 |
Here are some common alterations of each of the above harmonic intervals. Labeled theoretically in the top row, where "dim." is shorthand for the musical term diminished and "aug." represents the musical term augmented. Slang labels used to describe the harmonic intervals are in the second row. Example 5.
| minor 3rd | dim 5th | aug 5th | minor 7th | dim 9th | aug. 9th | aug. 11th | dim. 13th | aug. 15th |
| blue 3rd | blue 5th | sharp 5th | blue 7th | flat 9 | sharp 9 | sharp 11 | flat 13 | sharp 15 |
So where do we use these harmonic intervals? Well, mainly in creating chords that extend into the upper structure as in bars 35 and onward in the next idea. Example 6.
| C minor triad | C dim triad | C +5 | C 7+ 5 | C minor 7th |
| C 7b9 | C 7#9 | C maj 9#11 | C 7 #9b13 | C 6/9#11#15 |
Here is review of the harmonic intervals discussed so far. Example 7.
| pitches | interval | # of half steps | # of whole steps | commonly called |
| C up to D# | augmented 2nd | 3 | 1.5 | sharp two |
| C up to Eb | minor third | 3 | 1.5 | flat 3 / blue 3rd |
| C up to E | major third | 4 | 2 | major third |
| C up to Gb | diminished fifth | 6 | 3 | flat five / tritone / blue 5th |
| C up to G | perfect fifth | 7 | 3.5 | fifth |
| C up to G# | augmented fifth | 8 | 4 | sharp five |
| C up to Bb | minor seventh | 10 | 5 | flat seven / blue 7th |
| C up to B | major seventh | 11 | 5.5 | major seventh leading tone |
| C up octave to C | octave | 12 | 6 | octave |
| C up octave to Db | minor ninth | 13 | 6.5 | flat nine |
| C up octave to D | major ninth | 14 | 7 | ninth |
C up octave to D# |
augmented ninth | 15 | 7.5 | sharp nine |
C up octave to F |
perfect eleventh | 17 | 8.5 | eleventh |
C up octave to F# |
augmented eleventh | 18 | 9 | sharp eleven |
| C up octave to Ab | minor thirteenth | 20 | 10 | flat thirteen |
| C up octave to A | major thirteenth | 21 | 10.5 | thirteenth |
| C up octave to A# | augmented thirteenth | 22 | 11 | sharp thirteen |
| C up 2 octaves to C | major fifteenth | 24 | 12 | octave |
| C up 2 octaves + 1/2 step to C# | augmented fifteenth | 25 | 12.5 | sharp fifteen |
Knowledge of the intervals used to create chords helps in building chords when only a chord symbol is given in the written music. We find these symbols commonly in a lead sheet. Our ability to quickly and accurately spell our chords is improved with knowledge of the intervals as is our ability to understand the process of arpeggiating the harmony. In a practical sense, knowledge of the harmonic intervals is also handy when adjusting say a C 7 chord to a C 7b9, we simply locate the 9th in the arpeggio and flatten or lower it by half step. Cool with this? Pretty basic huh? Look to the workbook section to sharpen your understanding of harmonic intervals.
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Destiny is no matter of chance. It is a matter of choice. It is not a thing to be waited for, it is a thing to be achieved. Willian Jennings Bryan
