*     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. ... Or at least that's how it seemed to me at the time.


We would like to thank the following for their suggestions and/or encouragement during the development of the Sagittal notation system so far, (in alphabetical order): Gabor Bernath, Graham Breed, Paul Erlich, Mark Gould, Kraig Grady, Aaron Hunt, Marc Jones, Carl Lumma, Herman Miller, Alison Monteith, Joe Monzo, Ted Mook, Manuel Op de Coul, Joseph Pehrson, Keenan Pepper, Johnny Reinhard, Joel Rodrigues, Klaus Schmirler, Margo Schulter, Samara Secor, Gene Ward Smith, Dan Stearns, Jon Szanto, Robert Walker, Robert Wendell and Danny Wier.


We would also like to thank the following, who didn't know they were contributing to Sagittal at the time (in chronological order of their contribution): Pythagoras of Samos, Archytas of Tarentum, Didymus the musician, Claudius Ptolemy, Robert H M Bosanquet, Hermann von Helmholtz, Alexander Ellis, Richard Stein, Mildred Couper, Ervin M Wilson, Ivor Darreg, Ezra Sims, Gardner Read, Paul Rapoport and Daniel Wolf.


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. ... Or at least I thought that was my idea.


Anyway, George readily agreed to write this mythology, with the help of his daughter Samara, and it appears below for your enjoyment. But I'm wondering ... has anyone actually seen George Secor lately? ;-)


Dave Keenan, 2-Jul-2004



*     Read a mythical introduction to the Sagittal notation.


*     Or read the Xenharmonikon article (pdf) introducing the Sagittal notation.


*     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 use the free Bravura font, which contains the Sagittal symbols with the version 3 mapping (and many other music symbols).


*     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 your sound card.


*     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 charts.


*     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. 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. Cached copy.



The music that plays on loading this page is George Secor's 2009 piece Coming on Clouds, in a 16-tone subset of his 29-tone high-tolerance temperament, a 13-limit low-error temperament he devised in 1975.

<bgsound src="http://xenharmony.wikispaces.com/space/showimage/Clouds-29HTT4.mp3">