Zarlino and the C-c species

Paul Erlich wrote:

> still unsure as to why Zarlino favored the C-C over other octave
> species . . .

I dug up my notes I took from Zarlino and some other sources, finally.

First of all, Fogliano, in _Musica Theorica_, 1529, already presents a C-c
species for his monochord tuning. He acknowledges Ptolemy, and sets it out
like this:

C D E F G A B
10:9 9:8 16:15 9:8 10:9 9:8 16:15

|_____|___|____|
(Ptolemy's diaton syntonon)

[Interestingly, this tuning can be found even earlier, in _Musica
practica_ by Ramos de Pareja of Bologna, in 1482! He lays it out from A-a
though, as was standard in texts of the time. His student Spataro reported
that he arrived at this division independently from Ptolemy. It's indeed
unlikely Ramos would have had access to the Greek sources.]

So Zarlino, who acknowledges Fogliano as an excellent writer on music,
certainly knew Fogliano sets the octave division out from C to c. He gives
his division, which permutes the 9:8 and 10:9 from the beginning of
Fogliano's, and lists no less than 6 reasons why C-c should be considered
first, some better than others... Paraphrasing:

1) C-c is the model for pure tuning. (This he explains at length - all
the things about harmonic division, and ratios from the senario)

2) The second reason is a little unclear to me. It has to do with the
solmization syllables, and I think it's that if you start on "ut" you
don't have to mutate (i.e. if you had to sing A-c you can't call that
la-ut, you have to have switched to another hexachord by then).

3) A was probably only selected to be the first octave species
because it's the first letter of the alphabet [!] Thus we can discard the
ordering starting on A.

4) If you list the modes by their finals starting on C, you never jump
over a note: C-D-E-F-G-A is an unbroken chain, whereas D-E-F-G-A-C has a
skip.

5) Since the syllables for hexachordal solmization go "ut, re, mi, fa,
sol", then the modes should be arranged to reflect the same ordering.

6) This is a cool one: Zarlino tried to reconstruct the ordering of the
ancient Greek modes from Ptolemy. He misunderstood, and believed that
since Dorian and Phrygian, and Phrygian and Lydian, were a whole-tone
apart, they must be C-D-E. Since he wanted to call Dorian mode 1,
reflecting its importance in Greek theory, this means making C-c mode 1.
He gets the following names (this is from the Dimostrationi harmoniche,
1571):
C-c Dorian
D-d Phrygian
E-e Lydian
F-f Mixolydian
G-g Ionian
A-a Aeolian
which he thought reflected ancient Greek usage. (In reality the Greek
modes were like this: Dorian e-E, Phrygian d-D etc.)

He abandoned these names for the 2nd edition of the _Istitutioni
harmoniche_ in 1573 - I guess because he knew it was confusing when
everyone already knew a different set of names.

See you --Jon

Hi Jon -- you'll see the Fogliano and Ramos tunings mentioned in the _Gentle
Introduction to Periodicity Blocks_, part 2
(http://www.ixpres.com/interval/td/erlich/intropblock2.htm).

So it seems that several Renaissance theorists used the octave species from
C-c for theoretical demonstrations, even though the C mode was not yet
prevalent in the music.

Now I need to ask Margo for help -- I'm sure I haven't read her essays
closely enough, but perhaps a bit of naivite on my part may make for some
more generally enlightening answers from her:

Margo, you were saying that in the Renaissance, the harmonic progressions
were largely holdovers from Medieval ones, with the 3-limit dyads simply
completed into 5-limit triads, and the directed, "functional" harmonic
motion was still the major third resolving into the perfect fifth and the
minor third resolving into the unison (and the minor sixth resolving into
the perfect fourth and the major sixth resolving into the octave). (I take
it the minor seventh resolving into the perfect fifth and the major second
resolving into the perfect fourth had largely disappeared?) So it seems that
one could use these to "tonicize" the following modes:

C mode:
B-c
D-C

E mode:
d-e
F-E
or
A-B
F-E

F mode:
e-f
G-F
or
B-c
G-F

A mode:
F-E
G-A

while the D and G modes would require chromatic alterations? (Actually, even
if the m7-5 and M2-4 resolutions were still allowed, how would one
"tonicize" the D and G modes without any alterations? How was it done in
Medieval times (if such a concept of tonicization is at all applicable)?)

In any case, it is my belief that once thirds functioned as fully recognized
consonances for long enough, and bare 3-limit sonorities had been excluded
from the musical texture for long enough, these old directed resolutions
would have been overshadowed by the greater (in fact, maximal, among
diatonic possibilities,) incisiveness of the resolution from the diminished
fifth into the major third (or the augmented fourth into the minor sixth).
Thus the dominant directed progression became, sometime in the early or
middle Baroque,

F-e
B-c,

and this would clearly tonicize only the C mode. The notes C and E also
belong to the tonic triad of the A mode, though since the tonic A is not
part of the "goal" interval, a chromatic alteration is needed to fully
tonicize it. Thus the modern major and minor modes rose to prevalence.

