The Idea Behind SWING ARC
SWING ARC is a visual metronome that represents the time between Beats as continuous motion.
During development, I began experimenting with OFFSET: keeping the Beat and Subdivision timing the same while shifting their temporal relationship to the continuous motion.
A Simple Pattern
At certain OFFSET positions, a very simple timing structure appeared.
With straight eighth notes:
Beat → midpoint → Subdivision → midpoint → next Beat
These positions are evenly spaced.
Expressed as phase:
0° → 90° → 180° → 270° → 360°
In SWING ARC, two representative positions appear in the straight case: −25% and −75%.
These are not two different rules.
−25% corresponds to the midpoint on the Beat → Subdivision side.
−75% corresponds to the midpoint on the Subdivision → next Beat side.
So even with the same Beat and Subdivision timing, different candidate OFFSET positions appear depending on which side of the timing relationship is treated as the reference for the continuous motion.
This does not mean that 90°, 270°, −25%, or −75% have been proven to be naturally special positions for human rhythm perception.
They appear simply because the neighboring timing intervals are being divided in half.
What Changes with Swing?
Things become more interesting when Swing is introduced.
Swing moves the Subdivision.
If the important feature were a fixed phase such as 90° or 270°, the preferred position should stay in the same place.
But if the important feature is the relationship between the Beat and Subdivision, then the midpoint should move with the Subdivision.
For the Subdivision → next Beat side, for example:
- Straight eighth: Subdivision at 50% → midpoint at 75%
- Triplet swing: 66.7% → 83.3%
- Swing at 75%: 75% → 87.5%
This gives a simple testable prediction: if the reference is relational rather than fixed, changing Swing should move the relevant position.
Different Rhythms, Different Relationships
There may also be more than one useful Subdivision–Beat relationship within a rhythm.
In sixteenth-note grooves, for example, the most relevant relationship may sometimes involve the last Subdivision before the next Beat.
With 60% sixteenth-note Swing, that final Subdivision falls at about 80% of the Beat interval, placing its midpoint with the next Beat at 90%.
This is the current candidate position used for the Second Line FEEL preset.
With straight sixteenth notes, the final Subdivision falls at 75%, giving a midpoint of 87.5%. This is the current candidate used for the Funk preset.
These are not intended as definitions of Funk, Second Line, Jazz, or any other musical tradition.
They are working hypotheses generated by the model.
The Idea in One Sentence
The central idea is simpler:
People may organize musical time not only around discrete Beats and Subdivisions, but also around relative timing positions within continuous motion.
What About Body Movement?
The same question may apply to body movement.
When you walk, what moment do you actually experience as the rhythmic reference?
The instant the foot touches the ground?
The moment it leaves the ground?
The highest or lowest point of the body?
Even at the same tempo, rhythm may be experienced differently depending on which part of the movement cycle is being used as the reference.
What We Know — and What We Don’t
Existing research on rhythm, coordination, entrainment, continuous movement, and anticipatory timing is broadly compatible with this possibility.
But it does not yet establish that the specific midpoint positions predicted by SWING ARC are perceptually or physically important.
SWING ARC is not claiming that groove has been reduced to mathematics.
It is not claiming that a particular OFFSET defines a genre.
And it is not claiming that mathematical midpoints automatically become meaningful perceptual states.
The claim is much smaller:
During development, a simple and testable timing relationship appeared.
SWING ARC provides a way to see it, move it, and experience it directly.
Whether that relationship turns out to have broader perceptual, bodily, or musical significance is still an open question.