Following are four examples of the ear-training intonation exercises found in The Intonation Tutor.  Click on the links to download these audio tracks as MP3 files.  You may print this page to save the printed music for study and play-along.

1. Example of an equal-tempered Major 3^rd and a just-tuned major third.

    The interval pictured above , the major third, can be viewed as individual notes, f and a, with their individual sets of partials, as pictured in the example below.  (The open notes indicate the notes of the interval and the solid notes depict the upper partials.)  The two notes of the interval have a common partial at a².

    The "beating" of the equal-tempered major third takes place at this common, or intersecting partial. 

    When the major third is just-tuned, the partials match in frequency and the beating is eliminated, resulting in the pure-sounding just interval.

2. The Bb tuning reference note.

3. The C-major scale (for play-along).

    4.  Trio example: Play Part 1 with as the audio file plays parts 2 and 3.

The Intonation Tutor