Re: Sabat-Garibaldi's Dinarra -- 1/9 alpha

Hello, everyone, and on the basis of reading some of Eduardo
Sabat-Garibaldi's treatise, I can certainly confirm that his
instrument is tuned in a 1/9-schisma temperament with 53 frets per
octave -- a "virtually closed" system very close to 53-tET (as is a
53-note Pythagorean tuning just on the other side of the point of
precise mathematical closure).

Coming from a Pythagorean standpoint, I find the "nine steps to a
tone" readily comprehensible -- nine "commas" to a 9:8 whole-tone of
about 203.91 cents, or actually something very slightly smaller
because of the "microtempering" the fifths in the narrow direction by
1/9 of a 3-5 schisma.

His book is very interesting, and refers to the 3-5 schisma of ~1.95
cents as the "musical atom" known as Alpha, and the 3-7 schisma of
~3.80 cents as Beta-2. Beta-5 is the 5-7 schisma of ~5.75 cents. By
the way, Scala uses this terminology.

The idea of the tempering of the fifth by 1/9 of Alpha, the 3-5
schisma, is that a pure 6:5 or 5:3 is connected with a special effect
which Sabat-Garibaldi terms a _trino harmonico_ -- not a Gothic trine,
but a Spanish term for a kind of "trill" or similar effect.

Generally, he presents this 53-tone instrument as representing a kind
of affinity between the gamuts of Pythagoras and Ptolemy -- that is,
between Pythagorean tuning and 5-limit JI, through schismic
equivalence as we might say. Of course, this statement could apply to
anything close to Pythagorean; the choice of 1/9 Alpha seems to me a
distinguishable question from the general purpose and philosophy of
the tuning.

Most of the book seems to focus on factors of 3 and 5, with 5-limit
thirds and sixths preferred, and a notation developed based on the
53-tone system. The intonation of various intervals and sonorities is
described in terms of these "commas" or steps; for example 0-22-31
would be a sonority with a pure fourth and fifth in relation to the
lowest note, and a ~9:8 major second (9 commas) between the upper
notes.

There is a chapter on factors of 7, which includes an interesting table of
"triads" of intervals -- meaning sets of three versions of an interval a
"comma" apart such as major thirds at ~5:4, ~81:64, or ~9:7 (17, 18, or 19
commas), based on ratios of 3, 5, or 7. However, I'd say that the main
outlook is on a kind of harmonic style where a 5-limit ideal mostly
prevails.

He is very concerned with the problem of transposition -- or, as it
said in Spanish as well as at least some 16th-century Romance
languages, the "transport" of a sonority or scale pattern from one
step to another.

The question of a Dinarra playing together with a 12-tET instrument is
maybe a bit like the problem in the later 16th or early 17th century
of a meantone keyboard playing with a 12-tET lute. Theorists discuss
why it's not very appealing, but maybe the players could finesse it in
one way or another.

Dave, your question of just how much accuracy in fretting is
meaningful is an interesting point: with a 12-tET lute, the simple
rule of 18:17 turns out to be more accurate than the correct
logarithmic division because of the physics of fretting pressure.

Anyway, while Eduardo Sabat-Garabaldi's complete book may be the best
source on his instrument -- and I'd be very interested in his response
if he posts here to my attempt at a summary -- I can at least confirm
that 1/9 Alpha is the temperament, and a Pythagorean or 53-tET system
with a certain 5-limit outlook a more general theme.

Maybe I'm especially aware of this because the counting in "commas" is
quite congenial to my own outlook, but my neo-Gothic orientation would
lead me to emphasize different solutions. For example, he expresses a
strong preference for a major third of 17 commas (~5:4) rather the
usual Pythagorean ditone of 18 commas (~81:64).

If I were writing this, I might take 18 commas as the norm, with 17 as
a special effect (the diminished fourth), and 19 as a desirable choice
for many cadences where the major third (~9:7) expands to a fifth.

Whatever view one takes of the precise tuning desirable for a given
musical style (e.g. 1/15-Beta2 for 2-3-7-9?), or the best intonational
choices for that style, his Pythagorean system and 53-tone notational
concepts might apply nicely.

