As per Dave and others' suggestions, I've made a few revised diamonds, only involving the primes up to 13, but extending the odd limit to also include ratios of 45, which can be pretty important.
This one's Athenianlevel precision, so small intervals like the 13schismina ("mina") and 5schisma are effectively "virtually tempered out", that is, notationally ignored, so that 5/4 from D can be notated as either F or as G (with schismas, usually G)
The Athenian set also uses quite a few less symbols, so no for anyone interested, those are all simplified to Athenian precision symbols.
Hope there are no errors in this one, just been through my other two diamonds and found quite a few little mistakes, mostly involving accidentally reversing up and downshafts.
45 oddlimit 13prime limit diamonds in Athenian and beyond
 cam.taylor
 Posts: 51
 Joined: Thu Sep 03, 2015 11:55 am
45 oddlimit 13prime limit diamonds in Athenian and beyond
 Attachments

 45ODD 13PRIME LIMIT DIAMOND IN ATHENIAN SAGITTAL.docx
 (65.09 KiB) Downloaded 80 times
 cam.taylor
 Posts: 51
 Joined: Thu Sep 03, 2015 11:55 am
Re: 45 oddlimit 13prime limit diamonds in Athenian and beyond
Here is another version.
The same 13prime, 45odd limit diamond is represented in Herculean, adding some nonathenian flags, as well as the schisma accidentals to distinguish some interval pairs ~2c apart.
I have also made a 37prime 45odd limit diamond in both Olympian and MultiSagittal, but will start another thread for that, as there are quite a few more symbols for the higher primes involved  17, 19, 23, 29, 31, 37.
The same 13prime, 45odd limit diamond is represented in Herculean, adding some nonathenian flags, as well as the schisma accidentals to distinguish some interval pairs ~2c apart.
I have also made a 37prime 45odd limit diamond in both Olympian and MultiSagittal, but will start another thread for that, as there are quite a few more symbols for the higher primes involved  17, 19, 23, 29, 31, 37.
 Attachments

 45ODD 13PRIME LIMIT DIAMOND IN HERCULEAN SAGITTAL.docx
 (70.67 KiB) Downloaded 69 times
 Dave Keenan
 Site Admin
 Posts: 244
 Joined: Tue Sep 01, 2015 2:59 pm
 Location: Brisbane, Queensland, Australia
 Contact:
Re: 45 oddlimit 13prime limit diamonds in Athenian and beyond
That's great Cam. Thanks again!
I suggest completely omitting any alternative spellings from the Athenian chart that involve a schisma (approx 2c) approximation.
I suggest completely omitting any alternative spellings from the Athenian chart that involve a schisma (approx 2c) approximation.
 cam.taylor
 Posts: 51
 Joined: Thu Sep 03, 2015 11:55 am
Re: 45 oddlimit 13prime limit diamonds in Athenian and beyond
I thought about that, but it dawned on me that Athenian level notation already uses some other "approximations", possibly of a similar order of comma size. I had the schismatic spellings in brackets initially, but decided I'd include them as other approximations are surely already filling the diamond in other spots.
 Dave Keenan
 Site Admin
 Posts: 244
 Joined: Tue Sep 01, 2015 2:59 pm
 Location: Brisbane, Queensland, Australia
 Contact:
Re: 45 oddlimit 13prime limit diamonds in Athenian and beyond
That's one of the beauties of Athenian. In the the 45odd13primelimit diamond, I think the only one that actually needs a schisma approximation is 25/7, and of course its inverse. And I don't think there are any doublemina approximations needed. See the 13oddlimit diamond in Athenian in Figure 7 on page 14 of http://sagittal.org/sagittal.pdf. The filled notes are the approximations (all single mina, 0.4 c).cam.taylor wrote:I thought about that, but it dawned on me that Athenian level notation already uses some other "approximations", possibly of a similar order of comma size. I had the schismatic spellings in brackets initially, but decided I'd include them as other approximations are surely already filling the diamond in other spots.
It would be good if you could indicate which spellings involve approximations, and approximately how large the error is. e.g. colouring the nominal with saturated colours:
minas
0 black
1 blue
2 cyan
3 green
4 yellow
5 red (1 schisma)