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 any sagittals that are notating exactly half the alteration of a sharp or flat (most often ⁠ ⁠ ⁠ ⁠) are replaced by the Stein-Zimmermann semisharp ⁠ ⁠ and narrow reversed flat ⁠ ⁠, and the corresponding combinations (most often ⁠ ⁠⁠ ⁠ 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.

Scala

Sagittal notation is available in Scala.

Dorico

Because Dorico is built by Steinberg Media, the same company that maintains the SMuFL standard, it should support Sagittal.

Scores in Sagittal notation

• The Sagittal Songbook
  • One for All
  • Land Urchin
  • Clouds
  • Prayer of Thanks

• Sunday Pipes in 22tET by Mats Öljare
• Tibia in 22tET by Paul Erlich (Listen). Sagittal score in F||\ or in G (contains errors in measures 9, 19 and 20)
• On the Enharmonic Tetrachord (from Suite, Op. 62), in 22tET, by Ivor Darreg. Originally printed in the Spring 1975 issue of Xenharmonikon in quarter-tone notation. Transcribed to Sagittal by Juhani Nuorvala.(Listen)

Gallery

Spartan single-shaft

• 
  5:7 kleisma up
• 
  5:7 kleisma down
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  5 comma up
• 
  5 comma down
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  7 comma up
• 
  7 comma down
• 
  25 small diesis up
• 
  25 small diesis down
• 
  35 medium diesis up
• 
  35 medium diesis down
• 
  11 medium diesis up
• 
  11 medium diesis down
• 
  11 large diesis up
• 
  11 large diesis down
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  35 large diesis up
• 
  35 large diesis down

Spartan multi-shaft

• 
  Sharp 25S-down
• 
  Flat 25S-up
• 
  Sharp 7C-down
• 
  Flat 7C-up
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  Sharp 5C-down
• 
  Flat 5C-up
• 
  Sharp 5:7k-down
• 
  Flat 5:7k-up
• 
  Sharp
• 
  Flat
• 
  Sharp 5:7k-up
• 
  Flat 5:7k-down
• 
  Sharp 5C-up
• 
  Flat 5C-down
• 
  Sharp 7C-up
• 
  Flat 7C-down
• 
  Sharp 25S-up
• 
  Flat 25S-down
• 
  Sharp 35M-up
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  Flat 35M-down
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  Sharp 11M-up
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  Flat 11M-down
• 
  Sharp 11L-up
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  Flat 11L-down
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  Sharp 35L-up
• 
  Flat 35L-down
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  Double sharp 25S-down
• 
  Double flat 25S-up
• 
  Double sharp 7C-down
• 
  Double flat 7C-up
• 
  Double sharp 5C-down
• 
  Double flat 5C-up
• 
  Double sharp 5:7k-down
• 
  Double flat 5:7k-up
• 
  Double sharp
• 
  Double flat

Athenian extension single-shaft

• 
  7:11 kleisma up
• 
  7:11 kleisma down
• 
  17 comma up
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  17 comma down
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  55 comma up
• 
  55 comma down
• 
  7:11 comma up
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  7:11 comma down
• 
  5:11 small diesis up up
• 
  5:11 small diesis up down

Athenian extension multi-shaft

• 
  Sharp 5:11S-down
• 
  Flat 5:11S-up
• 
  Sharp 7:11C-down
• 
  Flat 7:11C-up
• 
  Sharp 55C-down
• 
  Flat 55C-up
• 
  Sharp 17C-down
• 
  Flat 17C-up
• 
  Sharp 7:11k-down
• 
  Flat 7:11k-up
• 
  Sharp 7:11k-up
• 
  Flat 7:11k-down
• 
  Sharp 17C-up
• 
  Flat 17C-down
• 
  Sharp 55C-up
• 
  Flat 55C-down
• 
  Sharp 7:11C-up
• 
  Flat 7:11C-down
• 
  Sharp 5:11S-up
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  Flat 5:11S-down
• 
  Double sharp 5:11S-down
• 
  Double flat 5:11S-up
• 
  Double sharp 7:11C-down
• 
  Double flat 7:11C-up
• 
  Double sharp 55C-down
• 
  Double flat 55C-up
• 
  Double sharp 17C-down
• 
  Double flat 17C-up
• 
  Double sharp 7:11k-down
• 
  Double flat 7:11k-up