Yahoo Tuning Groups Ultimate Backup tuning Sabat-Garibaldi's Dinarra (was: A new era in JI guitar design!)

I just learnt, thanks to John Chalmers and the Yahoo search engine (not the
YahooGroups search engine) that around 1978 Eduardo Sabat-Garibaldi
designed and had built, a JI guitar based on a linear microtemperament
(although he didn't describe it in those terms). It uses the conventional
EADGBE open string tuning. The guitar is 5-limit JI only.

Sabat-Garibaldi wished to have both accurate Pythagorean (3-limit JI) and
accurate Ptolemaic (5-limit JI) diatonic scales and to be able to modulate
them widely. See
http://members.nbci.com/drew_skyfyre/xe/dinarra.html

He rediscovered schismic temperament (where an octave-reduced chain of 8
perfect fourths gives a major third). He used the 5-limit MA optimum
generator, i.e. the generator which gives the minimum value for the maximum
of the absolute errors of all 5-limit intervals. This is a fourth widened
by 1/9 of the schisma, or equivalently a fifth narrowed by 1/9-schisma
(701.738c). A schisma is 32805/32768 = 2^-15 * 3^8 * 5^1 ~= 1.954 cents.

1/9-schisma temperament _is_ just. It has precise 5:6 minor thirds and has
fifths and major thirds which are only 0.2 c narrower than 2:3 and 4:5.

In case you were wondering, it has a max 7-limit error of 7.1c. The best
7-limit schismic temperament occurs with a 2/15-schisma _wide_ fifth, where
the max error is 4.3c. Not a microtemperament.

Numbers of notes for MOS are 5 (7) 12 (17 29 41) 53 (65) 118 ...

Sabat-Garibaldi chose to use 53 frets to the octave on his guitar (called
the Dinarra (pron. Deenarha)). He went to extraordinary lengths to obtain
accurate fret placement. I suspect this was largely a waste of time.

Given the limitations of even the best acoustic instruments, I doubt
whether even Johhny Reinhard could tell by listening to music played on it,
whether such a guitar was fretted for 1/9-schisma or 53-EDO, unless a
53-of-1/9-schisma "wolf" was played (7.7c wide). 53-EDO is approximately
1/29-schisma and has 0.1 c error in the fifths and 1.4c and 1.3c errors in
the major and minor thirds. The question of whether the chain of fifths is
open, or closed at 53, is not likely to be answered by modulation in any
ordinary piece of music.

Which brings me to the other thing I would have done differently, which is
to stop at 29 notes. Even a 5-limit melodic minor only spans 19 generators
and so 29 notes would allow its modulation through 9 different keys (majors
would have 17 keys available). Why anyone would feel that modulation
through 33 different keys was so desirable as to justify putting 53 frets
per octave on a guitar, is beyond me.

Although the 29 fret version would have the same minimum fret spacing
(20.9c) the larger spacings of 70.5c (as opposed to 28.7c for 53 frets)
would give more guidance as to finger placement and there would be only
half the work in building it.

That said, there is some very lovely music on that web page.

-- Dave Keenan
Brisbane, Australia
http://dkeenan.com

🔗Dave Keenan <D.KEENAN@UQ.NET.AU>

--- In tuning@y..., David C Keenan <D.KEENAN@U...> wrote:
> Why anyone would feel that modulation
> through 33 different keys was so desirable as to justify putting 53
frets
> per octave on a guitar, is beyond me.

I hadda thort.

Maybe he wants 53 notes to the octave, not for modulation, but for
_comma_drift_. Perhaps the intention is that, when performers play
pieces that would normally only work in 12-tET or meantone, they
should allow drift to happen.

Can anyone confirm or deny? John Chalmers?

Provided no comma pump is repeated too often in the same direction, or
you have enough rests in which to reset the tonic, 53 notes might be
enough for most pieces. But why not use 53-EDO? Then you can
comma-drift indefinitely. Presumably he believed that theoretical
maximum 0.2c errors would sound better than theoretical maximum 1.4c
errors, despite the reality of +-3c guitar intonation errors. Reminds
me a bit of the "Kellener vs. Werkmeister" thread.

-- Dave Keenan

🔗Paul Erlich <paul@stretch-music.com>

🔗Dave Keenan <D.KEENAN@UQ.NET.AU>

🔗Paul Erlich <paul@stretch-music.com>

🔗Dave Keenan <D.KEENAN@UQ.NET.AU>

--- In tuning@y..., "Paul Erlich" <paul@s...> wrote:
> --- In tuning@y..., "Dave Keenan" <D.KEENAN@U...> wrote:
> >
> > According to this argument there's no point in making a Blackjack
> > guitar (21 frets)? One might as well go straight to the proper
> Canasta
> > with 31?
>
> That's what I said at first.

Why did you change your mind?

> > But what's the point in having frets that you don't plan to use?
>
> (1) You can never plan for everything your compositional instinct
may
> require
> (2) Glissando
> (3) I'll bet that you can't play Graham Breed's Blackjack pump
> progression, in Joe Monzo's voicings, on the Blackjack guitar with
> only 21 frets . . . (getting ready to eat hat)

Your hat is safe, but for one note.

The chord progression is
G<sm7 E>sm7 Dsm7 C<sm7 A>mdim7 F]sm7 B[mdim7

I could play it just fine in a different voicing, which I think is
slightly better (same number of roots and fifths in the bass but only
one seventh in the bass instead of two). Just take Monzo's voicing and
transpose the two lowest voices up an octave (or equivalently the two
highest voices down an octave). Only the four middle strings are used,
so each voice gets a string.

Let me know if you want the tablature.

-- Dave Keenan

🔗BobWendell@technet-inc.com

I'm having trouble understanding this discussion, unless I assume
that no one realizes that 31 steps out of 53 is an astoundingly
accurate Perfect fifth. Fifty-three is the next cycle of fifths after
12 that comes out almost unison, much, MUCH closer than the
Pythagorean comma. The 53rd part of an octave is 22.64 cents, so it's
not hard to see why!

