Re: Zarlino's harmonic theory (thanks for corrections, Paul)

Hello, there, and thanks to Paul Erlich for some very important
corrections on my Zarlino article.

> The last "artifical arrangement" seems especially artificial, if you
> know what I mean. Shouldn't that be A3-D4-F4?

Absolutely, and I'm glad that someone caught this: my E3-G3-C4 is a
result of copying the first part of the table to use for the second
part, but not making the needed changes in the note names for the
second part.

>> C5 15
>> 8:5
>> G4 20

> that should be 8:6 . . .

Again, thanks for the perspicacious proofreading! Here I suspect that
when typing I was focusing on the minor sixth (indeed 8:5) which C5
forms with E4, but the interval we're looking at here is certainly an
8:6 fourth.

>> Might this tie in with Zarlino's opinion that C4-F4-A4 is "good,"
>> but C3-E3-A4 is "better"?

> This contradicts what you wrote above. Which was did Zarlino see it?

Fortunately, the contradiction here arises only from my typo or the
like in stating the last quoted sonority, which should be A3-C4-F4
(minor third below fourth), mentioned a bit earlier in this concluding
part of the article.

Zarlino, in sum, says that C3-F4-A4 is a more harmonious arrangement
of the _major_ third and fourth than F3-A3-D4; but finds a sonority
with the _minor_ third below and fourth above such as A3-C4-F4 yet
better. The converse arrangement with fourth below minor third,
e.g. A3-D4-F4, he finds the least harmonious of all these choices, and
"almost dissonant."

Maybe the rather tense qualities of the last combination makes it all
the more effective in a common type of 16th-century cadential
approach, typically leading into a 4-3 suspension:

F4 E4 D4
D4 C#4 D4
A3 D3

In this kind of Renaissance/Manneristic setting, the suspended 6:8:9
represents an increase in dissonance from the minor sixth sonority, so
tempered fifths and fourths may reinforce rather than compromise the
cadential grammar, so to speak.

Apart from the invaluable corrections, you also offer some fascinating
remarks that I'd like to address in a separate reply.

Anyway, your proofing is a real service, and I'm pleased to say that
I've made corrections in my original version for any future use.

Most appreciatively,

Margo Schulter
mschulter@value.net