Horizontal vs. vertical tuning

When notes sound simultaneously, we speak of "vertical tuning"; when
they follow each other melodically, we may use the term "horizontal
tuning" to describe the distance between them.

I've been struck with the thought that:

. For intervals of 7/6 and larger, vertical tuning is important
and horizontal tuning (melodic jumps) is unimportant.

. For intervals of 8/7 and smaller, vertical tuning is unimportant
and horizontal tuning (melodic steps) is important.

Those aren't meant as absolutes, but the relative importance seems to
switch places. Agree? Disagree?

(My tuning methods so far have emphasized vertical tuning and pretty
much neglected melodic intervals, and I'm trying to gain the
understanding to change this.)

JdL

>I've been struck with the thought that:

> . For intervals of 7/6 and larger, vertical tuning is important
> and horizontal tuning (melodic jumps) is unimportant.

> . For intervals of 8/7 and smaller, vertical tuning is unimportant
> and horizontal tuning (melodic steps) is important.

>Those aren't meant as absolutes, but the relative importance seems to
>switch places. Agree? Disagree?

I can't understand this at all. What exactly do you mean by "important" and
"unimportant"? BTW, I think horizontal tuning needs to conform to the
prevailing scale logic, regardless of interval size, and vertical tuning has
a lot to do with JI but no precise limit can be put on the complexity of the
ratio -- 8/7 might be reasonable in dyads for some timbres, but in chords of
three or more notes, more complex ratios can easily be appreciated.
Certainly there are vertical intervals larger, as well as smaller, than 8/7,
which escape easy JI interpretation.

On Wed, 29 Dec 1999 07:58:19 -0700, "John A. deLaubenfels"
<jadl@idcomm.com> wrote:

>I've been struck with the thought that:
>
> . For intervals of 7/6 and larger, vertical tuning is important
> and horizontal tuning (melodic jumps) is unimportant.
>
> . For intervals of 8/7 and smaller, vertical tuning is unimportant
> and horizontal tuning (melodic steps) is important.
>
>Those aren't meant as absolutes, but the relative importance seems to
>switch places. Agree? Disagree?

That sounds fair, but the actual point of the switchover could vary
depending on timbre, tempo, and other factors. Certainly, the first two
notes in the melody of Blackwood's etude in 16-note equal tuning sound
convincingly like a perfect fifth, even though the actual ratio is far from
3/2 and if the notes were sounded simultaneously would sound more like a
27:40, a dissonant interval. And one of the reasons I like about equal
tunings is that melodic intervals can be transposed to any scale degree and
still sound the same.
--
see my music page ---> +--<http://www.io.com/~hmiller/music/music.html>--
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>(My tuning methods so far have emphasized vertical tuning and pretty
>much neglected melodic intervals, and I'm trying to gain the
>understanding to change this.)

John, the procedure described at http://lumma.org/adaptive.txt achieves the
theoretical minimum pain possible with every vertical sonority just. Thus,
it achieves the theoretical maximum tonic drift. Perfect!

-Carl

[I wrote:]
>>I've been struck with the thought that:
>>
>> . For intervals of 7/6 and larger, vertical tuning is important
>> and horizontal tuning (melodic jumps) is unimportant.
>>
>> . For intervals of 8/7 and smaller, vertical tuning is unimportant
>> and horizontal tuning (melodic steps) is important.
>>
>>Those aren't meant as absolutes, but the relative importance seems to
>>switch places. Agree? Disagree?

[Paul Erlich, TD 463.17:]
>I can't understand this at all. What exactly do you mean by "important"
>and "unimportant"?

Sorry if I wasn't being clear. I mean, how much they can deviate from
"perfect" for a given level of "pain". So, I'm saying that a melodic
interval of a fifth can be mistuned by a few cents with less pain than
when the melodic interval of a major or minor second is mistuned by a
few cents. Whereas, when notes sound simultaneously, the mistuning of
a fifth by a few cents is more painful than the mistuning of a 9/8, say.

More clear?

[Paul:]
>BTW, I think horizontal tuning needs to conform to the prevailing
>scale logic, regardless of interval size,

If I understand you right, you're saying that the pain of melodic
imprecision is approximately constant with melodic interval, yes?

>and vertical tuning has a lot to do with JI but no precise limit can be
>put on the complexity of the ratio -- 8/7 might be reasonable in dyads
>for some timbres, but in chords of three or more notes, more complex
>ratios can easily be appreciated.

OK... I'm trying to be very careful not to make a "precise limit" here;
the dividing line is fuzzy. Your point about three or more notes
sounding is correct, I believe.

>Certainly there are vertical intervals larger, as well as smaller, than
>8/7, which escape easy JI interpretation.

True, and that clarification should be added.

JdL

[I wrote:]
>>(My tuning methods so far have emphasized vertical tuning and pretty
>>much neglected melodic intervals, and I'm trying to gain the
>>understanding to change this.)

[Carl Lumma, TD 464.5:]
>John, the procedure described at http://lumma.org/adaptive.txt achieves
>the theoretical minimum pain possible with every vertical sonority
>just. Thus, it achieves the theoretical maximum tonic drift. Perfect!

Carl, your ideas look interesting (I have to confess I'm not following
everything you're saying in the cited reference), but I'm not sure they
cover the range of possibilities found in real life sequences. As
always, I encourage you to put them to the test, difficult though that
may be.

Do you mean theoretical *minimum* tonic drift?

JdL

> From: "John A. deLaubenfels" <jadl@idcomm.com>

> When notes sound simultaneously, we speak of "vertical tuning"; when
> they follow each other melodically, we may use the term "horizontal
> tuning" to describe the distance between them.
>
> I've been struck with the thought that:
>
> . For intervals of 7/6 and larger, vertical tuning is important
> and horizontal tuning (melodic jumps) is unimportant.
>
> . For intervals of 8/7 and smaller, vertical tuning is unimportant
> and horizontal tuning (melodic steps) is important.
>
> Those aren't meant as absolutes, but the relative importance seems to
> switch places. Agree? Disagree?

In my ear-training classes, I encourage students to imagine the tuning of
the pitch to which they about to move--in other words, tune the two pitches
"simultaneously" (in imagination) on the basis of having sung the interval
in question many times before.

I begin the process by having them tune partials over a sustained
fundamental, first limiting the drill to 1:2, 2:3, 3:4, 4:5, 5:6 and later
including 6:7, 7:8, 8:9, 9:10 and even 10:11 (yes, the ear can lock it in,
even though it is "in the crack").

So, I suspect that the process of tuning vertically and horizontally is
essentially the same--but the latter having to use memory developed over
considerable practice. Nevertheless, when performing melodically within a
harmonic context containing changing roots, horizontal "targets" are subject
to vertical "correction" upon arrival. But then, life itself is a compromise
at times. :-)

Jerry

>>John, the procedure described at http://lumma.org/adaptive.txt achieves
>>the theoretical minimum pain possible with every vertical sonority
>>just. Thus, it achieves the theoretical maximum tonic drift. Perfect!
>
>Carl, your ideas look interesting (I have to confess I'm not following
>everything you're saying in the cited reference), but I'm not sure they
>cover the range of possibilities found in real life sequences. As
>always, I encourage you to put them to the test, difficult though that
>may be.

I will. It may take a year or two, though, since I have to learn a
practical language, like C, first. Feel free to write me on or off list
with any questions you have about the procedure, or any advice on how to
improve the explanation.

>Do you mean theoretical *minimum* tonic drift?

I meant maximum. If you have the minimum pain (which I take to mean
commatic adjustments), you will have the maximum overall tonic drift. I
was being sarcastic when I said, "perfect".

=Carl