Aren't we all familiar with 53-tone ET as the most perfect equal
temperament (unless we go to the next rational approximation of the
base two log of 3:2 = log(2) 1.5 after 7/12 and 31/53? (The next one
is some ungodly number of steps per octave, as if 53 weren't already
pretty messy from the standpoint of physical ergonomics!)

Partch built instruments (out of temperature-stable glass, since
nothing else would hold a tuning that accurate) to play it. It gives
everything so close to just it's ridiculous. Don't have my scientific
calc with me, but I believe I remember that even the most dissonant
intervals are within 3 or 4 cents of JI.

I do recall having seen 55 EDO mentioned in some threads in this
group. I wonder why anyone would bother with that division when 53
works so wonderfully well?

Respectfully yours,

Bob

--- In tuning@y..., "Paul Erlich" <paul@s...> wrote:
> --- In tuning@y..., "Dave Keenan" <D.KEENAN@U...> wrote:
> > --- In tuning@y..., David C Keenan <D.KEENAN@U...> wrote:
> > > Why anyone would feel that modulation
> > > through 33 different keys was so desirable as to justify
putting
> 53
> > frets
> > > per octave on a guitar, is beyond me.
> >
> > I hadda thort.
> >
> > Maybe he wants 53 notes to the octave, not for modulation, but
for
> > _comma_drift_. Perhaps the intention is that, when performers
play
> > pieces that would normally only work in 12-tET or meantone, they
> > should allow drift to happen.
>
> As far as I know, he's not into comma drift -- especially not when
a
> 12-tET guitar is accompanying!

🔗Paul Erlich <paul@stretch-music.com>

--- In tuning@y..., "Dave Keenan" <D.KEENAN@U...> wrote:
> --- In tuning@y..., "Paul Erlich" <paul@s...> wrote:
> > --- In tuning@y..., "Dave Keenan" <D.KEENAN@U...> wrote:
> > >
> > > According to this argument there's no point in making a
Blackjack
> > > guitar (21 frets)? One might as well go straight to the proper
> > Canasta
> > > with 31?
> >
> > That's what I said at first.
>
> Why did you change your mind?

I didn't! Until today -- see below.

> [To play Graham Breed's progression]
> Only the four middle strings are used,
> so each voice gets a string.

So presumably your fretting hand stays in pretty much the same
position the whole time? Awesome.

> Let me know if you want the tablature.
>
That might be cool if Monz were to include it on his Blackjack
webpage. Given this development, I might actually be in favor of
people just using 21 frets per octave, at least for a while (the
other 10 could always be added in later).

🔗Paul Erlich <paul@stretch-music.com>

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

> I'm having trouble understanding this discussion, unless I assume
> that no one realizes that 31 steps out of 53 is an astoundingly
> accurate Perfect fifth.

Don't worry -- we all realize this.
>
> Aren't we all familiar with 53-tone ET as the most perfect equal
> temperament

Depends how you define perfect. For 3-limit and 5-limit harmonies,
sure. Higher up, no. Also, see below.

> Partch built instruments (out of temperature-stable glass, since
> nothing else would hold a tuning that accurate) to play it.

Partch built 53-tET intruments? This will be news to the Partch
scholars on this list.
>
> I do recall having seen 55 EDO mentioned in some threads in this
> group. I wonder why anyone would bother with that division when 53
> works so wonderfully well?

The 53-division has some serious problems for common-practice music.
The whole tone comes in two sizes, which is rather awkward
melodically. Even more awkward are the "comma-pump" progressions like
C-Am-Dm-G-C and C-F-Dm-G-C. If you try to use good voice leading, the
final C chord is a comma lower than the initial C chord. The
alternative is to have at least one tone, usually D, shift by a comma
in the middle of the progression. This type of "correction" has a
disturbing effect, smacking of poor intontation (melodically, not
harmonically). A good, experienced choral group singing in adaptive
JI will spread the comma over all four chord changes, so that it
passes unnoticed, and there are no full-comma shifts or drifts.

The 55-division was never used in full, but was merely a convenient
way of describing a meantone tuning (whose advantages we are all well
aware) close to 1/6-comma meantone in the 18th century.
Instrumentalists (including Mozart), especially string and wind
players, were taught that the whole-tone was 9 parts (this applies to
_all_ whole-tones, not just the "major" ones as in 53), the diatonic
semitone was 5 parts, and the chromatic semitone 4 parts. Thus the 55-
division was used as a system of reckoning, not as a practical tuning
for instruments.

🔗BobWendell@technet-inc.com

Wow! Thanks, Paul! Very enlightening. I knew I joined this group for
a good reason.

Paul said:
Partch built 53-tET intruments? This will be news to the Partch
scholars on this list.

Bob Answers:
Well, I remember reading about it in the 60s. Anyone interested
should be able to find references to it at the Just Intonation
Network's Website. Don't have time right now to go get the link.
Sorry! I'll get to it later.

--- In tuning@y..., "Paul Erlich" <paul@s...> wrote:
> --- In tuning@y..., BobWendell@t... wrote:
>
> > I'm having trouble understanding this discussion, unless I assume
> > that no one realizes that 31 steps out of 53 is an astoundingly
> > accurate Perfect fifth.
>
> Don't worry -- we all realize this.
> >
> > Aren't we all familiar with 53-tone ET as the most perfect equal
> > temperament
>
> Depends how you define perfect. For 3-limit and 5-limit harmonies,
> sure. Higher up, no. Also, see below.
>
> > Partch built instruments (out of temperature-stable glass, since
> > nothing else would hold a tuning that accurate) to play it.
>
> Partch built 53-tET intruments? This will be news to the Partch
> scholars on this list.

