New Olympian diacritics

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Dave Keenan
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New Olympian diacritics

Post by Dave Keenan »

Many thanks to Xen-Gedankenwelt for helping to get the full set of Sagittal symbols up as "smilies" on this forum.
View more smilies

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 had
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	:`::(|\:	:`::(|\:
125L	:,::(|\:	:,::(|\:
7L	:.::(|\:	:.::/|):
625L	:,::.::(|\:	:,::.::(|\:

The smiley codes for the four Olympian extension diacritics use the back-quote (up) and the comma (down):
:`:   :`:
:,:   :,:
:``:  :``:
:,,:  :,,:

Their Sagispeak pronunciations are:
:`: mi
:,: mo
:``: mimi
:,,: momo

[Edit: Thanks to cmloegcmluin for this updated version of the following paragraphs, as discussed here.]

As a symbol, :`::|: mai :,::!: mao, the mina's primary role is the 5.7.13-schismina, 4095:4096, 0.423c, and it has a capture zone spanning from 0.211 to 0.773c (from 1.5 to 5.5 steps of 809EDA). Secondary roles within this capture zone include the 5⁴.7-schismina, 4374:4375, 0.396c. As a diacritic component of other symbols ( :`: mi- :,: mo- ) the mina changes the primary role of the core symbol by one of these two commas, or another comma of a similar size.

Similarly, :``::|: mimai :,,::!: momao, the 2 mina symbol, has a primary role as a (5.13):(7.11)-schismina, 2079:2080, 0.833c, and it has a capture zone spanning from 0.773 to 1.194c (from 5.5 to 8.5 steps of 809EDA). Secondary roles within this capture zone include the 13:5³-schismina, 255879:256000, 0.818c. As a diacritic component of other symbols ( :``: mimi- :,,: momo- ) the double mina changes the primary role of the core symbol by one of these two commas, or another comma of a similar size.

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cmloegcmluin
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Re: New Olympian diacritics

Post by cmloegcmluin »

Agreed. I moved the metallic/noble notations discussion here: viewtopic.php?f=7&t=427

Either of you two, please feel free to break out the tina mapping discussion if you'd like.

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Re: New Olympian diacritics

Post by cmloegcmluin »

I have also used my newfound gavel powers to extract some posts specific to the Bravura font to a thread where Dave and I continue that conversation without impinging upon discussion of the diacritics here.

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Dave Keenan
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Re: New Olympian diacritics

Post by Dave Keenan »

The tina mapping discussion has been moved to a new Magrathean diacritics topic.

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