Tritaves

Paul is/was correct. . .When I said the experiments with tritave
equivalence were failures, I meant in the sense that I/we still didn't
hear the tritave as a new kind of octave.

However, that doesn't mean cool music can't and hasn't been made with such
structures.

In general, theory may tell you you can't hear or preceive something, but
a good musician can still make magic with it.

>Paul is/was correct. . .When I said the experiments with tritave
>equivalence were failures, I meant in the sense that I/we still
>didn't hear the tritave as a new kind of octave.

But I do hear it in that sense in the Carpenter stuff.

-Carl

--- In tuning@yahoogroups.com, Carl Lumma <ekin@l...> wrote:
> >Paul is/was correct. . .When I said the experiments with tritave
> >equivalence were failures, I meant in the sense that I/we still
> >didn't hear the tritave as a new kind of octave.
>
> But I do hear it in that sense in the Carpenter stuff.
>
> -Carl

That would seem especially puzzling from Pierce's or Sethares's
standpoint, since Carpenter doesn't even bother to eliminate the even
harmonics from his timbres . . .

>> >Paul is/was correct. . .When I said the experiments with tritave
>> >equivalence were failures, I meant in the sense that I/we still
>> >didn't hear the tritave as a new kind of octave.
>>
>> But I do hear it in that sense in the Carpenter stuff.
>>
>> -Carl
>
>That would seem especially puzzling from Pierce's or Sethares's
>standpoint, since Carpenter doesn't even bother to eliminate the even
>harmonics from his timbres . . .

Yes, and as far as I'm concerned that part of the theory is incorrect.
I doubt any conditions (such as timbre but barring functional musical
context) can be concocted to make 3:1 sound *more* "equivalent" than
2:1. But it doesn't mean the 3:1 can't sound equivalent at all. As
David L. Burge says, 'many people confuse the perfect 5th and perfect
octave at first'.

-Carl

--- In tuning@yahoogroups.com, Carl Lumma <ekin@l...> wrote:
> >> >Paul is/was correct. . .When I said the experiments with
tritave
> >> >equivalence were failures, I meant in the sense that I/we still
> >> >didn't hear the tritave as a new kind of octave.
> >>
> >> But I do hear it in that sense in the Carpenter stuff.
> >>
> >> -Carl
> >
> >That would seem especially puzzling from Pierce's or Sethares's
> >standpoint, since Carpenter doesn't even bother to eliminate the
even
> >harmonics from his timbres . . .
>
> Yes, and as far as I'm concerned that part of the theory is
incorrect.
> I doubt any conditions (such as timbre but barring functional
musical
> context) can be concocted to make 3:1 sound *more* "equivalent" than
> 2:1. But it doesn't mean the 3:1 can't sound equivalent at all. As
> David L. Burge says, 'many people confuse the perfect 5th and
perfect
> octave at first'.
>
> -Carl

Of course, that would not be an example of 3:1 equivalence, but
rather a more general affinity or similarity (or equivalence, if you
insist) at very simple-integer ratios, such as 3:2 and 4:3. This, I
think, is very important, and leads to the notion of
omnitetrachordality . . .