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.

Rank Ratio

----------------

5 5

7 7

10 5x5

11 11

12 7/5

7x5

13 13

14 7x7

15 5x5x5

16 11/5

11x5

17 5x5/7

5x5x7

17

18 11/7

11x7

13/5

13x5

19 7x7/5

7x7x5

19

20 5x5x5x5

13/7

13x7

21 7x7x7

5x5/11

5x5x11

22 5x5x5/7

5x5x5x7

11x11

17/5

17x5

23 5x7/11

5x11/7

7x11/5

5x7x11

5x5/13

5x5x13

23

24 7x7/5x5

7x7x5x5

13/11

13x11

17/7

17x7

19/5

19x5

25 5x5x5x5x5

5x7/13

5x13/7

7x13/5

5x7x13

26 5x5x5/11

5x5x5x11

7x7x7/5

7x7x7x5

13x13

19/7

19x7

27 5x5x5x5/7

5x5x5x5x7

5x5/17

5x5x17

28 7x7x7x7

5x5x5/13

5x5x5x13

17/11

17x11

29 29

30 5x5x5x5x5x5

5x11/7x7

5x7x7/11

7x7x11/5

5x11x7x7

17/13

17x13

19/11

19x11

31 31

37 37

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.