Ben Johnston notation - a centered universe

Hello there,

Usual disclaimer: I've been traveling on my sabbatical, and haven't
checked in lately, so I'm replying to long-ago posts probably, mainly
having to do with Joe Pehrson's discussin of Ben Johnston's notation.

Being historically minded, one of the things I love about Ben's
notation is its connection to Renaissance practice. Just like 16th-
century JI and 12-pitch meantone (and even most forms of well
temperament), it is centered around the pitch C, and by extension the
CEG triad (or A and ACE if you want to think in minor). After all, the
original European scale was the "white-note" scale, not the 12-pitch,
and the accidentals - which raised or lowered pitches by 25/24 in 16th-
century Italian treatises, just as they do in Ben's notation - were
added to create extra ratios to those basic pitches, just as in Ben's
notation. The further you move from that central C tonality, the more
complex the accidentals get. I feel that because Ben's notation is
grounded in historical European tradition, it has deeper roots and a
more secure connection to earlier music than some makeshift system
newly concocted for the 20th century. I also prefer to work in a
musical universe with an implied center, no matter how arbitrarily
chosen, than to refer everything back to an equally arbitrary scale
like the 12-pitch Pythagorean.

The one counterintuitive thing about the notation is that, admittedly,
D:A is not a perfect fifth, nor is Bb:F. Personally, however, I never
had much trouble getting used to this one quirk of the system, and I
kind of like being forced to remember that, in the key of C, D and A *
aren't* a perfect fifth apart. (I'd rather do that than have to
remember that CEG isn't a major triad.)

How well the system works for performers depends on how complex you're
trying to get. For myself, as Joe notes, I've only used the tunings
electronically. Ben has worked for years with getting live performers
to play them, with varying degrees of success. His Chamber Symphony
uses relatively simple ratios, but even there, I thought Eric Grunen's
orchestra had a pretty rough time playing in tune. Ben's beautiful
Sixth String Quartet uses massively complex ratios, and the performers,
as I understand it, simply have to learn and memorize where every pitch
lies on the string - the notation is no help to an intuitive
understanding. On the other hand, the Fine Arts Quartet did a gorgeous
job with Ben's 22-pitch, 7-limit scale in the Amazing Grace quartet.

Ben's notation encourages harmonic rather than melodic thinking, and
his music always gives the players consonant pitches to tune each new
note to. If you don't think harmonically, as David Doty and I
manifestly do, the advantages of the notation may not be so obvious.

Kyle Gann

--- In tuning@y..., kgann@e... wrote:
>...it is centered around the pitch C, and by extension
the
> CEG triad (or A and ACE if you want to think in minor).

Hi Kyle,

I don't think it's accurate to say that it is centered around any note
unless it is F^ (F-half-sharp). It is really centered around the D-A
wolf.

Centering on D-A is fine (that's what Eb to G# meantone does) but I
feel that notations where D-A is a perfect fifth have deeper
historical roots (Pythagorean) than those where it is a wolf.

-- Dave Keenan

--- In tuning@y..., kgann@e... wrote:

> Being historically minded, one of the things I love about Ben's
> notation is its connection to Renaissance practice. Just like 16th-
> century JI

As used by whom?

> and 12-pitch meantone (and even most forms of well
> temperament), it is centered around the pitch C,

12-pitch meantone is usually centered around the fifth D-A:

Eb-Bb-F-C-G D-A E-B-F#-C#-G#

> and by extension the
> CEG triad (or A and ACE if you want to think in minor). After all,
the
> original European scale was the "white-note" scale, not the 12-
pitch,
> and the accidentals - which raised or lowered pitches by 25/24 in
16th-
> century Italian treatises, just as they do in Ben's notation - were
> added to create extra ratios to those basic pitches, just as in
Ben's
> notation. The further you move from that central C tonality, the
more
> complex the accidentals get

Actually D is the center in these respects.

> I feel that because Ben's notation is
> grounded in historical European tradition, it has deeper roots and
a
> more secure connection to earlier music than some makeshift system
> newly concocted for the 20th century. I also prefer to work in a
> musical universe with an implied center, no matter how arbitrarily
> chosen, than to refer everything back to an equally arbitrary scale
> like the 12-pitch Pythagorean.

The center is D is Daniel Wolf's notation as well.

>
> The one counterintuitive thing about the notation is that,
admittedly,
> D:A is not a perfect fifth, nor is Bb:F. Personally, however, I
never
> had much trouble getting used to this one quirk of the system, and
I
> kind of like being forced to remember that, in the key of C, D and
A *
> aren't* a perfect fifth apart.

Whose key of C? What composer, historically, wrote in the key of C
and _didn't_ expect D and A to be a perfect fifth apart?

> (I'd rather do that than have to
> remember that CEG isn't a major triad.)

It's easy to remember that you need to lower the major third by a
comma to get a 5-limit major triad.
>
> On the other hand, the Fine Arts Quartet did a gorgeous
> job with Ben's 22-pitch, 7-limit scale in the Amazing Grace >
quartet.

Is there a recording of this available?
>
> Ben's notation encourages harmonic rather than melodic thinking

I think it's important to facilitate both.

Dave,

Ben's tuning notation is centered around C in that the C major triad is
at the center, FAC and GBD are spaced symmetrically on each side, and
beyond that you get accidentals in each direction.

>
> Centering on D-A is fine (that's what Eb to G# meantone does) but I
> feel that notations where D-A is a perfect fifth have deeper
> historical roots (Pythagorean) than those where it is a wolf.

Also, I said that Ben's notation picks up where the Renaissance left
off, not the medieval era. Medieval French Pythagorean had all perfect
fifths, and in 14th century music such as Machaut's, you see him trying
to work major thirds into chords by every rhythmic subterfuge in the
book. The 15th century's English-inspired acceptance of 5-limit tuning
was, to my understanding of history, a major advance in theoretical
honesty and a concession to what was already being done in practice
anyway. Pythagorean may be an older tuning, but it was five-limit
tuning through which the history of European music developed to its
greatest potential. The tuning debates of the late 16th century took
five-limit tuning as their basis, not Pythagorean. And Ben, like so
many other mid-20th-century American composers (Partch, Cowell) picks
up where the Renaissance left off.

Kyle Gann

> 12-pitch meantone is usually centered around the fifth D-A:
>
> Eb-Bb-F-C-G D-A E-B-F#-C#-G#

The intervals may be symmetrical around the fifth D-A, but the
available keys are symmetrical around C. Ever look through a collection
of 16th-century keyboard music? The most common key is invariably C,
followed by F and G, then Bb and D, occasionally Eb or A. Very rarely
anything further out in the circle of fifths.

