Weird and missing notations in the pdf

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רועיסיני
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Weird and missing notations in the pdf

Post by רועיסיני »

I noticed lately that 130edo's notation in figure 8 on page 16 of the sagittal pdf has a double shaft symbol, :/||:, that is not an apotome complement of the matching single shaft symbol, which in this case is ://|:. That's the only time, except for the limma fraction notation, I've seen an official sagittal material where that happens. Also, it claims to use "all the spartan symbols", but :)||(: is spartan while :/||: is not, and there is also :(|): which is spartan but is not used there. Furthermore, there is a notation for the same edo on the next page doesn't use ://|: but :|\:. Is there a good reason for all of this or is it just a leftover from the time :|\: used to be spartan?

Also, 64edo and 49edo are said there to have alternative notations as subsets of 128edo and 147edo respectively, but I couldn't find agreed notations for these edos anywhere. The closest I could find was this post where there are suggestions from George that had not been reviewed by Dave. Are these the notations referred to in the pdf or are there other ones? Also, if these are the notations, then that post also contains a 135edo notation for 45edo to be (possibly) notated as a subset of, which makes it weird that the pdf says "a future 135edo notation".

Can anyone make sense of all of this? Thanks!
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Re: Weird and missing notations in the pdf

Post by Dave Keenan »

רועיסיני wrote: Sun May 28, 2023 5:11 am I noticed lately that 130edo's notation in figure 8 on page 16 of the sagittal pdf has a double shaft symbol, :/||:, that is not an apotome complement of the matching single shaft symbol, which in this case is ://|:. That's the only time, except for the limma fraction notation, I've seen an official sagittal material where that happens. Also, it claims to use "all the spartan symbols", but :)||(: is spartan while :/||: is not, and there is also :(|): which is spartan but is not used there. Furthermore, there is a notation for the same edo on the next page doesn't use ://|: but :|\:. Is there a good reason for all of this or is it just a leftover from the time :|\: used to be spartan?

Also, 64edo and 49edo are said there to have alternative notations as subsets of 128edo and 147edo respectively, but I couldn't find agreed notations for these edos anywhere. The closest I could find was this post where there are suggestions from George that had not been reviewed by Dave. Are these the notations referred to in the pdf or are there other ones? Also, if these are the notations, then that post also contains a 135edo notation for 45edo to be (possibly) notated as a subset of, which makes it weird that the pdf says "a future 135edo notation".

Can anyone make sense of all of this? Thanks!
Thank you for bringing those problems to my attention. The use of :/||: instead of :)||(: for the Spartan version of 130 is my failure to fully convert it from the non-Spartan version. The claim that it contains all Spartan symbols is also a mistake on my part. I will fix these soon.

There are not yet any agreed notations for 128, 135 or 147. The definitive list of EDO notations is here: https://github.com/Sagittal/sagittal-ma ... sag_et.par

So 128 and 147 were just as deserving of the "future" qualifier as was 135. Can you see anything wrong with the notations George proposed for them, or suggest any improvements?

The aim with Sagittal.pdf, is not to add anything new to it, but only to correct things that are wrong, and update things that become wrong due to carefully-considered changes to Sagittal. So I am inclined to never add any notations for 128, 135 or 147 to it. But I will remove the "future" qualification regarding 135.

I seem to remember that George was happy for 45 to be notated as a subset of 180, because we had a notation for 180 (12×15). I was not happy with that because I thought an EDO should be notated as a subset of only its smallest multiple that is 1:3:9-consistent, or equivalently has an error in its fifth that is less than ¼ of a step, in this case 135edo. But we didn't have a notation for 135 at the time. George was happy for 45 to be notated as a subset of 135 and not 180, once we had a notation for 135. I'm not sure why there was no such disagreement regarding 128 or 147 which we also didn't have notations for.
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Re: Weird and missing notations in the pdf

Post by רועיסיני »

Cool! I didn't find anything wrong with the 128, 135 and 147 notations, but I didn't really look. Also, seems like there are some notations that are not in the par file yet, like the mauve, cyan and yellow range notations, the extended trojan notations and the 2460edo notations. Should we ask Douglas to add them?
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Re: Weird and missing notations in the pdf

Post by רועיסיני »

Now I have looked for something wrong and improvenents, and indeed found some:

The 128edo notation violates double-shaft flag arithmetic, as
:~|\: - (:)~||: - :(|): - :)|:) + :/|: = 5 - (8 - 7 - 1) + 3 = 5 + 3 = 8 ≠ 6 = :/|\:.
I thought about replacing :~|\: with :(|~: for 5 steps, because it's similar to the apotome complement of :)|:, and is only approximated a bit less well, but its complement is :|\\: which should be used for 8 steps but voilates flag arithmetic because 2(:/|\: - :/|:) = 2(6 - 3) = 6 ≠ 8.
Replacing :/|: with :|): in addition will make the double shafts recapitulate a subsequence of the single shafts and also solve this issue, but I'm not sure this is worthwhile since 5 is a simpler prime than 7 and is approximated better in 128. Do you have any other suggestion?

