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Is there an edo that takes every Spartan accidental and nothing else?

Posted: Fri Jan 15, 2021 8:36 pm
by FloraC
Like this:
1\: :|(:
2\: :/|:
3\: :|):
4\: :/ /|:
5\: :/|):
6\: :/|\:

I checked the edo list in https://sagittal.org/sagittal.pdf. Curiously, there's not one.

Re: Is there an edo that takes every Spartan accidental and nothing else?

Posted: Fri Jan 15, 2021 10:25 pm
by yahya.abdal-aziz
I'd like to know more about your question. For example:
  • How did you think of it?(E.g. just as a curiosity, or for some potential advantage.)
  • Why does the answer matter to you?
  • What are its practical consequences for musicians?

Re: Is there an edo that takes every Spartan accidental and nothing else?

Posted: Fri Jan 15, 2021 10:45 pm
by FloraC
I wasn't suggesting it, but now you asked, there's potential advantage. Notation software developers tend to implement smufl by entire blocks. For example, what happened just now was that MuseScore team implemented the Spartan set, and only the Spartan set. So musicians will be practically rewarded if we make the fullest of Spartan.

Re: Is there an edo that takes every Spartan accidental and nothing else?

Posted: Fri Jan 15, 2021 11:25 pm
by Dave Keenan
Hi FloraC,

It is an alternative notation for both 130-edo and 137-edo. 130-edo has the more accurate fifth. The Spartan single-shaft symbols are arguably a superior notation for 130-edo and 137-edo in Evo Sagittal (Mixed Sagittal).

In Revo Sagittal (Pure Sagittal) the notation given in the XH article is superior because the flag sequence of its double-shaft symbols matches a subsequence of its single shaft symbols.

You can see some discussion of this here: viewtopic.php?f=5&t=421

This alternative wasn't considered when the XH article was written, because at that time :|\: was in the Spartan set.

Re: Is there an edo that takes every Spartan accidental and nothing else?

Posted: Sat Jan 16, 2021 1:31 am
by FloraC
because at that time :|\: was in the Spartan set.
Oh, no wonder! I also noticed 130edo was the closest match.

Will you "renovate" the XH article or publish something new in future?

Re: Is there an edo that takes every Spartan accidental and nothing else?

Posted: Sat Jan 16, 2021 6:22 am
by Dave Keenan
We are overdue to "renovate" the XH article for several other EDO notations as well. Thanks for giving us a nudge. :)

Re: Is there an edo that takes every Spartan accidental and nothing else?

Posted: Fri Mar 26, 2021 8:54 am
by Dave Keenan
@FloraC, I just realised (while updating the Xenharmonikon article, and thanks to a facebook post by Nicholas Denton Protsack) that 130edo and 137edo do not use every Spartan accidental as I claimed earlier. Sorry. They do not use :(|): because it is the same number of steps as :/|\: . Although they do match the list you gave, which only goes up to 6 steps.

To fully match Spartan, we need an EDO with 13 steps to the sharp, not 12 as in 130edo and 137edo. Although 135edo, 142edo and 149edo all have 13 steps to the sharp, and reasonably accurate fifths, the honour of using all of Spartan belongs to 142edo alone. 135edo has the best fifths of the three, but it tempers the 5-comma and 7-comma to the same number of steps (3 steps), and 149edo has a gap between the steps for the 5 and 7 commas (2 and 4 steps).

Only 142edo has all the Spartans as consecutive steps:

1\: :|(:
2\: :/|:
3\: :|):
4\: :/ /|:
5\: :/|):
6\: :/|\:
7\: :(|):
8\: :(|\:
9\: :)||(: or :\ \!::#:
10\: :||): or :!)::#:
11\: :||\: or :\!::#:
12\: :/||): or :!(::#:
13\: :/||\: or :#:

Of course you don't need to use :(|): in 142edo (or any tuning), since you could use :\!/::#: instead, just as you could use :\!)::#: instead of :(|\: .

However, 130edo is a far better model for a low-precision JI notation than is 142edo, because 130edo is 15-limit consistent while 142edo is only 9-limit consistent.