Magrathean diacritics
- cmloegcmluin
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Re: Magrathean diacritics
Sorry for the barrage of messy posts, and for not responding adequately to your recent post involving the latte
Yes, I did remember to go back and check that they were the top one in the list which was also LATE. I had little doubt that 2401/25n was LATE since its abs3exp was 1. But I'm doing it manually, i.e. working down the list for each comma, analyzing it, and if it's not LATE, moving on to the next. It's the kind of thing that's fast enough that I'm not even going to bother automatiing it.
121/1225n is our guy for 1 tina (George's)
N2D3P9 = 1258.08
319/7n is our guy for 2 tinas... I don't think we ever looked at this one before!
N2D3P9 = 599.602
3025/7n is our guy for 4 tinas (was our yellow highlghted one)
N2D3P9 = 539.178
for 0.5 tinas it's 13:4675n
N2D3P9 = 2391.61
that one was in our page 6 list.
(so we didn't end up making dinner yet because Lauren got sucked into a gaming event)
Yes, I did remember to go back and check that they were the top one in the list which was also LATE. I had little doubt that 2401/25n was LATE since its abs3exp was 1. But I'm doing it manually, i.e. working down the list for each comma, analyzing it, and if it's not LATE, moving on to the next. It's the kind of thing that's fast enough that I'm not even going to bother automatiing it.
121/1225n is our guy for 1 tina (George's)
N2D3P9 = 1258.08
319/7n is our guy for 2 tinas... I don't think we ever looked at this one before!
N2D3P9 = 599.602
3025/7n is our guy for 4 tinas (was our yellow highlghted one)
N2D3P9 = 539.178
for 0.5 tinas it's 13:4675n
N2D3P9 = 2391.61
that one was in our page 6 list.
(so we didn't end up making dinner yet because Lauren got sucked into a gaming event)
- cmloegcmluin
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Re: Magrathean diacritics
aaaaaaand I just got the "laté" joke. good one.
- Dave Keenan
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Re: Magrathean diacritics
Yeah. Maybe it would have been better if I'd written "LATÉ". But I'm impressed you got it anyway.
Thanks for those tina defs. The only worrying one is 2 tinas. I look forward to the monzo for that. I don't understand why we haven't seen it before.
Thanks for those tina defs. The only worrying one is 2 tinas. I look forward to the monzo for that. I don't understand why we haven't seen it before.
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Re: Magrathean diacritics
319/7n
5104/5103
[ 4 -6 0 -1 1 0 0 0 0 1 ⟩
0.339¢
maybe he gets some points for being superparticular?
I have to turn in for the night now. But I was thinking... why do we care so much about LATE for these primary commas? I think you recently pointed out that we don't care near as much about the EDO-ability of such tiny commas. So in the case of a tina which has a comma with much lower N2D3P9 but which just doesn't quite happen to be LATE, mightn't we prefer it? e.g. for the 0.5 tina, we've got
35/299n
76545/76544
[ -8 7 1 1 0 -1 0 0 -1 ⟩
0.023¢
which has N2D3P9 = 742.886, clearly much lower than 2391.61. Actually that's the 2,3-free class with the lowest N2D3P9 south of 0.75 tinas.
With abs3exp of 7, it's not quite LATE, but the one that beats it isn't tremendously better. It's just the 299/35C, the same thing but off by a 1C.
5104/5103
[ 4 -6 0 -1 1 0 0 0 0 1 ⟩
0.339¢
maybe he gets some points for being superparticular?
I have to turn in for the night now. But I was thinking... why do we care so much about LATE for these primary commas? I think you recently pointed out that we don't care near as much about the EDO-ability of such tiny commas. So in the case of a tina which has a comma with much lower N2D3P9 but which just doesn't quite happen to be LATE, mightn't we prefer it? e.g. for the 0.5 tina, we've got
35/299n
76545/76544
[ -8 7 1 1 0 -1 0 0 -1 ⟩
0.023¢
which has N2D3P9 = 742.886, clearly much lower than 2391.61. Actually that's the 2,3-free class with the lowest N2D3P9 south of 0.75 tinas.
With abs3exp of 7, it's not quite LATE, but the one that beats it isn't tremendously better. It's just the 299/35C, the same thing but off by a 1C.