The point to emphasize is that I think it is pure coincidence that Zarlino
and others focused on the C mode when they did, since they had no way of
knowing of its future ascendancy. Let alone Ptolemy.

Hi Paul,

> you'll see the Fogliano and Ramos tunings mentioned in the _Gentle
> Introduction to Periodicity Blocks_, part 2
> (http://www.ixpres.com/interval/td/erlich/intropblock2.htm).

ok - all I could find there were the phrases "was this Ramos?", referring
to one block, and Monz's comment likening a different block to Fogliano's
tuning.
But the Ramos and Fogliano monochord divisions are actually the same
tuning, up to modal rotation - why are they associated with two different
blocks here?
Btw Fogliano has at least one other division of the monochord, a 14-note
scale with 2 D's and 2 Bb's (it's interesting that these extra notes,
too, are symmetrically placed around C). Since having 2 of these is
impractical, he suggests splitting the difference in each case, to produce
a 12-note scale with D at sqrt(5):2 and Bb at 4:sqrt(5) above C.

> The point to emphasize is that I think it is pure coincidence that
> Zarlino and others focused on the C mode when they did, since they had
> no way of knowing of its future ascendancy. Let alone Ptolemy.

What do you mean by "Let alone Ptolemy" here? His tetrachordal division
that appears in these Renaissance tunings hasn't got anything to do with
the C mode.

I think "pure coincidence" is a bit strong. The part of Zarlino's reason
that has to do with the consistency of modal quality on scale degrees I IV
and V, i.e. them all being major triads, was surely a factor in the C
mode's eventual prevalence, I would imagine.

In any case, I don't know that it's true that the C mode was much less
prevalent then. When Fogliano displays the division of the C-c species, he
explains his choice as _more practicorum_ which means something like
"according to practice". I don't know the breakdown of modes offhand in
surviving compositions from the early 1500s -- and no one knows the
actual breakdown of all contemporary pieces, since most have disappeared.

best -jon

Jon Wild wrote,

>But the Ramos and Fogliano monochord divisions are actually the same
>tuning, up to modal rotation - why are they associated with two different
>blocks here?

I think you're mistaken. The Ramos tuning is quite different -- see
http://www.ixpres.com/interval/td/erlich/ramospblock.htm (if you haven't
already).

>> The point to emphasize is that I think it is pure coincidence that
>> Zarlino and others focused on the C mode when they did, since they had
>> no way of knowing of its future ascendancy. Let alone Ptolemy.

>What do you mean by "Let alone Ptolemy" here? His tetrachordal division
>that appears in these Renaissance tunings hasn't got anything to do with
>the C mode.

Exactly -- and yet you'll often find the "JI major scale" ascribed to
Ptolemy.

>I think "pure coincidence" is a bit strong. The part of Zarlino's reason
>that has to do with the consistency of modal quality on scale degrees I IV
>and V, i.e. them all being major triads, was surely a factor in the C
>mode's eventual prevalence, I would imagine.

My belief is that that is another common misconception . . . even Schoenberg
fell into this trap.

>In any case, I don't know that it's true that the C mode was much less
>prevalent then. When Fogliano displays the division of the C-c species, he
>explains his choice as _more practicorum_ which means something like
>"according to practice". I don't know the breakdown of modes offhand in
>surviving compositions from the early 1500s -- and no one knows the
>actual breakdown of all contemporary pieces, since most have disappeared.

I'm sure Margo or someone can address this . . .

> Message: 8
> Date: Tue, 14 Nov 2000 12:08:02 -0500
> From: "Paul H. Erlich" <PERLICH@ACADIAN-ASSET.COM>
> Subject: RE: RE: Zarlino and the C-c species
>
> Jon Wild wrote,
>
> >But the Ramos and Fogliano monochord divisions are actually the same
> >tuning, up to modal rotation - why are they associated with two different
> >blocks here?
>
> I think you're mistaken. The Ramos tuning is quite different -- see
> http://www.ixpres.com/interval/td/erlich/ramospblock.htm (if you haven't
> already).

Paul - the Ramos and Fogliano diatonic tunings are the same. The
periodicity blocks in the link you give extend to chromatic notes, which
are arrived at differently between the two systems. But we've been talking
about diatonic modes of the octave.

The relevant portion of the lattice you show for Ramos is as follows:

1:1
D----A----E----B
| | |
F----C----G

And here are Fogliano's string lengths for his monochord division, taken
from chapter 1 of book III of _Musica theorica_:

C 3600
D 3240
E 2880
F 2700
G 2400
A 2160
B 1920
C 1800

(the numbers are so large so that he can eventually add chromatic
divisions and stay in whole numbers). It's the same tuning.

Hello, there, and I'd like very briefly for now to respond to some of
Paul Erlich's questions about 16th-century music and modality.

First of all, 16th-century verticality is in its own category, with
traditional 3-limit progressions (especially m3-1, M3-5, M6-8) being
supplemented in practice and theory by newer developments such as
suspensions (e.g. 7-6, 4-3, 2-3), directed tritone resolutions (d5-M3,
A4-m6), and progressions between the bass and one of the upper parts
such as M3-8 (upper part ascending by step, bass falling a fifth or
rising a fourth).

