This Simple Formula Is All You Need
To Name Any Interval With Accuracy

To start with, let's look at some general examples of simple chromatic intervals:

Ex. Of Chromatic Intervals

I've chosen to show the above examples inside a variety of key centers because most music is written with key signatures.
But keys only influence why a composer wrote non-diatonic notes a certain way (like Fb instead of E) and have no real bearing on the naming of chromatic intervals.
We still need to be able to name any interval anywhere.

Here is part 1 of the formula for naming any interval:

  1. Pretend to make the lower note the tonic of It's own key. (if it is not one of the 15 key signature notes go to Part 2)
    Formula 1 pic
  2. Imagine that note's key signature for a moment (If the note happens to be Eb add 3 flats in your mind).
    Formula 2 pic
  3. Count the scale steps (in the imaginary scale) till you hit the line or space of the top note.
    Formula 3 pic
  4. The number you come up with is part of your interval name (even if the higher note turns out to be the same pitch).
    Formula 4 pic
  5. Compare the note of your imaginary scale (that would be on that step) with the actual higher note.
    Formula 5 pic
  6. Add the proper modifier to complete the process: Major, Minor, Perfect, Augmented, Diminished.
    Formula 6 pic

Here is the formula applied to the other chromatic interval examples shown at the top of this page:

Solution to chromatic interval examples

This formula may seem complicated and long but if you know your major scales and key signatures it is actually very quick and simple.
The most difficult part is probably step 6 where you have to choose the modifier, but if you remember the 2 groups, even that becomes routine.

Now, let's deal with the situation when the bottom note is not one of the 15 key signature notes but 1 of the remaining 6 note possibilities: D#, E#, G#, A#, B#, Fb.

Part 2 of the naming-any-interval formula:

Thankfully, this is relatively simple:

  1. Be aware that the bottom note is not one of the 15 possible key signature notes but one of these: D#, E#, G#, A#, B#, Fb
  2. To work out the interval name simply:
    LOWER or RAISE BOTH notes by a half step and then apply Part 1 of the formula. Be careful NOT to change the name of the lowered/raised notes to another letter:
    Ex 1: Interval = E# to C, lowering both notes = E to Cb (not B): Dim 6th
    Ex 2: Interval = Fb to A#, raising both notes = F to A## (not B): doubleAug 3rd
  3. Use this solution also if your bottom note is a Double Sharp or Double Flat. (Notes may be raised or lowered by a whole step if necessary)

Beware Of These Deceiving Looking Diminished Intervals:

Any minor interval that has been flattened by another step becomes diminished and not, as you might be tempted, double-diminished or "double-minor".

Diminished Intervals

The middle staff has been included for completeness and to

illustrate the difference between double lowered minor intervals and lowered perfect ones

About Inverting Intervals:

So far all my examples have shown intervals moving upwards from a lower note to a higher note. Of course the opposite is just as common.
The same principles that we just talked about apply in both situations.
Inverting an interval simply means raising the bottom note or lowering the top note by 1 octave.

The result of this in terms of simple steps on the staff means:

  • A UNISON inverts to an OCTAVE and an OCTAVE to UNISON (1 - 8 - 1)
  • A SECOND inverts to a SEVENTH and a SEVENTH to a SECOND (2 - 7 - 2)
  • A THIRD inverts to a SIXTH and a SIXTH to a THIRD (3 - 6 - 1)
  • A FOURTH inverts to a FIFTH and a FIFTH to a FOURTH (4 - 5 - 4)
  • Note that each single inversion adds up to 9

When we add the modifiers, we get:

  • MAJOR inverts to MINOR and the reverse
  • PERFECT inverts to PERFECT and the reverse
  • AUGMENTED inverts to DIMINISHED and the reverse
Inverted Intervals with Modifiers

Compound Intervals

Any distance between notes greater than an octave is called a compound interval.
It is rare that the span between notes goes beyond 2 octaves, and naming these leaps is, compared to everything else, quite simple.

Here is how to deal with compound intervals:

  • Work them out like any other diatonic or chromatic interval but their name will include the numbers 9 to 15 (or higher if necessary)
  • If it makes it any easier, lower or raise the target note by an octave (in your mind), figure out the interval type, then add 7 to the number you come up with.
    (ex: a Dim6th becomes a Dim13th)
Examples of compound intervals

Perfect are 1, 4, 5 and 8,
+1 step they're Aug and -1 Dim;
2, 3, 6, 7 are Major and +1 Augmented,
but -1 they're Minor and Minus 2 Dim.

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