In our very first post, I noted that music moves in two directions: vertically and horizontally. Music moves horizontally forward in various intervals of time – which we call rhythm. Simultaneously, music moves vertically up and down in various intervals of pitch. Individual notes and/or clusters of notes move in harmony in these two dimensions – creating a three dimensional feeling that causes us to move, emotionally and physically! It is an amazing gift from God – what would our lives be without music?
Here we will embark on a comprehensive review of pitch intervals. You already know most of the intervals of music if you’ve followed this blog up to this point. There are just a few left to discuss, which I felt important before continuing on with our discussions of chords and guitar fingerings.
Just as there are twelve notes in a chromatic octave, there are twelve intervals in music. While you are likely familiar with minor and major intervals, I’ve occasionally referred to some intervals as “Perfect”, and you’re probably asking what the heck is that? Perfect intervals have no minor or major variant – in other words there is no such thing as major or minor 4th or 5th or octave. There is only one type of each of these three intervals – Perfect – P4, P5, and P8:
Interval Ref Steps Frets Example
Perfect 4th P4 2 ½ 5 C - F Perfect 5th P5 3 ½ 7 C – G Perfect 8th P8 6 12 C - C
So where does the Tritone interval fit in? While there is indeed only one Tritone interval (three whole tones, the middle of the octave), Tritones are not normally referred to as Perfect. Protocol dictates referencing the Tritone interval as TT, or simply the word Tritone:
Interval Ref Steps Frets Example
Tritone TT 3 6 C - Gb
So, we have minor, major, perfect, and tritone intervals – every interval type in music. Before reviewing all twelve, its important for you to understand the concept of inversions. Inverting intervals or chords in the purist sense simply means moving the bottom (lowest) note up to the top. This is especially important to understand when referring to chords. In the case of single note intervals, it appears the two notes are simply exchanging positions. Here’s what happens when we invert a minor 2nd, in this case we’ll invert E – F and make it F – E:
Interval Ref Steps Frets Example
Minor 2nd mi2 ½ 1 E - F Major 7th ma7 5 ½ 11 F - E
Below is a chart showing all twelve intervals and their inversions, beginning with the smallest (1/2 step) to largest (6 steps)
Interval Ref Steps Frets Example Inversion Interval Steps Frets
Minor 2nd mi2 ½ 1 C - Db Db - C ma7 5 ½ 11
Major 2nd ma2 1 2 C - D D - C mi7 5 10
Minor 3rd mi3 1 ½ 3 C - Eb Eb - C ma6 4 ½ 9
Major 3rd ma3 2 4 C - E E - C mi6 4 8
Perfect 4th P4 2 ½ 5 C - F F - C P5 3 ½ 7
Tritone TT 3 6 C - Gb Gb - C TT 3 6
Perfect 5th P5 3 ½ 7 C – G G - C P4 2 ½ 5
Minor 6th mi6 4 8 C - Ab Ab - C ma3 2 4
Major 6th ma6 4 ½ 9 C - A A - C mi3 1 ½ 3
Minor 7th mi7 5 10 C - Bb Bb - C ma2 1 2
Major 7th ma7 5 ½ 11 C - B B - C mi2 ½ 1
Perfect 8th P8 6 12 C - C C - C P8 6 12
A few observations worth noting:
major inverts to minor
minor inverts to major
2nd inverts to 7th
7th inverts to 2nd
3rd inverts to 6th
6th inverts to 3rd
Perfect intervals invert to each other
The Tritone interval inverts to itself - as do octaves
Therefore:
mi2 = ma7 ma2 = mi7 mi3 = ma6 ma3 = mi6 P4 = P5 P5 = P4 TT = TT P8 = P8
We previously learned that scales are patterns of 1/2 and 1 step intervals. These are the 2nd intervals: mi2 = 1/2 step, ma2 = 1 step.
We then learned that chords are patterns of 3rds: mi3 = 1.5 steps, ma3 = 2 steps.
All other intervals are components found within scales, arpeggios, and chords. Most importantly, intervals play a major role in strong melody and harmony, and are immeasurably important to understand for composition and improvisation. Repetitive patterns of scales or arpeggios are redundant and boring to listen to – while beautiful melodies contain a balance of various intervals of all sizes.
In Summary: We’ve learned that there are 12 intervals in all of music. We know that the smallest interval is a mi2, and is 1/2 step in size. An octave represents 6 whole-steps, or 12 half-steps, and is called P8. Perfect intervals have no minor or major variants – while all other intervals do. The Tritone is the very center of the octave – 3 whole steps (6 half-steps), and is called TT – although it does share the individualist quality of Perfect intervals. Inversions are created by moving the bottom note to the top. Minor inverts to major and vice versa. P4 inverts to P5, vice versa. TT inverts to itself – as does P8.
Now that we know all the intervals in music, we’re ready to move forward learning more chords, as well as fretboard fingerings and shapes. Until next time, I remain
Musically yours,
Al Dinardi
by Al Dinardi
11 Sep 2010 at 15:44
Thank you for your comments and taking the time to respond. I stand corrected in thinking the dia in diatonic had to do with seven tones, as I believe pentatonic refers to five tone scales – it was not only an assumption on my part, but on previous music instructors who mistakenly believe the same thing.
Regarding enharmonic equivalent intervals, those early posts were aimed at beginners, and in hind sight was probably too early on to introduce the concepts of double sharps or flats or enharmonic equivalents. I do however always suggest a simple way of avoiding that when writing out scales or chords: write the alpha names first, then add the appropriate flats or sharps to fit the scale structure. Similarly, I always suggest writing out the 3rd intervals of a chord, and filling in the appropriate # or b. If a student were to adhere to this practice, they would never encounter inadvertently writing notes outside of keys or chords. i.e. writing a C diminished chord is a two step process: write the alpha 3rd intervals: C E G B then fill in the flats to fit the chord structure: C Eb Gb Bbb. I emphasize these practices for both scales and chords throughout the posts – perhaps you missed them.
Regarding perfect intervals, that was illuminating and I plan on changing that post accordingly – though I will likely drop the discussion as to why they are called perfect for now and save it for a more advanced post.
One of the goals here is simplicity – I want to keep as many readers engaged as possible. So, I am constantly attempting a tight focus throughout each post, and not get too detailed. That is a discipline that is difficult at times – finding myself going further into details that could or should have been saved for later posts. Saying that, I definitely welcome your comments, and in most cases will probably strike that part of the discussion from the post – saving it for a later discussion. So by all means, keep it coming – I appreciate your thoughts, research, and writing – I need it as I am not perfect. As stated in the About posts “I absolutely encourage comments and questions, and guarantee one way or another we’ll find the answer to every music theory question. As with most things in life, there are multiple ways of viewing the same thing – and I hope to present all known views – perhaps discovering a few new ones along the way:) Thanks.
Al