An app for visualizing consonance and dissonance

Download: iPad and Mac app via the Apple Store

The main screen of “A Glass Bead Game”

The graph
Each axis of the graph above represents the frequency of a musical tone across the span of two and a half octaves. The tick-marks along these axes represent one semitone of pitch change, and note names representing a diatonic scale in C is added for reference.

The horizontal and vertical lines of the graph represent intervals of a “just intoned” musical scale where the moving tone forms a consonance compared to a static drone tone, as is described in the page An Atlas of Consonance. The diamonds are points in the graph where the two moving tones and the drone all form consonances with each other. Every possible arrangement of 3 notes (a chord) is represented as a point on this graph.

The big red diamond represents middle C, and is the pitch of the drone. This is where the scales start as well. They have a range of one octave under the drone, and an octave and a half above the drone.

The top toggle to the right of the graph control the display of diamonds (this should usually be on). The Harmonics selector controls the number of harmonics in the musical tone used to calculate the scales that are shown on the graph. Higher numbers of harmonics make for more complex scales. Finally the View button rotates the graph in ways that may make more sense to you. Most screens are small enough that square makes the clearest display.

An Apple pencil produces the most controllable sound, but this is limited to the iPad. You can also use finger touch. A mouse is supported on the Mac. Tapping the screen starts the sound.

Audio output
When you tap on one of these diamonds you should hear these tones rendered by the app. If not you may need to adjust the volume on your device. You can enable or disable the drone and the two moving tones using the buttons to the right of the graph. Turning these on and off may make it easier to understand how the graph works. The “Use Internal Synth” button lets you disable the internal synth engine.
The internal synth is able to produce very accurate pitches to match scale intervals.

Accuracy

The pen on the iPad will produce the cost accurate and controllable experience. Larger screens will also allow more accurate control.
Snap
The “Snap” toggle turns on snapping pitch to the nearest scale interval. Turning this off allows you to play tones in the blank spaces between the diamonds. Moving in and out of consonance makes for an interesting and dynamic experience.

Pedal

The pedal toggle causes the musical tones to continue after the pen is raised or the mouse click is finished.

MIDI output
The app can also send MIDI data to a connected synthesizer, ideally a synthesizer that supports MIDI Polyphonic expression (MPE). The buttons to the side of the graph allow you to enable MIDI, MPE, and to select which midi output device you want to send MIDI data to. In the screenshot above the app is connected to a Eurorack MIDI interface module called “Univer Inter” which works well for me.

Be aware that your synth may not track pitch as accurately as the internal synth in the app. MPE is much better at tracking pitch than vanilla MIDI is but still may not be perfect. Having said that I’ve been surprised how accurate analog modules can be.

Tune MIDI

This button sends MIDI note on messages for middle C on MIDI channels 0 through 2. This is useful when you are setting up several oscillators to play the same pitch.

Test

The Test button sends a full range midi signal that you can use to confirm that your receiving module is set correctly. Usually MPE pitchbend should be set to 24 semitones. Vanilla MIDI usually tops out at 12 semitones, and if your settings in the app don’t enable MPE the graph will only work for an octave up and an octave down.