New Olympian diacritics

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Dave Keenan
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New Olympian diacritics

Postby 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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