Most respectfully,

Margo Schulter
mschulter@value.net

In a message dated 8/14/01 2:17:56 AM Eastern Daylight Time,
MSCHULTER@VALUE.NET writes:

> Hello, everyone, and on the basis of reading some of Eduardo
> Sabat-Garibaldi's treatise, I can certainly confirm that his
> instrument is tuned in a 1/9-schisma temperament with 53 frets per
> octave -- a "virtually closed" system very close to 53-tET (as is a
> 53-note Pythagorean tuning just on the other side of the point of
> precise mathematical closure).
>

Thank you, Margo, for checking out his book. Eduardo is trying to get it
translated into English, but no one has picked it up as yet. Although you
have read specific theory, in a week of working with the Uruguayan tuning,
12-tET fit right in...not at a 9/8.

> The question of a Dinarra playing together with a 12-tET instrument is
> maybe a bit like the problem in the later 16th or early 17th century
> of a meantone keyboard playing with a 12-tET lute. Theorists discuss
> why it's not very appealing, but maybe the players could finesse it in
> one way or another.
>

There was no finessing for tuning. Eduardo encouraged 12-tET guitars for the
Dinarra accompanying. The players told me it was regular 12 with much in
between.

Question: when the Dinarra was made, were the original guitar frets pulled
out and reset? I do not think so. Does it say in the book?

Best, Johnny Reinhard

--- In tuning@y..., Afmmjr@a... wrote:

>
> There was no finessing for tuning. Eduardo encouraged 12-tET
guitars for the
> Dinarra accompanying. The players told me it was regular 12 with
much in
> between.

I suspect that was meant in general, rather than exact, terms.

> Question: when the Dinarra was made, were the original guitar frets
pulled
> out and reset? I do not think so. Does it say in the book?
>
> Best, Johnny Reinhard

Johnny, if you are correct that the whole tones are split into 9
parts, making 54 tones per octave, wouldn't _half_ of the 12-tET
frets need to be pulled out?

Anyhow, we have a serious discrepancy between (a) everything Eduardo
has written on his website and on this list, and (b) the impression
he gave you verbally. Why don't we contact him and find out what the
deal is with the Dinarra?

Boy, now I'm really confused!... Thought it was 53 from earlier
statements in this thread. That would make good sense! To my mind, 54
is NUTS! It not only messes up the amazingly just tunings of 53t-ET,
but eliminates compatibility with half of 12t-ET as Paul indicates
here.....!!!!!!???????

Regards,

Bob

P.S. Please ready my previous comment in this thread about 53t-ET if
you haven't already.

--- In tuning@y..., "Paul Erlich" <paul@s...> wrote:
> --- In tuning@y..., Afmmjr@a... wrote:
>
> >
> > There was no finessing for tuning. Eduardo encouraged 12-tET
> guitars for the
> > Dinarra accompanying. The players told me it was regular 12 with
> much in
> > between.
>
> I suspect that was meant in general, rather than exact, terms.
>
> > Question: when the Dinarra was made, were the original guitar
frets
> pulled
> > out and reset? I do not think so. Does it say in the book?
> >
> > Best, Johnny Reinhard
>
> Johnny, if you are correct that the whole tones are split into 9
> parts, making 54 tones per octave, wouldn't _half_ of the 12-tET
> frets need to be pulled out?
>
> Anyhow, we have a serious discrepancy between (a) everything
Eduardo
> has written on his website and on this list, and (b) the impression
> he gave you verbally. Why don't we contact him and find out what
the
> deal is with the Dinarra?

--- In tuning@y..., BobWendell@t... wrote:

> Boy, now I'm really confused!... Thought it was 53 from earlier
> statements in this thread. That would make good sense!

Sabat-Garibaldi's treatise, and his posts to this list, all indicate
a slightly unequal 53-tone tuning (a chain of 52 fifths, each
tempered by 1/9 schisma).

> To my mind, 54
> is NUTS! It not only messes up the amazingly just tunings of 53t-
ET,
> but eliminates compatibility with half of 12t-ET as Paul indicates
> here.....!!!!!!???????

Agreed.