Prime Period Diacritics — Overview
Prime Period Diacritics (PPD) is a standalone diacritic system for marking sub-period positions on any base figure, derived from PPT's prime family structure.
Prime Period Diacritics
What Prime Period Diacritics is
PPD is a standalone diacritic system for marking sub-period positions on any base figure. It is derived from PPT’s prime family structure and is applicable wherever a period needs to be subdivided — pitch notation, rhythmic duration markers, amplitude or effect envelopes, or any parameter that varies across a repeating cycle.
It is used by Uniform Solfège as its microtonal extension layer, but is specified independently so it can be applied to other notational contexts.
Core principle
Any period has a base position (0) and an Axis position (+1/2, the point equidistant between adjacent bases). Between these two poles, positions are defined by prime-ratio subdivision. Diacritics mark deviation from base within the range (−1/2, +1/2], where −1/2 is excluded by periodicity (it is equivalent to the prior period’s +1/2).
The prime families
| Family | Prime (p) | Unique forms needed | Positions |
|---|---|---|---|
| Du | 2 | 1 | +1/2 (Axis only) |
| Tri | 3 | 1 (+mirror) | ±1/3 |
| DuTri | 2×3 | 1 (+mirror) | ±1/6 |
| Qui | 5 | 2 (+mirror) | ±1/5, ±2/5 |
| Sep | 7 | 3 (+mirror) | ±1/7, ±2/7, ±3/7 |
| Undec | 11 | 5 (+mirror) | ±1/11 … ±5/11 |
Note: DuTri is a fractal compound — Du applied within a Tri segment — not a base prime. The naming convention Du[Family] generalises: DuQui = ±1/10, DuSep = ±1/14, etc. Glyph forms for non-Du fractal compounds are reserved for future extension; the principle is defined here but glyphs are not yet specified.
Axis-proximity design principle
When a position’s proximity to Axis (1/2) exceeds its proximity to Base (0), the diacritic should visually inherit from the Axis glyph form rather than the Base glyph form.
Threshold: position > 1/4. This applies explicitly in Sep (+3/7 ≈ 0.429) and Undec (+4/11 ≈ 0.364, +5/11 ≈ 0.455).
Fractal Du depth (Du family only)
The Du diacritic (Axis stroke) supports fractal subdivision to four levels, encoding depth via small triangle offsets on the Axis stroke itself:
| Depth | Position | Fraction |
|---|---|---|
| 1 | ±1/2 | Axis |
| 2 | ±1/4 | Du of Axis |
| 3 | ±1/8 | Du of Du of Axis |
| 4 | ±1/16 | Du of Du of Du of Axis |
Fractal depth for non-Du families is theoretically defined but not currently specified in glyph form.
See Glyph Forms for visual specifications.