45/32

>>> >> >It seems to me that if it is still possible for 45/32 to sound
>>> >> >spookily-dead-on, it must be possible for 20/13, tuned very
>>> >> >precisely, to have the same effect. Moreover if 45/32 can
>>> >> >somehow manage to be beatless, a pure 9/7 ought to be able to
>>> >> >also.
>>> >>
>>> >> Why?
>>> >
>>> >It's much higher on the consonance totem-pole, obviously.
>>>
>>> That's not obvious, or even necessarily true. Tenney height
>>> stops working as the numbers get large.
>>
>>9/7 isn't large, but obviously it has to stop working, because the
>>rational numbers are dense. However, the claim was that 45/32 was
>>spookily dead-on; this can hardly be the case if 9/7 isn't.

>There are a lot of things that could happen here. 9/7 can be
>in the field of attraction of 5/4, and when it is it usually
>sounds terrible. 45/32 is in a realm that enjoys a lot of
>flexibility, like the minor third realm.

All the harmonic entropy work makes this seem perilously far-fetched.
Sure, 11/9 can have lower entropy than several simpler ratios, and
thus be a candidate for being "spookily dead-on" -- but 45/32 is far,
far, far beyond the realm of ratios that can be "spookily dead-on",
regardless of whether its harmonic entropy is low or high. Even if
it's rather low, or if the area around it is devoid of high
peaks, "spookily dead-on" seems way off.

>>>> >> >It seems to me that if it is still possible for 45/32 to sound
>>>> >> >spookily-dead-on, it must be possible for 20/13, tuned very
>>>> >> >precisely, to have the same effect. Moreover if 45/32 can
>>>> >> >somehow manage to be beatless, a pure 9/7 ought to be able to
>>>> >> >also.
>>>> >>
>>>> >> Why?
>>>> >
>>>> >It's much higher on the consonance totem-pole, obviously.
>>>>
>>>> That's not obvious, or even necessarily true. Tenney height
>>>> stops working as the numbers get large.
>>>
>>>9/7 isn't large, but obviously it has to stop working, because the
>>>rational numbers are dense. However, the claim was that 45/32 was
>>>spookily dead-on; this can hardly be the case if 9/7 isn't.
>
>>There are a lot of things that could happen here. 9/7 can be
>>in the field of attraction of 5/4, and when it is it usually
>>sounds terrible. 45/32 is in a realm that enjoys a lot of
>>flexibility, like the minor third realm.
>
>All the harmonic entropy work makes this seem perilously far-fetched.
>Sure, 11/9 can have lower entropy than several simpler ratios, and
>thus be a candidate for being "spookily dead-on" -- but 45/32 is far,
>far, far beyond the realm of ratios that can be "spookily dead-on",
>regardless of whether its harmonic entropy is low or high. Even if
>it's rather low, or if the area around it is devoid of high
>peaks, "spookily dead-on" seems way off.

All of the above assumed 45/32 could be "dead on". Assuming that
doesn't in itself make it true for 9/7, was my point.

-Carl

--- In harmonic_entropy@yahoogroups.com, Carl Lumma <ekin@l...> wrote:
> >>>> >> >It seems to me that if it is still possible for 45/32 to
sound
> >>>> >> >spookily-dead-on, it must be possible for 20/13, tuned very
> >>>> >> >precisely, to have the same effect. Moreover if 45/32 can
> >>>> >> >somehow manage to be beatless, a pure 9/7 ought to be able
to
> >>>> >> >also.
> >>>> >>
> >>>> >> Why?
> >>>> >
> >>>> >It's much higher on the consonance totem-pole, obviously.
> >>>>
> >>>> That's not obvious, or even necessarily true. Tenney height
> >>>> stops working as the numbers get large.
> >>>
> >>>9/7 isn't large, but obviously it has to stop working, because
the
> >>>rational numbers are dense. However, the claim was that 45/32 was
> >>>spookily dead-on; this can hardly be the case if 9/7 isn't.
> >
> >>There are a lot of things that could happen here. 9/7 can be
> >>in the field of attraction of 5/4, and when it is it usually
> >>sounds terrible. 45/32 is in a realm that enjoys a lot of
> >>flexibility, like the minor third realm.
> >
> >All the harmonic entropy work makes this seem perilously far-
fetched.
> >Sure, 11/9 can have lower entropy than several simpler ratios, and
> >thus be a candidate for being "spookily dead-on" -- but 45/32 is
far,
> >far, far beyond the realm of ratios that can be "spookily dead-
on",
> >regardless of whether its harmonic entropy is low or high. Even if
> >it's rather low, or if the area around it is devoid of high
> >peaks, "spookily dead-on" seems way off.
>
> All of the above assumed 45/32 could be "dead on". Assuming that
> doesn't in itself make it true for 9/7, was my point.
>
> -Carl

Well, maybe I'm misunderstanding you, but I just mean that I can't
see how it would be possible, for a given timbre and register, for
45/32 to be "dead on"-able while 9/7 isn't.

>Well, maybe I'm misunderstanding you, but I just mean that I can't
>see how it would be possible, for a given timbre and register, for
>45/32 to be "dead on"-able while 9/7 isn't.

This thread started when Brad said he thought the 9/7 sounded
bad, and then later, in another case, that 45/32 sounded dead
on. Gene tried to say this amounts to some sort of contradiction,
and I'm saying it doesn't. There's nothing more to it; it's
pointless to discuss it further.

-Carl

Are you guys talking about single pitches 45/32 and 9/7?

If so, what's the problem? 45/32 can easily be heard as dead-on relative to 9/8 or 15/8 for example, while 9/7 would not be.

If not, how about using the right notation for dyads, to avoid confusion. e.g. 32:45 and 7:9.