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Re: Magrathean diacritics
I've been meaning to point out for some time that the best notating comma for the 1/1 class is not [ -19 12 ⟩, but [ 0 ⟩ or no comma at all. And the symbol for the 1/1 class is not but or no symbol at all. I note that (a bare shaft) is not a symbol.
The 0.5 tina as 13:4675n is very inaccurate too, at 0.73 tinas. But I'm not sure if I care about that.
What do we get if we require the whole tinas to be ±0.25 tinas and the half tina to be ±0.125 tinas?
But no. LATE (lowest absolute three exponent) has nothing to do with EDO-ability. It's LAAS (lowest absolute apotome slope) that relates to EDO-ability. LATE relates to JI-ability because it tells you how likely it is that you will need to combine the comma symbol with a sharp or flat, which is undesirable.
Maybe "he" loses points for being very inaccurate, at 2.414 tinas.cmloegcmluin wrote: ↑Fri Sep 04, 2020 4:13 pm 319/7n
5104/5103
[ 4 -6 0 -1 1 0 0 0 0 1 ⟩
0.339¢
maybe he gets some points for being superparticular?
The 0.5 tina as 13:4675n is very inaccurate too, at 0.73 tinas. But I'm not sure if I care about that.
What do we get if we require the whole tinas to be ±0.25 tinas and the half tina to be ±0.125 tinas?
I'm tempted to say, "So we damn-well get this over with, and get on to more important things".... why do we care so much about LATE for these primary commas? I think you recently pointed out that we don't care near as much about the EDO-ability of such tiny commas. So in the case of a tina which has a comma with much lower N2D3P9 but which just doesn't quite happen to be LATE, mightn't we prefer it?
But no. LATE (lowest absolute three exponent) has nothing to do with EDO-ability. It's LAAS (lowest absolute apotome slope) that relates to EDO-ability. LATE relates to JI-ability because it tells you how likely it is that you will need to combine the comma symbol with a sharp or flat, which is undesirable.
I don't understand in what sense that could be considered 0.5 tinas. It looks like 0.16 tinas to me. But I understand it was LATE when you posted that.e.g. for the 0.5 tina, we've got
35/299n
76545/76544
[ -8 7 1 1 0 -1 0 0 -1 ⟩
0.023¢
- Dave Keenan
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Re: Magrathean diacritics
Here's a thort. We can list more than one comma against a tina in the SMuFL doc. See the first few Athenian entries here:
https://w3c.github.io/smufl/gitbook/tab ... ntals.html
This might be the way forward for hard-to-decide cases like 2 tinas and 0.5 tinas.
https://w3c.github.io/smufl/gitbook/tab ... ntals.html
This might be the way forward for hard-to-decide cases like 2 tinas and 0.5 tinas.
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Re: Magrathean diacritics
I'll patch my code for those two issues.Dave Keenan wrote: ↑Fri Sep 04, 2020 11:40 pm I've been meaning to point out for some time that the best notating comma for the 1/1 class is not [ -19 12 ⟩, but [ 0 ⟩ or no comma at all. And the symbol for the 1/1 class is not but or no symbol at all. I note that (a bare shaft) is not a symbol.
FWIW, despite having been working on the code for months now, precise conceptual representations of Sagittal per our discussions (such as the differences between accents and the symbols which consist only of an accent and a bare shaft) have not been my priority. The way things are now are mostly pragmatic. For a while there I was agonizing over planning, trying to get my ERD just right w/r/t elements, levels, etc. before diving into work on the code. But more pressing things came up, and we needed some answers about bounds, tiny commas, popular ratios, and so on. I do eventually plan to review all my notes from conversations with you and ensure the code base faithfully embodies its design and thinking, such that it could potentially even serve as a secondary resource for understanding the system (at least for the subset of our user base which understands JavaScript).
True. And error actually matters.Maybe "he" loses points for being very inaccurate, at 2.414 tinas.maybe he gets some points for being superparticular?
We definitely don't have to keep masculinizing these commas. Don't do it for my sake anyway. For whatever reason "is our guy" just came out when I was frantically scrawling down notes last night and I just pasted it onto the forum.
Good question.The 0.5 tina as 13:4675n is very inaccurate too, at 0.73 tinas. But I'm not sure if I care about that.
What do we get if we require the whole tinas to be ±0.25 tinas and the half tina to be ±0.125 tinas?
