Macrotonal Tuning System

Microtonal music divides the octave into steps smaller than the standard semitone, giving quarter-tones, eighth-tones, and beyond. Macrotonal music does the opposite: its basic step is larger than a semitone. Rather than slipping between the keys, the scale strides across them.

In this system each step is 1¼ semitones. That is 125 cents, or five quarters of a standard semitone. The ratio 5/4 describes this directly: five pitch octaves are compressed into four keyboard octaves, so every key you play sounds a proportionally wider interval than it would in standard tuning. Four physical octaves on the keyboard span five actual octaves of pitch space, and that compression ratio gives the system its name.

Fig. 0: Key scaling ratios. Click any line on the graph to hear that scale on the keyboard. The teal 5/4 line is the Macro system: four physical octaves span five octaves of pitch space.

The system divides 1500 cents (an octave plus a minor third) into twelve equal steps of 125¢. Each step is exactly five quarters of a standard semitone, which gives the system its working name, 5/4: four macrotonal degrees span five semitones. The grid therefore realigns with standard tuning at every perfect fourth (500¢), and in between, every pitch still lands on the 25¢ eighth-tone grid, so the whole system can be written with ordinary accidentals plus three small markings.

It is macrotonal twice over: the step is wider than a semitone, and the cycle is wider than an octave. Octave equivalence is abandoned; what repeats instead is the 1500¢ cycle. The intervals that survive near just intonation (the fourths) anchor the harmony, while the rest sit deliberately between the cracks, close enough to familiar intervals to beat against them. That interference is the music, and the mark.

Fig. 1: The 100¢ grid (above) laid against the 125¢ grid (below). The two coincide at 0, 500, 1000 and 1500¢: the stacked-fourth skeleton, marked red. Every other degree drifts from its nearest standard pitch by +25, −50 or −25 cents. Tap a degree to hear it against the root.

Degrees are numbered 1–12 from the root. Node colours follow the notation code of §04: the dashed triangle joins the red degrees 1 → 5 → 9, the cycle of fourths. Select a degree to hear it against the root.

Every degree is written as its nearest standard pitch plus one of four adjustments, each assigned a fixed colour. At the exact quarter-tone midpoint (degrees 3, 7 and 11) the upper neighbour is always taken and flattened; the system never uses a quarter-sharp.

Because 125¢ advances the offset by +25¢ (mod 100), the colour of a degree is simply its position mod 4: the code cycles red → yellow → green → blue every four steps, and the red degrees are exactly the fourth-cycle of §03.

Fig. 2: The colour cycle across one full cycle of degrees.

One consequence does most of the practical work: since octaves and all transposition modes shift the result by a whole number of semitones, the adjustment (and therefore the colour) is fixed by the input note alone. C is always red, C♯ always yellow, D always green, D♯ always blue, in every octave and every mode. This single invariant is what lets the MuseScore colour plugins, the parts, and the rehearsal tools stay consistent across the whole ensemble.

Scores and MIDI are written chromatically: each written semitone is one degree. Play a chromatic scale and the macrotonal scale sounds; a written major third sounds a pure fourth; a written octave sounds the 1500¢ cycle. The table below converts any written note to its sounding pitch and marking.

The seven transposition modes shift the sounding result by a fixed standard interval, placing material in the right register for each instrument. Because the shift is a whole number of semitones, markings and colours are untouched; the input note still decides everything.