>
> > and by extension the
> > CEG triad (or A and ACE if you want to think in minor). After all,
> the
> > original European scale was the "white-note" scale, not the 12-
> pitch,
> > and the accidentals - which raised or lowered pitches by 25/24 in
> 16th-
> > century Italian treatises, just as they do in Ben's notation - were
> > added to create extra ratios to those basic pitches, just as in
> Ben's
> > notation. The further you move from that central C tonality, the
> more
> > complex the accidentals get
>
> Actually D is the center in these respects.

Ditto above

>
> >
> > The one counterintuitive thing about the notation is that,
> admittedly,
> > D:A is not a perfect fifth, nor is Bb:F. Personally, however, I
> never
> > had much trouble getting used to this one quirk of the system, and
> I
> > kind of like being forced to remember that, in the key of C, D and
> A *
> > aren't* a perfect fifth apart.
>
> Whose key of C? What composer, historically, wrote in the key of C
> and _didn't_ expect D and A to be a perfect fifth apart?

As late as Anton Bruckner's theoretical writings in the mid-19th-
century, he states that the fifth between the second and sixth scale
degrees is to be treated as a dissonance, and resolved accordingly.

>
> > (I'd rather do that than have to
> > remember that CEG isn't a major triad.)
>
> It's easy to remember that you need to lower the major third by a
> comma to get a 5-limit major triad.

It may be easy to remember, but in composing I wouldn't like the look
of it.

> >
> > On the other hand, the Fine Arts Quartet did a gorgeous
> > job with Ben's 22-pitch, 7-limit scale in the Amazing Grace >
> quartet.
>
> Is there a recording of this available?

There was one on Gasparo - may no longer ba avilable.

> >
> > Ben's notation encourages harmonic rather than melodic thinking
>
> I think it's important to facilitate both.

I never denied that.

Kyle gann

--- In tuning@y..., kgann@e... wrote:

/tuning/topicId_22032.html#22032

> Usual disclaimer: I've been traveling on my sabbatical, and
> haven't checked in lately, so I'm replying to long-ago posts
> probably, mainly having to do with Joe Pehrson's discussin
> of Ben Johnston's notation.

Hi Kyle,

Good to see you back on the list. We've had *quite* a heavy
discussion here of Ben, his notation, and his music in the
last three weeks. There's a good chance you missed something.

In case you need a pointer to help catch up, here's the
question posed by Joe Pehrson which started it all:
/tuning/topicId_20929.html#20929

Follow the "replies" links at the bottom to see only a very
few of the further installments. I actually would recommend
viewing the archives on the internet starting with #20929
and scrolling thru each post, because a lot of what was
posted in the two weeks after that had to do not only specifically
with Ben's notation, but with the larger question of microtonal
notational systems. I think you'll find it profitable.

(Quite a bit of my and Paul Erlich's posts discuss important
aspects of my favored "HEWM" notation. Thought I'd mention
that too, since I know you are very interested in my own work.
There's even an mp3 I created of an excerpt from Ben's
_8th Quartet_... it's gotten rave reviews from Joe Pehrson.)

-monz
http://www.monz.org
"All roads lead to n^0"

In a message dated 5/4/01 6:18:11 AM, kgann@earthlink.net writes:

<< the Fine Arts Quartet did a gorgeous
> > job with Ben's 22-pitch, 7-limit scale in the Amazing Grace >
> quartet.
>
> Is there a recording of this available?

There was one on Gasparo - may no longer ba avilable. >>

In a message dated 5/4/01 6:18:11 AM, kgann@earthlink.net writes:

<< the Fine Arts Quartet did a gorgeous
> > job with Ben's 22-pitch, 7-limit scale in the Amazing Grace >
> quartet.
>
> Is there a recording of this available?

There was one on Gasparo - may no longer ba avilable. >>

It's out of print. Try a university library. I've heard this one and it
puts the Kronos recording to shame.

--- In tuning@y..., kgann@e... wrote:
> > 12-pitch meantone is usually centered around the fifth D-A:
> >
> > Eb-Bb-F-C-G D-A E-B-F#-C#-G#
>
> The intervals may be symmetrical around the fifth D-A, but the
> available keys are symmetrical around C. Ever look through a
collection
> of 16th-century keyboard music? The most common key is invariably
C,
> followed by F and G, then Bb and D, occasionally Eb or A. Very
rarely
> anything further out in the circle of fifths.

Kyle,

Referring to the set of natural ("white") notes as "the key of C" is
a later 17th century development. Until then, many different modes
were given equal stature:

D dorian
E phrygian
F lydian
G mixolydian

. . . all with the same set of notes. Regarding D dorian in
particular, a dissonant D-A seems wholly inappropriate.

> > >
> > Whose key of C? What composer, historically, wrote in the key of
C
> > and _didn't_ expect D and A to be a perfect fifth apart?
>
> As late as Anton Bruckner's theoretical writings in the mid-19th-
> century, he states that the fifth between the second and sixth
scale
> degrees is to be treated as a dissonance, and resolved accordingly.

Kyle, your own history of tuning page is perhaps the best one out
there. Surely you can see that these kinds of abstractions have
little to do with the actual history and progress of music. Bruckner
is a very idiosyncratic example. In practice, the D minor triad is
not treated as a dissonance by any composer, from the beginning of 5-
limit harmony onward, other than a few odd exceptions like Bruckner
who over-theorized in a certain direction. In fact, in the key of C
major, it is the E minor triad that seems to have been
handled "differently" by classical composers.

> > > > On the other hand, the Fine Arts Quartet did a gorgeous
> > > job with Ben's 22-pitch, 7-limit scale in the Amazing Grace >
> > quartet.
> >
> > Is there a recording of this available?
>
> There was one on Gasparo - may no longer ba avilable.

This is very sad. I have the Kronos recording but I'm sure the
intonation could be better.

-Cheers!

>
> Referring to the set of natural ("white") notes as "the key of C" is
> a later 17th century development. Until then, many different modes
> were given equal stature:
>
> D dorian
> E phrygian
> F lydian
> G mixolydian
>
> . . . all with the same set of notes. Regarding D dorian in
> particular, a dissonant D-A seems wholly inappropriate.

Well, I don't want to start splitting hairs, but I know my modes, and
it was frequently acknowledged in publications of the day that the
modal system, though still theoretically in effect, had pretty much
fallen apart by the late 16th century, and left us with basically major
and minor usage. The point is that you almost never see more than three
sharps or three flats in a key signature from that period, and the
midpoint between three sharps and three flats is zero sharps or flats,
or what we think of as C major.

>
> > > >
> > > Whose key of C? What composer, historically, wrote in the key of
> C
> > > and _didn't_ expect D and A to be a perfect fifth apart?
> >
> > As late as Anton Bruckner's theoretical writings in the mid-19th-
> > century, he states that the fifth between the second and sixth
> scale
> > degrees is to be treated as a dissonance, and resolved accordingly.
>
> Kyle, your own history of tuning page is perhaps the best one out
> there. Surely you can see that these kinds of abstractions have
> little to do with the actual history and progress of music. Bruckner
> is a very idiosyncratic example. In practice, the D minor triad is
> not treated as a dissonance by any composer, from the beginning of 5-
> limit harmony onward, other than a few odd exceptions like Bruckner
> who over-theorized in a certain direction. In fact, in the key of C
> major, it is the E minor triad that seems to have been
> handled "differently" by classical composers.

