Intervals

A musical INTERVAL is simply the distance between 2 notes.

Not exactly a tough thing to wrap your head around but INTERVALS are ABSOLUTELY CRITICAL to musical understanding and create the patterns that underpin music theory.

This is easily the most important page on the entire website and well worth taking your time to work through and understand. Because if you can, the rest of this website is going to make a lot more sense!

This page contains the following sections:

Whether keys, scales, chords or modes, they all rely heavily on INTERVAL patterns.

HOW INTERVALS WORK

The easiest way to understand INTERVALS is by starting with the CHROMATIC scale. The CHROMATIC scale is unique in that it contains every half-tone within a single octave – but, it is not an OCTAVE! A scale is not automatically an octave by default. An octave occurs when the TONIC (or ROOT note) is added to the end of the scale. Try playing a scale without the ending tonic and you’ll quickly hear why octaves are considered the norm. The scale seems to hang in mid-air waiting to be completed.

Which, according to your brain – it is!

From the time you came out of dear ‘ol mom kicking and screaming to the moment you read this sentence, your brain has been learning what sounds normal and what doesn’t. Without that trailing tonic, there’s no resolution to the scale. It’s basic cognitive fluency in audio form.

chromatic-scale-octave

So the formula becomes: SCALE + TONIC/ROOT = OCTAVE

Now you may be asking yourself, “how can an octave, which is Latin for eighth (8th), be equal to 13 half-tones?” Well grasshopper, welcome to the weirdness that causes people so much pain and confusion when trying to get a grip on music theory. OCTAVE is basically a catchall term describing any scale that starts and ends on the same note. Technically, it’s based on the 7 note HEPTATONIC scale with an added TONIC.

So, 7 notes + TONIC = OCTAVE.

As you can see from the following graphic, there is a single half-tone INTERVAL between each of the notes. In musical parlance, a single half-tone INTERVAL is known as a minor 2nd (m2).

chromatic minor 2nds

INTERVAL ABBREVIATIONS

I can smell brain fry!

I know, it’s kind of weird thinking about the number 2 representing 1 of anything, but that quirkiness runs throughout the interval naming system as demonstrated by the following graphic showing INTERVAL name abbreviations.

interval-abbreviations

This means that a Perfect 5th (P5) would be 7 steps (scale degrees) from P1 (AKA “unison”). A MAJOR 3rd (M3) would be 4 steps from P1.  A minor 7th (m7) would be 10 steps from P1 and so on. Finally, you round out the OCTAVE with a Perfect 8th (P8) located exactly 12 steps from P1.

I created a free PDF file of the above graphic with a couple of additions that can be downloaded and printed. It’s probably a good idea to keep it handy while reading through this website because from here on – INTERVAL abbreviations are used A LOT! Click here to download

SEEKING PERFECTION

Next, we jump from the CHROMATIC scale to the HEPTATONIC (AKA diatonic) scale. If you don’t know what a HEPTATONIC scale is, read (or reread) the page on SCALES and then come back.

The above INTERVAL abbreviations graphic makes it easy to see the relationship between the scale degrees and the INTERVAL names when starting on the ROOT of the scale (in this case C). Of particular interest are the INTERVAL names that start with the letter ‘P’. These are considered PERFECT INTERVALS and are the most consonant. P1 is the ONLY INTERVAL that consists of a single note and will always be the most PERFECT INTERVAL. The rest break down like so: P4 sounds good, P5 sounds better and P8 sounds second best after P1 because it uses the same tones an OCTAVE apart.

The following graphic of the C MAJOR scale shows the perfect INTERVALS common to all MAJOR scales.
perfect-intervals
Remember, to find the INTERVAL you need to count the spaces between the notes – not the actual notes!

  • C to F consists of 5 half-tone INTERVALS ( 2 + 2 + 1) or a P4
  • C to G consists of 7 half-tone INTERVALS (2 + 2 + 1 + 2) or a P5
  • C to C consists of 12 half-tone INTERVALS (2 + 2 + 1 + 2 + 2 + 2 + 1) or a P8.

The above graphic also exposes an EXTREMELY IMPORTANT pattern concerning CHORD PROGRESSIONS. If you were to play a I / IV / V / I chord progression (easily the most common progression containing more than 2 chords) in ANY MAJOR KEY, you’d actually be playing the following scale degrees.

