Well tempered

5 limit

Pitch Fever

Exploring the roots of harmony

Compare the sounds of different scales by clicking and dragging in the white area below. Double click to keep playing a note (you can drag it around), and click it again to stop it. Explore how pitch is built up into scales with the controls on the left.

Tag and drag in the white area below to listen. Explore how pitch is built up into scales with the controls on the left.

I had some early experience with the problems of a well-tempered scale. Within a few months of learning guitar, it seemed some chords just didn't sound good unless the guitar was tuned especially for them. This got me interested in the way harmonies and scales are constructed from pitches and frequencies.

In short, harmonies are groups of notes that sound good together, and they tend to be based on simple fractions. Scales built on those simple fractions end up having combinations where the notes collide and don't sound as nice. A well tempered scale compromises on harmony, but avoids the nastiest collisions.

But what do they really sound like? That's what this page is for. By clickingtouching and dragging in the white area, you can hear the pitches in each scale. Cross from top to bottom to hear the same note from the different scales. As you play, you can see the shape of the combined frequencies: consonant harmonies tend to have simpler, symmetrical patterns that repeat quickly.

You can choose the scale by choosing "Just" or "Well-tempered" on the left. Toggle "Chromatic" to decide between do-re-mi-fa-so-la-ti-do or a twelve note scale. Choose between two different types of just intonation by selecting "Pythagorean" or the classical "5-limit", and transpose them to different keys. Comparing the same scale transposed reveals some particularly jarring collsions. Or explore the ratios that drive harmony by selecting "Fractions", and set how many divisions there will be. Or you can just cut loose by selecting "Free", and watch the sine wave at the top respond.