Explaining how all these elements interact with the norm of 5-limit
saturation, an integral element of theory as well as practice by the
time of Vicentino (1555) and Zarlino (1558), would call for a major
post, or maybe a series. It's a worthy project, maybe when I'm a bit
further along with the neo-Gothic series.

For now, I would emphasize that the total musical effect is quite
different than either 14th-century or 18th-century verticality. As a
medievalist, I may focus on the medieval elements, while people
oriented to major/minor tonality often read 18th-century
interpretations into 16th-century progressions later incorporated into
the key system.

For example, Vicentino and Zarlino discuss the resolution of tritone
tension (e.g. d5-M3) as a pleasing feature of style, but this is just
one cadential possibility, as opposed to _the_ defining element of
cadentiality or modality.

Note generally that in standard 16th-century styles (as contrasted to
avant-garde compositions near the end of the century), seconds and
sevenths are more restricted than in either 13th-14th century or
17th-century and later practice. It's interesting that a bold
progression such as m7-5 occurs boldly both in Machaut and in the late
Manneristic modality of the early 17th century, but is foreign to
orthodox 16th-century style, where prominent sevenths occur mainly as
more restrained suspensions.

Glareanus and Zarlino recognize 12 modes: the usual eight medieval
ones, plus authentic and plagal versions of Aeolian (A-A) and Ionian
(C-C). Zarlino specifically states that Ionian is the most popular
mode in Italy for dances. Both also note that the Aeolian and Ionian
modes are older in practice than in theory, a point on which I could
enlarge. An important point is that these modes -- unlike major and
minor keys which appear to be based on similar octave-species -- are
open to the usual fluid accidental inflections, e.g. B/Bb or F/F#.

An important point about Zarlino's harmonic aesthetic: he generally
urges that composers alternate the harmonic division of the fifth
(string-ratio 15:12:10, major third below minor third) with the
arithmetic division (6:5:4, minor third below major third). This
fluidity is one of the most pleasing features, at least to me, of
16th-century verticality.

Also, for Zarlino, the principal degrees of a mode on which to place
cadences are the first, third, and fifth -- e.g. C, E, and G in
Ionian or D, F, and A in Dorian. This invites a discussion of
traditional schemes of finals and confinals, another topic; but I did
want to clarify which degrees Zarlino generally considers primary.

To conclude for now, I would emphasize the importance of viewing the
whole picture: the variety of basic two-voice progressions, old and
new; the plurality of modes; the balance of conjunct and disjunct bass
motions; the fluidity of accidental inflections both in orthodox and
not-so-orthodox styles.

Since 16th-century music grows out of medieval traditions and provides
the basis for 17th-century developments leading to the key system of
Corelli (c. 1680), it has resemblances to both systems, but its own
special qualities (e.g. the rather homogenous 5-odd-limit textures, as
opposed to the bolder contrasts of concord/discord or "harmonic
entropy" in earlier as well as later styles).

Zarlino's modal ethos focuses both on the division of the fifth
(harmonic or arithmetic) above the final, and on the structure of
pentachords and tetrachords making up an octave species. Thus
Mixolydian (G-G) shares with Ionian (C-C) and Lydian (F-F) the more
"natural" and "joyful" harmonic division above the final; and it
shares with Dorian (D-D) the upper tetrachordal structure T-S-T
(Mixolydian D-E-F-G; Dorian A-B-C-D).

This is an attempt to be quick, fragmentary, but maybe responsive to
some of the immediate questions raised.

Most appreciatively,

Margo Schulter
mschulter@value.net

>Paul - the Ramos and Fogliano diatonic tunings are the same. The
>periodicity blocks in the link you give extend to chromatic notes, which
>are arrived at differently between the two systems. But we've been talking
>about diatonic modes of the octave.

Well, I was talking about the full 12-tone systems these authors proposed.

--- In tuning@egroups.com, "M. Schulter" <MSCHULTER@V...> wrote:

http://www.egroups.com/message/tuning/15527

>
> Explaining how all these elements interact with the norm of 5-limit
> saturation, an integral element of theory as well as practice by the
> time of Vicentino (1555) and Zarlino (1558), would call for a major
> post, or maybe a series. It's a worthy project, maybe when I'm a bit
> further along with the neo-Gothic series.
>
>>
>For example, Vicentino and Zarlino discuss the resolution of tritone
>tension (e.g. d5-M3) as a pleasing feature of style, but this is just
>one cadential possibility, as opposed to _the_ defining element of
>cadentiality or modality.

This is so very interesting! And it would be particularly
interesting to listen to Renaissance music where there are 5-limit
triadic sonorities that are not functioning in an 18th century
"tonal" way...I would enjoy citations of particular pieces with such
effects....

Well, actually, come to think of it, Lasso (Lassus) seems to do some
of this... and it is one of the most exciting aspects of his music,
if I am not mistaken...

________ ___ __ _
Joseph Pehrson