### 140th mina

Posted:

**Tue Apr 07, 2020 12:32 pm**[Moderator note: this thread was broken out from the JI Notation Spreadsheet thread. The last post there is reproduced as a quote below.]

Wow! Thanks for all that.

That bug is interesting. Well spotted! It relates to something I noticed a week or so ago:

The upper boundary of the largest single-shaft symbol in Olympian is currently the nearest odd half-tina to 139.5 minas, which is 68.08453 ¢, as you noted.

But the upperbound for single-shaft sagittals should be the same as the upperbound for large-dieses. This is the apotome-complement of the lower-bound for medium-dieses, and is given in footnote 7 on page 8 of http://sagittal.org/sagittal.pdf as sqrt([-30 19⟩) = 68.57250822 ¢.

That's one mina higher than the upperbound of the current largest single-shaft symbol.

That suggests there ought to be one more single-shaft Olympian, at the 140th mina, namely . Its primary comma (default interpretation) should be 25:77L, which is the apotome-complement of the 93rd mina, 25:77M. That is so that every medium diesis has a single-shaft complement. Currently 25:77M is the only one that doesn't. Or equivalently, it is so that we have single-shaft symbols for all large-dieses.

I think its upper bound should be the aforementioned 68.57250822 ¢ even though that is not on a half-tina. But that's not entirely clear to me. Perhaps it should be symmetrical with the upperbound [Edit: Oops! That should be "lowerbound". Thanks Douglas] of the 93rd mina 25:77M, about the half-apotome.

In any case, this would require changing the symbol for 25:77M (the 93rd mina) from to to agree with the apotome-complement rules.

Perhaps George thought that the former was a better symbol for 25:77M based on sum-of-flags. Or perhaps it is the effect it might have on the related 45.6 cent Herculean or Athenian boundary that led to his choice. This deserves investigating. But I can't justify the time at present.

cmloegcmluin wrote: ↑Tue Apr 07, 2020 1:56 am Sagittal Standard JI Notation Calculator Spreadsheet.xlsx

(attachment last edited: May 2nd, 2020)

Alright, I’ve updated the JI calculator spreadsheet to use the new Olympian diacritics (linked above). While I was at it I also updated it to:

I made a few other tweaks here and there too, such as switching the names of each level to be based on their precision instead of the Greek proper names for their maximum symbol set.

- include pure notation
- include the Unicode characters so if you have the Bravura font installed you can see the symbols (pending the Olympian diacritics getting implemented in SMuFL)
- report the error between your pitch and the default pitch of suggested symbols
- report the count of fifths each pitch is away from 1/1
- hide the guts of the calculator on other tabs to clean up the UI
- patch what I suspect was a bug where the calculator would suggest instead of simply *

These changes are not a strict win. Perhaps to some people the pure version, the unicode, or the accuracy measurements are just clutter. So please let me know what you think or if there any revisions you would like to see made. Otherwise I hope it works for you and you enjoy notating some JI in Sagittal!

* You can test this for yourself by entering C as your 1/1, -4 as your count of 3's, and 1 as your count of 5's. I found that you can fix the problem by increasing the upper bound of symbol suggestion from 68.08453082 to 68.8, but I was not sure if that might cause other problems, so instead I simply added a layer at the end where if it ever suggests it swaps it out for (and the equivalent problems for flat, double sharp, and double flat).

Wow! Thanks for all that.

That bug is interesting. Well spotted! It relates to something I noticed a week or so ago:

The upper boundary of the largest single-shaft symbol in Olympian is currently the nearest odd half-tina to 139.5 minas, which is 68.08453 ¢, as you noted.

But the upperbound for single-shaft sagittals should be the same as the upperbound for large-dieses. This is the apotome-complement of the lower-bound for medium-dieses, and is given in footnote 7 on page 8 of http://sagittal.org/sagittal.pdf as sqrt([-30 19⟩) = 68.57250822 ¢.

That's one mina higher than the upperbound of the current largest single-shaft symbol.

That suggests there ought to be one more single-shaft Olympian, at the 140th mina, namely . Its primary comma (default interpretation) should be 25:77L, which is the apotome-complement of the 93rd mina, 25:77M. That is so that every medium diesis has a single-shaft complement. Currently 25:77M is the only one that doesn't. Or equivalently, it is so that we have single-shaft symbols for all large-dieses.

I think its upper bound should be the aforementioned 68.57250822 ¢ even though that is not on a half-tina. But that's not entirely clear to me. Perhaps it should be symmetrical with the upperbound [Edit: Oops! That should be "lowerbound". Thanks Douglas] of the 93rd mina 25:77M, about the half-apotome.

In any case, this would require changing the symbol for 25:77M (the 93rd mina) from to to agree with the apotome-complement rules.

Perhaps George thought that the former was a better symbol for 25:77M based on sum-of-flags. Or perhaps it is the effect it might have on the related 45.6 cent Herculean or Athenian boundary that led to his choice. This deserves investigating. But I can't justify the time at present.