How is 2460edo *actually* notated?

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FloraC
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How is 2460edo *actually* notated?

Post by FloraC »

Is there actual material showing it, such as what basic symbols are used and how the diacritics are applied.

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cmloegmcluin
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Re: How is 2460edo *actually* notated?

Post by cmloegmcluin »

@FloraC The Extreme precision level of Sagittal's standard JI notation is modeled after 2460-EDO, which uses the full Olympian symbol set, so the notation for 2460-EDO is just every Olympian symbol in order.

Dave has corrected the above crossed-out statements in the next post. Sorry for any confusion.

Normally you could find that in the data tabs of the standard JI notation calculator spreadsheet, but the one that's linked on the site presently is out-of-date (specifically I noticed it's missing the very last step here, the :``::)|\ \: ). I suspect it got reset to an older backup version of itself or something when we did a server upgrade last month. Perhaps you knew this already and checked there but were confused by what you found — if so, very sorry about that! Thanks for alerting us to the problem and I'll update it ASAP. Unfortunately this caused me to realize I've lost access to updating it, too, but that's another issue :) Anyway, I still have all the source information in my repo...

The above crossed-out stuff has also been dealt with. Never mind.

....so here you go.

I first used Dave's Athenian-preference to choose between the two options. That worked in 5 out of 6 cases (the 2 other cases of the 8 split minas — the ones above the half-apotome mirror — are not separate cases because for those we just choose the apotome complement of the one we choose below the mirror).

The only tough case was between :`::'::/|): and :.::/|\: . I next checked if their primary commas were consistently mapped in 2460. They were; both the 625M and 11/5M map to 105\2046 as they should. So that didn't break the tie.

Next I checked their complexity using our favorited metric, N2D3P9:
https://en.xen.wiki/w/N2D3P9#Table_of_T ... _by_N2D3P9
Which places the 5/11M above the 625M. So that makes :.::/|\: win.
Which is just as well because the :`::'::/|): requires not just one, but two accents.

By the way:
1439 steps in a CG (fifth)
418 steps in a CD (whole tone)
233 steps in a # (chromatic semitone)
185 steps in a BC (diatonic semitone)

0 (:h:)
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 :.::~|(:
27 :`::.::~|(:
28 :,,::~|(:
29 :,::~|(:
30 :~|(:
31 :`::~|(:
32 :,,::|~:
33 :,::|~:
34 :|~:
35 :`::|~:
36 :~~|:
37 :`::~~|:
38 :``::~~|:
39 :,::.::/|:
40 :.::/|:
41 :)|~:
42 :,,::/|:
43 :,::/|:
44 :/|:
45 :`::/|:
46 :``::/|:
47 :.::)/|:
48 :'::/|:
49 :`::'::/|: keep
:,,::)/|: strike
50 :,::)/|:
:)/|: strike
51 :,::.::|): keep
52 :.::|):
53 :`::.::|):
54 :,,::|):
55 :,::|):
56 :|):
57 :`::|):
58 :``::|):
59 :,::'::|):
60 :'::|):
61 :`::'::|):
62 :,::)|):
63 :)|):
64 :.::(|:
65 :|\:
66 :`::|\:
67 :,::(|:
68 :(|:
69 :`::(|:
70 :``::(|:
71 :,::'::(|:
72 :'::(|: keep
:,::~|): strike
73 :~|):
74 :`::~|):
75 :,::.::(|(:
76 :.::(|(:
77 :'::~|):
:/|~: strike
78 :,,::(|(: keep
79 :,::(|(:
80 :(|(:
81 :`::(|(:
82 :~|\:
83 :,::.::/ /|:
84 :.::/ /|:
85 :`::.::/ /|:
86 :,,::/ /|:
87 :,::/ /|:
88 :/ /|:
89 :`::/ /|:
90 :``::/ /|:
91 :,::'::/ /|:
92 :'::/ /|:
93 :,,::)/ /|:
94 :,::)/ /|:
95 :)/ /|:
96 :`::)/ /|:
97 :``::)/ /|:
98 :,,::/|):
99 :,::/|):
100 :/|):
101 :`::/|):
102 :(|~:
103 :,::'::/|):
104 :'::/|):
:`::'::/|): strike
105 :.::/|\: keep
106 :`::.::/|\:
107 :,,::/|\:
108 :,::/|\:
109 :/|\:
110 :`::/|\:
111 :,::(/|:
112 :(/|:
:`::(/|: strike
113 :'::/|\: keep
114 :`::'::/|\:
115 :,::)/|\:
116 :)/|\:
117 :`::)/|\:
118 :``::)/|\:
119 :,::.::(|):
120 :.::(|): keep
:,::|\): strike
121 :|\):
122 :`::|\):
123 :,::(|):
124 :(|):
125 :`::(|):
126 :``::(|):
127 :,::'::(|):
128 :'::(|): keep
:,::.::(|\: strike
129 :.::(|\:
130 :`::.::(|\:
131 :|\ \:
132 :,::(|\:
133 :(|\:
134 :`::(|\:
135 :``::(|\:
136 :,,::)|\ \:
137 :,::)|\ \:
138 :)|\ \:
139 :`::)|\ \:
140 :``::)|\ \:

I believe you can take it from there but if you have any other questions let me know.

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Dave Keenan
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Re: How is 2460edo *actually* notated?