🔗Paul Erlich <paul@stretch-music.com>

🔗BobWendell@technet-inc.com

🔗Paul Erlich <paul@stretch-music.com>

--- In tuning@y..., BobWendell@t... wrote:
> Paul said:
> The alternative is to have at least one tone, usually D, shift by a
> comma in the middle of the progression. This type of "correction"
has
> a disturbing effect, smacking of poor intontation (melodically, not
> harmonically).
>
> Bob comments:
> Maybe in fixed-pitch instruments this could be disturbing,

Yes -- 53-tone organs were built in the 19th century and the comma
shifts made many observers feel that the music came out "slimy" --
likely due to the non-constancy of melodic pitches.
>
> THIS HAPPENS ALL THE TIME WITH GOOD STRING PLAYERS. I have never
> heard anyone comment on it, although admittedly typical musicians
do
> not fairly represent the august company in this group.

String players can use a combination of sliding, vibrato, and very
tiny amounts of temperament to finesse these adjustments. Also,
they'll make them motivically meaningful, by mimicking these effects
in similar melodic phrases that immediately precede and follow the
problematic ones in a piece of music. For the most part, though,
string players won't have an opportunity to play triple-stopped
chords with open strings, so I would say that string players with a
sensitivity to JI harmonies as well as to melody would, most often,
tend to use adaptive JI instead, rather than strict JI with its full
commas.

However, perhaps sadly, most professional string players are not
sensitive to JI harmonies anyway. They've been taught to play 12-tET
intervals, with a shading of tendency tones away from, rather than
towards, their meantone/adaptive JI directions. For example, for the
last two centuries, string players have been taught to play G#
_higher_ than Ab. As a simplification, it's often stated that string
players use Pythagorean tuning -- though when the pitches are
measured, the typical result is much too varied to be pinned down to
anything as rigid as Pythagorean or 12-tET. It's fair to say, though,
that anything resembling just thirds is the exception rather than the
rule in classically-trained string players today. You'll find far
more just-leaning thirds in Celtic and Appalachian fiddle playing,
for example.

🔗BobWendell@technet-inc.com

Paul said:
However, perhaps sadly, most professional string players are not
> sensitive to JI harmonies anyway. They've been taught to play 12-
tET
> intervals, with a shading of tendency tones away from, rather than
> towards, their meantone/adaptive JI directions. For example, for
the
> last two centuries, string players have been taught to play G#
> _higher_ than Ab.

Bob's comment:
Well, I sadly must agree. The whole thing about leading tones needing
to be so skinny really irritates me, though! That whole idea flies
directly in the face of good intonation, and it's a common idea among
string players. Yuck!

I'm a violinist of sorts, although I truly hesitate to say it these
days. In spite of my lack of virtuosity, however, I do tend to play
justly tuned double and triple stops, and in baroque music it is not
so unusual to find chord sequences where the comma is right in your
face as in the example I gave. It doesn't really bother my ear to
shift the comma melodically like that, which you MUST do in so many
instances on the violin, but it DEFINITELY bothers my ear to fail to
make the shift and leave the harmony out by a comma. A lot of triple
stop sequences do use open strings, in spite of the slight misnomer
this implies, since only two and sometimes one of the strings are
actually stopped.

If you listen to the famous Heifetz recordings of the Bach
Unaccompanied Partitas and Sonatas in old RCA mono, you will hear a
LOT of just tuning even in the melodic scale passages, and most
definitely in the double stopping. Superb ear! I find that Perlman
and Zuckerman also tend to play just harmonies a high percentage of
the time, although it is most definitely adaptive as you indicate.

Also, as I'm sure you must be aware, most if not all the original
instrument groups in Europe use authentic period tunings and the best
of them have string players with pretty sensitive auricular apparati
intonation-wise.

🔗Paul Erlich <paul@stretch-music.com>

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

> It doesn't really bother my ear to
> shift the comma melodically like that,

Is this in the context of a particular piece of music, played at an
appro? I feel that melody is of stronger importance than harmony in
most actual music, while the "aesthetics" of isolated chord
progressions may be different.

> which you MUST do in so many
> instances on the violin,

"MUST" . . . in your opinion.

> but it DEFINITELY bothers my ear to fail to
> make the shift and leave the harmony out by a comma.

Well, you can do a number of things in-between these two extremes.
For example, you can have each of the harmonies out by 1/3-comma, in
opposite directions, and thereby reduce the melodic shift to only 1/3-
comma. That's "adaptive tuning", and sounds better to me than either
of the extremes you put forth, if the notes are participating in
melodic lines in an actual piece of diatonic music.
>
> If you listen to the famous Heifetz recordings of the Bach
> Unaccompanied Partitas and Sonatas in old RCA mono, you will hear a
> LOT of just tuning even in the melodic scale passages, and most
> definitely in the double stopping. Superb ear!

Heifetz is definitely a fan of narrow leading tones, though, at least
in other repertoire.

> I find that Perlman
> and Zuckerman also tend to play just harmonies a high percentage of
> the time, although it is most definitely adaptive as you indicate.

Perlman is a master of intonation. Forget about Isaac Stern, though.

> Also, as I'm sure you must be aware, most if not all the original
> instrument groups in Europe use authentic period tunings and the
best
> of them have string players with pretty sensitive auricular
apparati
> intonation-wise.

Yes, very true. But determining just what "authentic period tunings"
are is a very controversial issue for string players. Meantone? JI
with comma shifts and/or drifts? I would say, some form of adaptive
tuning, respecting the best in each of those alternatives but
adhering to neither, is what flows most naturally from the strings of
sensitive players of Renaissance and early Baroque music, whether
today or in the period in question.

The problems of strict JI were well-recognized in the Renaissance,
and one solution was offered by Vicentino in his second tuning of
1555 (implemented on two extended 1/4-comma meantone keyboards tuned
1/4-comma apart, allowing for vertical justness in all triads and
reducing horizontal shifts to a barely audible 1/4-comma). If one had
to point to an "authentic period tuning" to recommend to players of
flexible-pitch instruments, this would have to be it. Margo's recent
62-tone proposal on this list is simply an extension of this system,
to take advantage of the approximate closure of 1/4-comma meantone
when extended to 31 notes.

