Updated April 2020.


Sad news: Our friend George Secor, who gave us the gift of Sagittal notation, passed away on the 2nd of March 2020, aged 76, after a long battle with cancer.


We have a beautiful new Sagittal SMuFL Character Map thanks to volunteer Douglas Blumeyer. Download the Excel or LibreOffice version below.


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.


*     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.


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


*     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.


*     Scala

*     MicroABC

*     Mus2


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


*     Keenan and Secor Honored (cached copy). It seems the gods have been having a bit of fun with us. Apparently we have been honored already! Although what kind of honor it is, when Keenan is described as "offensive" and Secor as "a rookie", I'm not sure. Not to mention that they got our first names wrong, and those photos don't really do us justice. Thanks to Aaron Hunt for bringing this extraordinary "coincidence" to our attention.