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581EDO - The Sagittal forum

581EDO

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cam.taylor
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581EDO

Postby cam.taylor » Tue Jun 21, 2016 4:10 pm


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cam.taylor
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Re: 581EDO

Postby cam.taylor » Tue Jun 21, 2016 4:23 pm

I'd like to emphasise the 23-prime limit, so not that keen to use higher primes unless it makes things a whole lot easier. Thanks.

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George Secor
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Re: 581EDO

Postby George Secor » Thu Jun 23, 2016 6:19 am

I have a solution for notating 1deg581: Define the symbol :'::|::.: as 17:121n (the 17:121-schismina, 1088:1089). This is slightly larger than 5:19n (1215:1216, ~1.424c), which is notated :.::)|: and vanishes in 581-EDO.

This combination of opposite-altering diacritics (or accent marks) may then be added to various unaccented symbols to alter those by 1deg581. For example, :/|: is 11deg581, so :'::/|::.: may be 12deg581 and :.::/|::': may be 10deg581. Since :|): is 13deg581, :.::|)::': might be used instead for 10deg581, so there would need to be a method for deciding between such alternatives (such as preferring augmentation of an unaccented symbol to its diminution).

Some combinations would need to be avoided, e.g., :'::|(::.: for 3deg581, since this symbol is already defined as 1225k (19600:19683) and would be 5deg581. Since :.::~|::': is not presently defined, that could be used instead.

It's evident that 581 is going to take a bit of time and effort to get it done, but it's far better to have the problem of deciding between two alternatives for a given number of degrees than not being able to find anything that works.

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George Secor
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Re: 581EDO

Postby George Secor » Thu Jun 23, 2016 7:02 am


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cam.taylor
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Re: 581EDO

Postby cam.taylor » Sat Jun 25, 2016 7:33 pm

Thanks for all this George, for taking the time to look into this so deeply. I wouldn't have thought it would be quite this tricky, since 581 is not too far from 23- and 25-limit JI, and with 270 looking not too radical, I thought 581 would be only a bit of gap-filling from there. Obviously, I was wrong. Does that mean a notation for 311 would also be rather dificult, as 581=270+311?

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George Secor
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Re: 581EDO

Postby George Secor » Sun Jun 26, 2016 6:00 am


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Re: 581EDO

Postby George Secor » Fri Apr 14, 2017 5:03 am

I posted the following, regarding notation of 581-EDO, on 9 April 2017 to a thread in the Facebook group Xenharmonic Alliance Mathematical Theory, and am reposting it here at Dave Keenan's request. Although most of this already appears in my previous postings here, my suggestion of the 85:121 schismina as a possible interpretation of :|::': is new:

<< Scott Dakota, do you have a ratio for 1\581? The principal problem for notating 581 with Sagittal is defining a symbol for the single degree. The 5-schisma (32768:32805) :'::|: maps to 2\581, but is not particularly useful. The 17:121-schismina (1088:1089) maps to a single degree, but would be notated as :'::|::.: -- rather clumsy, but the simplest ratio for that symbol (not defined for olympian level, hence theoretically in a "super-olympian" extension). The difference between these two small intervals, the 85:121 schismina (61952:61965), would then be 1\581, notated as :|::': -- rather convoluted in that it's valid only as a secondary ratio that's far down the list.

I previously had 581 in my notes, where I chose '|. as 17:121n for 1\581, with the first few members of the symbol sequence being:
581 :'::|::.: :|(: :'::)|::.: :.::~|::': :~|: :)~|: ... >>

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Re: 581EDO

Postby Dave Keenan » Sat Apr 15, 2017 6:57 pm

It seems wrong to me, for 581-EDO notation to use schismina accents. 612 and 624-EDO notations don't need them. However it seems unavoidable that 581 will need to use _some_ kind of accents. I believe 494-EDO is the largest that we can notate without accents. As with 612 and 624, I think we should use schisma accents for 581, but in the case of 581 we need to accept that they will not represent the 5-schisma.

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George Secor
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Re: 581EDO

Postby George Secor » Wed Apr 19, 2017 11:55 am


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Re: 581EDO

Postby Dave Keenan » Thu Apr 20, 2017 12:59 am

That's quite a tour de force, George. I don't doubt that it is valid, however I find it unsatisfying. Of course it's easy to criticise, and much harder to come up with an alternative. It's unsatisfying that there is no regularity that might reduce the amount of information that needs to be remembered or looked up -- or at least none that I can discern. In particular, there is no consistent assignment of numbers-of-steps to all flags, and the double-shaft symbols do not repeat a flag sequence of the single-shaft symbols. And there are so many different core symbols.


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