## Magrathean diacritics

cmloegcmluin
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Real Name: Douglas Blumeyer (he/him/his)
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### Re: Magrathean diacritics

Oy, I had another ridiculous thought while falling asleep last night, along the same lines as the thing I suggested which Dave posted a post-mortem re: miscommunication over here. I thought that when tallying metacomma occurrences, we should have ignored counting occurrences for already-occupied zones. In other words, or how about a specific example, let's say we're currently looking at the metacommas with the 1/19C,  , which is the 41st mina. When we find the metacomma between it and the best comma for the zone 9 tinas higher than it, we should tally it as an occam for that comma (the metacomma) in the 9 tina bucket of candidates. However, the zone 9 tinas higher than is already occupied by another ultracore, i.e. that's the 44th mina (9 tinas up = 3 minas up) which is the 1/5C,  .Now... I guess we'd only want to ignore such already-occupied occurrences if we thought of ourselves as searching for tina commas that help us exactly zones in the Insane precision notation which won't inherit their symbols from a lower level. But I suppose there's an argument that we care as well about finding metacommatic relationships between existing symbols and that these should contribute to our sense of what the tinas should represent, even if in that case there'd be no chance that it'd come to pass that the corresponding tina symbol would actually be used in application to the ultracore in question in order to with exact sum-of-elements notate the best comma found in that zone. Anyway, I'm sure we could continue to invent ways to doubt our process (we never double-checked the perfection of our badness metric either), but I'm glad to call it a wrap.

Dave Keenan
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### Re: Magrathean diacritics

cmloegcmluin wrote: Sun Nov 08, 2020 1:04 pm Oy, I had another ridiculous thought ...
Anyway, I'm sure we could continue to invent ways to doubt our process (we never double-checked the perfection of our badness metric either), but I'm glad to call it a wrap.
Thanks for being thorough. But it feels better to me, that the way we ultimately made the decision, depends less on the specific existing choices of comma and more on the ideal choices according to a reasonable badness function that nevertheless fits those existing choices fairly well. I'm not sure what you mean by "perfection" here, but please check on it if you can.

Dave Keenan
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### Re: Magrathean diacritics

Yes, that's a wrap! We have submitted it to the W3C Music Notation Community Group, and had it acknowledged, and we should see it in the SMuFL 1.4 update, expected before the end of the year. Hoorah.

It only took us 8.5 months.

Along with me, my mental simulation of George Secor is smiling, and wants to thank everyone who contributed to this 22 page thread, and the closely related 49 page thread, although he does think you're a little crazy. Many thanks to @Ash9903b4, @cmloegcmluin, @volleo6144 and @herman.miller.

Those final default comma definitions again:

1 tina: 10241/5n first proposed by Ash9903b4
2 tinas: 1/5831n first proposed by Ash9903b4
3 tinas: 1/455n first proposed by George Secor
4 tinas: 3025/7n first proposed by George Secor
5 tinas: 2401/25n first proposed by George Secor
6 tinas: 65/77n first proposed by George Secor
7 tinas: 7/425n first proposed by Ash9903b4
8 tinas: 187/175n first proposed by Ash9903b4
9 tinas: 1/539n first proposed by George Secor
1/n tina (default is 1/2 tina): 77/185n first proposed by Dave Keenan using Douglas' find-commas script.

And of course thanks to Douglas for finding the N2D3P9 metric that allowed us to finally make a decision.

And I leave you with a recurring theme: Von Neumann's elephant, a cautionary tale about overfitting of models to data. See the fifth paragraph of https://www.nature.com/articles/427297a

And the Disney remake, a cautionary tale about mind altering substances.

cmloegcmluin
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Real Name: Douglas Blumeyer (he/him/his)
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### Re: Magrathean diacritics

To cap off this effort, I've added some new smileys to the forum, so you can now use Magrathean accents in your sagittations.

(I expect this post to be used as a reference until we get some formal Sagittal documentation ready, so for those coming to this page for the first time, it should be noted that the Magrathean symbol extension and corresponding Insane precision level JI notation are surely the most esoteric cranny of the Sagittal notation system, unlikely to be needed by most mortals, more useful for theoretical discussion than actual practice. We've invested our time this year in order to wrap up this subproject that Dave and George started so long ago, and moving forward we'll stop fiddling and concentrate on explaining how to use the simpler aspects of Sagittal.)

