Re: stuff (Paul E.)

>Actually, David, you have found the "problem of the syntonic comma" which
>explains why 5-limit just intonation never gained much importance in Western
>music.

No! It explains why the diatonic scale was not tuned in 5-limit just
intonation on most western keyboards and guitars.

5-limit JI is a big place, present in some form in many meantone tunings.
Using the term synonymously with some 7-tone scale by Ptolemy is a big loss.

>Coprime and relatively prime are synonymous. So Carl and I were really
>saying the same thing.

Yes of course. But I don't recall writing that in response to anything you
said.

>Carl was thinking, much as you are now, that while odd-limit may be
>appropriate for dyads, prime-limit may be appropriate for larger chords. I
>demonstrated to him with some examples (check the archives) that I thought
>this was an illusion. He appears to have bought my argument, as he is now
>using it "against" you.
>
>What Carl is saying:

I didn't say it better myself.

>>To me, there's a difference between a lattice metric and a lattice
>>visualization of a complexity metric.
>
>Can it hurt to try to make them coincide as closely as possible? Then one
>kills two birds with one stone.

The stone only kills one bird -- it's not my fault that shorest-route
metrics have nothing to do with dyadic consonance and dissonance!

The shortest-route metrics are equivalent to change-making problems. What
is the least number of coins you can use to make 33 cents change? Forget a
quarter, nickel, and three pennies, Erlich mints a 33-cent piece on the spot!

>The advantage of using primes is that each note appears in one and only
one >place

Yes, but using logs on an odd factor lattice, all locations have the same
value. Multiple locations may still be a pain visually, but probably not
so much as wormholes...

Carl

Carl Lumma wrote,

>>Actually, David, you have found the "problem of the syntonic comma" which
>>explains why 5-limit just intonation never gained much importance in
Western
>>music.

>No! It explains why the diatonic scale was not tuned in 5-limit just
>intonation on most western keyboards and guitars.

Don't forget harps -- if I'm not mistaken harps were pretty much diatonic in
Renaissance and Baroque times, so would have been natural for meantone. One
harpist tackles the tuning issue at
http://users.uniserve.com/~tzhoskin/tuning.htm.

>5-limit JI is a big place, present in some form in many meantone tunings.

Strictly speaking, only 1/3 or 1/4 of the notes in a meantone tuning can
coincide with 5-limit JI.

>Using the term synonymously with some 7-tone scale by Ptolemy is a big loss

Amen. But many do. Perhaps I should have said that David's conception of
tuning never gained much importance in Western music.

>>Coprime and relatively prime are synonymous. So Carl and I were really
>>saying the same thing.

>Yes of course. But I don't recall writing that in response to anything you
>said.

That's right -- I was just clarifying things for Joe Monzo.

>>Can it hurt to try to make them coincide as closely as possible? Then one
>>kills two birds with one stone.

>The stone only kills one bird -- it's not my fault that shorest-route
>metrics have nothing to do with dyadic consonance and dissonance!

Your fault? Anyway, it seems that Tenney and I both tried to kill the two
birds with one stone and came to similar strategies. The differences are
probably because I assumed octave-equivalence and Tenney didn't.

>The shortest-route metrics are equivalent to change-making problems. What
>is the least number of coins you can use to make 33 cents change? Forget a
>quarter, nickel, and three pennies, Erlich mints a 33-cent piece on the
spot!

Eh?

> Don't forget harps -- if I'm not mistaken harps were pretty much diatonic in
> Renaissance and Baroque times, so would have been natural for meantone. One
> harpist tackles the tuning issue at
> http://users.uniserve.com/~tzhoskin/tuning.htm.

I'll check that out sometime when real life isn't interfering with theory
-- I've got a chorister facing a death threat from a racist right now.
BUT: I tune to all kinds of fancy theories on harpsichords and pianos, but
when I tune my celtic harp, I pretty much make sure the octaves and fifths
aren't too bad and play tunes, move things around that sound bad. Tuning a
diatonic instrument is at least an order of magnitude different from
tuning one with 12 notes. Add bray pins to the harp like they did in the
Renaissance, try to imagine the differential equations matters. It's
impossible to tune a celtic harp so it doesn't sound pretty. Harpists, in
addition, usually have flowing blonde hair. Just look at the pictorial
record from the renaissance. Just intonation is beside the point.

Back to dealing with the police department.

Judy