🔗BobWendell@technet-inc.com

Yes, Paul, I hear you (all puns intended...chuckle)! Isaac Stern I
did forget about long ago. Never liked him much on intonation or on
many other apsects of musicality, especially his performances of
Baroque works in the fully soupy, romantic style of the "old school"
(which, amazingly, many people still love and prefer).

And yes, Perlman is indeed a master on intonation and many other
aspects of musicality.

Also 'MUST' I suppose is a bit strong, and you're right. The violin
is not a fixed pitch instrument and I'm sure I play the games to
which you refer to diguise the shift as much as possible. Just as in
singing, string players have a lot of options this way.

As an experiment, I tempered my violin last night to 1/4-comma
meantone and played a compromise E against the G and A open strings
and it didn't sound half bad (all puns intended again). Further, the
barest move disguised the problem completely as a normal miniscule
melodic nuance.

I agree on the importance of whether the harmonic or melodic nature
of a passage plays a dominant role, and the progression I had in mind
when commmenting is indeed harmonic and minimally melodic in nature.

You folks are a veritable wealth of historical information on tuning.
I am extremely pleased with what I'm learning here. The commnet on
the 1/4-comma shift between two keyboards and the 31 EDO
approximation of the same principle leading to 62-tET is highly
fascinating!

Thanks once again!

Bob

--- In tuning@y..., "Paul Erlich" <paul@s...> wrote:
> --- In tuning@y..., BobWendell@t... wrote:
>
> > It doesn't really bother my ear to
> > shift the comma melodically like that,
>
> Is this in the context of a particular piece of music, played at an
> appro? I feel that melody is of stronger importance than harmony in
> most actual music, while the "aesthetics" of isolated chord
> progressions may be different.
>
> > which you MUST do in so many
> > instances on the violin,
>
> "MUST" . . . in your opinion.
>
> > but it DEFINITELY bothers my ear to fail to
> > make the shift and leave the harmony out by a comma.
>
> Well, you can do a number of things in-between these two extremes.
> For example, you can have each of the harmonies out by 1/3-comma,
in
> opposite directions, and thereby reduce the melodic shift to only
1/3-
> comma. That's "adaptive tuning", and sounds better to me than
either
> of the extremes you put forth, if the notes are participating in
> melodic lines in an actual piece of diatonic music.
> >
> > If you listen to the famous Heifetz recordings of the Bach
> > Unaccompanied Partitas and Sonatas in old RCA mono, you will hear
a
> > LOT of just tuning even in the melodic scale passages, and most
> > definitely in the double stopping. Superb ear!
>
> Heifetz is definitely a fan of narrow leading tones, though, at
least
> in other repertoire.
>
> > I find that Perlman
> > and Zuckerman also tend to play just harmonies a high percentage
of
> > the time, although it is most definitely adaptive as you indicate.
>
> Perlman is a master of intonation. Forget about Isaac Stern, though.
>
> > Also, as I'm sure you must be aware, most if not all the original
> > instrument groups in Europe use authentic period tunings and the
> best
> > of them have string players with pretty sensitive auricular
> apparati
> > intonation-wise.
>
> Yes, very true. But determining just what "authentic period
tunings"
> are is a very controversial issue for string players. Meantone? JI
> with comma shifts and/or drifts? I would say, some form of adaptive
> tuning, respecting the best in each of those alternatives but
> adhering to neither, is what flows most naturally from the strings
of
> sensitive players of Renaissance and early Baroque music, whether
> today or in the period in question.
>
> The problems of strict JI were well-recognized in the Renaissance,
> and one solution was offered by Vicentino in his second tuning of
> 1555 (implemented on two extended 1/4-comma meantone keyboards
tuned
> 1/4-comma apart, allowing for vertical justness in all triads and
> reducing horizontal shifts to a barely audible 1/4-comma). If one
had
> to point to an "authentic period tuning" to recommend to players of
> flexible-pitch instruments, this would have to be it. Margo's
recent
> 62-tone proposal on this list is simply an extension of this
system,
> to take advantage of the approximate closure of 1/4-comma meantone
> when extended to 31 notes.

🔗BobWendell@technet-inc.com

In my previous statement below:

"The comment on the 1/4-comma shift between two keyboards and the 31
EDO approximation of the same principle leading to 62-tET is highly
fascinating!"

Oops! For the record, didn't mean 62-tET. Obviously two 31-tET
keyboards tuned 1/4 comma apart do NOT constitute 62-tET. A quarter
comma is roughly 5.5 cents and half a fifth-tone in 31-tET is about
19.5 cents.