For 135, I think it may be better to replace :)|(: with :~|: for 1 step and ://|: with :)//|: for 5 steps, as it simplifies the notation with 2:~|: = :~~|:, keeps the double shafts recapitulating the single shafts and prevents the "even" sagittal ://|: from notating an odd number of steps. The only problems I can see with this are that the corresponding commas are approximated worse than the previous proposed commas in 135edo (but are still valid, of course), and that the new notation is not consistent with the proposed 270edo notation, which I think is perfect and we should accept as-is.

For 147, :~|): is invalid for 5 degrees as 49/48, since it maps to 4.362347084935664 degrees if you only temper the 3, so unless you can find a better secondary comma in the e-mail I think it should be replaced by something else, maybe :(|(:. This also makes the proposal consistent with double-shaft flag arithmetic, which it previously wasn't - in the original proposal
:/||\: - :/|\: + 2(:~|): - (:/|): - :/|:)) = 14 - 7 + 2(5 - (8 - 3)) = 7 + 2(5 - 5) = 7 ≠ 9 = :~~||:
but in my proposal, you can assign
:)|: = 0, :|(: = 1, :~|: = 1, :/|: = 3, :|): = 3, :|\: = 4, :(|: = 4
and get correct values for all the accidentals from that. It may also be better to use :|(: for 1\147 instead of :)|(:, as it makes the souble shafts recapitulate the single shafts, although it is approximated less well.

So, to summarize, these are my variants of George's suggestions:
128edo (unsatisfying):
:)|:	:~|(:	:|):	:(|(:	:(|~:	:/|\:	:(|):	:|\\:	:~||(:	:||):	:(||(:	:(||~:	:/||\:
1	2	3	4	5	6	7	8	9	10	11	12	13
135edo:
:~|:	:~~|:	:|):	:~|):	:)//|:	:/|\:	:(|):	:)|\\:	:~~||:	:||):	:~||):	:)//||:	:/||\:
1	2	3	4	5	6	7	8	9	10	11	12	13
147edo:
:|(:	:~|(:	:/|:	:|\:	:(|(:	:/|):	:/|\:	:(|\:	:~||(:	:/||:	:||\:	:(||(:	:/||):	:/||\:
1	2	3	4	5	6	7	8	9	10	11	12	13	14
Also, 270edo:
:|(:	:)|(:	:~|(:	:~~|:	:/|:	:|):	:|\:	:~|):	:(|(:	:/ /|:	:/|):	:/|\:	:)/|\:	:(|):	:(|\:
1	2	3	4	5	6	7	8	9	10	11	12	13	14	15
	:)||(:	:~||(:	:~~||:	:/||:	:||):	:||\:	:~||):	:(||(:	:/ /||:	:/||):	:/||\:
	16	17	18	19	20	21	22	23	24	25	26
(George's exact suggestion)

Any thoughts?
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Re: Weird and missing notations in the pdf

Post by Dave Keenan »

רועיסיני wrote: Tue May 30, 2023 1:38 am ... seems like there are some notations that are not in the par file yet, like the mauve, cyan and yellow range notations,
Did you perhaps mean the green, cyan and yellow range notations? The mauve, now called purple, range is complete with 26, 45, 52 and 64 (:/|): = 1/3 and 1/2, :(|\: = 2/3), which are all included in sagittal.pdf and sag_et.par.

The green, cyan and yellow apotome fraction notations have not been thoroughly checked, except for EDOs below 72. There remain questions such as: Should 117 be yellow or cyan? Should 170 be yellow or pink? The current noble colour boundaries may need to be changed.
the extended trojan notations and the 2460edo notations. Should we ask Douglas to add them?
There are a number of reasons I am not inclined to do so, yet. 1. "The paint is still wet" on some of them. 2. There are currently no accented notations in sag_et.par. 3. Adding them to sag_et.par implies (eventually) asking Manuel Op de Coul to support them in Scala, and EDOs whose Sagittal notations require accents are unlikely to ever be used.

I am happy to consider that if a notation is not given in one of the .par files on github, then this forum is the next most authoritative source.

What Sagittal needs much more than the standardising of notations for 3 digit EDOs, is the hiding of such complexity and the increasing of access to the simpler aspects of Sagittal, through educational material that uses only the starter (72edo 11-limit-JI) set followed by the Spartan set, and by providing templates for popular notation software such as Dorico, and by adding Sagittal staff notation to Xenharmonic wiki articles for popular (2-digit) EDOs. And bringing old resources like https://sagittal.org/SagittalJI.gif up to date.
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Re: Weird and missing notations in the pdf

Post by Dave Keenan »

I have updated https://sagittal.org/sagittal.pdf to correct the errors you found in figures 8 and 9. Thanks @רועיסיני.

