Yahoo Tuning Groups Ultimate Backup tuning interval names: rational 'tritones'

Paul, what an informative post! You've got to cut this out, man. I really
can't afford the time to stay here much past our solving the high third
mystery. If you keep this up, I'll be more hooked than I already am. So
please cut it out!!! LOL
>
> Jerry wrote,
>
>>I"m beginning to suspect that this "problem" is grounded in theorists (and
>>perhaps microtonalists, as well) intent on providing a rational system of
>>fixed pitches that relate directly to a tonal center.

Paul:
>
> Even in the fixed-pitch interpretation of the diatonic scale that Monz gave,
> the D-A fifth is 27:40, and the D-F minor third is 27:32. Clearly this is an
> example of what you are talking about. There had to be a way to sidestep
> this problem on Renaissance and Baroque (and later!) keyboard instruments
> (necessarily of fixed pitch); the solution was meantone temperament.
> Unfortunately for Jerry, meantone temperament has very dissonant dominant
> seventh chord. During the meantone period, a keyboard continuo was quite
> common and it is doubtful that many vocalists would have made the ~35-cent
> change necessary to make 4:5:6:7 dominant seventh chords. But I guess we'll
> never know for sure.

Of course, you are right. But also consider that vocal composition was
primary until well into the seventeenth century. Ears were relatively free
to seek satisfying pitch relations. (I'll mp3 a great recording of a
Gabrielli polychoral motet that was not likely to have been "corrupted" by
meantone interference. Unfortunately, it was not recorded circa 1610. :-)

Renaissance singers had little "interference" from keyboards since the only
instruments that were used _with_ singing were somewhat flexible in
tuning--viols (if they weren't fretted) and recorders. Then violins hit the
scene and took over the responsibility for "ear" tuning.

Also, consider that harpsichords (like pianos) produce a decaying sound,
making it possible for well-tuned singing and string playing to maintain
well-tuned performances in spite of theoretical dissonances.

Me:

>>Interest in allowing
>>for "scale step" deviations to accommodate root changes seems minimal, and
>>appears to result in compromised intervals having high-number ratios.

Paul:
>
> The type of theory you're describing here is one that I've always lashed out
> against.

Have I found a new soul mate? LOL

> You'll find a lot of theorists doing that sort of thing, including
> Yasser of all people, but those high-number ratios are almost always
> irrelevant.

(?)

> The adaptive tuning algorithms John deLaubenfels has been
> implementing and I and others have been discussing aim to tune almost all
> simultaneities in simple-integer ratios; each "scale step" will fluctuate
> over the course of the piece, > though John's program tries to keep sudden,
> drastic changes (which would be disturbing in performance) to a minimum.

I dig it!

> Meanwhile, John Link and others seems to like sudden, drastic changes,
> particularly in scale step 2 in the major scale, but in my opinion they're
> clinging too strongly to an essentially fixed-pitch interpretation like the
> one Monz gave (augmented with an additional "D" at 10/9 to make a consonant
> D minor triad).

Perhaps "John Link and others" will respond to this. It should be
informative.

Me:
>
>>To me, the functional "augmented fourth" in a dominant 7th chord is _not
>>synonymous with "tritone." The former is larger and specifically has the
>>leading tone on top and the latter is the keyboard's compromised ambiguous
>>version of both "inversions."

Paul:
>
> "Tritone" literally means three tones,

Yes.

> or three major seconds,

Yes.

> or an
> augmented fourth.

No.

The term "tritone" could only be spawned by a 12-tET keyboard concept of
music. In fact, the concepts of "whole step" and "half step" requires a
keyboard mentality for validity. In keyboard terms, both "augmented fourth"
and "diminished fifth" are (uuuuuughhhhhhgggggg!!!!!!!) "tritones." Keyboard
tritones are invertible. Acoustic "tritones" are not.

In response to an earlier post, I said:
>
>>Why not 600 cents? Aren't we talking keyboard here?

Paul:
>
> Ellis was one of the "high-number ratio" people we both take issue with. His
> 590 cents is the 45:32. For practical purposes, the keyboard tuning would
> indeed be relevant -- as it happens, one variety of meantone, 1/6-comma
> meantone, has exactly this 590-cent augmented fourth.

Okay. There's that meantone business again. Can be bury meantone? I guess
not, since we really should honor the past. On the other hand we bury our
fathers. I'm really confused on this. LOL
>
>>In any case, is 7 cents
>>considered "quite close"? The difference between a keyboard "tritone" and an
>>acoustic 5:7 diminished fifth or 7:10 augmented fourth is aurally quite
>>considerable.
>
> There are meantone tunings, though, where the augmented fourth would
> coincide with Jerry's "diminished fifth"; namely, 583 cents. Most of the
> historical meantone tunings come closer to this than 1/6-comma meantone.

