[phpBB Debug] PHP Warning: in file [ROOT]/includes/bbcode.php on line 494: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead
[phpBB Debug] PHP Warning: in file [ROOT]/includes/bbcode.php on line 494: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead
[phpBB Debug] PHP Warning: in file [ROOT]/includes/bbcode.php on line 494: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead
[phpBB Debug] PHP Warning: in file [ROOT]/includes/bbcode.php on line 494: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead
[phpBB Debug] PHP Warning: in file [ROOT]/includes/bbcode.php on line 494: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead
[phpBB Debug] PHP Warning: in file [ROOT]/includes/bbcode.php on line 494: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead
[phpBB Debug] PHP Warning: in file [ROOT]/includes/bbcode.php on line 494: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead
[phpBB Debug] PHP Warning: in file [ROOT]/includes/bbcode.php on line 494: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead
[phpBB Debug] PHP Warning: in file [ROOT]/includes/bbcode.php on line 494: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead
[phpBB Debug] PHP Warning: in file [ROOT]/includes/bbcode.php on line 494: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead
[phpBB Debug] PHP Warning: in file [ROOT]/includes/bbcode.php on line 494: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead
[phpBB Debug] PHP Warning: in file [ROOT]/includes/bbcode.php on line 494: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead
[phpBB Debug] PHP Warning: in file [ROOT]/includes/bbcode.php on line 494: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead
[phpBB Debug] PHP Warning: in file [ROOT]/includes/bbcode.php on line 494: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead
[phpBB Debug] PHP Warning: in file [ROOT]/includes/bbcode.php on line 494: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead
[phpBB Debug] PHP Warning: in file [ROOT]/includes/bbcode.php on line 494: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead
[phpBB Debug] PHP Warning: in file [ROOT]/includes/bbcode.php on line 494: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead
[phpBB Debug] PHP Warning: in file [ROOT]/includes/bbcode.php on line 494: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead
[phpBB Debug] PHP Warning: in file [ROOT]/includes/bbcode.php on line 494: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead
[phpBB Debug] PHP Warning: in file [ROOT]/includes/bbcode.php on line 494: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead
[phpBB Debug] PHP Warning: in file [ROOT]/includes/bbcode.php on line 494: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead
[phpBB Debug] PHP Warning: in file [ROOT]/includes/bbcode.php on line 494: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead
[phpBB Debug] PHP Warning: in file [ROOT]/includes/bbcode.php on line 494: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead
[phpBB Debug] PHP Warning: in file [ROOT]/includes/bbcode.php on line 494: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead
[phpBB Debug] PHP Warning: in file [ROOT]/includes/bbcode.php on line 494: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead
[phpBB Debug] PHP Warning: in file [ROOT]/includes/bbcode.php on line 494: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead
[phpBB Debug] PHP Warning: in file [ROOT]/includes/bbcode.php on line 113: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead
[phpBB Debug] PHP Warning: in file [ROOT]/includes/functions.php on line 5312: Cannot modify header information - headers already sent by (output started at [ROOT]/includes/functions.php:3925)
[phpBB Debug] PHP Warning: in file [ROOT]/includes/functions.php on line 5312: Cannot modify header information - headers already sent by (output started at [ROOT]/includes/functions.php:3925)
[phpBB Debug] PHP Warning: in file [ROOT]/includes/functions.php on line 5312: Cannot modify header information - headers already sent by (output started at [ROOT]/includes/functions.php:3925)
45 odd-limit 13-prime limit diamonds in Athenian and beyond - The Sagittal forum

45 odd-limit 13-prime limit diamonds in Athenian and beyond

User avatar
cam.taylor
Posts: 51
Joined: Thu Sep 03, 2015 11:55 am

45 odd-limit 13-prime limit diamonds in Athenian and beyond

Postby cam.taylor » Wed May 18, 2016 11:53 am

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 Athenian-level precision, so small intervals like the 13-schismina ("mina") and 5-schisma are effectively "virtually tempered out", that is, notationally ignored, so that 5/4 from D can be notated as either F:\!::#: or as G:b: (with schismas, usually G:'::|::b:)

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 down-shafts.
Attachments
45-ODD 13-PRIME LIMIT DIAMOND IN ATHENIAN SAGITTAL.docx
(65.09 KiB) Downloaded 66 times

User avatar
cam.taylor
Posts: 51
Joined: Thu Sep 03, 2015 11:55 am

Re: 45 odd-limit 13-prime limit diamonds in Athenian and beyond

Postby cam.taylor » Wed May 18, 2016 3:00 pm

Here is another version.

The same 13-prime, 45-odd limit diamond is represented in Herculean, adding some non-athenian flags, as well as the schisma accidentals to distinguish some interval pairs ~2c apart.

I have also made a 37-prime 45-odd limit diamond in both Olympian and Multi-Sagittal, 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
45-ODD 13-PRIME LIMIT DIAMOND IN HERCULEAN SAGITTAL.docx
(70.67 KiB) Downloaded 54 times

User avatar
Dave Keenan
Site Admin
Posts: 239
Joined: Tue Sep 01, 2015 2:59 pm
Location: Brisbane, Queensland, Australia
Contact:

Re: 45 odd-limit 13-prime limit diamonds in Athenian and beyond

Postby Dave Keenan » Wed May 18, 2016 3:09 pm

That's great Cam. Thanks again!

I suggest completely omitting any alternative spellings from the Athenian chart that involve a schisma (approx 2c) approximation.

User avatar
cam.taylor
Posts: 51
Joined: Thu Sep 03, 2015 11:55 am

Re: 45 odd-limit 13-prime limit diamonds in Athenian and beyond

Postby cam.taylor » Wed May 18, 2016 3:14 pm

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.

User avatar
Dave Keenan
Site Admin
Posts: 239
Joined: Tue Sep 01, 2015 2:59 pm
Location: Brisbane, Queensland, Australia
Contact:

Re: 45 odd-limit 13-prime limit diamonds in Athenian and beyond

Postby Dave Keenan » Wed May 18, 2016 4:09 pm



Return to “Just Intonation notations”

Who is online

Users browsing this forum: No registered users and 0 guests

cron