--- In tuning@y..., BobWendell@t... wrote:
> Yes, Paul, I hear you (all puns intended...chuckle)! Isaac Stern I
> did forget about long ago. Never liked him much on intonation or on
> many other apsects of musicality, especially his performances of
> Baroque works in the fully soupy, romantic style of the "old
school"
> (which, amazingly, many people still love and prefer).
>
> And yes, Perlman is indeed a master on intonation and many other
> aspects of musicality.
>
> Also 'MUST' I suppose is a bit strong, and you're right. The violin
> is not a fixed pitch instrument and I'm sure I play the games to
> which you refer to diguise the shift as much as possible. Just as
in
> singing, string players have a lot of options this way.
>
> As an experiment, I tempered my violin last night to 1/4-comma
> meantone and played a compromise E against the G and A open strings
> and it didn't sound half bad (all puns intended again). Further,
the
> barest move disguised the problem completely as a normal miniscule
> melodic nuance.
>
> I agree on the importance of whether the harmonic or melodic nature
> of a passage plays a dominant role, and the progression I had in
mind
> when commmenting is indeed harmonic and minimally melodic in
nature.
>
> You folks are a veritable wealth of historical information on
tuning.
> I am extremely pleased with what I'm learning here. The commnet on
> the 1/4-comma shift between two keyboards and the 31 EDO
> approximation of the same principle leading to 62-tET is highly
> fascinating!
>
> Thanks once again!
>
> Bob
>
>
>
> --- In tuning@y..., "Paul Erlich" <paul@s...> wrote:
> > --- In tuning@y..., BobWendell@t... wrote:
> >
> > > It doesn't really bother my ear to
> > > shift the comma melodically like that,
> >
> > Is this in the context of a particular piece of music, played at
an
> > appro? I feel that melody is of stronger importance than harmony
in
> > most actual music, while the "aesthetics" of isolated chord
> > progressions may be different.
> >
> > > which you MUST do in so many
> > > instances on the violin,
> >
> > "MUST" . . . in your opinion.
> >
> > > but it DEFINITELY bothers my ear to fail to
> > > make the shift and leave the harmony out by a comma.
> >
> > Well, you can do a number of things in-between these two
extremes.
> > For example, you can have each of the harmonies out by 1/3-comma,
> in
> > opposite directions, and thereby reduce the melodic shift to only
> 1/3-
> > comma. That's "adaptive tuning", and sounds better to me than
> either
> > of the extremes you put forth, if the notes are participating in
> > melodic lines in an actual piece of diatonic music.
> > >
> > > If you listen to the famous Heifetz recordings of the Bach
> > > Unaccompanied Partitas and Sonatas in old RCA mono, you will
hear
> a
> > > LOT of just tuning even in the melodic scale passages, and most
> > > definitely in the double stopping. Superb ear!
> >
> > Heifetz is definitely a fan of narrow leading tones, though, at
> least
> > in other repertoire.
> >
> > > I find that Perlman
> > > and Zuckerman also tend to play just harmonies a high
percentage
> of
> > > the time, although it is most definitely adaptive as you
indicate.
> >
> > Perlman is a master of intonation. Forget about Isaac Stern,
though.
> >
> > > Also, as I'm sure you must be aware, most if not all the
original
> > > instrument groups in Europe use authentic period tunings and
the
> > best
> > > of them have string players with pretty sensitive auricular
> > apparati
> > > intonation-wise.
> >
> > Yes, very true. But determining just what "authentic period
> tunings"
> > are is a very controversial issue for string players. Meantone?
JI
> > with comma shifts and/or drifts? I would say, some form of
adaptive
> > tuning, respecting the best in each of those alternatives but
> > adhering to neither, is what flows most naturally from the
strings
> of
> > sensitive players of Renaissance and early Baroque music, whether
> > today or in the period in question.
> >
> > The problems of strict JI were well-recognized in the
Renaissance,
> > and one solution was offered by Vicentino in his second tuning of
> > 1555 (implemented on two extended 1/4-comma meantone keyboards
> tuned
> > 1/4-comma apart, allowing for vertical justness in all triads and
> > reducing horizontal shifts to a barely audible 1/4-comma). If one
> had
> > to point to an "authentic period tuning" to recommend to players
of
> > flexible-pitch instruments, this would have to be it. Margo's
> recent
> > 62-tone proposal on this list is simply an extension of this
> system,
> > to take advantage of the approximate closure of 1/4-comma
meantone
> > when extended to 31 notes.

🔗Eduardo Sabat-Garibaldi <ESABAT@ADINET.COM.UY>

--- In tuning@y..., Afmmjr@a... wrote:
> Hi Dave
>
> Actually, the NY debut of Eduardo Sabat-Garibaldi's Dinarra from
Montevideo,
> Uruguay took place during Microthon 2000. He stayed here a week.
The major
> seconds of a whole tone scale are divided into 9 parts.

>>Johnny, this is not correct, as it would imply 54 tones per octave.
>>In fact, there are 53, coming from a single chain of 1/9-schisma
>>tempered fifths.
-------------------------------------------------

Dear friends, Johnny, Paul, Dave, Margo, Wim, Kris, Bob, Joe, and
everybody else.
Firstly, I am overwhelmed by the fact that such a fine collection of
people
have discussed the Dinarra over the Internet.

I would answer your many questions, but please be patient.
----------------------------------

To Paul and Johnny:

I don't understand exactly what you mean when you say that there are 54
notes per Octave. Though 6 tones in the Octave multiplied by 9 commas
equals 54, the case of the Dinarra is different. The systematic of the
Dinarra is Pithagoric (with some peculiarities), thus I count 5 tones
of 9 commas each (45) plus 2 semitones of 4 commas each (8), resulting
53 commas.
These 53 commas are enclosed in 54 notes in the Octave but the first and
the last notes have the same note-name (one duplicate the frequency of
the other).
The 53 notes are defined by a row of 52 fifths. This row of fifths I
call
Estructura Pitagorica. By comparison the Diatonic Pithagorean Structure
is formed by a row of 6 fifths that make 7 note-names that are closed
in the 8 notes per Octave.
The semitonic scale is formed by 11 fifths, and has 12 note-names closed
in 13 notes per Octave. Therefore, the Dynamic Scale (Gama Dinamica) is
formed
by 52 fifths, has 53 Omega Notes (or Dynamics Notes) that are closed in
54 notes per Octave.
I didn't use above the term Cromatic Pithagoric Scale instead of
"semitonic" because this name is reserved for the scale of 21
note-names.(According with "La Gamme" by Richard P., France, and some
comments made in this list a time ago).

My question is the following: "is number 54 as I use it the same as your
?
-------------------------------------

To Johnny,
Quote "So, it is like the French system, with 9 commas to the
equal-tempered whole tone."
Unquote: I nodded yes.

But please excuse me if I wrongly nodded yes. I believe I didn't
understand. You know my difficulties with the English language.

What's the meaning of "French System"?