Excuse me if I say "So what."
>
>>Sounds like a whopping difference. I'll go with the one that best describes
>>what ears hear. It appears to me that the 5-limit concept is simply a
>>compromised apology to 12-tET tradition.
>
> The 5-limit concept is much older than 12-tET tradition. The 5-limit
> concept, combined with the consensus ears of musicians, brought about the
> adoption of meantone tuning in the late 15th century. The dominant seventh
> chord was born in this 5-limit, meantone environment. In that environment,
> it was the augmented sixth chord, not the dominant seventh chord, that
> approximated the 4:5:6:7 chord. In fact, if you look at the historical
> literature, you'll find people discussing ratios of 7 in the context of
> augmented sixth chords and on their own merits long before ratios of 7 were
> ever discussed in the context of dominant seventh chords. And this wasn't
> the result of any over-abstract theory -- Tartini could play the ratios of 7
> on his violin (we know because he reported hearing the then-unknown
> difference tones in the correct places) and yet considered these ratios to
> be foreign (in a good way!) to diatonic music rather than part of an
> already-existing practice involving dominant seventh chords.

This paragraph makes me want to live another 65 years so I can catch up to
Paul. How old are you, Paul? 130? Do you have a day job? What do you do
every day other than pore over old manuscripts? No wife saying "why don't
you spend more time with me"? No time clock to punch? No stacks of exam
papers to grade? Must be nice!

Jerry

🔗Joe Monzo <monz@juno.com>

> [Jerry Eskelin, TD 530.2]
>
>> Paul [Erlich]:
>> "Tritone" literally means three tones,
>
> [Jerry]
> Yes.
>
>> [Paul]
>> or three major seconds,
>
> [Jerry]
> Yes.
>
>> [Paul]
>> or an augmented fourth.
>
> [Jerry]
> No.
>
> The term "tritone" could only be spawned by a 12-tET keyboard
> concept of music.

Jerry - I'm sorry, but you are WRONG here!

You must have missed the post I sent explaining this
http://www.onelist.com/messages/tuning?archive=528
where I say, among other things (including an answer to
a question *you* posed to me):

> [me, monz, TD 528.23]
> But the original meaning, which is obvious from the word's
> etymology, is to define an interval composed of *3 tones*.
> The term developed at a time which stipulated a Pythagorean
> context (help me on the history, Margo), and so thus the
> interval was (9/8)^3 = 512:729 = ~611.73 cents. This is
> exactly synonymous with 'augmented 4th' in Pythagorean tuning.

The term 'tritone' is *far* older than any 12-tET theory,
and in fact probably predates keyboards too, which, remember,
were not tuned even approximately in 12-tET until around 1500
at the very earliest.

As far as I know, the Greeks did not use the term, and it
developed with Latin theory c 1000 - waaaaaaay before 12-tET.

-monz

Joseph L. Monzo Philadelphia monz@juno.com
http://www.ixpres.com/interval/monzo/homepage.html
|"...I had broken thru the lattice barrier..."|
| - Erv Wilson |
--------------------------------------------------

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🔗Joe Monzo <monz@juno.com>

> [Jerry Eskelin, TD 530.2]
> Renaissance singers had little "interference" from keyboards
> since the only instruments that were used _with_ singing were
> somewhat flexible in tuning--viols (if they weren't fretted)
> and recorders. Then violins hit the scene and took over the
> responsibility for "ear" tuning.

But viols had frets!!

As you point out, it's not until around the 1600s that
the excellence of the fretless violin family, constructed by
the Cremona masters such as Stradivari, begins to usurp the
prime position in the ensemble from the viols.

Certainly, viols exitsted which did not have frets, but
the norm was the fretted version. Info from anyone more
historically informed would be appreciated - maybe someone
knows of a viol discussion list to which this post can
be forwarded?

And you are correct to note that recorders were used and
are not fixed pitch.

But keyboards were certainly a frequent part of the ensemble,
and something you're really overlooking: lutes were ubiquitous
during the Renaissance, and they were fixed-pitch but not
meantone, tuned generally in something close to 12-tET and
in at least one important case (Dowland) in a circulating or
well-temperament:
http://interval/monzo/fngrbds/dowland/dowland.htm

> [Jerry]
> Also, consider that harpsichords (like pianos) produce a
> decaying sound, making it possible for well-tuned singing
> and string playing to maintain well-tuned performances in
> spite of theoretical dissonances.

Good point. To my mind, it's very likely that singers accompanied
by a keyboard continuo could sing a note at the pitch given by
the keyboard, then slide it upward or downward as the keyboard
sound decays, to make it approach vertical JI better.

Ta da! - an adaptive JI stemming from meantone, as advocated
by Paul Erlich. (see his many posts on this to John deLaubenfels)

And something that I think Jerry feels is natural but Paul
might balk at is the ability of good singers to sing whatever
damn pitch they want to, regardless of what's going on around
them. A great example is Robert Johnson's total disregard
for the 12-tET pitches being produced by his guitar while
he sings microtonal pitches all over the place:
http://www.ixpres.com/interval/monzo/rjohnson/drunken.htm

-monz

interval names: rational 'tritones'

🔗Gerald Eskelin <stg3music@earthlink.net>

🔗Joe Monzo <monz@juno.com>

🔗Joe Monzo <monz@juno.com>