These aren't abstractions, I'm arguing from musical usage. Of course
D:A was in tune - that's why meantone was adopted. But it's interesting
that Zarlino's keyboard design, which (I'm out of town and away from my
reference books here, so forgive my memory if faulty) I believe dates
from the 1580s, has the usual five-limit ratios for C, E, F, G, A, and
B, and two different D keys - 10/9 and 9/8. This hardly points to
Dorian mode having equality with Ionian, but points to the second scale
degree as being the problematic one - an intuition that must have been
deeply grounded if it survived as late as Bruckner, no matter how
idiosyncratic Bruckner was to still be sensitive to it.

>
> > > > > On the other hand, the Fine Arts Quartet did a gorgeous
> > > > job with Ben's 22-pitch, 7-limit scale in the Amazing Grace >
> > > quartet.
> > >
> > > Is there a recording of this available?
> >
> > There was one on Gasparo - may no longer be avilable.
>
> This is very sad. I have the Kronos recording but I'm sure the
> intonation could be better.

Ben thinks the Fine Arts did a much better job, tuning-wise, than the
Kronos.

Kyle

--- In tuning@y..., kgann@e... wrote:
> >
> > Referring to the set of natural ("white") notes as "the key of C"
is
> > a later 17th century development. Until then, many different modes
> > were given equal stature:
> >
> > D dorian
> > E phrygian
> > F lydian
> > G mixolydian
> >
> > . . . all with the same set of notes. Regarding D dorian in
> > particular, a dissonant D-A seems wholly inappropriate.
>
> Well, I don't want to start splitting hairs, but I know my modes,
and
> it was frequently acknowledged in publications of the day that the
> modal system, though still theoretically in effect, had pretty much
> fallen apart by the late 16th century, and left us with basically
major
> and minor usage.

Margo Schulter puts the date at about 1680, about a century later than
you.

The point is that you almost never see more than
three
> sharps or three flats in a key signature from that period, and the
> midpoint between three sharps and three flats is zero sharps or
flats,
> or what we think of as C major.

. . . or A minor.
>
>
> These aren't abstractions, I'm arguing from musical usage. Of course
> D:A was in tune - that's why meantone was adopted. But it's
interesting
> that Zarlino's keyboard design, which (I'm out of town and away from
my
> reference books here, so forgive my memory if faulty) I believe
dates
> from the 1580s, has the usual five-limit ratios for C, E, F, G, A,
and
> B, and two different D keys - 10/9 and 9/8.

This keyboard design was very much an abstraction and Zarlino proposed
2/7-comma meantone for keyboards performing the music of his day.

> This hardly points to
> Dorian mode having equality with Ionian, but points to the second
scale
> degree as being the problematic one - an intuition that must have
been
> deeply grounded if it survived as late as Bruckner, no matter how
> idiosyncratic Bruckner was to still be sensitive to it.

Again, I argue that it's not a musical intuition at all, but only an
over-theoretical invention arrived at only by those theorists who
insisted on pinning strict JI ratios on each of the degrees of the
major scale. Bruckner and Zarlino were two such theorists. My point of
view is that adaptive JI or meantone temperament forms a better model
of diatonic thinking by common-practice composers that strict JI. From
1500 on, four fifths was always a consonant major third.
>
> Ben thinks the Fine Arts did a much better job, tuning-wise, than
the
> Kronos.

Oh how, oh how, can I hear a recording of this?

> > Well, I don't want to start splitting hairs, but I know my modes,
> and
> > it was frequently acknowledged in publications of the day that the
> > modal system, though still theoretically in effect, had pretty much
> > fallen apart by the late 16th century, and left us with basically
> major
> > and minor usage.
>
> Margo Schulter puts the date at about 1680, about a century later than
> you.

Well, I don't know who Margo Schulter is, but I've taught Renaissance
counterpoint with Josquin's works as a model, and I've taught it with
Palestrina's works as a model, and I don't see how anyone can deny that
by the 1560s or '70s, somewhere between Josquin and Palestrina, the
modal system had been altered by chromatic inflections to be equivalent
to the major/minor system. Any theorist or historian who tries to pin
the breakdown of the modal system to a specific year is faking. Perhaps
there was some theoretical admission of key centers that late, but
Monteverdi's music of a much earlier period falls consistently into
major and minor keys.

But my curiosity is piqued on one issue. You mention that the iii chord
was treated differently than the other major or minor triads. How? It
does strike me that ii appears in first inversion more commonly than I,
IV, V, or vi. How is iii different?

Kyle

--- In tuning@y..., paul@s... wrote:
> --- In tuning@y..., kgann@e... wrote:
>
> > Being historically minded, one of the things I love about Ben's
> > notation is its connection to Renaissance practice. Just like 16th-
> > century JI
>
> As used by whom?
>
> > and 12-pitch meantone (and even most forms of well
> > temperament), it is centered around the pitch C,

To begin with, Ludovico Fogliano in his *Musica theorica* of 1529, and
Vincenzo Galilei in his *Discorso intorno all'opere...* of 1589, who
base their scale charts on a C major scale and give their musical
examples in what we would call the key of C.

Kyle

--- In tuning@y..., kgann@e... wrote:

> Well, I don't know who Margo Schulter is,

I thought you would know since you mention her on your own page on historical tuning systems.
In any case, she's back with us on this list (yippee!), so I'll let her respond to this:

> but I've taught Renaissance
> counterpoint with Josquin's works as a model, and I've taught it with
> Palestrina's works as a model, and I don't see how anyone can deny that
> by the 1560s or '70s, somewhere between Josquin and Palestrina, the
> modal system had been altered by chromatic inflections to be equivalent
> to the major/minor system. Any theorist or historian who tries to pin
> the breakdown of the modal system to a specific year is faking.

I did not mean to suggest that Margo was pinning it a a specific year -- only that she places the
time about 100 years later than you do. I have no strong feelings one way or the other.

> Perhaps
> there was some theoretical admission of key centers that late, but
> Monteverdi's music of a much earlier period falls consistently into
> major and minor keys.

I know Margo has a response to this, so I'll leave it to her.
>
> But my curiosity is piqued on one issue. You mention that the iii chord
> was treated differently than the other major or minor triads. How? It
> does strike me that ii appears in first inversion more commonly than I,
> IV, V, or vi. How is iii different?