Greetings
Eduardo

--
Eduardo Sabat-Garibaldi
Simon Bolivar 1260
11300 Montevideo
Uruguay
Phone: (598)(2) 7080952
Webpage (Spanish): http://www.geocities.com/dinarra2000/dinarra.html
Webpage (English): http://members.nbci.com/drew skyfire/xe/dinarra.html
IFIS Webpage: http://www.invention-ifia.ch
look for patent 101

🔗Paul Erlich <paul@stretch-music.com>

🔗Eduardo Sabat-Garibaldi <ESABAT@ADINET.COM.UY>

🔗Dave Keenan <D.KEENAN@UQ.NET.AU>

--- In tuning@y..., Eduardo Sabat-Garibaldi <ESABAT@A...> wrote:
> Re: TD 1520 and 1521.
> Dear Mr. Dave Keenan,
> To understand fully your points of view and ideas I need to know in
your terms the meaning of
> different topics.

Greetings Eduardo,

> How does it generate the scale of 29 notes ?

Using the same fifth as the Dinarra, 1/9-schisma narrow of 2:3, make
the scale as an octave reduced chain of only 28 of them, instead of
52. We call both of these "schismic" scales.

The one with 29 note names will have only two step-sizes, as does the
Dinarra. Its smallest step will be the same as that of the Dinarra,
but it will not require as much work to build it and it will still
give plenty of room for modulation before hitting any wolves.

> What is the 21 Blackjack guitar and Canasta 31 ?

Blackjack and Canasta are not intended for playing music in the
standard western major and minor scales. These scales consist of
octave-reduced chains of respectively 20 and 30 minor seconds of 116.7
cents. They have only two step sizes and they approximate many ratios
of odd numbers up to 11 (and their octave equivalents), within 3.3
cents.

The schismic scales approximate ratios of odd numbers up to 5 within
0.2 cents, but I claim that such accuracy is not available from a
guitar, nor is it required by human ears.

> >despite the reality of +-3c guitar intonation errors.
> What the meaning of that?
> From where did you got this information?

http://www.izzy.net/~jc/PSTInfo/fretbd.html

Regards,
-- Dave Keenan

🔗Eduardo Sabat-Garibaldi <ESABAT@ADINET.COM.UY>

Dear Mr. Dave Keenan:

>The one with 29 note names will have only two step-sizes, as does the
>Dinarra. Its smallest step will be the same as that of the Dinarra,
>but it will not require as much work to build it.

About 30 years ago I invented the Gama Dinamica 28, an arrangement of 28

notes names made with Pithagoric fifths of 3/2 each.
After I substitute the pure Pith. values by others related with 5, but
as a puzzle
because in those moments I wasn't dicovered yet the deep relation for
the harmonics
3 and 5. (i.e. 16/15, 8/5, 6/5 and 9/5 are by fifths).
In my files I must have the list of the numbers that I copyrighted.
But in those times I said "if I would know the deep reason of 5 and 3 I
might do a complete arrangement by commas", because in those moments
and now I thought and think that the rational scale of the future must
be by commas.

The system you propose of 29 notes is interesting but in my opinion the
future is waiting for new news.
Try to make a design for a Dinarra-29. I am sure you will note that
there must be
some or many uncompleted frets, and in order to make an arrangement of
an all
complete frets you must arrive to a design by commas.

>Blackjack and Canasta are not intended for playing music in the
>standard western major and minor scales. These scales consist of
>octave-reduced chains of respectively 20 and 30 minor seconds of 116.7
>cents. They have only two step sizes and they approximate many ratios
>of odd numbers up to 11 (and their octave equivalents), within 3.3
>cents.

OK, thanks, I didn't know them. Most of the gray matter used through
history was
trying to reconcile theory of the intonation and its practice.

>The schismatic scales approximate ratios of odd numbers up to 5 within
>0.2 cents,

The couple 6/5-5/3 is just, 8/5-5/4 and 9/5-10/9 are at 0.2 cent, and
16/15-15/8 at
0.4 cent. from the just value.
In my book "Principios de la Gama Dinamica" there is the Chapter "El
armonico 7".
There are around 15 enharmonic notes (for harm. 7) that give from 0.4 to
1.3 cent
for "mayor" ratios and others for "minor". The others have around 7
cents.
In the Dinarra the "mayor" spaces of the fingerboard (that are 12 per
Octave) gives
an Harm. 7 to the open string almost just. This is one of the reason
that explain why
I choice the Omega variant to the 53 root of two.

>but I claim that such accuracy is not available from a
>guitar, nor is it required by human ears.
Yes, by first time theory is over the practice, and fixed.
Now we must improve many topics about fretting and strings.

> >despite the reality of +-3c guitar intonation errors.
> What the meaning of that?
> From where did you got this information?

http://www.izzy.net/~jc/PSTInfo/fretbd.html

Thanks,
Yes, guitar makers and luthiers must consider the new system.

Greetings
Eduardo
--
Eduardo Sabat-Garibaldi
Simon Bolivar 1260
11300 Montevideo
Uruguay
Phone: (598)(2) 7080952
Webpage (Spanish): http://www.geocities.com/dinarra2000/dinarra.html
Webpage (English): http://members.nbci.com/drew skyfire/xe/dinarra.html
IFIS Webpage: http://www.invention-ifia.ch
look for patent 101

🔗Dave Keenan <D.KEENAN@UQ.NET.AU>

--- In tuning@y..., Eduardo Sabat-Garibaldi <ESABAT@A...> wrote:
> Dear Mr. Dave Keenan:

Just call me Dave.

> The system you propose of 29 notes is interesting but in my opinion
> the future is waiting for new news.
> Try to make a design for a Dinarra-29. I am sure you will note that
> there must be
> some or many uncompleted frets, and in order to make an arrangement
> of an all complete frets you must arrive to a design by commas.