The smilies can be accessed from the expanded smilies panel per usual by clicking "View more smilies" on the right. You can also type these smileys directly using their smiley codes, which you can find in the table below. I also realize we've still never shared out the glyph descriptions for these accents; I've mentioned a few of them like "horn" and "wedge" without formally introducing them. We also haven't yet formally introduced Sagispeak for the Magratheans. Well, here they are:

newexisting
smileysmileyglyphglyphschismas
codecodesmileyimagedescriptionSagispeaktinasminas(ultrinas)
:':tick (up)bi141
:@1:horn (up)qui1
:@2:wedge (up)quiqui2
:@3:::wing (up)mi31
:@4:hornwing (up)quimi4
:@5:wedgewing (up)quiquimi5
:@6:::bird (up)mimi62
:@7:hornbird (up)quimimi7
:@8:wedgebird (up)quiquimimi8
:@9:wingbird (up)mimimi9(3)
:@.:dot (up)i¹⁄n
:.:tick downbo-14-1
:l1:horn downquo-1
:l2:wedge downquoquo-2
:l3::,:wing downmo-3-1
:l4:hornwing downquomo-4
:l5:wedgewing downquoquomo-5
:l6::,,:bird downmomo-6-2
:l7:hornbird downquomomo-7
:l8:wedgebird downquoquomomo-8
:l9:wingbird downmomomo-9(-3)
:l.:dot downo-¹⁄n

Those are lower-case L's for all the down symbols.

The ASCII form can be found by simply removing the colons from either side of the Smiley code.

A tina is approximately 1/809th of an apotome, 1/8539th of an octave (a zeta-peak EDO), or 0.14 cents. The fractional-tina is generally half a tina but is intentionally arbitrary, because if you need any more precision than that, I have a bottle of Da' Bomb Beyond Insanity Hot Sauce with your name on it. The exact values of the tinas can be found in the previous post from Dave, or in many different forms in the table at the bottom of this post.

The Insane precision level of the JI notation has not yet been developed, so the exact combinations of these accents and symbol cores which are valid and invalid have not not yet been determined. However, there are some rules about combining them which are already established, which you should follow:
1. No more than one schisma accent (tick).
2. No more than one integer-tina or mina accent. The 1-mina accent is identical to the 3-tina accent and the 2-mina accent is identical to the 6-tina accent, because 1 mina = 3 tinas. In a sense, then, Magrathean and Olympian are alternative extensions: use one or the other, rather than Magrathean added atop Olympian.
3. No more than one fractional-tina accent (dot) when the fraction is ½ or ⅓. No more than floor(n/2) for ¹⁄n.
4. It's okay to have a mina or integer-tina accent pointing in the opposite direction as a tick, e.g.  . However, if you have a fractional-tina dot and an integer-tina accent they must go in the same direction when the fraction is ½. No more than floor((n-1)/2) dots can go in the opposite direction for ¹⁄n.
5. Smaller pitch alterations to the left. So: dots if any, mina or integer-tina accent if any, then tick if any.
So the maximum accent alteration you could have on a single core would be one ½-tina dot, one wingbird, and one tick, like this:  . That would make a total 23½ tinas in alteration (½ + 9 + 14).

If you are wondering how I showed the smiley codes here without them resolving to the smileys, I used a technique to "escape" the codes which I learned from Dave. You can learn it here.

Why "@" and a lower-case "L"? According to Dave:
...they are the only [ASCII characters] that haven't been used yet... Magrathean is the least useful part of Sagittal, so it should get the dregs. And we have a rule that when an up/down pair consists of a letter and a special character, the letter is down and the special character is up. The archetypes being b# and v ^.
You may have noticed that I've included the Herculean accents for comparison. Previously they were referred to as "acute" and "grave", but we decided it was preferable — now that we have so many accents — for the up and down versions of each to have the same name. The SMuFL class names will not be changing.

