Tartini fractional sharp aren't

The first and third symbols from the left here
http://upload.wikimedia.org/wikipedia/commons/4/4c/Partial_accidentals.svg
have been attributed to Guiseppe Tartini (1692-1770) on this list for as long as I can remember. We refer to them as such in the Sagittal Xenharmonikon article. But while writing his thesis, Tony Salinas asked George and I whether we could substantiate that. And we found that we could not! In fact the earliest use we can find described by a reputable source is by Richard Stein in the 20th century (described in Prof. Gardner Read's book, "20th century microtonal notation").

However they seem such obvious symbols that it is hard to believe they were not proposed sooner. And we have not been able to learn what fractional sharp symbols Tartini did use.

Does anyone else have, or can anyone else else find, any evidence on this, one way or the other?

-- Dave Keenan

I think I hit the jackpot. A scan of Tartini's Tratato di Musica from 1754 (MDCCLIV)
http://erato.uvt.nl/files/imglnks/usimg/2/2d/IMSLP91212-PMLP187470-Tartini_-_Trattato_di_musica.pdf
Many thanks to the anonymous scanner.

You can check for yourself that Tartini's Tratato di Musica, 1754, does _not_ contain anything even remotely resembling the 3-stroke semi-sharp (quartertone) symbol that we have been attributing to him for decades.

Instead he uses a simple 2-stroke san-serif "x" as his semi-sharp, which you can see notating an 11th harmonic on page 95 and an enharmonic tetrachord on page 121. This is quite logical when you notice that his sharp symbol is similar to ours but rotated 45 degrees (except when used in a key signature).

I see no sesqui-sharp symbol (3/4 tone).

So now we're looking for the earliest usage by Adriaan Fokker (or anyone else) to see if they have priority over Richard Stein.

According to George Secor, Gardner Read in his "20th Century Microtonal Notation" says "It is significant, as well as being historically pertinent, that these two modified symbols [the 3-stroke and 5-stroke semi and sesqui sharps] were used in the first quarter-tone composition of our century to be commercially published,­ the 1909 __Zwei Konzertstucke fur Violoncello und Klavier_ of Richard Stein. The Harvard Dictionary of Music says Stein pulished this quartertone piece in 1906.
http://books.google.com.au/books?id=02rFSecPhEsC&pg=PA510&lpg=PA510&dq=Richard+stein+quartertones&source=bl&ots=Uk5ZOISkSN&sig=nUOls089VEsOsftPUsqWt4mPm_M&hl=en&sa=X&ei=xP-XT6z6LqWViQeSm4DcBQ&ved=0CDwQ6AEwBA#v=onepage&q=Richard%20stein%20quartertones&f=false

-- Dave Keenan http://dkeenan.com

I forgot to note that Kurt Stone is quoted as saying Tartini first used these symbols in 1756 and I have only shown that Tartini did not use them in his 1754 publication. However I can find no record of anything published by Tartini in 1756. Could Stone have transposed his Roman numerals --
MDCCLIV versus
MDCCLVI ?

No chance for Fokker having priority over Stein. Fokker only started studying music theory in 1942.

So it seems we cannot call them the "Tartini-Couper" symbols any longer, but must call them the "Stein-Couper" symbols, although I would still dearly like to know what source Kurt Stone cites for his Tartini attribution.

By the way, Richard Stein (a Rumanian composer) also has priority over Mildred Couper for the backwards-flat semi-flat (but not the merged backwards+forwards sesqui-flat). But if, like me, you prefer the unmerged version (where backwards and forwards flats have separate shafts which are merely close together) then it could be argued that this is not a new symbol at all and so this could simply be called the Stein set (even though Stein never notated a sesqui-flat). I note that George Secor and I prefer that the backwards flat is narrower than the forwards flat, so it looks more like a half of a flat. This modified Stein set is included in the sagittal font.

I really enjoyed this conversation. :-)

--- In tuning@yahoogroups.com, "dkeenanuqnetau" <d.keenan@...> wrote:
>
> I think I hit the jackpot. A scan of Tartini's Tratato di Musica from 1754 (MDCCLIV)
> http://erato.uvt.nl/files/imglnks/usimg/2/2d/IMSLP91212-PMLP187470-Tartini_-_Trattato_di_musica.pdf
> Many thanks to the anonymous scanner.
>
> You can check for yourself that Tartini's Tratato di Musica, 1754, does _not_ contain anything even remotely resembling the 3-stroke semi-sharp (quartertone) symbol that we have been attributing to him for decades.

