For those of you who, like me, are interested in microtonal music, figuring how how to communicate it effective can be the biggest challenge.
Microtonal music, as the term is typically used, is really any pitch organization besides the 12 note-per-octave equal temperament that modern pianos are set up to use. This includes other equal temperaments, just intonation-based scales, mean-tone temperaments, and virtually anything else, too. As such, it is really way too vague of a term for productive discussion. When I end up talking about such music, I never refer to ‘microtonality’ any more, but to the more specific terminology: 31-Equal Temperament, or 5-limit Just Intonation, or some other more descriptive term.
In musical terms, usage of any of the microtonal systems has a very obvious benefit: to expand the possible color palette with which we composers and performers can create music; to make the music a lot more potentially interesting to listen to. The tricky thing is in how to communicate it between musicians. In particular, notating the various forms of microtonality can be a real challenge.
I have had to do a bit of research about this, because I am interested in the specific form of microtonality called just intonation. One of the first people to come up with an elegant way of incorporating the harmonic language of just intonation into readable notation was Ben Johnston, whose notation system of additional accidentals bears his name: Johnston Notation. It really is a pretty good system, and has been the basis for several other systems that came after it. The biggest problem with his system is the manuscript: he uses separate accidentals for each change in pitch that may affect a note, which can sometimes end up producing some rather complex accidental-chains before a note; and some of the accidentals actually are not very easy to read on a 5-line staff, the ‘+’ and ‘-‘ in particular. It turns out that this problem between precision and legibility is a pretty tough problem to solve.
It is not a problem that I have to solve by myself, however. After a bit of looking around (in truth, a couple of years) I believe that the team that produced Sagittal notation has come up with the best solution I’ve seen between precision and legibility. Tuning purists will say that these two systems have a major difference in how they assume the 5-line staff is organized. Johnston Notation assumes a 5-limit C major scale, and Sagittal notation assumes a Pythagorean major scale. This can produce some differences in when a certain type of accidental (representing the Syntonic Comma) is used in each system, but in my humble opinion this is really not an important difference. Both scales work just fine, and roughly equally well. The best argument I’ve seen over whether to use the 5-limit or the Pythagorean major scale is not the usage of accidentals, but the more regular spacing of whole and half steps in the Pythagorean version, which actually may produce some benefits in dealing with complex enharmonics.
The major difference, however, is simply how the accidentals are written on the staff. Whereas Johnston notation uses a different accidental for every pitch adjustment and accidentals in front of a note are added together, Sagittal uses a system of vertical arrows and arrow parts to represent combinations of pitch adjustments, combining them into exactly one accidental per note. Because none of the parts of their accidentals are horizontal to the lines of a staff, they are much more legible, and they spent an incredible amount of time refining the representation of the different parts of the symbols to be as clear as possible in visually representing how much of a pitch change the accidental represents.
For more information on the Sagittal notation system, visit their website. My preference for this system is with how it is useful in notating just intonation, but it can be applied to many other forms of microtonality as well. Sagittal was developed by George Secor and Dave Keenan.