Perfect intervals

Intervals measure musical distance.

At bottom, they represent a frequency ratio. For instance, pretend you’re rotating a fan twice per second and someone next to you is rotating a fan once per second.

If you speed that up enough, we’ll exit the realm of rhythm and enter the realm of harmony, and you’ll hear an octave, because the frequency ratio of the octave is 2:1. So every time something vibrates twice as fast as something else, you’ll hear an octave.

Now the fifth happens when you rotate something 50% faster than something else, with a ratio of 3:2.

All of the intervals come in 2 different forms, harmonic and melodic. If you hear the 2 notes of the interval at the same time, it’s a harmonic interval, because it forms a harmony. If you hear the 2 notes one after the other, it’s a melodic interval, because it forms a melody. When melodic, it can either be ascending or descending.

Before we move on to other intervals, let me just give you this one piece of advice for finding 5ths quickly on the keyboard, since you need them a lot when building chords. A 5th, 83.3 % of the time, will end up on the same note color as its fundamental. The only fundamentals where the 5th ends up switching color are B and Bb. So if your note is called B or Bb, you should go from a white key to a black key, or vice versa. But any other note name will generate a 5th that is on the same note color. That, combined with the size of your hand, which (probably) has 5 fingers, gives you an automatic fifth, is much faster than counting 7 half steps.

All fifths land on the same note color as their fundamental, except for B♭ and B.

In the orchestra, all of the strings tune their instruments in ascending fifths. on a violin say, the lowest string is G, then D, then A then E. This is why you get this very open and airy sound when instruments are getting tuned at the beginning of a concert. Only the the double bass tunes its strings in leaps of 4ths.

The 4th, which has a ratio of 4:3, is the only interval missing to complete the set of perfect intervals. These intervals are called perfect because they don’t have a minor and a major version. They are set in stone, so to speak.

Let’s clear a confusion from the start. You don’t count intervals the same way you count half steps. When you count half steps, you count the distances in between the notes. But when you count intervals, you include the first and last note of the interval in your count. Intervals are inclusive: you include everyone involved. If there are 4 note names total in your interval, it’s a fourth. If there are 5 note names involved, it’s a fifth. That’s the best advice I can give you for intervals. Count the note names, and then, you can fine tune your answer based on the number of half steps.

If we zoom in and count the number of half-steps:

• Octave: 12 half-steps, just like the number of zodiac signs and the number of months in a year.
• Fifth: 7 half-steps, the number of divine perfection and the number of colors in a rainbow.
• Fourth: 5 half-steps, which feels a bit counterintuitive, but it is what it is.

As some of you might have noticed already, with C and G, you can get both a 5th and a 4th, it just depends on which note you put on top. That’s because these 2 intervals are inversions of each other.

These 3 intervals form the set of perfect intervals. If anyone is wondering who is this guy on the left, this is the unison. A unison is simply when 2 voices sing the same note. So one could say that the inversion of the octave is the unison, which is kind of the zeroth point of intervals.

Soundwise they are very consonant, open, somewhat cold. They are called perfect because they have a stable state that they are in most of the time. Debussy’s La Cathédrale Engloutie makes a great use of these open fifths.