RE: [tuning] Diatonic?

I wrote,

>> With regard to your V-IV-I progression, it seems like you're proposing a
>> "diatonic" scale of
>>
>> 1/1 9/8 7/6 4/3 3/2 14/9 7/4 (2/1)

Johnny wrote,

>Paul, I don't believe this is the best meaning of "diatonic."

If you mean the intervals are wrong, that's why I put the word in quotes!

>(Perhaps this
>is the beginning of a new thread.) Minor is not the opposite of major, in
>the tonal sense.

Who said it is???

Kraig wrote,

>It seems that if you start on the 7/6 you have a Major like scale that I
have used for years as a diatonic scale.

1/1 8/7 9/7 4/3 3/2 12/7 27/14 (2/1)?

I'm not interested in debating terminology when there are matters of
substance to discuss.

William Annis wrote,

>In my own notes I refer
>to the base or core scale as the "diatonic" version of the system I'm
>working in.

OK, and did you see the 7-note scale I identified as the "diatonic" version
of the 12-tone scale you mentioned? If so, I think there may be better
choices for the larger system. . . .

>Kraig wrote,
>
>>It seems that if you start on the 7/6 you have a Major like scale that I
>have used for years as a diatonic scale.
>
>1/1 8/7 9/7 4/3 3/2 12/7 27/14 (2/1)?

Ooh! And it gives you a scale with the same tetrachords on
1/1 and 3/2... cool. I'll have to play with this... Imitative
couterpoint sounds a bit wonky when your bottom and top tetrachords
are shuffled variants of each other.

--
wm

>>In my own notes I refer
>>to the base or core scale as the "diatonic" version of the system I'm
>>working in.
>
>OK, and did you see the 7-note scale I identified as the "diatonic" version
>of the 12-tone scale you mentioned? If so, I think there may be better
>choices for the larger system. . . .

Yes, I did. That's what I'm using as the base scale, with a
transposition available a 6:7 away. I've not yet tried incorporating
the bottom system into the chords built using the top one. That is,
using this shape:

<14:9> <7:6> <7:4> <21:16> ; first three,
<4:3> <1:1> <3:2> <9:8> ; all four
<8:7> <12:7> <9:7> <27:14> ; "chromatic"

I haven't yet tinkered with chords using the bottom row, although
using the bottom two, you get everything you get in the top one, just
down 7/6. I realize this is obvious to many on this list, but it's
still a new way of thinking for me.

By restricting myself to the 12 notes above I have no doubt
I'm missing a lot of interesting possibilites, which I'm sure I'll be
seeing in forthcoming email :), but as I said earlier, I have to start
somewhere.

At some point I want to try a suite of pieces using the system
above enriched with chromatics giving the 10:12:15 minors, and
flipping back and forth between those in much the same way a baroque
dance suite might wander between Dmaj and Dmin and see what happens,
since the 10:12:15 has such a different feel.

--
wm

>
> > With regard to your V-IV-I progression, it seems like you're proposing a
> > "diatonic" scale of
> >
> > 1/1 9/8 7/6 4/3 3/2 14/9 7/4 (2/1)
>
> Paul, I don't believe this is the best meaning of "diatonic." (Perhaps
this
> is the beginning of a new thread.) >
>

This scale happens to be based on permutations of Archytas's diatonic
tetrachord (Ptolemy's "tonic diatonic"). You can't get much more diatonic
than that!

I second all of Daniel's points here. Good show!

P.S. What is tuning@egroups.com <mailto:tuning@egroups.com> , and how on
earth did it get in my "to" list?

-----Original Message-----
From: Daniel Wolf [mailto:djwolf@snafu.de]
Sent: Monday, April 03, 2000 7:15 AM
To: tuning@onelist.com; Gerald Eskelin
Subject: [tuning] Diatonic?

Hello:

I think your last posting to the tuning list was not quite right; in fact it
may qualify for one of your "lies"!

<Johnny, if you think about it, the term "diatonic" (consisting of whole
<steps and half steps) is really a 12-tET concept.

"Diatonic" was one of the three classical Greek and Hellenistic genera for
the division of a tetrachord, and the only of the three to survive, in
scalar form with a disjunction between the tetrachords into medieval
European music. It consists of two intervals of one tone (Gk. _tonoi_,
ranging in size from 10/9 to 8/7, possibly as wide as 7/6 (Aristoxenus)) and
the interval which remains when two tones are subtracted from a perfect
fourth, a semitone. The 12-tet "lie" of modern music theory, if you will,
is that a tone divides equally into two semitones. Of course there is no
proportion in just intonation which will do that.

<Both modes are dependent on the dominant seventh chord for participation in
<the major/minor system (as opposed to "modal music")

One can find and compose for oneself perfectly acceptable tonal compositions
in Major or minor without sevenths in the dominant chords. American
vernacular harmony may indeed differ on this point, but in parts of that
repertoire sevenths sometimes function classically, as dissonances to be
resolved, and sometimes as ordinary chord members without dissonance
treatment. However it is striking that one may also play a good deal of
vernacular repertoire with all of the sevenths dropped (indeed, some of the
earliest recorded examples of 12-bar blues consist only of simple major
triads).

<The business of "three minor scales" is basically nonsense that was
invented
<by music educators who chose to "teach" melody before harmony. This
<prevented countless music students (many of whom are now teachers) from
<realizing that the reason for choosing flat 6 & 7 or natural 6 & 7 had
<nothing to do with going up or down, but rather with what harmony is
<prevailing. The dominant chord requires the leading tone while tonic and
<subdominant does not.

While I agree that music educators do turn a generalization about scalar
forms into an unnecessary rule, teaching melody before harmony is certainly
not to be criticized. The idea of making a chorale harmonization without
knowing the chorale melody inside and out, and without trying to make the
individual lines as melodically attractive as possible is both unmusical and
ahistorical. Classically, one mastered counterpoint before learning harmony,
that is to say, figured bass; even in the chaconne form, with a fixed
harmonic progression, the rules of contrapuntal voice leading had precedence
over consistent restatements of the harmony. Your last statements are
unsustainable -- melodies have generally preceded their harmonization. (And
before the common practice era, _ficta_ was determined on melodic criteria,
often with remarkable harmonic results). Again, there may be exceptions to
this in American vernacular practice, but you offer no qualification on this
point.

Dr. Daniel Wolf
djwolf@snafu.de <mailto:djwolf@snafu.de>
http://home.snafu.de/djwolf/ <http://home.snafu.de/djwolf/>
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