I've seen a great many treatises and articles on tonal music which claim that in common-practice
harmony, the iii chord is a "non-functional" chord in a major key. Although this struck me as odd at
first, I must admit that the evidence from Classical and Romantic period music tends to support
this view -- a first-inversion iii chord often acts as the dominant (so should be analyzed as a V),
etc. . . . while the ii chord is a functional chord like the I, IV, V, vi, and viio. Personally, I like the iii
chord, but I grew up with the Beatles . . .

--- In tuning@y..., kgann@e... wrote:
> --- In tuning@y..., paul@s... wrote:
> > --- In tuning@y..., kgann@e... wrote:
> >
> > > Being historically minded, one of the things I love about Ben's
> > > notation is its connection to Renaissance practice. Just like 16th-
> > > century JI
> >
> > As used by whom?
> >
> > > and 12-pitch meantone (and even most forms of well
> > > temperament), it is centered around the pitch C,
>
> To begin with, Ludovico Fogliano in his *Musica theorica* of 1529, and
> Vincenzo Galilei in his *Discorso intorno all'opere...* of 1589, who
> base their scale charts on a C major scale and give their musical
> examples in what we would call the key of C.

Hi Kyle, and if you mean these men posited a C major scale in terms of the usual JI ratios, I still
question the connection with "Renaissance practice" as opposed to "Renaissance theory".

For example, already in the 16th century, musican/physicist Giovanni Battista Benedetti
understood the problems with this Ptolemaic ratio-model when applied to existing Western
5-limit diatonic practice -- look in the archives at message #19304 and scroll down to Part 4 of
that message. The debate has been going on ever since, but I side with Benedetti (while
disagreeing with his particular conclusion) and Blackwood (check out Blackwood's book if you
haven't yet) rather than Fogliano and Bruckner.

--- In tuning@y..., paul@s... wrote:
> --- In tuning@y..., kgann@e... wrote:
>
> > Well, I don't know who Margo Schulter is,
>

> I thought you would know since you mention her on your own page on historical tuning systems.

Well, years of Aspartame overdoses have reduced my memory to a shadow,
but while I remembered where I'd seen the name as soon as I e-mailed
you, I still don't know Margo as more than a name. Very interesting
about the iii chord - I'll keep an eye on it as I teach theory next
fall. I've been calling the iii6 chord a dominant in Chopin's music for
many years, of course (especially in the form G:F:B:E in the key of C),
but I've seen many root-position iii chords in earlier music, and never
noticed anything unusual about them - especially as they sometimes turn
into V/vi chords and lead to vi, in which case they seem quite
functional indeed. All this veers far away from the point I intended to
make - that Ben Johnston's notation is based on the so-called Ptolemaic
sequence and uses ratio values for sharps and flats that were
acknowledged at least as early as Benedetti's *Diversarum speculationum
mathematicarum* of 1585. Since Ben himself explains his notation as
being centered around C major and cites Renaissance precedents, I
thought I was stating obvious truths and never dreamed I was inciting
controversy.

Yours,

Kyle

> > But my curiosity is piqued on one issue. You mention that the iii chord
> > was treated differently than the other major or minor triads. How? It
> > does strike me that ii appears in first inversion more commonly than I,
> > IV, V, or vi. How is iii different?
>
> I've seen a great many treatises and articles on tonal music which claim that in common-practice
> harmony, the iii chord is a "non-functional" chord in a major key. Although this struck me as odd at
> first, I must admit that the evidence from Classical and Romantic period music tends to support
> this view -- a first-inversion iii chord often acts as the dominant (so should be analyzed as a V),
> etc. . . . while the ii chord is a functional chord like the I, IV, V, vi, and viio. Personally, I like the iii
> chord, but I grew up with the Beatles . . .

--- In tuning@y..., kgann@e... wrote:
> --- In tuning@y..., paul@s... wrote:
> > --- In tuning@y..., kgann@e... wrote:
> >
> > > Well, I don't know who Margo Schulter is,
> >
>
> > I thought you would know since you mention her on your own page on historical tuning
systems.
>
> Well, years of Aspartame overdoses have reduced my memory to a shadow,
> but while I remembered where I'd seen the name as soon as I e-mailed
> you, I still don't know Margo as more than a name. Very interesting
> about the iii chord - I'll keep an eye on it as I teach theory next
> fall. I've been calling the iii6 chord a dominant in Chopin's music for
> many years, of course (especially in the form G:F:B:E in the key of C),
> but I've seen many root-position iii chords in earlier music, and never
> noticed anything unusual about them - especially as they sometimes turn
> into V/vi chords and lead to vi, in which case they seem quite
> functional indeed.

Yes, a V/vi chord would be a major chord functioning as a secondary dominant. But the iii in its
natural chord as a minor chord is something many theorists regard as not having a function of its
own, and acting in some other capacity when it occurs in music -- these theorists where probably
focusing only on the period from Bach to the late Romantic, though.

> All this veers far away from the point I intended to
> make - that Ben Johnston's notation is based on the so-called Ptolemaic
> sequence and uses ratio values for sharps and flats that were
> acknowledged at least as early as Benedetti's *Diversarum speculationum
> mathematicarum* of 1585.

Benedetti of course rejects the so-called Ptolemaic sequence as describing Renaissance
practice, and with good reason. Even if one wants to claim, with Johnny Reinhard, that
Benedetti's argument is invalid because drift did in fact occur and was desired in the music, one
still will be confronted with the usage of the D-A fifth and the D minor triad as consonances in the
vast majority of the Renaissance and common-practice repertoire.

Again I ask: Have you read Blackwood's book?

Kyle Gann wrote:

> I still don't know Margo as more than a name.

Now, that's a cryin' shame. Search the Tuning List archives for "neo-Gothic." You'll end up with what is the equivalent of 333 single-space typed pages (I've copied it into a single Word document) of
masterful, engaging, and thoroughly scholarly work. Also, search for the names of medieval and Renaissance theorists such as Zarlino, Vicentino, Marchettus, etc. for loads more. She has also published some
web pages about early music theory.

I think she also may be up for the "Nicest Person In The World" award.

--
David J. Finnamore
Nashville, TN, USA
http://personal.bna.bellsouth.net/bna/d/f/dfin/index.html
--

------------------------------------------------
Ben Johnston notation and historical context:
A response to the Paul Erlich-Kyle Gann dialogue
------------------------------------------------

Hello, there, and having become something of a topic as well as a not
disinterested reader of the fascinating dialogue regarding matters of
broad music history and notational utility involving Paul Erlich and
Kyle Gann, I would like to respond especially on two questions of
historical style and intonation.

Please let me begin by thanking Paul Erlich warmly for quoting my
views pertinently and accurately, and also Kyle Gann for raising some
very reasonable questions and differences of view with a widespread
currency among musicologists and others.

