Preface

The word
"sagittal" (pronounced "SAJ-i-tl" /ˈsædʒ ɪ təl/) means
"arrow-like". Think of Sagittarius the archer; the centaur with bow
and arrow that the ancients saw in the night sky.

The
Sagittal notation system is a comprehensive system for notating musical pitch
in all possible scales and tunings - a universal set of microtonal accidentals,
equally suited to extended just intonation, equal divisions of the octave (or
of any other interval), or any of the non-just non-equal "middle
path" tunings or temperaments. It is called Sagittal because, you guessed
it, it uses various arrow-like symbols, pointing up or down to indicate raising
or lowering of pitch.

Sagittal
was developed by George Secor and myself, with a
major early contribution from Gene Ward Smith, and in cooperation with many
others on the Yahoo Groups *tuning* and *tuning-math*.

At some
stage during the development of the notation, I suggested to George that we
should provide an entertaining introduction by means of some mythology.

George readily
agreed to write this mythology, with the help of his daughter Samara, and it
appears below for your enjoyment.

Dave
Keenan, 2-Jul-2004

Read
a mythical introduction to the Sagittal
notation.

Or
read the Xenharmonikôn article
(pdf) introducing the Sagittal notation.

Register
with the Sagittal forum for news,
support and discussion.

In
cooperation with Steinberg's SMuFL (Standard Music Font Layout) initiative, we have
devised a font mapping for Sagittal, that makes it easier to find the more
common symbols. View the **Sagittal-SMuFL Character
Map** online as a PDF, or download it as
a spreadsheet in either Excel or LibreOffice format.
You must install the *Bravura Text*
font before the spreadsheets will display the correct symbols. The character
map tabulates an enormous amount of information about the complete set of
Sagittal and Sagittal-compatible accidentals. Many thanks to Douglas Blumeyer for all his hard work in compiling and presenting
this information.

The
Sagittal symbols are now part of Steinberg's free *Bravura* and *Bravura Text* fonts.

For
those of you who prefer mixed Sagittal but are frustrated by the limitations of
current notation software when it comes to compound accidentals, we have
created the *BravuraMSS* font. MSS stands for Mixed Spartan
Sagittal. This is version 1.18 of the Bravura font with the multi-shaft Spartan
Sagittal accidentals replaced by the corresponding mixed-Sagittal combination
of accidentals, as single characters. And they have also been mapped to all the
letters of the alphabet, lower and upper case. The natural is mapped to zero.

See
the Sagittal notation on the staff as you hear the chords played, in Andrew Meronek's Sagittal
chord list videos.

You can read about the Prime
Factor Sagittal Just Intonation notation.

If you want to use one of Sagittal's standard JI notations (and of course we recommend following our standards!)
then you can just input your JI pitches into this spreadsheet and it will calculate which nominal (ABCDEFG) and accidental(s) you should use to notate each of them.
The results are automatically shown with both Evo flavor and Revo flavor as options, and at each precision level (Medium, High, Ultra, and Extreme — generally choose the simplest one that doesn't unwantedly conflate two of your pitches).
For more information on the precision levels, here's a chart showing the accidentals for the various precision
levels of Single-Sagittal Just Intonation notation. Please note
that the lower two levels are considered sufficient for most mortals. And note
that the Olympian level is out-of-date. It needs to be updated to use breves on the left instead of accents on the right.

Read
about Sagispeak, a tuning independent, and language
independent, way of naming and pronouncing the Sagittal symbols.

You
can hear the notation example from the top of this
page played in various tunings. At this stage they are in MIDI files so the
tuning accuracy and timbre is dependent on JavaScript MIDI playback.

Graham
Breed has done some brilliant work to let you use Sagittal in Lilypond.
Visit his website to
learn how.

Download
Jacob Barton's amazing Sagibelius 2.0 scripts
that let you use Sagittal symbols with the Sibelius music notation software. It
wasn't easy, but he found a way. The zipfile includes
a modified version of the Sagittal-2 font. The documentation and examples will
be educational even if you're not using Sibelius.

See
how Prent Rodgers has used Sagittal to notate the 15-limit tonality diamond.

While
the *Bravura* font can be used with
notation software such as Dorico, Sibelius, Finale or
Lilypond, just like any other notation font, the
following software products provide explicit support for the Sagittal system.

What the sagittal symbols really
represent. This will be of interest to anyone implementing software to play
sagittal notations.

Check out
*The Sagittal Songbook*, including 48 pieces for 1-5 voices each,
written by 15 different composers in a variety of tunings, edited by Jacob Barton.

A farewell to George Secor, our friend who gave us the gift of Sagittal notation

Play George Secor's
2009 piece *Coming on Clouds*

It's in a 16-tone subset of his 29-tone high-tolerance temperament, a 13-limit temperament
he devised in 1975.

Updated September 2024.