Here's my design. This is the optimal fretting in cents for 29 of
5-limit-schismic temperament (Dinarra-29) when the open string tuning
is the standard EADGBE. That's 407.0 cents between the G and B
strings, 498.3 cents between the others).

fret
tuning spacing
(cents) (cents)
0.0 20.9
20.9 70.5
91.3 20.9
112.2 70.5
182.6 20.9
203.5 20.9
224.3 70.5
294.8 20.9
315.6 70.5
386.1 20.9
407.0 70.5
477.4 20.9
498.3 20.9
519.1 70.5
589.6 20.9
610.4 70.5
680.9 20.9
701.7 20.9
722.6 70.5
793.0 20.9
813.9 70.5
884.4 20.9
905.2 20.9
926.1 70.5
996.5 20.9
1017.4 70.5
1087.8 20.9
1108.7 70.5
1179.1 20.9
1200.0

-- Dave Keenan

🔗Eduardo Sabat-Garibaldi <ESABAT@ADINET.COM.UY>

Re: [tuning] Digest Number 1549

Dave and all the tuning friends,
In order to set our terminology I'll make some commentaries.
The 53 Pithagoric as per and the 53 schismic (as you call) have two kinds of
commas. In both cases there is set of 12 different commas than the other 41.
I call Harmonic commas to the 12 said and Enharmonic to the other 41.
In the case of the just Pith. the 12 enharm. are smaller than the others.
In the case of the 53-schismic (or Omega as I call) scale the 12 enharm. are bigger
than the others.
In case of the Dinarra, it can see at sight the 12 spaces bigger than the surrounding
ones. Those are the 12 enharm. commas.

Pith. Harm. Comma --- (3/2) raised 12 equals 23,46 cents.
Pith. Enharm. Comma --- (3/2) raised (-41) (raised minus 41) equals 19,84 cents.

Omega Harm. Comma --- Omega fifth raised 12 equals 20,9 cents.
Omega Enharm. Com-- Omega fifth raised (-41) equals 28,7 cents.

The bigger space of Dinarra-29 is formed by 2 times 20,9 plus 28,7
equals 70,5 cents.

Greetings
Eduardo

🔗Dave Keenan <D.KEENAN@UQ.NET.AU>

--- In tuning@y..., Eduardo Sabat-Garibaldi <ESABAT@A...> wrote:
> In my book "Principios de la Gama Dinamica" there is the Chapter "El
> armonico 7".
> There are around 15 enharmonic notes (for harm. 7) that give from
0.4 to
> 1.3 cent
> for "mayor" ratios and others for "minor". The others have around 7
> cents.
> In the Dinarra the "mayor" spaces of the fingerboard (that are 12
per
> Octave) gives
> an Harm. 7 to the open string almost just. This is one of the
reason
> that explain why
> I choice the Omega variant to the 53 root of two.

Ah yes! What I've been calling 5-limit schismic _does_ have an
accurate approximation of 4:7, as a chain of 39 perfect fifths. Since
the 4:5 is a chain of 8 perfect fourths, we need 48 notes in the chain
before we can get a single 4:5:6:7 chord. So the Dinarra, with 53
notes, has 6 of these chords with 0.4 c accuracy.

But if 14 perfect fourths are used as the approximation to 4:7 then
the error is about 7 cents, perceptibly non-just.

-- Dave Keenan

🔗Eduardo Sabat-Garibaldi <ESABAT@ADINET.COM.UY>

Tuning Digest 1551

Dave,
>> The bigger space of Dinarra-29 is formed by 2 times 20,9 plus 28,7
>> equals 70,5 cents.

>Yes, certainly. Is there a problem with that?

Not, it was just a commentary, a confirmation of your numbers with the
Dinarra
numbers.

>I'm claiming that (apart from the obvious glissandi) most of the
>pieces of music played on the Dinarra could be played on a Dinarra-29
>with exactly the same intonation, but without the trouble of having to
>fit 53 frets per octave. Do you agree, Mr Eduardo Sabat-Garibaldi?

I would say "many" instead of "most" and "almost exactly" instead of
"exactly".
It depends on your ear. But I suspect (to not say I'm sure) that if you
had had a
53-Dinarra during more than 20 years, as I did, your opinion on the
exactness of
intonation of the music would be different.
--------------------------------------------------
What's the problem with to fit 53 frets instead of 29?
Is it a problem on the price?, What's the trouble?
--------------------------------------
According some commentaries you have made I guess you have some
intellectual
material different than my web pages have.
What do you have about "Correccion por la pisada de la cuerda"
(Correction due to
the press down of the string), and also the drawing I call "Telarana
Pitagorica"
(Pithagoric spider web) with both the "Ptolemaic Spider" and "Harm. 7
Spider" ?
------------------------------------
Have you made an electric or acoustic Dinarra 29?

Greetings
Eduardo

🔗Dave Keenan <D.KEENAN@UQ.NET.AU>

--- In tuning@y..., Eduardo Sabat-Garibaldi <ESABAT@A...> wrote:
> What's the problem with to fit 53 frets instead of 29?
> Is it a problem on the price?, What's the trouble?

Yes. I imagine it would be cheaper, but whether by much I don't know.
But I also imagine it would be easier to play without so much choice
of where to put one's fingers. I am not much of a guitarist.

But as you point out, with only 29 we would miss out on those accurate
7th harmonic intervals.

> According some commentaries you have made I guess you have some
> intellectual
> material different than my web pages have.
> What do you have about "Correccion por la pisada de la cuerda"
> (Correction due to
> the press down of the string),

I know nothing about this, and have not read yours. Can you give the
web page? I started with a guitar already fretted for 12-tET and
assumed they had those frets about right. I measured them all from the
nut and interpolated using a best-fit hyperbola to find the positions
for the new frets.

> and also the drawing I call "Telarana
> Pitagorica"
> (Pithagoric spider web) with both the "Ptolemaic Spider" and "Harm.
7
> Spider" ?