-----------------------------------------------------------------
1. General concerns: 5-limit notations and historical transitions
-----------------------------------------------------------------

Before getting into the deeper historical intricacies of 14th-century
style and Pythagorean intonation (e.g. Machaut), or the fluid and
often ambiguous modality of the late 16th and early 17th centuries
based in my view mainly on a meantone model, I'd like briefly to
address the primary matter at issue in this dialogue, and also to echo
your caution, Kyle Gann, about taking _any_ convenient date as a
precise and absolute line or demarcation between two eras or
approaches such as modality and major/minor tonality.

-------------------------------------------------
1.1. Notational projects and historical precedent
-------------------------------------------------

First, regarding notations for a system such as 5-limit just
intonation (JI) where any solution will involve some compromises and
arguable "anomalies," I would say pragmatically that whatever people
find most comfortable and convenient is best.

Since different people evidently find different notations most
"natural," some diversity may be the most reasonable or, I might say,
"ecologically" appropriate solution.

If we are to take 16th-century musical notation as a precedent or
model, however, then we encounter a complication: this notation, as
used by composers and theorists including Zarlino (champion of the
syntonic diatonic as a model of _vocal_ intonation), does not attempt
explicitly to show syntonic comma adjustments or to distinguish 9:8
and 10:9 whole-tones. Rather such adjustments -- however negotiated --
are left implicitly to the performers.

Playing a 16th-century piece on a keyboard with a 15-note octave
modelled after Zarlino's scheme, I must realize the notation by
playing the right notes to make either G-D or D-A a pure fifth rather
than one a syntonic comma narrow. Here there is _not_ a one-to-one
correspondence between notation or spelling and the tuning system
itself. Karol Berger's dissertation on chromatic and enharmonic
theories in late 16th-century Italy nicely addresses this point.

Thus the project of developing a 5-limit notation which _expressly_
indicates syntonic comma distinctions is something outside of usual
16th-century practice, which seems to me most closely to reflect
either meantone or some "unwritten" form of adaptive tuning
adjustments for purer consonances. On this point, Paul, we seem much
in agreement.

As to what system is best for such a project, I may not be the best or
most informed judge, since I'm accustomed mostly to what I term
"equitonal" systems such as Pythagorean intonation, meantone, and
neo-Gothic temperaments where all regular major seconds have the same
size and a major third is equal to four fifths up.

If one is seeking a literal notation for classic 5-limit JI which
keeps count of all the syntonic commas, then I might personally go
with the Helmholz-Ellis-Wolf-Monzo system (HEWM), also used by Easley
Blackwood (albeit as a critic rather than an exponent of this form of
intonation).

However, if the Ben Johnston notation is comfortable for performers
and helps them find the right notes, then that's fine, also.

Here I would emphasize that neither Johnston nor HEWM notation needs
the ratification of any historical precedent: if the notational shoe
fits the musical foot, then why not wear it?

---------------------------------------
1.2. Transitions and conventional dates
---------------------------------------

In response to Paul's accurate quote of my view that the transition
from modality to major/minor tonality had become an established
feature of "modern" practice by around 1680 (the era of Corelli and
Werckmeister), Kyle questions the validity of giving _any_ precise
date for such a transition, as well as proposing the late 16th-century
era of Palestrina, say a century earlier, as a better estimate.

While saving the issue of modality in the late 16th and early 17th
centuries for discussion below (Section 3), I would like very much to
agree that any date such as 1680 is merely an arbitrary reference
point for a process of transition.

What we have during the Manneristic era of around 1540-1640 or
Rore-Monteverdi, in my viewpoint, is a fluid and very creative
practice based on a 12-mode system both enriched and sometimes blurred
by liberties including direct chromaticism and sometimes also
diesisism (Vicentino). An important point is that the new inflections
often fit _neither_ the "classical" Renaissance practice of a composer
such as Josquin, nor the constraints of major/minor tonality.

By the third quarter of the 17th century, composers such as Stradella
are moving in a tonal direction, so that one might place the
transition somewhere around 1660-1680, with Corelli's music taken as a
confirmation and consolidation of this trend.

One advantage of the approximate date 1680 is that it closely
coincides with Werckmeister's publication of his well-temperaments
(1681 and later), as well his views that only two basic modes (major
and minor) were needed to describe modern practice. At the same time,
this date also agrees with one 20th-century view of the major/minor
period as ranging roughly from 1680 to 1900 (say Corelli-Puccini).

In my opinion, a balanced view of the problem should recognize not
only that some elements introduced in the late modal practice of
around 1600-1640 become usual elements of major/minor tonality, but
also that some modal concepts remain important in the theory of around
1700, when we would agree that tonality has clearly become the norm.

Similarly, to propose (as Mark Lindley does, very reasonably in my
view) that the transition from Pythagorean to meantone on keyboards
may have occurred sometime around 1450 is not to say that it happened
suddenly in that precise year or even decade, but that clues such as
the style of a keyboard composer such as Conrad Paumann suggest this
epoch as a likely one.

Traditional "great dates" of historiography may be placed in fuller
perspective without losing their significance. The year 1600 (or its
surrounding decade or so), for example, continues to symbolize the
import of such events as the new dissonance treatment of Monteverdi
and his colleagues, or the advent of continuo-based forms, even if we
choose to describe this transition as "Early/Late Manneristic" rather
than "Renaissance/Baroque."

To sum up, Kyle, I'm much in agreement with you that any quoted date
for a transition between two musical eras, styles, or tuning systems
is at best a convention and convenience -- although a galvanizing
composition or treatise may often provide a ready date _symbolizing_
such a transition and making its flavor more tangible.

----------------------------------------------
2. Pythagorean intonation and the 14th century
----------------------------------------------

In this dialogue, Machaut's prominent use of major thirds was briefly
mentioned, and I'd like to comment in my view that this practice is
quite consistent with the Pythagorean intonation described by
musicians of the Ars Nova era such as his contemporary Johannes Boen
(1357).

As long as thirds and sixths are treated as decidedly _unstable_
intervals, often inviting standard cadential resolutions although
often also used in a freer or more "coloristic" fashion, Pythagorean
tuning fits such a role of "imperfect concord" or _relative_ blend.

An interesting passage in Boen explains the role of parallel thirds
and sixths in approaching a cadence: these intervals serve as
"forerunners and handmaidens" of the stable or "perfect" concords of
the fifth and octave. Thus I find that a late Gothic idiom of this
kind can be very pleasing in Pythagorean tuning, with C4 here showing
middle C in a "MIDI-like" fashion:

A4 G4 F4 E4 F4
E4 D4 C4 B3 C4
C4 Bb3 A3 G3 F3

As Mark Lindley writes, the complex thirds and sixths give this kind
of texture a "sinuous" quality.

In fact, I often enjoy passages of this kind in 29-tone equal
temperament (29-tET) with major thirds and sixths somewhat wider than
Pythagorean. Going much beyond this, however, some Setharean timbre
adjustments may be in order to keep these unstable intervals
_relatively_ blending; with such adjustments, 17-tET can also be
delightful.