Alright, for the 2 tina we get:
1/5831n
5832/5831
[ 3 6 0 -3 0 0 -1 ⟩
0.297¢
2.11 tinas
17-limit
N2D3P9 = 688.382
it was our yellow-highlighted comma ...and it's superparticular after all
And for the 0.5 tina we get:
1/20735n
20736/20735
[ 8 4 -1 0 -1 -1 0 0 0 -1 ⟩
0.083¢
0.59 tinas
29-limit
N2D3P9 = 4175.80
...and it's superparticular too hehehehe
(so I'm not sure how the "full stop" business is going to figure in to the SMuFL description... perhaps not at all)
By the way, I realized a couple flaws in the work I did last night:
- The default maxes I had set for prime limit, max SoPF>3, and max CoPF>3 were at 47, 61, and 555 respectively. I'd taken a note to have the scripts alert you to these settings each run, but hadn't gotten to making it so; sure wish I had though, since that would have been helpful to be reminded of. Another thing that would have spared me from this mistake would be if I had managed to get to the point of turning on the linter rule for disallowing magic numbers except in dedicated constants submodules, as is my preference in other mature projects of mine. Anyway, enough about implementation details... In other words, there was some possibility that a comma with a competitive N2D3P9 but bad prime limit, SoPF>3, or CoPF>3 was not showing up for consideration. I could get the CoPF>3 limitation out of the way, but SoPF>3 is how it determines which monzos to search. The highest I could get max SoPF>3 without it crashing is 127, and it doesn't make much sense to set the prime limit any higher than the SoPF>3 of course. Johnny Reinhard might be disappointed that we didn't quite make it into the 8th octave of the harmonic series except, oh wait, of course he won't... he may, in fact, be the single person on the planet least interested in assigning commas to tinas, insofar as his interest is probably the most negative of anyone I can think of. (We still love you, Johnny)
- This one's even more subtle. In the second phase of LATE verification, I was neglecting to filter commas with sizes greater than a half-apotome. So those commas might have been disqualifying other commas as not LATE when really they were.
For 1 tina, I found a new comma with better N2D3P9 than the one we found previously, George's 121/1225n, which had 1258.08. This comma has N2D3P9 = "only" 451.241. It is 59-limit though, haha:
59/7n
14337/14336
[ -11 5 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 1 ⟩
0.121¢
0.86 tinas
(and superparticular!)
The reason we didn't look at it before is that it has SoPF>3 of 66, which was outside our threshold (and I didn't suggest it yesterday because it was outside my code's threshold).
For 4 tinas, 3025/7n is still the winner.
For 5 tinas, 2401/25n is still the winner.
To summarize, the work has been redone with new searches that were more limited in the right ways (less max abs tina error allowed) and less limited in the right ways (no false negatives for LATE; less undesired prime-limit-, SoPF>3-, and/or CoPF>3- based disqualifications that otherwise could have had competitive N2D3P9). The commas for tinas 3, 6, 9, 7, and 8 are all w/in 0.25 tinas of their whole tina (the 7 tina just barely at 7.245, but hey, I'll take it) and since we got those ones from the absolute top list by N2D3P9 we know there can't be any better ones.
By the way, I also checked that every one of these commas mapped to the right tina count under the zeta-peak optimal EDO, 8539.00834-EDO, which starts off ⟨ 8539 13534 19827 ... ].
Here's the full val I used, up to the 59-limit, if you'd like to double-check it. Graham Breed's tool (http://x31eq.com/temper/net.html) seems to be not working for me, but it wasn't hard to find it myself.
Code: Select all
⟨ 8539 13534 19827 23972 29540 31598 34903 36273 38627 41482 42304 44484 45748 46335 47431 48911 50232 50643 51798 52513 52855 53828 54437 55296 56357 56855 57096 57565 57794 58238 59676 60058 60610 60789 61645 61809 62289 62751 63050 63484 63904 64041 64704 64832 65085 65209 65931 66612 66831 66939 67152 67466 67568 68069 68360 68644 68922 69014 69283 69460 ]
1 [ -11 5 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 1 ⟩ maps to 1 tina, so is consistent
2 [ 3 6 0 -3 0 0 -1 ⟩ maps to 2 tinas, so is consistent
3 [ 12 -2 -1 -1 0 -1 ⟩ maps to 3 tinas, so is consistent
4 [ -4 -3 2 -1 2 ⟩ maps to 4 tinas, so is consistent
5 [ -5 -1 -2 4 ⟩ maps to 5 tinas, so is consistent
6 [ 5 -3 1 -1 -1 1 ⟩ maps to 6 tinas, so is consistent
7 [ -2 5 -2 1 0 0 -1 ⟩ maps to 7 tinas, so is consistent
8 [ -12 4 -1 0 1 0 0 0 1 ⟩ maps to 8 tinas, so is consistent
9 [ 17 -5 0 -2 -1 ⟩ maps to 9 tinas, so is consistent
Perhaps the way I make you repeat explanations like that throughout the forum may serve as another secondary resource for learning Sagittal!LATE (lowest absolute three exponent) has nothing to do with EDO-ability. It's LAAS (lowest absolute apotome slope) that relates to EDO-ability. LATE relates to JI-ability because it tells you how likely it is that you will need to combine the comma symbol with a sharp or flat, which is undesirable.