Post by Dave Keenan »

Hi FloraC. I'm afraid Douglas is mistaken. The Olympian (Extreme precision) symbol set contains 8 more symbols than are needed for 2460edo, and a decision has not previously been made as to which symbol should be used in those cases where there is a choice of two symbols. If you look at the "Boundaries" tab in the JI Notation spreadsheet, you will see these pairs hilited.
FloraC wrote: Sat Oct 23, 2021 10:06 pm Is there actual material showing it, such as what basic symbols are used and how the diacritics are applied.
No, there is no such material. But we could decide it here and now.

In the "Commas" tab of that spreadsheet you will see the primary comma (37-limit) for each symbol. You could convert these to prime-count vectors and then apply the simple map for 2460edo to them, to check that they map to the expected degree of 2460edo, since, strictly speaking, Olympian is based on 233-EDA (apotome), not 2460-EDO.

In choosing which of two valid Olympian symbols to use for a degree of 2460edo, I would favour those whose core symbol is Athenian.

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Re: How is 2460edo *actually* notated?

Post by cmloegmcluin »

@Dave Keenan and @FloraC I have corrected my previous post. Hope I've got it in decent order now. Sorry for goofing up in the first place.

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Re: How is 2460edo *actually* notated?

Post by Dave Keenan »

Thanks Douglas. That looks good.

It would also be interesting (some time) to see if it is possible to make a notation for 2460edo using the new Stoic symbols plus the Herculean and Olympian accents. That would be equivalent to dropping all symbols with non-Athenian (Promethean-extension) cores and filling in the gaps by adding more accents to the Athenian cores, then replacing the Athenians with Stoics.

FloraC
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Re: How is 2460edo *actually* notated?

Post by FloraC »

Uh, first, there's no left diacritics vs right diacritics? Then https://sagittal.org/SagittalJI.gif is seriously out of date.

Second, why is promethean involved at all? I figured it's possible to do this
1\ :`::|:
2\ :``::|:
3\ :,::'::|:
4\ :'::|:
5\ :`::'::|:
6\ :``::'::|:
7\ :,::.::|(:
8\ :.::|(:
9\ :`::.::|(:
10\ :,,::|(:
11\ :,::|(:
12\ :|(:
And so on.

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Dave Keenan
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Re: How is 2460edo *actually* notated?

Post by Dave Keenan »

FloraC wrote: Tue Oct 26, 2021 7:02 pm Uh, first, there's no left diacritics vs right diacritics?
That's correct. There is no longer any need to use right diacritics/accents, particularly now that the Olympian accents are in SMuFL and Bravura. See viewtopic.php?f=10&t=254 and see the last paragraph on page 24 of https://sagittal.org/sagittal.pdf
Then https://sagittal.org/SagittalJI.gif is seriously out of date.
Yes! Douglas has had a partly-completed updated version of that chart in the works for many months now, but has been distracted by our Regular Temperament Theory simplification/pedagogy project.
Second, why is promethean involved at all? I figured it's possible to do this
1\ :`::|:
2\ :``::|:
3\ :,::'::|:
4\ :'::|:
5\ :`::'::|:
6\ :``::'::|:
7\ :,::.::|(:
8\ :.::|(:
9\ :`::.::|(:
10\ :,,::|(:
11\ :,::|(:
12\ :|(:
And so on.
Yes. That's the kind of thing I was suggesting above, as a stepping stone to a possible accented-Stoic notation. But I agree that such an accented-Athenian notation could be used in it's own right, if it could be made to work. However there is a problem where there are more than 13 steps of 2460edo between some pairs of consecutive (unaccented) Athenians. This occurs as follows:
:~|(: 14 steps :/|: 14 steps :|):
:(|: 14 steps :(|(:
and worst of all
:/|\: 17 steps :(|):

Using symbols from the Promethean extension, such as :)/|\: between :/|\: and :(|): , is one way to solve this problem. Another is to allow double schisma accents, in the combinations :,::'::': and :'::': and their inversions, which have not previously been required.

FloraC
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Re: How is 2460edo *actually* notated?

Post by FloraC »

:~|(: 14 steps :/|: 14 steps :|):
:(|: 14 steps :(|(:
and worst of all
:/|\: 17 steps :(|):
:/|: to :|): is 12 steps just as :h: to :|(:, right? Same as :(|: to :(|(: .
:~|(: to :/|: is 14 steps.
:/|\: to :(|): is 15 steps.

For any 14- or 15-step gap I might go for :,::'::': , but I do hope to save all the mess by :@9::': .

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Dave Keenan
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Re: How is 2460edo *actually* notated?

Post by Dave Keenan »

FloraC wrote: Sat Oct 30, 2021 1:49 am
:~|(: 14 steps :/|: 14 steps :|):
:(|: 14 steps :(|(:
and worst of all
:/|\: 17 steps :(|):
:/|: to :|): is 12 steps just as :h: to :|(:, right? Same as :(|: to :(|(: .
:~|(: to :/|: is 14 steps.
:/|\: to :(|): is 15 steps.

For any 14- or 15-step gap I might go for :,::'::': , but I do hope to save all the mess by :@9::': .
You are so right. I went and made the same mistake Douglas did initially. Thanks FloraC.

Yes, you could use the 9-tina accent as a 3-mina accent.

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