As Carl Dahlhaus has written, there is a neat correspondence between
the "acoustical surface" of Pythagorean tuning and the musical
style of the 13th and 14th centuries, with octaves, fifths, and
fourths serving as the primary concords but various unstable intervals
also playing a very prominent role.

By the later 15th century, however, there is a gap between Pythagorean
theory and current practice -- although some students of this era have
recently suggested that singers may have often leaned toward
Pythagorean intonation in performances of composers such as Ockeghem,
even as meantone keyboards were becoming the norm.

Notationally speaking, musicians finessed the transition by sticking
with what one might call an intonationally generic and "equitonal"
notation corresponding closely to either the old Pythagorean or the
new meantone system, but not explicitly recognizing the complication
of the syntonic comma for flexible-pitch performers negotiating the
tertian styles now in vogue with thirds at or close to 5:4 or 6:5.

----------------------------------------------------------
3. Modality, centers, and intonation: Vicentino-Monteverdi
----------------------------------------------------------

During the era of 1540-1640, music is based on a very flexible system
of 12 modes, sometimes freely ornamented and mixed together in manners
advocated in the earlier part of this period by the composer and
theorist Nicola Vicentino (1555), and in the latter part by such
musicians as Claudio Monteverdi and his brother Giulio Cesare
Monteverdi (1607).

Here I would like to focus on the general question of accidentalism,
the matter of Zarlino's experimental JI keyboard, and my views of the
modes in practice around 1600.

------------------------------------------------------
3.1. Accidentalism in Manneristic modality (1540-1640)
------------------------------------------------------

In viewing the accidentalism of the 16th and early 17th centuries,
including the direct chromaticism of a Vicentino or Gesualdo as well
as the routine inflections taken for granted by Zarlino, it is very
important to place this question in the perspective of earlier Gothic
practice and theory.

While the accidentals Eb, F#, and C# -- in addition to the fluid step
B/Bb (German H/B) of the regular gamut -- are in use by the era of
Perotin around 1200, these inflections plus G# become a routine
feature of the early Ars Nova in the era around 1300.

Such accidentals are frequently mandated by the pattern of "closest
approach" -- the norm that unstable intervals should resolve to "the
nearest consonance." Thus a third expanding to a fifth or sixth
expanding to an octave by contrary motion should be major, while a
third contracting to a unison should be minor.

This convention calls for a regular use of _musica ficta_, "invented
notes" outside the regular gamut of diatonic notes plus Bb.

In 16th-century modality, such inflections are one side of a modal
system also routinely using accidentals by the 1520's to obtain major
thirds above the lowest voice in closing sonorities -- the use of
thirds in such sonorities becoming increasingly the norm.

From my perspective, at least, a balanced view of our Manneristic
period from Rore and Vicentino to Monteverdi and Frescobaldi should
take account of at least three factors:

(1) The modal system, including its creative ambiguities and
affinities between related modes with similar species of fifths and
fourths (or pentachords and tetrachords);

(2) The element of vertical sonority, now clearly shifted in practice
and theory from the Gothic trine (2:3:4) to the _harmonia perfetta_ of
Zarlino's "third plus fifth or sixth" (e.g. 4:5:6); and

(3) The often guiding role of "closest approach" and related
progressions, some borrowed from the Gothic era, in directing the flow
of saturated tertian sonorities.

Obviously a 16th-century system of meantone, or of adaptive JI with
minute adjustments to finesse the syntonic comma while maintaining
pure vertical concords, neatly fits item (2). However, musicians such
as Netherlands just intonation advocate Peter van Marissing have
suggested a more subtle connection between intonation and vertical
organization.

In meantone, major and minor thirds are pure or nearly pure, and the
late modal style of organization often features relationships between
sonorities with lowest notes a third apart. Such relations are common
in medieval chant and polyphony, but take on new aspects in a tertian
environment, some of them involving striking forms of accidentalism
including direct chromaticism.

At the same time, the late Gothic principle of "closest approach" also
takes on new forms, as such a scholar as Carl Dahlhaus has found in
his study of compositions around 1600.

Consider a progression in a setting in E Phrygian like this:

E4 F#4 G4
B3 D4 E4
G#3 A3 C4
E3 D3 C3

8 - 10 - 12

Here there is no direct chromaticism -- the use of chromatic semitone
steps -- but a use of accidentals producing three consecutive
sonorities with what Zarlino terms harmonic divisions of the fifth
(fifth plus major third above the bass).

From one viewpoint, we might focus on the stepwise contrary motion of
the outer parts from octave to major tenth to twelfh. The smoothly
conjunct motion prevailing has a "late tertian/modal flavor" of its
own.

Taking the perspective of closest approach, we note that the first
sonority is connected to the second by a major third expanding to a
fifth between the lower pair of voices (E3-G#3 to D3-A3), and the
second sonority to the third by a similar expansion of major tenth to
twelfth between the outer voices (D3-F#3 to C3-G3).

Thus does a familiar 14th-century cadential progression take on new
sonorous shape, Pythagorean intonation compellingly reflecting the
original context, and meantone or adaptive just intonation the
16th-century adaptation.

While the beauty of this progression speaks for itself, we might add
from a free modal perspective that the motion of the bass E3-D3-C3
connects the Phyrgian final E, the note of repose, with the common
confinal or "co-final" C, often favored for intermediate cadences.
This "third-related" connection is a delightful aspect of Manneristic
practice sometimes inspiring boldly direct chromaticism.

For example, consider a progression like this:

A4 A4
F4 E4
C4 C#4
F3 A3

Such idioms have a logic of their own, constrained neither by the
earlier modal practice of a composer such as Josquin, nor by the
major/minor key system established in the later 17th century.

In his analysis of Monteverdi, Carl Dahlhaus concludes that many of
his progressions fit the "closest approach" paradigm mentioned as a
basic element of counterpoint by such an early 17th-century "modern"
as Agazzari in his presentation on continuo (1607), but not the
expectations of key tonality, citing especially examples like the
following:

E4 F#3 G4 A4
B3 D4 D4 F4
G#3 A3 B3 C4
E3 D3 or G3 F3

These progressions again involve the common expansion of major third
to fifth in contexts where Dahlhaus remarks that major/minor tonality
would suggest a different treatment. He comments that while
conventional histories often look for instances where inflections
seem to fit a "major/minor" pattern, they may disregard choices which
seem to have the opposite effect, but fit the concept of "closest
approach" as applied in a tertian setting.

At the same time, Dahlhaus emphasizes that such compositions do not
conveniently fit either classic 16th-century modal theory or
18th-century tonal theory. In their manifesto of 1607, the Monteverdi
brothers themselves declare that this music belongs to a tradition of
freely mixing modes in order to express the words and affections
(i.e. emotions) of a text, an ethos for which we have an eloquent
statement in Vicentino.

