Re: a few things for Joseph

Joseph said :

>
>
> ****Hi George. Well you *certainly* make good use of your lunch hour
> (!) Personally, I'm lucky if I can just get through part of the
> newspaper... :)
>

You may have more success with food. And later stated...

> It seems however, regrettably, that the "appetite" for
> acoustic instruments is actually on the wane, and for "traditional"

yowsers, food is cheaper too!.

In a different post you said...

> ***But does it really make sense to notate a 12-tET G:B the *same
> way* as a 1/4 comma meantone G:B, for instance?
>
> It would seem the notation would not be so specific in that case, yes?

THIS is the crux of the matter. G->B is going up 4 fifths and octave
reducing. We should call this a ditone. In a meantone, it is also the
best (5/4), (or "major third"), which is true whether 1/4 comma or 1/11
comma [12et]. In the well temperments, you may find a variety of pretty
good (5/4), all of which are best compared to notes of different numbers
of chromatic steps.

It does not include 72, since the ditone is not the best (5/4).

I had a discussion with my brother who put together his own theory primer
for his young students. Basically the whole book was explaining the note
names and trying to get them to know where the half-steps are. I was
somewhat baffled since if you just forget about steps and do everything
from the primary unit (single chromatic step), it can be a sensible
system. You can show the step size patterns for the major scale, walk
through the addition of sharps and flats and watch as rotations of the
scale appear on different degrees, see the modes in the process. Finally
you can hitch it back up to the note names and apologize that it doesn't
make so much sense anymore, but neither do "dots" and "double dots" or
a lot of other things in music notation. When I was done, HE was
completely baffled.

Bob Valentine

--- In tuning@y..., Robert C Valentine <BVAL@I...> wrote:

/tuning/topicId_33919.html#33919

On digestibles:

(!) Personally, I'm lucky if I can just get through part of the
> > newspaper... :)
> >
> > You may have more success with food. And later stated...
>
> > It seems however, regrettably, that the "appetite" for
> > acoustic instruments is actually on the wane,

****Bob. Thanks so much for your commentary and I can see now I will
have to "eat my words" as well!

> In a different post you said...
>
> > ***But does it really make sense to notate a 12-tET G:B the *same
> > way* as a 1/4 comma meantone G:B, for instance?
> >
> > It would seem the notation would not be so specific in that case,
yes?
>
> THIS is the crux of the matter. G->B is going up 4 fifths and octave
> reducing. We should call this a ditone. In a meantone, it is also
the best (5/4), (or "major third"), which is true whether 1/4 comma
or 1/11 comma [12et]. In the well temperments, you may find a
variety of pretty good (5/4), all of which are best compared to notes
of different numbers of chromatic steps.
>
> It does not include 72, since the ditone is not the best (5/4).
>

****Sure, so 72-tET *never* makes a very good meantone, and the 5/4
is an "approximation" as well. However, the major thirds in 72-tet
are pretty *good* approximations, only off by about three cents, yes?

JP

Hi Bob,

> From: Robert C Valentine <BVAL@IIL.INTEL.COM>
> To: <tuning@yahoogroups.com>
> Sent: Sunday, February 10, 2002 4:09 AM
> Subject: [tuning] Re: a few things for Joseph
>
>
> Joseph said :
>
> >
> > ****Hi George. Well you *certainly* make good use of your lunch hour
> > (!) Personally, I'm lucky if I can just get through part of the
> > newspaper... :)
> >
>
> You may have more success with food.

<:E (that's supposed to be me LMAO)

this one was hilarious!

> > ***But does it really make sense to notate a 12-tET G:B the *same
> > way* as a 1/4 comma meantone G:B, for instance?
> >
> > It would seem the notation would not be so specific in that case, yes?
>
> THIS is the crux of the matter. G->B is going up 4 fifths and octave
> reducing. We should call this a ditone. In a meantone, it is also the
> best (5/4), (or "major third"), which is true whether 1/4 comma or 1/11
> comma [12et]. In the well temperments, you may find a variety of pretty
> good (5/4), all of which are best compared to notes of different numbers
> of chromatic steps.

and don't forget that well-temperaments a l s o give a variety of
pretty good 81:64s ("Pythagorean major 3rds") too! The "3rds" of
well-temperament run thru the whole spectrum from 3- to 5-limit,
with approximately 5/4 and 81/64 at either end of the spectrum.

