Re: [tuning] Re: harmonic entropy continuing

Paul Erlich wrote,

> (in the 3-limit they're the same),

Wouldn't this be the case for any single interval chain, say the
16:20:25 and the 1/(25:20:16) for example?

Dan

Carl Lumma wrote,

> is there a similarity between the differences? Does the 1/(4:5:6:7)
sound like a "minor" version of the 4:5:6:7?

I think so, or at least I can 'hear it' that way... didn't someone say
that they thought this was the "Tristan Chord" a while back? BTW,
doesn't it make more sense to write these subharmonic chords with the
identity in reverse order, i.e., the 1/1 7/6 7/5 7/4 as a 1/(7:6:5:4)?

> BTW- major and minor 3-limit chords are not the same. Perfect
fourth vs. perfect fifth?!

I think that Paul meant that a 2:3, or a 4:6:9 are the same as a
1/(3:2) and a 1/(9:6:4), or using the augmented example that I gave, a
16:20:25 is the same as a 1/(25:20:16)... either that or I've confused
or missed some basic part of the discussion.

Dan

D.!
I always thought so. Wagner would have pled on the microtones if he would have had them.
CPS would also attracted him for their constant suspension of a set tonic

"D.Stearns" wrote:

> the 1/(4:5:6:7)
> sound like a "minor" version of the 4:5:6:7?
>
> I think so, or at least I can 'hear it' that way... didn't someone say
> that they thought this was the "Tristan Chord" a while back? BTW,
> doesn't it make more sense to write these subharmonic chords with the
> identity in reverse order, i.e., the 1/1 7/6 7/5 7/4 as a 1/(7:6:5:4)?
>
>
> Dan

-- Kraig Grady
North American Embassy of Anaphoria island
www.anaphoria.com

I wrote,

>> (in the 3-limit [otonal and utonal are] the same),

Dan Stearns wrote,

>Wouldn't this be the case for any single interval chain, say the
>16:20:25 and the 1/(25:20:16) for example?

Yes, as well as chords like 12:14:18:21 and 8:10:12:15, but I think we were
talking about complete consonant chords of a given limit.

Carl Lumma wrote,

>BTW- major and minor 3-limit chords are not the same. Perfect fourth
>vs. perfect fifth?!

Major and minor? Well, if you're talking about otonal and utonal, 3:2 and
1/2:1/3 are both perfect fifths, and 4:3 and 1/3:1/4 are both perfect
fourths. It is certainly not the case that the perfect fifth is otonal and
the perfect fourth is utonal.

>What I'm driving at here is... does minor sound sad? Major happy? Do
>the chords alone sound that way, or only in context of the diatonic scale?
>Tritone explains why two modes were selected during the developement of
>tonal music, but not why they sound different. That difference must come
>from the psychoacoustic quality of the tonic triad...

You're probably right. But the utonal 9-limit pentad, 1/9:1/7:1/6:1/5:1/4,
doesn't sound sad to me . . . maybe because it sounds like a dominant ninth
with a _sharp_ major third . . .

Carl wrote,

>I can't seem to remember if this web
>page has already been discussed...

>http://www.sohl.com/sohl/mt/maptone.html

Yup, I think I mentioned that it approaches the problem of triadic
consonance from what one might call the Helmholtz/Plomp/Sethares angle, and
so fails to differentiate between otonal and utonal . . .

>Another thing -- by my proposed definition of minor, all ASS's would be
>minor.

OK -- what's your proposed definition of minor again?

On Thu, 25 May 2000, Paul H. Erlich wrote:

> OK -- what's your proposed definition of minor again?

Interesting question, and I know **I** am not whom you are asking. But at
the beginning of the Baroque there were Dorian and Phrygian minors, two
each. And at the end there was only Aeolian minor, with an augmented
second thrown in for excitement just below the leading tone. And some kind
of an idea of adding a Dorian sixth on the way up but not on the way down.
Obviously the idea of minor is a very malleable one. But in an emotional
sense, people seem to need it.

Judy

Carl Lumma wrote,

> What I'm driving at here is... does minor sound sad? Major happy?

Assuming "sad" and "happy" to be ultra generalization, yes, I'd say
that I more or less agree with that...

> Do the chords alone sound that way, or only in context of the
diatonic scale?

Again, I'd more or less say yes (to both)...

> Tritone explains why two modes were selected during the developement
of tonal music, but not why they sound different. That difference
must come from the psychoacoustic quality of the tonic triad...

Hmm, I'd more tend to say that they're different because they're
different... in other words, is there some analogous "happy" and "sad"
when the otonal utonal, "major" "minor" analogy is reversed as with
the 6:7:9 and the 1/(9:7:6)? Maybe so (though I think most folks find
the 1/(9:7:6) to be an acutely unhappy "major" triad!), but I don't
think that you'd have to look very long before you find some instances
where this analogy just doesn't stretch so well.

Personally I think that too much emphasis placed upon the musically
uncontextual, or psychoacoustically isolated observation, can
sometimes lead (even brilliant minds) to what seem to me to be some
musically -- call that "artistically" if you must -- dubious
extrapolations:

"The major mode is well suited for all frames of mind which are
completely formed and clearly understood, for strong resolve, and for
soft and gentle or even for sorrowful feelings, when the sorrow has
passed into the condition of dreamy and yielding regret. But it is
quite unsuited for indistinct, obscure, unformed frames of mind, or
for the expression of the dismal, the dreary, the enigmatic, the
mysterious, the rude, and whatever offends against artistic
beauty;--and it is precisely for these that we require the minor mode,
with its veiled harmoniousness, its changeable scale, its ready
modulation, and less intelligible basis of construction. The major
mode would be an unsuitable form for such purposes, and hence the
minor mode has its own proper artistic justification as a separate
system." (Helmholtz, "On the Sensations of Tone," p. 302)

Dan