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

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

Post 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.

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yahya.abdal-aziz
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Real Name: Yahya Abdal-Aziz

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

Post 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?

Regards,
Yahya

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

Post 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.

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

Post 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.

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

Post 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?

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

Post by Dave Keenan »

We are overdue to "renovate" the XH article for several other EDO notations as well. Thanks for giving us a nudge. :)

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

Post 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.

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