> It does not include 72, since the ditone is not the best (5/4).
>
> I had a discussion with my brother who put together his own theory primer
> for his young students. Basically the whole book was explaining the note
> names and trying to get them to know where the half-steps are. I was
> somewhat baffled since if you just forget about steps and do everything
> from the primary unit (single chromatic step), it can be a sensible
> system. You can show the step size patterns for the major scale, walk
> through the addition of sharps and flats and watch as rotations of the
> scale appear on different degrees, see the modes in the process. Finally
> you can hitch it back up to the note names and apologize that it doesn't
> make so much sense anymore, but neither do "dots" and "double dots" or
> a lot of other things in music notation. When I was done, HE was
> completely baffled.

you just gave a pretty good description of at least part of the
reason why 12edo (or simply 12-tone thinking in general, even for
other tunings) was so easy to adopt. it's the smallest unit that
gives you the entire rotational set of diatonic scales and modes
in terms of half- and whole-steps. in 12edo, they literally
a r e all half- and whole-steps.

it's not surprising that both of you were baffled by
each other's explanations. the notation grew up around
Pythagorean thinking, as i explain at the beginning of
<http://www.ixpres.com/interval/dict/hewm.htm>,
then was adapted for use in meantone. in both of those
cases there has to be a distinction between # and b
-- meantone essentially reverses the Pythagorean meaning
of the symbols, but they're still distinct.

in 12edo (or something close to it) there is no distinction
between # and b, and so the half-step/whole-step business
is a little harder to explain using the Pythagorean/meantone
symbols. it's much easier to do it your way, Bob, simply
starting from the basic fact that everything in 12edo is
generated from the semitone, and to show all the "half-steps"
and "whole-steps" as 1 and 2 semitones respectively.

i find in teaching my piano students that the best way to
get them to understand the key system of our mishmash hybrid
Pythagorean/meantone-notation-and-12edo-tuning system
is to use the "circle of 5ths" in conjunction with the
idea of tetrachordal similarity. they learn each "major
scale" on the piano by using four fingers of each hand,
so the pattern is (use "expand messages" to view this
on the Yahoo web interface):

C D E F G A B C notes
LH: 5 4 3 2 RH: 2 3 4 5 fingers
1 1 1/2 1 1 1 1/2 steps between
\________/ \/ \________/
lower tone upper
tetrachord of tetrachord
disjunction

each hand playing an intervallically identical tetrachord,
with the "tone of disjunction" falling between hands.

then to move to the key and scale a "5th" higher,
they simply switch the right hand with the left and
copy the same pattern of "whole-whole-half" starting
a "tone" higher for the new tetrachord in the right hand,
which simply requires raising the 4th finger a "half-step".

i draw the "circle of 5ths" for them as they go thru
this procedure, and when we finish the key of C#, we
start over again on C and go around the other way to
do the flat keys, where the hand-switching is a bit
different.

i find that by using this method, my students get a
very quick understanding of the whole standard system
of keys as they are ordinarily used, and there is no
confusion over the three pairs of keys which are
enharmonically equivalent (Cb/B, Gb/F#, Db/C#).
the student understands the derivation of each of those
from both sides of the circle, so it all makes sense.

of course, thru all of this i'm always emphasizing to
them that i t o n l y w o r k s i n
T H I S t u n i n g !

my hope is that they'll get interested enough to want
to learn about other tunings ... but until they do show
an interest in that, i just discreetly keep reminding
them that the tuning on their piano is only one out of
a huge number that could be chosen, and that in many of
those other tunings we get flats which are different
from sharps, and the key of Gb might not be the same
as the key of F#.

-monz

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