New Olympian diacritics

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Dave Keenan
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New Olympian diacritics

Post by Dave Keenan » Sun Nov 06, 2016 12:17 am

Many thanks to Xen-Gedankenwelt for helping to get the full set of Sagittal symbols up as "smilies" on this forum.
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None of the recently uploaded symbols will be of any interest to those of you using the "mixed" Sagittal notation, as this only requires the single-shaft symbols, and all those recently uploaded were 3-shaft and X-shaft symbols, equivalent to single-shaft symbols added to sharps and double-flats, or subtracted from flats and double-sharps.

But anyone interested in the Olympian (extreme precision) JI notation (mixed or pure), should note the new section at the very end entitled :olympian:, with four tiny diacritical marks. These are an alternative representation for one or two "minas" up or down. A mina (pronounced meena) is approximately 0.4 cents in size. The mina was first defined as the difference between the primary (or exact) meaning of :(|\: as the 35-large-diesis (8505/8192), and its secondary (or approximate) meaning as the 13-large-diesis (27/26).

When it was first decided that we should have a diacritical mark to symbolise this difference, and thereby allow an exact symbol for the 13-large-diesis, it was expedient to simply re-use the grave and acute diacritics that we used on the left for 5-schisma alterations (~2.0 cents), by declaring that if they appeared to the right of a symbol they were to be interpreted as mina diacritics (~0.4 cents). So we have
Diesis	Symbol	Smiley code
35L	:(|\:	:(|\:
13L	:(|\::':	:(|\::':
125L	:(|\::.:	:(|\::.:
7L	:.::(|\:	:.::/|):
625L	:.::(|\::.:	:.::(|\::.:
See the right-hand end of http://sagittal.org/SagittalJI.gif for their ratios.

However this violates the rule that the smallest alteration should be the furthest from the notehead, and allows for left/right confusion. So when Tony Salinas (J.A.Martin Salinas) asked for a way to notate even smaller alterations, for compositions that involved precisely-controlled beating effects, we decided the mina should have a diacritic whose shape and size differed from that of the schisma diacritic, and so could be placed on the left of a symbol, and to the left of any schisma diacritic. It should also allow for a possible future extension using other diacritic shapes, for alterations in multiples of about 0.14 cents that we call "tinas" -- the mythical Magrathean extension.

After ridiculous amounts of discussion and testing, George and I agreed (3 years ago) that the new mina diacritics should look like a slanted breve -- something like a miniature version of this symbol :/|): without its shaft, and only about half the height of the schisma diacritic. So we now have:
Diesis	Symbol	Smiley code
35L	:(|\:	:(|\:
13L	:n::(|\:	:n::(|\:
125L	:u::(|\:	:u::(|\:
7L	:.::(|\:	:.::/|):
625L	:u::.::(|\:	:u::.::(|\:
The smiley codes for the four Olympian extension diacritics are:
:n: :n:
:u: :u:
:nn: :nn:
:uu: :uu:

Their Sagispeak pronunciations are:
:n: mi
:u: mo
:nn: bi
:uu: bo

:n::|: mi-ai :u::!: mo-ao, 1 mina, has a primary role as a 5.7.13-schismina, 4095:4096, 0.422716c
and a secondary role as a 5⁴.7-schismina, 4374:4375, 0.395756c.

:nn::|: bi-ai :uu::!: bo-ao, 2 minas (a bi-mina), has a primary role as a (5.13):(7.11)-schismina, 2079:2080, 0.832524c
and a secondary role as a 13:5³-schismina, 255879:256000, 0.818472c.

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Dave Keenan
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Re: New Olympian diacritics

Post by Dave Keenan » Wed Dec 26, 2018 9:29 pm

Magrathean Diacritics

I received the following query by email:
... I noticed SMuFL had a range for Magrathean Sagittal. Just wondering about the current state of the project, and what it would be like.
I had difficulty finding what George and I had agreed on, about 5 years ago. So I thought I should put the answer here, so the work is not lost.

The main reason we have never before published it, is that it is kind of embarrassing that it even exists. :oops: Some people already complain that Sagittal has too many symbols, often failing to appreciate that 99% of what anyone ever wants to do microtonally can be notated with the Spartan subset of 8 symbols.

But since we are dealing here with symbols (specifically diacritical marks or accents) having a resolution of a half-tina or 0.07 cents (completely inaudible except in very special circumstances), we needed a name for some beings that were more powerful than the Olympian gods, and yet were ridiculous. : D The Magratheans of Douglas Adams' comedy sci-fi The Hitchhikers Guide to the Galaxy were ideal for this.

To ensure that the symbols were as distinct as possible given their necessarily-small size, George and I used the discipline of forcing ourselves to represent them in as few pixels as possible. You can see the final result here, at two different resolutions. The 3, 6 and 9 tina symbols are identical to the 1, 2, and 3 mina symbols described in the previous post. To these we add 1 and 2 tina symbols and a dot to represent a half-tina. The intention is that, in a proper outline font, the 1, 2 and 3 tina symbols should be something like miniature versions of the following symbols without their shafts :)|: :)|(: :/|): , and the half-tina dot should be circular.

Magrathean-GS17.gif
Magrathean-GS17.gif (2.64 KiB) Viewed 682 times

George came up with the following definitions, with the help of a comma list produced by Gene Ward Smith. The ratios below have had their powers of 2 and 3 removed. These can be found if necessary, since we know the approximate size in cents. The trailing "n" is the symbol for "schismina" (our name for commas smaller than 1.8075 cents).

0.5 tina: 49:9765625n
1 tina: 121:1225n
1.5 tinas: 121:5359375n
2 tinas: 13:6655n
2.5 tinas: 343:15625n
3 tinas, 1 mina: 455n (~4375n)
3.5 tinas: 11:47n
4 tinas: 7:3025n
4.5 tinas: (no definition)
5 tinas: 25:2401n (~343:14641n)
5.5 tinas: (no definition)
6 tinas, 2 minas: 65:77n (~13:125n)
6.5 tinas: 13:37n
7 tinas: 143:1715n
7.5 tinas: 3125:5929n
8 tinas: 420175n
8.5 tinas: (no definition)
9 tinas: 539n
9.5 tinas: (no definition)

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