Right, that makes total sense.
Nyuk, nyuk, nyuk.I don't understand in what sense that could be considered 0.5 tinas. It looks like 0.16 tinas to me. But I understand it was LATE when you posted that.e.g. for the 0.5 tina, we've got
35/299n
76545/76544
[ -8 7 1 1 0 -1 0 0 -1 ⟩
0.023¢
Right. Those are among the commas which you told me to include as "protected secondary commas". I still haven't written tests to protect them, but it's in the TODO list.Dave Keenan wrote: ↑Sat Sep 05, 2020 12:58 am Here's a thort. We can list more than one comma against a tina in the SMuFL doc. See the first few Athenian entries here:
https://w3c.github.io/smufl/gitbook/tab ... ntals.html
This might be the way forward for hard-to-decide cases like 2 tinas and 0.5 tinas.
Sure, that's fine with me.
Whoa, I didn't see that post until this morning. But yes, great observation, and it was quickly confirmed!Dave Keenan wrote: ↑Fri Sep 04, 2020 12:32 pm If you calculate the N2D3P9 of the (2,3-free ratios notated by the) remaining metacommas on my list, and take the maximum, that's an upper bound on how high you will need to go in N2D3P9 to get all the whole tinas as commas.
Oh okay. I do vaguely remember that. In my defense, it looks like you were in the midst of a seven-post-in-a-row run there. I must have apportioned my attention-votes among themDave Keenan wrote: ↑Wed Sep 02, 2020 3:15 pmDifferent thread. Sorry. viewtopic.php?p=1636#p1636Let me know if you find [apportioning votes between commas for the same 2,3-free ratio]. I just reviewed the thread and couldn't find it.
Seriously though, that's cool stuff. It'll go in the book that gets written about Sagittal one day.
That's right! Thank you.Dave Keenan wrote: ↑Thu Sep 03, 2020 2:00 pm The word you are looking for is "schisma". THE schisma is 5s, the difference between 5C and 3C, the syntonic and Pythagorean commas.
I wonder if you've been wondering what it might look like to work our way up the zeta peaks, for each one seeing, for each of its 'inas is the lowest N2D3P9 2,3-free class with a LAAS comma of its size, and see what all these precision levels would look like, and compare them with Sagittal's existing precision level notation.Dave Keenan wrote: ↑Fri Sep 04, 2020 11:48 am So we shouldn't be looking at metacommas at all! We should just go up the N2D3P9 list until we find actual commas of the right size, i.e. as the single best comma for some 2,3-equivalence class.
Again, clearly neither of us would have gotten here without the other to bounce the problem back and forth with.We'll probably need the 307 list (maybe more) to get all the tinas. But it's a much simpler problem. Thanks!
What reason(s) exactly do you mean, then?I've often encouraged less agonising over these defs, but not exactly for that reason.so why would we even agonize over exact notation at this stage at all?!
Okay, so perhaps we should prepare a final table, and after producing it, tag the other people who have been involved in this thread, and give a few days for them to chime in? I'd hardly feel satisfied to pull the trigger without the folks who have been big helps here having a say.
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Re: Magrathean diacritics
Ah. I missed the connection to "our guy". Duh.cmloegcmluin wrote: ↑Sat Sep 05, 2020 7:21 am We definitely don't have to keep masculinizing these commas. Don't do it for my sake anyway. For whatever reason "is our guy" just came out when I was frantically scrawling down notes last night and I just pasted it onto the forum.
