Sagittal notation

Sagittal notation is a musical notation system capable of notating almost any conceivable tuning. It was developed by Dave Keenan and George Secor with significant contributions from numerous others.

Flavors of Sagittal notation

Sagittal notation comes in two mutually compatible flavors.

Evo

The Evo flavor (short for "evolutionary", previously called "mixed") uses only single-shaft Sagittal symbols, e.g. ⁠ ⁠ ⁠ ⁠ ⁠ ⁠ ⁠ ⁠, alone or in combination with conventional sharps and flats and their doubles. Only the large variant of the double sharp ⁠ ⁠ (U+E47D) is considered to be stylistically-compatible with Sagittal symbols. Evo is much easier to learn, but it results in a greater number of symbols on the sheet, which can give it a more cluttered appearance, particularly with chords, and it may be confusing when two symbols alter the same note in opposite directions.

A sub-flavor of Evo is Evo-SZ (Evo with Stein-Zimmermann). This is where the arrow-like 11M up and down symbols ⁠ ⁠ ⁠ ⁠ are replaced by the Stein-Zimmermann semisharp ⁠ ⁠ and narrow reversed flat ⁠ ⁠. This should only be done when the 11M symbols notate exactly half the alteration of a sharp or flat. Similarly, the combinations ⁠ ⁠⁠ ⁠ and ⁠ ⁠⁠ ⁠ are replaced by ⁠ ⁠ and ⁠ ⁠. The narrow variants of the fractional flats ⁠ ⁠ (U+E284) and ⁠ ⁠ (U+E285) are preferred because they preserve the Sagittal principle that the visual size of a symbol should indicate the relative size of its alteration.

Revo

The Revo flavor (short for "revolutionary", previously called "pure") only requires one accidental per note. Revo therefore takes up less space on the sheet and presents a cleaner appearance, and it clearly indicates the direction of the overall alteration. It discards the conventional sharps and flats and their doubles and replaces them with these multi-shaft arrow-like symbols: ⁠ ⁠ ⁠ ⁠ ⁠ ⁠ ⁠ ⁠. Adding a sharp or flat to a Sagittal is achieved by adding two more shafts, e.g. ⁠ ⁠⁠ ⁠ becomes ⁠ ⁠ and ⁠ ⁠⁠ ⁠ becomes ⁠ ⁠. When the Sagittal part alters in the opposite direction to the sharp or flat part, the rules are not so simple, e.g. ⁠ ⁠⁠ ⁠ becomes ⁠ ⁠ and ⁠ ⁠⁠ ⁠ becomes ⁠ ⁠; one must simply learn these apotome complements.

Resources

Official site
Sagittal Forum
File:Sagittal.pdf – The original Xenharmonikon article (download: [ Sagittal.pdf])
Gift of the Gods: a Mythical introduction to Sagittal notation
spreadsheet-based calculator for Sagittal JI notation
Sagittal-SMuFL-Map, a table of every Sagittal symbol
Pain free guide to Sagittal by William Lynch
File:24 Edo.pdf – Sagittal notation guide for 24edo by William Lynch (download: 24_Edo.pdf)
Introductory examples by Hans Straub
Sagittal chord chart by Andrew Meronek

Notation software support

Sibelius

Sagibelius 2.0 - plugins for using Sagittal notation in Sibelius 4 and up. By Jacob Barton. Hosted on this wiki. Donationware.

Sagibelius_2.0.zip

Lilypond

Plugin for Sagittal notation in Lilypond by Graham Breed

MuseScore

Sagittal accidentals are available in MuseScore via the Bravura font which implements the SMuFL standard. They can be accessed by opening the Master Palette and finding them in the Symbols section at the end.