A "polymodal" approach to composers such as Monteverdi and Gesualdo,
like any theoretical approach, must fall short of a full appreciation
of the music, but seems to me both enticing and evocative, with
"closest approach" as discussed by Dahlhaus providing one historical
foundation for what in the 21st century remains justly famed as a
radically innovative style.

-----------------------------------------------
3.2. Zarlino's JI keyboard and the modal system
-----------------------------------------------

As Paul Erlich has remarked, Zarlino's JI keyboard with its 16 notes
per octave (including two versions of D, Bb, F#, and Eb) is presented
by Zarlino himself as an experimental instrument, difficult to play
and much less practical than a temperament such as his own 2/7-comma
meantone.

The main conclusion I draw from playing a 15-note variation on
Zarlino's instrument mapped to two keyboard manuals is that managing
any piece in any mode that frequently calls for fifths at both D-A and
G-D is likely indeed to be "difficult," just as Zarlino observes.
These fifths are likely to occur in any of the modes, not only in the
obvious D Dorian or G Mixolydian.

For a few pieces calling for only one of these fifths (interestingly
including a favorite D Dorian piece where G-D happens not to occur),
or where in my two-manual arrangement the fifths or fourths in
question happen fortuitously to call for the right hand at the most
convenient time, this kind of JI can be as easy as meantone.

Otherwise, as Zarlino says, temperament is more practical; and he also
observes that singers, unlike such special keyboards in the syntonic
diatonic, can strive for pure consonances without the complication of
"small intervals" such as the syntonic comma. Could this be a hint
that adaptive JI was at least sometimes practiced?

Like his predecessor Glareanus, Zarlino favors a system of 12 modes,
with an authentic and plagal form for each of six basic octave-species
(D, E, F, G, A, and C).

From the perspective of either middle to late 16th-century practice,
or of later developments, we may duly note that while in 1558 he
follows the traditional numbering of the modes starting with authentic
and plagal Dorian (Modes I and II), by the early 1570's he proposes
giving the Ionian or C modes pride of place. This renumbering would
follow the order of the natural hexachord C-A (C ut, D re, E mi, F fa,
G sol, A la).

However, Zarlino is _not_ proposing a reduction of the 12 modes to
two, or the abolition of the Dorian mode because the fifth D-A
presents complications in a realization of his syntonic diatonic model
on a fixed-pitch instrument.

Similarly, Zarlino groups the modes (1558) into two families based on
the natural vertical division of the fifth above the final: in Dorian,
Aeolian, and Phrygian (D-D, A-A, E-E), the arithmetic division
prevails with minor third below and major third above (string ratio
6:5:4); while in Lydian, Ionian, and Mixolydian (F-F, C-C, G-G) the
harmonic division obtains with major third below and minor third above
(string ratio 15:12:10).

He describes the harmonic division with the major third above the
final as more "natural" or "joyful," and the arithmetic division with
the minor third as more "sad" or "gentle."

This harmonic/arithmetic distinction is also expressed in the later
contrast between major and minor keys, but under different musical
conditions and with often different organizational structures and
patterns.

While Zarlino proposes a renumbering of the 12 modes, incidentally,
musicians of this and the immediately succeeding generation prefer to
retain the customary numbering as expounded and expanded by
Glareanus (1547).

The question, "What is the center of the system?" may be based on the
premise that there is necessarily a specific "center." One might
argue that there are multiple centers, depending on how one chooses to
view the system at a given moment.

For example, the Dorian and Mixolydian modes might represent one kind
of center, located midway between Lydian and Phyrgian in the set of
modes (a distinct Lydian being least common in the 16th century):

F C G D A E
Lydian Ionian Mixolydian | Dorian Aeolian Phyrgian
------------------------ ------------------------
harmonic division arithmetic division

If we take account of Zarlino's harmonic/arithmetic groupings, then
Mixolydian and Dorian are the adjacent members of the two groupings,
sharing the affinity of an upper tetrachord T-S-T (T for whole-tone, S
for semitone), D-E-F-G or A-B-C-D.

Of course, Zarlino's theoretical model of the syntonic diatonic and
his renumbering of the modes suggest C as a center of interest, while
going back to earlier medieval practice, one could argue on the
concrete evidence of usual musical clefs that F and C, the diatonic
notes located immediately above mi-fa semitones (C-fa or F-fa), are
both salient points of orientation.

Applying solmization in a different way, we could point to the
symmetry of Dorian as a special attraction, with two T-S-T tetrachords
(re-mi-fa-sol):

D E F G A B C D
re mi fa sol re mi fa sol
T S T T T S T

The attraction of multiple centers both in theory and in practice
lends much charm to the music of this era, along with the element of
fluid degree inflection inspired by both melodic and vertical
considerations often differing from those of later tonal styles.

The typical 12-note meantone compass Eb-G# nicely accommodates the
usual accidental inflections of the 12 modes, with modal variety
providing a rich system within a relatively modest range of
transpositions.

It is in the late 17th century, when major/minor tonality becomes the
established paradigm, that Werckmeister's well-temperaments serve to
accommodate the greater range of routine transpositions compensating
for the "bipolar" rather than "multipolar" world of the new system.

-------------------------------------------
3.3. Fluid modality in practice around 1600
-------------------------------------------

As a very perceptive historian, Julius Lester if I recall correctly,
has observed, debates about the "modal" or "tonal" nature of early
17th-century music are inevitably colored by the viewpoints of the
participants.

I have experienced this at first hand, when playing a piece from a
German keyboard manuscript of this era identified as in the "First
Tone" (Mode I, D Dorian) for a friend more accustomed to later Baroque
music, and a far more skilled keyboardist by the way.

What I experienced as routine cadences or momentary focuses on various
degrees of the mode, she noted as "modulations." In other music from
this period, she expressed surprise at events which for me seemed less
remarkable.

Reading efforts of 20th-century theorists to "explain" progressions
which seem to me a part of the usual late modal vocabulary also
suggests that one's musical background and preferences may shape much
of the analysis.

Recognizing these inevitable and stimulating differences, I would myself
join with such authors as Arthur Merritt (_Sixteenth Century Polyphony: A
Basis for the Study of Counterpoint_) and Knud Jeppesen (often cited by
Joseph Pehrson in counterpoint-related threads) in viewing the music of
Palestrina, Lasso, and Victoria as indeed modal, with an interplay of
multiple centers which Merritt considers a special attraction of this
period.

In composers of the early 17th-century era such as Giovanni Gabrieli
and Frescobaldi, I can recognize, for example, "Dorian" idioms; while
the Phrygian mode has its charms not only in vocal liturgical settings
such as those of Victoria, but in keyboard music with a distinctly
"modern" flavor.