It can (kind of) figure in to the characters' names: accSagittalFractionalTinaUp, accSagittalFractionalTinaDown.(so I'm not sure how the "full stop" business is going to figure in to the SMuFL description... perhaps not at all)
So, young Jedi. Right to be skeptical I was. When write I did:By the way, I realized a couple flaws in the work I did last night:
- The default maxes I had set for prime limit, max SoPF>3, and max CoPF>3 were at 47, 61, and 555 respectively. ... In other words, there was some possibility that a comma with a competitive N2D3P9 but bad prime limit, SoPF>3, or CoPF>3 was not showing up for consideration.
- In the second phase of LATE verification, I was neglecting to filter commas with sizes greater than a half-apotome. So those commas might have been disqualifying other commas as not LATE when really they were.
Wouldn't it still be a good idea to compare the results of these two methods, in case there are other bugs lurking.Dave Keenan wrote: ↑Fri Sep 04, 2020 12:59 pm I don't understand how the above command can guarantee to find the LATE-comma with the lowest N2D3P9.
...
I don't see how you can be confident unless you generate LATE commas for all 2,3-equivalence-classes with N2D3P9 < 1258.09.
By the way, apotome-complements have the same absolute slope. They differ only in the sign of the slope.
OK. But shouldn't you also rerun the earlier n.0±0.5, 0.5±0.25 case, with these bugs fixed.So I redid the work for tinas 1, 4, and 5 as well.
Hmm. It looks like we can't avoid working up a badness measure (combining error, abs3exp and N2D3P9)Good question.What do we get if we require the whole tinas to be ±0.25 tinas and the half tina to be ±0.125 tinas?
Alright, for the 2 tina we get:
1/5831n
5832/5831
[ 3 6 0 -3 0 0 -1 ⟩
0.297¢
2.11 tinas
17-limit
N2D3P9 = 688.382
it was our yellow-highlighted comma ...and it's superparticular after all
And for the 0.5 tina we get:
1/20735n
20736/20735
[ 8 4 -1 0 -1 -1 0 0 0 -1 ⟩
0.083¢
0.59 tinas
29-limit
N2D3P9 = 4175.80
...and it's superparticular too hehehehe
OK. Interesting. We can't reject it merely because it is 59-limit. We have to go with N2D3P9, which takes prime limit into account. And similarly we can't favour superparticulars per se. But I believe N2D3P9 combined with LATE does favour them.For 1 tina, I found a new comma with better N2D3P9 than the one we found previously, George's 121/1225n, which had 1258.08. This comma has N2D3P9 = "only" 451.241. It is 59-limit though, haha:
59/7n
14337/14336
[ -11 5 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 1 ⟩
0.121¢
0.86 tinas
(and superparticular!)
The reason we didn't look at it before is that it has SoPF>3 of 66, which was outside our threshold (and I didn't suggest it yesterday because it was outside my code's threshold).
I'm thankful for these small mercies.For 4 tinas, 3025/7n is still the winner.
For 5 tinas, 2401/25n is still the winner.
I still don't trust it.To summarize, the work has been redone with new searches that were more limited in the right ways (less max abs tina error allowed) and less limited in the right ways (no false negatives for LATE; less undesired prime-limit-, SoPF>3-, and/or CoPF>3- based disqualifications that otherwise could have had competitive N2D3P9).
Yeah. I trust those.The commas for tinas 3, 6, 9, 7, and 8 are all w/in 0.25 tinas of their whole tina (the 7 tina just barely at 7.245, but hey, I'll take it) and since we got those ones from the absolute top list by N2D3P9 we know there can't be any better ones.
Excellent. Thank you.By the way, I also checked that every one of these commas mapped to the right tina count under the zeta-peak optimal EDO, 8539.00834-EDO, which starts off ⟨ 8539 13534 19827 ... ].
I checked it up to prime 59 and I concur.Here's the full val I used, up to the 59-limit, if you'd like to double-check it. Graham Breed's tool (http://x31eq.com/temper/net.html) seems to be not working for me, but it wasn't hard to find it myself.