I haven't seen these. Can you give the web page?

> Have you made an electric or acoustic Dinarra 29?

No. Only a 12-of-meantone (1/4 comma or 31-tET) with split frets, so
far.

-- Dave Keenan

🔗Eduardo Sabat-Garibaldi <ESABAT@ADINET.COM.UY>

SECOND E-MAIL, CORRECTED

Tuning Digest 1551

Dave,
>> The bigger space of Dinarra-29 is formed by 2 times 20,9 plus 28,7
>> which equals 70,5 cents.

>Yes, certainly. Is there a problem with that?

Not, it was just a comment, a confirmation of your numbers with the
Dinarra
numbers.

I would say "many" instead of "most" and "almost exactly" instead of
"exactly".
It depends on your ear. But I suspect (not to say I'm sure) that if you
had had a
53-Dinarra during more than 20 years, as I did, your opinion on the
exactness of
intonation of the music would be different.
--------------------------------------------------
What's the problem with to fit 53 frets instead of 29?
Is it a problem on the price?, What's the trouble?
--------------------------------------
According to some comments you have made I guess you have some
intellectual
material different from the one my web pages have.
Do you have something about "Correccion por la pisada de la cuerda"
(Correction by means of
pressing down the string), and also about the drawing I call "Telaran~a
Pitagorica"
(Pithagoric spider web) with both the "Ptolemaic Spider" and "Harm. 7
Spider" ?
------------------------------------
Have you made an electric or acoustic Dinarra 29?

Greetings
Eduardo

🔗Paul Erlich <paul@stretch-music.com>

🔗Eduardo Sabat-Garibaldi <ESABAT@ADINET.COM.UY>

Wim,
Merci beaucoup for your comments.
We took two Dinarras to Microthon 2000.
Alejandro Sanchez preferes strings "11" instead of the "9" ones.
("11" stands for 0.011 inches for the first string, E).
Like you and me, all the other guitar players that have played electric

Dinarra prefer strings number 9.
I would like to know what do you mean by the word "bend",
I guess it means bar of finger, am I riight?
.
Greetings
Eduardo

-------------------------------------------
>>>>>>>Message: 21 TUNING DIGEST 1528 >>>>>>>>>>>
Date: Thu, 16 Aug 2001 09:45:17 +0200
From: "Wim Hoogewerf" <wim.hoogewerf@fnac.net>
Subject: Re : Re: Sabat-Garibaldi's Dinarra (was: A new era in JI guitar
design!)

I actually played a little on the Dinarra after the Microthon 2000
concert.
Eduardo told me that the system was not exactly 53-tet and that the main

musical purpose was to give expression to intervals in the same way
singers
can do, even when they are accompanied by a 12-tet instrument like the
piano
or a guitar. This is exactly what was happened during the concert, even
if
one of the background-guitars had an E-string which didn't stop to slip
away. Eduardo's guitarist mainly played latin-jazz standards, I think
there
was even The Girl from Ipanema.

The guitar itself was not really difficult to play. It had extremely
heavy
strings, which made it impossible to play bends. However, it didn't
mater
how narrow the space was between two frets. The string picked it up
always
very neatly. So it felt almost like a fretless guitar with a very good
sustain, no special electronic devices needed, just the clean sound,
straight from the pick-up. I don't think you get lost on this guitar.
With a
good background harmony, your ears tell you where to go and you don't
really
need to look at your fingers. Playing for instance a 24-tet guitar is
much
more difficult in my experience.

--Wim Hoogewerf

Sabat-Garibaldi's Dinarra (was: A new era in JI guitar design!)

🔗David C Keenan <D.KEENAN@UQ.NET.AU>

🔗Dave Keenan <D.KEENAN@UQ.NET.AU>

🔗Paul Erlich <paul@stretch-music.com>

🔗Paul Erlich <paul@stretch-music.com>

🔗Dave Keenan <D.KEENAN@UQ.NET.AU>

🔗Dave Keenan <D.KEENAN@UQ.NET.AU>

🔗Paul Erlich <paul@stretch-music.com>

🔗Dave Keenan <D.KEENAN@UQ.NET.AU>

🔗BobWendell@technet-inc.com

🔗Paul Erlich <paul@stretch-music.com>

🔗Paul Erlich <paul@stretch-music.com>

🔗BobWendell@technet-inc.com

🔗Paul Erlich <paul@stretch-music.com>

🔗BobWendell@technet-inc.com

🔗Paul Erlich <paul@stretch-music.com>

🔗BobWendell@technet-inc.com

🔗Paul Erlich <paul@stretch-music.com>

🔗BobWendell@technet-inc.com

🔗BobWendell@technet-inc.com

🔗Eduardo Sabat-Garibaldi <ESABAT@ADINET.COM.UY>

🔗Paul Erlich <paul@stretch-music.com>

🔗Eduardo Sabat-Garibaldi <ESABAT@ADINET.COM.UY>

🔗Dave Keenan <D.KEENAN@UQ.NET.AU>

🔗Eduardo Sabat-Garibaldi <ESABAT@ADINET.COM.UY>

🔗Dave Keenan <D.KEENAN@UQ.NET.AU>

🔗Eduardo Sabat-Garibaldi <ESABAT@ADINET.COM.UY>

🔗Dave Keenan <D.KEENAN@UQ.NET.AU>

🔗Dave Keenan <D.KEENAN@UQ.NET.AU>

🔗Eduardo Sabat-Garibaldi <ESABAT@ADINET.COM.UY>

🔗Dave Keenan <D.KEENAN@UQ.NET.AU>

🔗Eduardo Sabat-Garibaldi <ESABAT@ADINET.COM.UY>

🔗Paul Erlich <paul@stretch-music.com>

🔗Eduardo Sabat-Garibaldi <ESABAT@ADINET.COM.UY>

🔗David Beardsley <davidbeardsley@biink.com>