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Ear Training & Interval Arithmetic

Ear Training is learning to recognize what we are hearing. There are generally two skills to hone:

Absolute Pitch - the recognition of individual Notes by name (all 12 of them); because they are literally different Frequencies, it is similar to distinguishing one Hue from another (e.g.: unless one is color blind, Red is noticeably different from Green).

Relative Pitch - the recognition of the Intervals between Notes, of which there are two types:

1. Melodic Intervals - the relationship between two consecutive Notes

Did it go from low-to-high (Ascending), or from high-to-low (Descending)? In other words, did the following Note shift up or down in Pitch from the last, and if so, by how much (a 2nd, a 3rd, etc.)?

2. Harmonic Intervals - the relationship between two simultaneous Notes

What is the quality (Major or minor, Perfect or diminished) that they make?

If you play an instrument, learning to recognize any Interval up or down from any Note is helpful for many reasons, including Ear Training. A good way to learn this is through what we will call "Interval Arithmetic".

First, learn to quickly recognize these four Intervals:

Half-Step
Whole-Step
Octave
Perfect 5th

On a piano, Half-Steps and Whole-Steps are simple:

Image adapted from one in the book Everything You Need To Know To Play The Piano Or Keyboard by Karen Ramirez

Whole-Steps are shown in Green; Half-Steps are shown in Orange.

A Half-Step is from one key to the next key with no key in-between. A Whole-Step is from one key to another key with one key in-between. They may be either white keys or black keys.

If there is ever an occassion in which you have to count Half-Steps and Whole-Steps, count along the top of the keys where they are all about the same width, instead of counting from key-to-key as you play them. However, rather than counting out Half-Steps or Whole-Steps each time that we want to know a larger Interval, we can combine the four Intervals mentioned above in the following ways:

Interval Formula
Unison (P1) N/A
minor 2nd (m2) Half-Step
Major 2nd (M2) Whole-Step
minor 3rd (m3) Whole-Step + Half-Step
Major 3rd (M3) Whole-Step + Whole-Step
Perfect 4th (P4) Perfect 5th - Whole-Step
diminished 5th (dim5) Perfect 5th - Half-Step
Perfect 5th (P5) Memorize
minor 6th (m6) Perfect 5th + Half-Step
Major 6th (M6) Perfect 5th + Whole-Step
minor 7th (m7) Octave - Whole-Step
Major 7th (M7) Octave - Half-Step
Octave (P8) Memorize