Code: Select all
⟨ 8539 13534 19827 23972 29540 31598 34903 36273 38627 41482 42304 44484 45748 46335 47431 48911 50232 50643 51798 52513 52855 53828 54437 55296 56357 56855 57096 57565 57794 58238 59676 60058 60610 60789 61645 61809 62289 62751 63050 63484 63904 64041 64704 64832 65085 65209 65931 66612 66831 66939 67152 67466 67568 68069 68360 68644 68922 69014 69283 69460 ]
I don't recall saying that. I think it would be better if it mapped to 0 tinas according to the "tinic" temperament's mapping, as given above. But I don't think it's a deal-breaker.0.5 [ 8 4 -1 0 -1 -1 0 0 0 -1 ⟩ maps to 1 tina btw but I think you said we don't care about this
Ah. But I think I sidetracked you from your actual point, which was, "Why do we care so much about tina commas being either LAAS or LATE (which are after all the same thing for tina-sized commas)? Why can't we use non-LAAS non_LATE commas?".Perhaps the way I make you repeat explanations like that throughout the forum may serve as another secondary resource for learning Sagittal!LATE (lowest absolute three exponent) has nothing to do with EDO-ability. It's LAAS (lowest absolute apotome slope) that relates to EDO-ability. LATE relates to JI-ability because it tells you how likely it is that you will need to combine the comma symbol with a sharp or flat, which is undesirable.
Right, that makes total sense.
Which is a good question, and leads us back to having to come up with a comma-usefulness metric after-all, and then combining that with error to get a badness metric.
I'd like to see the "Secor complexity" of these commas, as kindly reverse-engineered by @volleo6144 here:
viewtopic.php?p=1659#p1659
Notice how George included a term that attempted to correct for the balance-blindness of SoPF>3. Perhaps we can replace the first two terms with some function of N2D3P9 and simplify the last two terms into one term, given that abs3exp and absApotomeSlope are the same thing here.
OK. But can you please explain why you proposed a 0.16 tina comma as a 0.5 tina comma. Was it simply a mistake?Nyuk, nyuk, nyuk.I don't understand in what sense that could be considered 0.5 tinas. It looks like 0.16 tinas to me. But I understand it was LATE when you posted that.e.g. for the 0.5 tina, we've got
35/299n
76545/76544
[ -8 7 1 1 0 -1 0 0 -1 ⟩
0.023¢
No.I wonder if you've been wondering what it might look like to work our way up the zeta peaks, for each one seeing, for each of its 'inas is the lowest N2D3P9 2,3-free class with a LAAS comma of its size, and see what all these precision levels would look like, and compare them with Sagittal's existing precision level notation.
Reasons very close to what you mentioned, but not exactly the same. I was just avoiding seeming to claim some prescience I didn't have.What reason(s) exactly do you mean, then?I've often encouraged less agonising over these defs, but not exactly for that reason.so why would we even agonize over exact notation at this stage at all?!
The main reason not to agonise over them is that there are many more important things to be done, and probably no one will care, because no one will use them. Or the first person to use them will have their own reasons to find their own definitions for them.
You seem to be under the mistaken impression that you and I have agreed on all the required definitions. At the very least, 2 and 0.5 are still up in the air for me.Okay, so perhaps we should prepare a final table, and after producing it, tag the other people who have been involved in this thread, and give a few days for them to chime in? I'd hardly feel satisfied to pull the trigger without the folks who have been big helps here having a say.
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Re: Magrathean diacritics
Yes, Master Keenan. (not far off from Qui-Gon! "Padawan Blumeyer" doesn't have quite the right ring to it.)Dave Keenan wrote: ↑Sat Sep 05, 2020 10:50 am Wouldn't it still be a good idea to compare the results of these two methods, in case there are other bugs lurking.
Ooh, yeah, that makes sense. Good tip.By the way, apotome-complements have the same absolute slope. They differ only in the sign of the slope.
Let me know if you wanted to try some tricks exploiting that... or if it was truly just a "by the way".
That's what I meant to get across, that I had done that already. The comma results for 0.5, 1, 2, 4, and 5 should all be in the same tier w/r/t your trust level. 3, 6, 9, 7, and 8 should all be together in the other higher trust tier.OK. But shouldn't you also rerun the earlier n.0±0.5, 0.5±0.25 case, with these bugs fixed.So I redid the work for tinas 1, 4, and 5 as well.
Yeah, I was worried a bit about that too. Possibly also a punishment for inconsistency with the patent val.Hmm. It looks like we can't avoid working up a badness measure (combining error, abs3exp and N2D3P9)
Word. To be clear, I wasn't necessarily hoping to get away with 37, despite the entire forum topic originally dedicated to achieving it. There, it turned out a 37 limit was rightful in the case of the Extreme precision level. If it turns out 59 is rightful for the Insane level, so be it.We can't reject [59/7n for 1 tina] merely because it is 59-limit. We have to go with N2D3P9, which takes prime limit into account.
