By the way, anyone can edit a copy of the Bravura font
, to add whatever Sagittal combinations ("ligatures" in font jargon) you need, using the free cross-platform font-editing program called FontForge
. FontForge is the work of one man, George Williams, who deserves some kind of award for it. Its graphical user interface is one of the most elegant and consistent I have ever used, and it is well documented. But even so, it does take some time to get up to speed with how fonts work.
All of SMuFL
is in what is called the Unicode Private Use Area from U+E000 to U+F8FF because SMuFL has no official standing within Unicode
, as yet. The Sagittals go from U+E300 to U+E41F (288 code-points, not all of them occupied). In Mus2
these appear in ranges 455 and 456. The SMuFL committee has set aside a sort of even-more-private-use area within the Private Use Area, for non-SMuFL ligatures and stylistic variations, from U+F400 to U+F8FF (1280 code-points). So that is where any multi-Sagittal ligatures should go. The Bravura font already uses 405 of these, from U+F400 to U+F595, and may use more in future. So I suggest starting the multi-Sagittals at U+F5E0.
[Edit: I originally wrote: That will give us 800 code points for the following 80 combinations of primes above 3. We only need to consider primes above 3 because prime 2 is the octave, and prime 3 is taken care of by the nominals, sharps and flats. But we need 10 code-points for each combination of primes below, because each can appear with double-flat, flat, sharp and double-sharp as well as appearing alone (5 combinations) and each of these will be accompanied by its inverse.]
That will give us 800 code points. This allows for the following 80 combinations of primes above 3, and 20 more that might be found useful in future (100 combinations). We only need to consider primes above 3 because prime 2 is the octave, and prime 3 is taken care of by the nominals, sharps and flats. But we need 8 code-points for each combination of primes, because each can appear alone, subtracted from sharp, added to sharp and subtracted from double-sharp (4 combinations) and each of these will be accompanied by its inverse (8 combinations).
A simple way of enumerating the combinations of primes, in such a way that popular combinations tend to come before less popular combinations, is to rank them according to a weighted sum of the absolute values of the exponents of the primes, where the weight for each prime-exponent is the prime itself. Or putting it another way: When the ratio is expressed as its prime factorisation (as they are below), replace all multiply and divide signs by plus-signs to obtain the rank. When several ratios have the same rank, list them in order of prime limit, and when they have the same prime limit list division before multiplication. It's remarkable how well this matches the ranking obtained from the Scala archive statistics
The last few are incomplete in the sense that there may be other combinations with the same rank, however they are complete in the sense that all ratios which are more popular than prime 37, according to the Scala archive stats, are included.