Scale explorer

A scale is the set of pitch classes a piece of music draws on, numbered from the tonic as scale degrees. Choose a tonic and a scale or mode, see the same set on a pitch-class circle and on a keyboard, play it in equal temperament or just intonation, and watch a live chromagram of what you hear.

Scale
Tuning:

Choose Custom in the menu, then click positions on the circle to add or remove pitch classes; the tonic always stays. Note names use sharps throughout.

The circle is the chromatic clock: 12 pitch classes with C at the top, the tonic in orange, and the scale's members joined into a shape. Moving the shape round the circle changes the tonic; changing the shape changes the mode. Click a position to hear that pitch class. The chromagram beside it uses the same twelvefold space: its 12 bars are the pitch-class energy of the sound the app is making right now, measured from its own output and folded into one octave, as the chapter describes.

Two octaves from C4 (261.6 Hz) to C6. Highlighted keys belong to the scale, with the degree printed on the key; the tonic is orange, and the note sounding now is yellow. Click a key to hear it in the current tuning.

Degrees

Semitones and cents are measured from the tonic, and the frequency is that of the degree in the octave above the tonic shown on the keyboard. In just intonation each degree sits at a small whole-number ratio to the tonic; the last column says how far that is from the equal-tempered degree, positive meaning sharper. The diatonic degrees take the 5-limit ratios 1/1, 9/8, 5/4, 4/3, 3/2, 5/3 and 15/8; the chromatic degrees take 16/15, 6/5, 45/32, 8/5 and 9/5, the same ratios as in the Interval lab.

Things to try: compare Lydian with major and listen for the one degree that differs. Step through the seven modes with the same tonic and watch which positions on the circle switch on and off. Play the major pentatonic over a drone and hear that no note clashes. Keep the drone on, play the major scale in equal temperament and then in just intonation, and listen to the third: the just third locks with the drone, the equal-tempered one beats gently. Watch the chromagram while the drone plays: the tonic and its fifth carry most of the energy even though the melody visits every degree.