Oh right! Sorry ugh it gets hard to hold all these things in mind at once.I don't recall saying that. I think it would be better if it mapped to 0 tinas according to the "tinic" temperament's mapping, as given above. But I don't think it's a deal-breaker.0.5 [ 8 4 -1 0 -1 -1 0 0 0 -1 ⟩ maps to 1 tina btw but I think you said we don't care about this
Perhaps we need to mosey back on over to the "developing a notational comma popularity metric" topic then? viewtopic.php?f=4&t=493But I think I sidetracked you from your actual point, which was, "Why do we care so much about tina commas being either LAAS or LATE (which are after all the same thing for tina-sized commas)? Why can't we use non-LAAS non_LATE commas?".
Which is a good question, and leads us back to having to come up with a comma-usefulness metric after-all, and then combining that with error to get a badness metric.
I'd like to see the "Secor complexity" of these commas, as kindly reverse-engineered by @volleo6144 here:
viewtopic.php?p=1659#p1659
Notice how George included a term that attempted to correct for the balance-blindness of SoPF>3. Perhaps we can replace the first two terms with some function of N2D3P9 and simplify the last two terms into one term, given that abs3exp and absApotomeSlope are the same thing here.
Sorry I forgot to actually address that point. Yes, I wasn't thinking clearly about including a lower bound for cents on it when I ran the script.can you please explain why you proposed a 0.16 tina comma as a 0.5 tina comma. Was it simply a mistake?
True. For example: me. I think I would need Magrathean accents to differentiate between some intervals in one of my tunings, and I recently checked and some of the pitches are like in the 4000's of N2D3P9, so there's little chance they'll work out to be included. I'll just have to state them in a key up top.Or the first person to use them will have their own reasons to find their own definitions for them.
A guy could hopeYou seem to be under the mistaken impression that you and I have agreed on all the required definitions. At the very least, 2 and 0.5 are still up in the air for me.
Right-o. I'll get that list of LATE commas up through N2D3P9 encompassing that 1 tina. Though I note that the 0.5 tina candidate has N2D3P9 of 4175.80. But I have significant doubts I'll be able to actually find the top ~4000 most popular ratios. Or it might be one of those things that would take days to run and require some refactoring.
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Re: Magrathean diacritics
It was just a "by the way". But something I'm curious about, when you have an idle moment is how often, and for what classes, particularly for low N2D3P9, is the LATE comma different from the LAAS comma? This is not particularly related to this thread.cmloegcmluin wrote: ↑Sat Sep 05, 2020 11:52 amOoh, yeah, that makes sense. Good tip.Dave Keenan wrote: ↑Sat Sep 05, 2020 10:50 am By the way, apotome-complements have the same absolute slope. They differ only in the sign of the slope.
Let me know if you wanted to try some tricks exploiting that... or if it was truly just a "by the way".
Ah. OK. Thanks.That's what I meant to get across, that I had done that already. The comma results for 0.5, 1, 2, 4, and 5 should all be in the same tier w/r/t your trust level. 3, 6, 9, 7, and 8 should all be together in the other higher trust tier.
If we are forced to go for a comma usefulness, then yes. But there's still hope. I'll wait until your "trust upgrade" is complete and you've summarised the results for both ±0.5/±0.25 and ±0.25/±0.125.Perhaps we need to mosey back on over to the "developing a notational comma popularity metric" topic then? viewtopic.php?f=4&t=493
Hold on to the dream.A guy could hope
https://www.youtube.com/watch?v=g73YPFD ... u.be&t=140
Or perhaps this part is more relevant:
https://www.youtube.com/watch?v=g73YPFD ... u.be&t=269
Awesome. Thanks.Right-o. I'll get that list of LATE commas up through N2D3P9 encompassing that 1 tina.
No need to go there. If the run up to an N2D3P9 of 1258.09 doesn't reveal any discrepancies between that and your other search method, then I'm happy to trust the other method re 0.5 tina commas.Though I note that the 0.5 tina candidate has N2D3P9 of 4175.80. But I have significant doubts I'll be able to actually find the top ~4000 most popular ratios. Or it might be one of those things that would take days to run and require some refactoring.