Updated Dec-2019.


On loading this page we used to play George Secor's 2009 piece Coming on Clouds
in a 16-tone subset of his 29-tone high-tolerance temperament, a 13-limit temperament he devised in 1975.
In these days of smart phones it would be rude to play it automatically,
but by popular request you can still hear it by hitting the play button below.


*     Preface


The word "sagittal" (pronounced "SAJ-i-tl") 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 Xenharmonikon article (pdf) introducing the Sagittal notation.


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


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


*     Here's a chart showing the accidentals for the various levels of Just Intonation notation available in Sagittal. Please note that the lower two levels are considered sufficient for most mortals.


*     In cooperation with Steinberg's SMuFL (Standard Music Font Layout) initiative, we have devised a version 3 font mapping for Sagittal, to make it easier to find the more common symbols. Here is the Sagittal section of the SMuFL 0.9 documentation showing the new mapping. Sagittal is now released under the SIL Open Font License. New users of Sagittal should not use the version 2 Sagittal fonts below, but should download Steinberg's free Bravura font, which contains the Sagittal symbols with the version 3 mapping (and many other music symbols).


*     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 modified Bravura to become the free BravuraMSS font. MSS stands for Mixed Spartan Sagittal. This is a version of the Bravura font where the multi-shaft Spartan Sagittal accidentals have been replaced with the corresponding mixed-Sagittal compound accidentals, as single characters. And they have been mapped to all the letters of the alphabet, lower and upper case. The natural is mapped to zero.


*     Download the free Sagittal-2 TrueType font (.ttf). Install it by dragging it to your Fonts folder or control panel.


*     Or download the free Sagittal-2 PostScript font, either as a single OpenType file (.otf), or as separate Type 1 binary outlines (.pfb) and metrics (.afm) files. You may need to right click and choose "Save Link As ...".


*     View the Sagittal-2 Character Map online as a PDF or download it as a spreadsheet in either Excel or OpenOffice format. Thanks to Herman Miller for the OpenOffice conversion. You must install the Sagittal-2 font before the spreadsheets will display the correct symbols. This tabulates an enormous amount of information about the complete set of unaccented Sagittal (and other) 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. Updated to use the Sagittal 2.0 font mapping and to allow most of the Athenian subset. The zipfile includes a modified version of the 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.


*     See Andrew Meronek's Sagittal chord lists.


*     While the Sagittal font can be used with notation software such as 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.