We're making an effort to call all of these "accents" now, instead of diacritics. Mostly, it's just simpler. I was just too lazy to go back and change the name of this topic on every single post. Here's what Dave had to say on it:
Dave Keenan wrote: I think, for pedagogical reasons we should not be purists about the term "accent" which, strictly-speaking only refers to the three diacritics: grave , acute ´, and circumflex ˆ. In any case, the 1 mina up symbol looks a bit like a circumflex.

I know it was me who pushed for such purism in the first place. But I've seen the error of my ways.

So, rather than the 4 syllable "diacritic", I think we should use the 2 syllable "accent", to refer to tina, mina and schisma diacritics.
And rather than the 5 syllable "diacriticised", I think we should use the 3 syllable "accented".
Also it seems that generally for natural language, accents are considered a subtype of diacritic which are for altering pitch, so that seems relevant; in fact, the "cent" part of accent's etymology comes from Latin "cantus" for song. Accent is also nice because it is similar enough in look and sound to accidental without being so close that it should be easily confused.

And finally, here are the tinas' primary commas (with the ultrina primary comma for comparison):





















2,3-free
2,3-free
2,3-free
2,3-free
2,3-free

comma

quotient
















apotome
prime
class
class
class
class
tina
name
cents
       n
/
d
  2
  3
  5
  7
 11
 13
 17
 19
 23
 29
 31
 37
slope
limit
name
CoPFR
SoPFR
N2D3P9
14
5s
1.954¢
   32805
/
32768
[
-15
  8
  1









⟩
  7.880
  5
$$\{5\}_{\scriptsize{2,3}}$$
  1
  5
   1.389
1
7²⋅11⋅19/5n
0.169¢
   10241
/
10240
[
-11
  0
 -1
  2
  1
  0
  0
  1




⟩
 -0.010
 19
$$\{\frac{10241}{5}\}_{\scriptsize{2,3}}$$
  5
 49
2252.072
2
1/(7³⋅17)n
0.297¢
    5832
/
5831
[
  3
  6
  0
 -3
  0
  0
 -1





⟩
  5.982
 17
$$\{5831\}_{\scriptsize{2,3}}$$
  4
 38
 688.382
3
1/(5⋅7⋅13)n
0.423¢
    4096
/
4095
[
 12
 -2
 -1
 -1
  0
 -1






⟩
 -2.026
 13
$$\{455\}_{\scriptsize{2,3}}$$
  3
 25
  82.153
4
5²⋅11²/7n
0.572¢
    3025
/
3024
[
 -4
 -3
  2
 -1
  2







⟩
 -3.035
 11
$$\{\frac{3025}{7}\}_{\scriptsize{2,3}}$$
  5
 39
 539.178
5
7⁴/25n
0.721¢
    2401
/
2400
[
 -5
 -1
 -2
  4








⟩
 -1.044
  7
$$\{\frac{2401}{25}\}_{\scriptsize{2,3}}$$
  6
 38
 324.209
6
65/77n
0.833¢
    2080
/
2079
[
  5
 -3
  1
 -1
 -1
  1






⟩
 -3.051
 13
$$\{\frac{77}{65}\}_{\scriptsize{2,3}}$$
  4
 36
 200.818
7
7/(5²⋅17)n
1.018¢
    1701
/
1700
[
 -2
  5
 -2
  1
  0
  0
 -1





⟩
  4.937
 17
$$\{\frac{425}{7}\}_{\scriptsize{2,3}}$$
  4
 34
 234.144
8
11⋅17/(5²⋅7)n
1.135¢
  382976
/
382725
[
 11
 -7
 -2
 -1
  1
  0
  1





⟩
 -7.070
 17
$$\{\frac{187}{175}\}_{\scriptsize{2,3}}$$
  5
 45
 572.351
9
1/(7²⋅11)n
1.255¢
  131072
/
130977
[
 17
 -5
  0
 -2
 -1







⟩
 -5.077
 11
$$\{539\}_{\scriptsize{2,3}}$$
  3
 25
  82.347
¹⁄n
77/(5⋅37)n
0.081¢
 1515591
/
1515520
[
-13
  9
 -1
  1
  1
  0
  0
  0
  0
  0
  0
 -1
⟩
  8.995
 37
$$\{\frac{185}{77}\}_{\scriptsize{2,3}}$$
  4
 60
1626.744