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The Sagittal forum • New Olympian diacritics
Page 1 of 1

New Olympian diacritics

Posted: Sun Nov 06, 2016 12:17 am
by Dave Keenan
Many thanks to Xen-Gedankenwelt for helping to get the full set of Sagittal symbols up as "smilies" on this forum.


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

See the right-hand end of 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:

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.