I also added a link at the end, that will take the reader to the original published version of this paper, in case it is of historical interest.
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Re: Weird and missing notations in the pdf

Post by רועיסיני »

Dave Keenan wrote: Wed May 31, 2023 11:23 am
רועיסיני wrote: Tue May 30, 2023 1:38 am ... seems like there are some notations that are not in the par file yet, like the mauve, cyan and yellow range notations,
Did you perhaps mean the green, cyan and yellow range notations?
Yes, I probably confused one almost-too-bad-fifths range with the other.
Dave Keenan wrote: Wed May 31, 2023 11:23 am The green, cyan and yellow apotome fraction notations have not been thoroughly checked, except for EDOs below 72. There remain questions such as: Should 117 be yellow or cyan? Should 170 be yellow or pink? The current noble colour boundaries may need to be changed.
Makes sense. I may check some of them soon, especially the 88edo one, but I'm not sure. If only the boundaries need to be decided it may be already worth it to add to the par file the notations for edos that are sums of other established ones in the same range, i.e. 83 for green, 81, 88, 93 and 100 for cyan, and 86, 98, 110, 122, 129, 134, 141, and 153 for yellow. Also, I noticed that 79 already has a notation there that is not the one derived from the yellow color (which makes some sense since small yellow EDOs have :/|: tempered out). Maybe it'll be better to move it to pink?
For searchability purposes (i.e. because when I searched "88edo" in the forum that post didn't show up), I'll add that there are not yet reviewed notations there for 74edo, 76edo, 81edo, 83edo, 86edo, 88edo, 93edo, 98edo, 100edo, 105edo, 110edo, 117edo, 122edo, 129edo, 134edo, 141edo and 153edo, excluding the ones that may change if 79edo changes color, which are 146edo and 158edo.
Dave Keenan wrote: Wed May 31, 2023 11:23 am
the extended trojan notations and the 2460edo notations. Should we ask Douglas to add them?
There are a number of reasons I am not inclined to do so, yet. 1. "The paint is still wet" on some of them. 2. There are currently no accented notations in sag_et.par. 3. Adding them to sag_et.par implies (eventually) asking Manuel Op de Coul to support them in Scala, and EDOs whose Sagittal notations require accents are unlikely to ever be used.

I am happy to consider that if a notation is not given in one of the .par files on github, then this forum is the next most authoritative source.
Makes total sense. Thanks!
Dave Keenan wrote: Wed May 31, 2023 11:23 am What Sagittal needs much more than the standardising of notations for 3 digit EDOs, is the hiding of such complexity and the increasing of access to the simpler aspects of Sagittal...
I understand, and I'll think twice before I post here about 3-digit EDOs in the future, but I think these 3 specific EDOs, i.e. 128, 135 and 147, are more important than the rest, since they are listed in the pdf as ways of notating smaller EDOs which are less than 72, so I'd like you (or someone else, if they happen to read this) to check the notations I gave for them (and George's notation for 270 which is just too good to pass on IMO) and possibly improve them even more, with the goal of then eventually being added to sag_et.par.
Dave Keenan wrote: Wed May 31, 2023 2:43 pm I have updated https://sagittal.org/sagittal.pdf to correct the errors you found in figures 8 and 9. Thanks @רועיסיני.
You're welcome! It looks good now.
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Re: Weird and missing notations in the pdf

Post by Dave Keenan »

You make a good case for standardising those EDO. I would also be honouring a commitment I made to George. But first I have some earlier messages of yours I need to respond to. Sorry I am so slow responding.
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Re: Weird and missing notations in the pdf

Post by רועיסיני »

Cool, no pressure. In the meanwhile I think I may try to make a notation for 128 I'm more satisfied with.
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Re: Weird and missing notations in the pdf

Post by רועיסיני »

I tried to make a notation for 128 that would (only use primary commas and) comply with double shaft flag arithmetic, while using :/|: for 3 steps, and I got completely stuck. I had to either use ://|: for 6 steps, which is approximated really badly, or use :(|:, :/|): or :(/|: for 5 steps, which are all either approximated really badly or inconsistent with the 11-limit patent val or both.
Because of that, and because the relative error of the fifth in 128edo is almost 20% (greater than 72's), and the double shaft flag arithmetic violation I found in George's original suggestion is fairly convoluted, I think I like it better than anything I could create for 128, so I prefer
128edo:
:)|:	:~|(:	:/|:	:(|(:	:~|\:	:/|\:	:(|):	:)~||:	:~||(:	:||\:	:(||(:	:(||~:	:/||\:
1	2	3	4	5	6	7	8	9	10	11	12	13
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