Small mistake, Quantum take

>>So sound is, at this otherwise not very interesting sub/atomic level,
>>ultimately conveyed by photons. The invention of a new particle, the
>>phonon, seems to be no more than a pointless complication that side-steps
>>well-accepted physical models for no apparent reason.

This appeared at the bottom of my last post, "Re: Tuning Digest 1285". What
didn't appear there was my reply...

The invention of a new particle is just a way to treat a group of properties
in Quantum mechanics. You can model nine-geese-a-laying in Quantum
Mechanics if you come up with a particle for it.

..as it seems to have been forgotten in the clipboard.

Paul Erlich has said...

>>That is, the truly astonishing things about quantum mechanics reside at a
>>much deeper level and force us to throw away our customary "pictures" of
>>physical phenomena, which rely on philosophical assumptions such as
>>Einstein's reality principle, which has been shown experimentally to be false
>>(via Bell's theorem).

Einstein's reality principle?

>>If one finds a way of accepting the crazy axioms of
>>quantum mechanics, or just takes them for granted, one can construct the most
>>verifiably accurate physical theory known to mankind (general relativity has
>>been verified slightly more accurately in some contexts).

Granted.

>>and your classical way of viewing things is only
>>valid at the macroscopic level, where it emerges as an approximation.

Give me a break! Everything is an approximation -- Quantum Mechanics too.
One that doesn't, by the way, provide many corrections on the macroscopic
level, where the "classical way" is so dreadfully approximate.

>Any pitch in a score is participating in both vertical and horizontal
>relationships

Right.

>unless the score is one-dimensional.

Huh?

>Therefore it doesn't make sense to talk about having different sets of
pitches >for horizontal and vertical sonorities.

But it makes sense to talk about having the *same* pitch set for horizontal
and vertical sonorities? I quote from your post on Friday December 12th, to
Tuning Digest #1264...

>You can't deny that most Western music derives much of its beauty and
>contrapuntal versatility from having both vertical and horizontal sonorities
>taken from the same pitch set. These pitch sets have characteristic dissonant
>intervals which allow a "tonic" to be defined and when the pitch set changes,
>so does the tonic. In this way non-diatonic notes can anticipate a change of
>tonality before that tonality also arrives.

..and now, back to yesterday's...

>Of course, homophony provides for one "melody" and one can reserve a
>subset of the pitches for this and another subset for everything else.
>But even so, the non-melody parts will have horizontal movement of their
>own, as well as diagonal ("cross-") relations with the melody itself.

True. But this doesn't take away from the fact that there is one line of
notes heard, without a doubt, as "the" melody, being backup up with chords.
Go get the 1974 YES album, "Relayer", and listen to the second track from
time index 5.30 to 6.15 for an excellent example of melody and harmony
coming from different pitch sets.

This concept is very important in Barbershop, which is, by definition,
melody being backed up with chords. The melody is usually sung in something
roughly close to 12-tone Pythagorean (3-limit), while the notes used for the
chords fit almost exactly in the 7-limit.

>In contrapuntal music, all harmony is generated by the melody
>intertwining with its own imitations. In such a context, one needs a
>single set of pitches to provide all the melodic, harmonic, and diagonal
>ingredients of the piece.

Granted. Most all classical music has elements of contrapuntalness.
There's quite a bit in the midi files on my web page.

>>}4(P5) - M3 - 2(T) = X
>>
>>}Is this a
>>}good definition of the syntonic comma?
>>
>>There is another possible definition:
>>
>>3(P5)-M6-T=X
>>
>>The two definitions are often equivelent, but in the case of tunings not
>>consistent within the 5-limit (such as 20tet) they are unequal. In such a
>>case I say that the syntonic comma is not well-defined in that tuning.

Aha! Thanks! I was looking at your post with the asci diagrams, and I
agree that the diagonals work much better than a square grid (as in the JI
Primer). I was looking at the two D's, and realized that 3(P5)+(min3) =
4(P5)-(Maj3) is not true for temperaments without a consistent 5-limit
triad. In your 20TET example...

(36 + 5) /= (48 - 6)

So you would simply say the syntonic comma is not well defined? Cool.
Working on your septimal comma stuff...

John Chalmers has said...

>and, of course Bosanquet's original work on the
>general theory of the octave and the generalized keyboard.

Where to get Bosanquet's original work? Erv recommended his book
"Temperament" but it is out of print.

>I doubt any universal acoustic waves could exist at the present epoch,
>but there must have been some before and just after the inflationary
>period.

How are you going to have a standing wave in the universe? Wouldn't it have
to be a higher-dimentional wave? That is, if you look thru the strongest
telescope, do you see the back of your head?

Carl


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