Mode Rotation Calculator
The modes of the major scale are not seven different scales — they are one scale started in seven places. Say that as arithmetic and it generalises immediately: any sequence of steps adding to twelve has as many modes as it has degrees, unless the scale maps onto itself under rotation, in which case it has fewer. The whole-tone scale has six degrees and exactly one mode, and this shows you why.
What this generator does
Treats the scale as a cyclic sequence of steps and produces every rotation of it, giving each mode's step pattern, its degrees in semitones from the root, and its name where it has one. It then counts the rotations that reproduce the scale exactly, which is what decides how many modes are genuinely distinct.
How to use this tool
- Enter your scale as steps in semitones, adding up to 12.
- Press Work it out.
- Read every rotation with its steps and degrees.
- Read how many are genuinely distinct, and why.
Understanding the controls
- Scale steps
- The gaps between consecutive notes in semitones, separated by spaces or commas. They must add up to 12 so the scale closes at the octave — 2 2 1 2 2 2 1 is the major scale.
Common use cases
- Finding all the modes of an unfamiliar scale
- Understanding why the whole-tone and diminished scales feel rootless
- Checking that a scale you have invented adds up to an octave
- Seeing which rotations of a scale have names and which do not
- Teaching modes as rotation rather than as seven things to memorise
How this generator works
Starting a scale on its second degree and continuing to the octave gives the same notes in a different order, which is exactly a rotation of the list of steps. Every rotation is a mode. Where a scale maps onto itself under some rotation — as the whole-tone scale does under every rotation, and the octatonic under every second one — the modes repeat, and the number of distinct ones is the number of degrees divided by the number of symmetries. Before display every mode is confirmed to be a genuine rotation rather than a rearrangement, each is checked to span exactly twelve semitones, its degrees are re-derived from its own steps, and the symmetry count is recomputed and confirmed to divide the degrees exactly.
Randomness and fairness
Nothing here is random. A scale has exactly one set of rotations, computed rather than sampled — the scale and melody generators are the ones that produce something new.
For how randomness is produced across the whole site, see how Generate Random works.
Limitations and good to know
- Only twelve-tone scales are handled, since the steps must add to twelve. Microtonal and non-octave scales are a different problem.
- Names are given for the modes in common use; most of the hundreds of possible scales have no name and that is not a fault.
- Rotation says nothing about which mode sounds like what — that depends on harmony and emphasis rather than on the intervals alone.
- Enharmonic spelling is ignored: the degrees are given as semitones and as sharps, which is not always how a musician would write them.
Privacy and your data
The calculation runs in your browser and the scale you enter is never transmitted, stored or included in analytics.
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