  • I = TONIC (P1)
  • IV = SUB-DOMINANT (P4)
  • V = DOMINANT (P5)
  • I = TONIC (P1)

Which makes the whole progression about as consonant as you can get because of its bent towards perfection.

STACKED INTERVALS

The building blocks of TRIADS and 7ths.

“Stacked” INTERVALS are just what they sound like they should be – groups of INTERVALS stacked one on top of the other.

A couple of examples of stacked INTERVALS are MAJOR and minor triads. A TRIAD is simply a 3 note chord. In the case of the MAJOR triad, it is comprised of stacked 3rds and has the following INTERVALS: P1(ROOT), M3, m3. In the following graphic, note how the last note of the M3 INTERVAL (e) acts as the ROOT note of the m3 INTERVAL (from e to G).

stacked-intervals

For a minor TRIAD the 3rds are inverted creating the P1(ROOT), m3, M3 combination. This new INTERVAL pattern actually causes the KEY to change because of the introduction of the Eb, Ab and Bb notes. In this case, it would change to C MAJOR’s parallel KEY – c minor

stacked-c-minor-triad

But stacking INTERVALS is not the only way a TRIAD can be described.

ROOTED INTERVALS

Same result, different method..

The following graphic shows the same C MAJOR TRIAD but this time, the INTERVALS are calculated from the ROOT note. In this example, the TRIAD is comprised of the P1, M3 just like the “stacked” version, but the last note in the TRIAD (G) is calculated from P1 (C) instead of m3 (Eb) thus making it a P5.

root-position-intervals

Which confuses the crap out of people – unnecessarily.

Some articles I’ve read use STACKED INTERVALS while others will use ROOTED INTERVALS. In reality, it’s a good idea to learn both methods. It’s not really that hard if you break it into small pieces and remember a few simple rules.

BREAKING IT DOWN

AKA – divide and conquer!

A simple method of learning INTERVALS is to try to memorize the PERFECT intervals first. P1 is always considered the ROOT note of the INTERVAL. P8 is always the same note 12 scale degrees away. P4 is always equal to 5 half-tone INTERVAL steps and P5 is always equal to 7 half-tone INTERVAL steps. You can reinforce this concept by playing the I / IV / V / I chord progression (in any KEY) and saying the INTERVAL name and count out loud as you play its corresponding chord.

major scale perfect intervals

Next, try to memorize the MAJOR intervals.

major-scale-intervals

For MAJOR scales, if it ain’t PERFECT – it’s MAJOR. If it’s neither, it ain’t a MAJOR scale! Minor scales on the other hand aren’t quite so easy to remember. Take the following PARALLEL minor scale of C MAJOR (C minor).

minor-scale-intervals

The only MAJOR INTERVAL is M2. Everything else is either PERFECT or minor.

An interesting and useful pattern emerges from the above graphics. Notice how if the INTERVAL is minor, the scale degree is MAJOR and if the scale degree is MAJOR, the INTERVAL is minor. They are inverted.

INTERVAL RULES

INTERVALS can also be calculated with the following simple rules.

  • MAJOR = MAJOR (M)
  • minor (m) = MAJOR minus 1 half-tone
  • AUGMENTED (A) = MAJOR or PERFECT plus 1 half-tone
  • diminished (d) = PERFECT or minor minus 1 half-tone, MAJOR minus 2 half-tones

If it’s PERFECT, MAJOR or AUGMENTED, use a CAPITAL letter when writing it out, otherwise, use lowercase. It’s also important to point out that PERFECT intervals have no MAJOR or minor intervals associated with them – only AUGMENTED and diminished. In other words, a PERFECT 4th has an Augmented 4th and a diminished 4th, but not a MAJOR 4th or minor 4th. The same rule applies to the PERFECT 5th.

HARMONIC vs MELODIC

And last, but not least..

INTERVALS are divided into 2 basic types – melodic and harmonic. A MELODIC INTERVAL (think “linear”) is an interval that occurs between 2 adjacent notes. A HARMONIC INTERVAL is between notes that occur simultaneously.

Think MELODIC for scales and modes and HARMONIC for chords.

It’s just that simple.