Also, a radical musician such as Fabio Colonna (1618) demonstrates the
transpositions of various modes, including Dorian with its symmetrical
solmization, on his 31-note _Sambuca Lincea_ or harpsichord dividing
each tone into five equal parts (a model suggesting a circulating
1/4-comma temperament or the later 31-tET).

In proposing an often free intermixture of the 12 modes, or
"polymodality," as one standpoint from which to approach this era --
and in 1655, Christoph Bernhard presents a 12-mode system while
discussing many of the new idioms of Monteverdi and his age -- I would
not wish to suggest that "modality" is the only or most important
factor in this music.

Vertical euphony, closest approach, chromatic idioms, and sheer
inspiration all play a role in giving this music its character. As one
historian wrote of a different question, the "medieval/Renaissance"
distinction, there is enough material here for advocates or "modal"
and "tonal" analyses alike to keep busy for some time, and possibly to
find inspiration for the creation of much new music.

Most respectfully,

Margo Schulter
mschulter@value.net

>
> Again I ask: Have you read Blackwood's book?

No.

Dear Margo,

Thanks for your detailed exposition of the topics at hand, which I have
savored and saved for future reference. I'd like to repeat, not so much
for your benefit as to sum up for others, the points I originally
intended to make: that

1. The 5-limit premises of Ben Johnston's notation, mixing 5/4 major
thirds and 3/2 fifths, have multiple precedents in late Renaissance
writings and practice (no matter how many opposing views the
contentious late Renaissance itself may have harbored);

2a. Ben's notation is centered around a C major tonality (a fact that I
have been discussing with Ben for 18 years);

2b. There is a long European history in the 16th through 18th centuries
of taking C major as central, evident in both the practice of tuning C
and E as the central reference interval in meantone tuning (which Owen
Jorgensen documents and recommends, though others may have started
elsewhere) and in C:E being the narrowest third, and the closest to
386.3 cents, in several well temperaments, though admittedly not in all
of them.

It doesn't strike me that any of these assertions are contradicted in
what you say or elsewhere; I regard 2a as uncontradictable, since Ben
has the authority to say what key he centered his notation around. I
will continue to prefer Ben's notation, not because it is easier for
performers, but because it is centered in a tonality rather than in a
string of intervals; and because this fact makes it more analogous to
Harry Partch's monophonic system, which is based on G 1/1 of 392 cps.

I have, of course, enjoyed many of your writings before, and thank you
again for this one.

Yours,

Kyle

--- In tuning@y..., kgann@e... wrote:
>
> >
> > Again I ask: Have you read Blackwood's book?
>
> No.

I highly recommend, if at all possible, you seek out his book

_The Structure of Recognizable Diatonic Tunings_.

If you have access to a good library, you might find it.

Study it well -- it's not the friendliest read but more than rewards
the thought you put into it.

From Benedetti to Barbour to Blackwood, there's a whole other side to
the story that Ben tells.

And in Vicentino and our own John DeLaubenfels, we have a synthesis
of the seemingly opposing points of view.

--- In tuning@y..., paul@s... wrote:
> From Benedetti to Barbour to Blackwood, there's a whole other side to
> the story that Ben tells.

Ben was my mentor. I've known him for 18 years. I've written many pages
about him, and have interviewed him several times. He is a practicing
composer, and while he has evolved a few theories about pitch
perception, he has (unlike myself) never harbored pretensions as a
musicologist. I can assure you that any "story" that you believe Ben
tells is a product of the imaginations of others.

Kyle Gann

--- In tuning@y..., kgann@e... wrote:

> I can assure you that any "story" that you believe Ben
> tells is a product of the imaginations of others.

Hi Kyle. I'm afraid you must have misunderstood me here. I was simply
referring to your claim that Ben Johnston's notation, with its
dissonant D-A, reflects Renaissance practice, and to Ben Johnston's
remarks in a couple of interviews I've read. I do sense that this
discussion is getting rather heated, given your sentence above. No
one is misrepresenting Ben Johnston or you or intending any
disrespect toward either one of you. Let us all take a deep breath,
collect ourselves, and do some serious reading and thinking. Or
perhaps even better, let us go make some good microtonal music -- I
sure like yours!

-Paul

--- In tuning@y..., paul@s... wrote:
> Hi Kyle. I'm afraid you must have misunderstood me here.

Paul,

Many pardons. I see where my misunderstanding arose. I've never heard
Ben make more than a stray comment or two about the Renaissance, and I
can't imagine he has any deeply held views on the subject. I have
sensed some mild resentment toward him on the tuning list. Many of
those of us who worked with him regard him as something of a musical
saint, the John Cage of the Midwest.

Incidentally, I do know the arguments for temperament, and for the
prevalence of temperament during the Renaissance. Every other year when
I teach my tuning class, I use Benedetti's demonstrations for the
necessity of temperament, and play examples of simple chord
progressions shifting by syntonic commas. I realize Benedetti was not
pushing JI, and I've read Barbour. But with vocal music still so
dominant in the 16th century, I cannot believe that just intonation was
never practiced in Renaissance music. And I remain interested in
connections between Ben's notation and Renaissance ideas that no other
modern tuning notation duplicates.

Yours,

Kyle

--- In tuning@y..., kgann@e... wrote:

/tuning/topicId_22032.html#22292

> ... with vocal music still so dominant in the 16th century,
> I cannot believe that just intonation was never practiced
> in Renaissance music.

I think Kyle is making a really important point here, Paul.

> And I remain interested in connections between Ben's notation
> and Renaissance ideas that no other modern tuning notation
> duplicates.

Hmmm... that's an interesting perspective.
Gives me a little more respect for Ben's notation.

-monz
http://www.monz.org
"All roads lead to n^0"

--- In tuning@y..., kgann@e... wrote:
> --- In tuning@y..., paul@s... wrote:
> > Hi Kyle. I'm afraid you must have misunderstood me here.
>
> Paul,
>
> Many pardons. I see where my misunderstanding arose. I've never
heard
> Ben make more than a stray comment or two about the Renaissance,
and I
> can't imagine he has any deeply held views on the subject. I have
> sensed some mild resentment toward him on the tuning list.

I certainly haven't sensed anything of the sort, having read 95% of
the posts here for about five years.
>
> Incidentally, I do know the arguments for temperament, and for the
> prevalence of temperament during the Renaissance. Every other year
when
> I teach my tuning class, I use Benedetti's demonstrations for the
> necessity of temperament, and play examples of simple chord
> progressions shifting by syntonic commas. I realize Benedetti was
not
> pushing JI, and I've read Barbour. But with vocal music still so
> dominant in the 16th century, I cannot believe that just intonation
was
> never practiced in Renaissance music.

I completely agree with you if you mean _vertical_ just intonation.
Perhaps you are unaware that with Vicentino's proposals
(specifically, his second tuning of 1555), we can overcome
Benedetti's objections and preserve _vertical_ JI in the great
majority of Renaissance music.