Generator

The tritone, resolving

Two dominant sevenths that contain the very same tritone, each resolving. Every voice is drawn moving to its nearest note of the target chord, and the two notes of the tritone are the ones that move by a semitone — both of them converging in the registers laid out here, since nearest-note motion decides the direction and the registers decide which note is nearest. What does not depend on the register is that the same two frequencies are led to different notes, which is why one tritone serves two keys.

Drawn above with its standard settings, which is almost never how an essay draws it: an essay states the numbers it is arguing about, so the figure a reader meets there is about that argument rather than about the drawing in general. Every option a placement passes is checked against the ones this function actually reads, because an option it does not read is silently ignored and the figure quietly draws what is above instead.

It makes a noise. 4 of its 4 placements carry sound, built from the same numbers as the drawing, offering these buttons: D♭7 → G♭ major, D♭7, the substitution → C major, G7 → A minor, G7 → C major, The bare tritone, twice, an A♭ German sixth → G major.

Called by 1 essay

the blast radius of changing it

Every interval, and what it becomes when it is turned over. Each interval within the octave paired with its inversion — the interval left when the lower note is raised by an octave. The two always add to twelve semitones, so exactly one interval can be its own inversion, and it is the one at six.

The interval that inverts to itself

Six is the only number that divides twelve into two equal halves, so the tritone is the only interval unchanged by being turned over. That symmetry is not a curiosity — it is why one tritone belongs to two dominant chords, and why they resolve to keys a tritone apart.

harmony · The triad

All figures · What can be heard