Bravo, Dave!

> Instead he uses a simple 2-stroke san-serif "x" as his semi-sharp, which you can see notating an 11th harmonic on page 95 and an enharmonic tetrachord on page 121. This is quite logical when you notice that his sharp symbol is similar to ours but rotated 45 degrees (except when used in a key signature).

These symbols are not original with Tartini (see below).

> I see no sesqui-sharp symbol (3/4 tone).
>
> So now we're looking for the earliest usage by Adriaan Fokker (or anyone else) to see if they have priority over Richard Stein.
>
> According to George Secor, Gardner Read in his "20th Century Microtonal Notation" says "It is significant, as well as being historically pertinent, that these two modified symbols [the 3-stroke and 5-stroke semi and sesqui sharps] were used in the first quarter-tone composition of our century to be commercially published,­ the 1909 __Zwei Konzertstucke fur Violoncello und Klavier_ of Richard Stein. The Harvard Dictionary of Music says Stein pulished this quartertone piece in 1906.
> http://books.google.com.au/books?id=02rFSecPhEsC&pg=PA510&lpg=PA510&dq=Richard+stein+quartertones&source=bl&ots=Uk5ZOISkSN&sig=nUOls089VEsOsftPUsqWt4mPm_M&hl=en&sa=X&ei=xP-XT6z6LqWViQeSm4DcBQ&ved=0CDwQ6AEwBA#v=onepage&q=Richard%20stein%20quartertones&f=false
>
> -- Dave Keenan http://dkeenan.com

For the record, I would like to supply some additional information that came up in the course of our discussion off-list with Tony Salinas last year. Here are a couple of paragraphs from my messages of 24 and 25 March 2010 (with my present comments in [square brackets] added for clarification):

<< In the chapter on fifth-tones and the 31-tone scale, [Gardner] Read discusses the symbols of "Nicola Vincentino" (sic, should be Vicentino) & Fabio Colonna (pp. 116-117, with illustrations), and he also mentions that the semi-flat usually credited to Tartini (1754) was proposed by Quirinius van Blankenburg in 1739. However, in Read's illustration of van Blankenburg's notation (p. 117) there is no sesqui-flat symbol shown. Since Read is typically quite thorough about these things, I believe that this absence is significant and that we can conclude that the 31-tone sesqui-flat symbol (used by Fokker & attributed to Tartini), and thus the underlying logic behind the fractional flat symbols, was indeed original with Tartini -- until proved otherwise. (I believe that we have a parallel here with fractional flats in that: van Blankenburg is to Tartini as [Richard] Stein is to [Mildred] Couper; the former created [a] semi-flat symbol, while the latter employed logic linking the [new] semi-flat and [existing] flat symbols to [create a new] sesqui-flat symbol. [The parallel is not exact, however; read on!])

... It's also clear that Couper devised the sesqui-flat (in [her composition entitled] _Dirge_) prior to using the (backwards-flat) semi-flat. If we assume that she probably didn't know about Stein's symbols [since she reported that she got her fractional sharp symbols from Vyschnegradsky, without any mention of Stein], then we can probably also assume that she independently devised the (backwards-flat) semi-flat, since there is no earlier occurrence of it in Read's book apart from Stein. Her name should therefore be used for the [fractional flat] symbol set, not only because she originated the sesqui-flat, but also because she originated the logical connection between the sesqui-flat and [re-invented] semi-flat symbols.

… In case you're wondering, van Blankenburg's semi-sharp is a simple "x" and his sharp resembles a modern sharp rotated about 45 degrees, more or less [exactly what we find in Tartini's treatise, so van B. has precedence]. Also, no double-sharp or double-flat symbols are shown in Read's illustration, so I'm concluding that van Blankenburg didn't propose any symbols altering more than an apotome. >>

I hope I haven't overly muddied the waters with all of this "clarification". :-)

--George