practical Pythagorean tuning puzzle

Can anyone explain why when last night I was trying to put a pure
third on the Italian-style harpsichord I at first ended up with a
Pythagorean one?

In other words, I could tune 81/64 rather accurately by ear. I found
this out by tuning up pure fifths above the root and then comparing
with the third I had got - which clearly wasn't pure 5/4, but seemed
to be nonetheless directly tunable.

The main feature of this instrument is that lower harmonics above the
fundamental are fairly weak, but there are a lot of high harmonics in
the initial attack. Still, the 64th harmonic is certainly inaudible
for me or almost anyone in the middle of the keyboard!!

The way I found the Pythagorean third seemed to be by listening to
some sort of interference or combination tone, then when this tone
started to sound higher than the third itself it is too high and the
interval starts to have some character of being a fourth.

All very odd.

~~~T~~~

Could it be that you were trying to achieve a perfect fourth between E-A?

Oz.

----- Original Message -----
From: "Tom Dent" <stringph@gmail.com>
To: <tuning@yahoogroups.com>
Sent: 15 Haziran 2007 Cuma 18:19
Subject: [tuning] practical Pythagorean tuning puzzle

>
> Can anyone explain why when last night I was trying to put a pure
> third on the Italian-style harpsichord I at first ended up with a
> Pythagorean one?
>
> In other words, I could tune 81/64 rather accurately by ear. I found
> this out by tuning up pure fifths above the root and then comparing
> with the third I had got - which clearly wasn't pure 5/4, but seemed
> to be nonetheless directly tunable.
>
> The main feature of this instrument is that lower harmonics above the
> fundamental are fairly weak, but there are a lot of high harmonics in
> the initial attack. Still, the 64th harmonic is certainly inaudible
> for me or almost anyone in the middle of the keyboard!!
>
> The way I found the Pythagorean third seemed to be by listening to
> some sort of interference or combination tone, then when this tone
> started to sound higher than the third itself it is too high and the
> interval starts to have some character of being a fourth.
>
> All very odd.
>
> ~~~T~~~
>
>

I certainly hope not! Allow me to believe I can distinguish between a
perfect fourth and a Pythagorean third. Actually, following a bit of
arithmetic, I think I had hit on 19:15 - which should now be well
known as very close to 81:64.

What would you call a tuning which had the fourth root of 19:15 as a
generator?

~~~T~~~

--- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@...> wrote:
>
> Could it be that you were trying to achieve a perfect fourth between
E-A?
>
> Oz.
>
> ----- Original Message -----
> From: "Tom Dent" <stringph@...>
> To: <tuning@yahoogroups.com>
> Sent: 15 Haziran 2007 Cuma 18:19
> Subject: [tuning] practical Pythagorean tuning puzzle
>
>
> >
> > Can anyone explain why when last night I was trying to put a pure
> > third on the Italian-style harpsichord I at first ended up with a
> > Pythagorean one?
> >
> > In other words, I could tune 81/64 rather accurately by ear. I found
> > this out by tuning up pure fifths above the root and then comparing
> > with the third I had got - which clearly wasn't pure 5/4, but seemed
> > to be nonetheless directly tunable.
> >
> > The main feature of this instrument is that lower harmonics above the
> > fundamental are fairly weak, but there are a lot of high harmonics in
> > the initial attack. Still, the 64th harmonic is certainly inaudible
> > for me or almost anyone in the middle of the keyboard!!
> >
> > The way I found the Pythagorean third seemed to be by listening to
> > some sort of interference or combination tone, then when this tone
> > started to sound higher than the third itself it is too high and the
> > interval starts to have some character of being a fourth.
> >
> > All very odd.
> >
> > ~~~T~~~
> >
> >
>

if you tune in a series of fifths (3/2) you get 81/64
--
Kraig Grady
North American Embassy of Anaphoria Island <http://anaphoria.com/index.html>
The Wandering Medicine Show
KXLU <http://www.kxlu.com/main/index.asp> 88.9 FM Wed 8-9 pm Los Angeles

I meant to say, that you might have been tuning in for 4:3 down from 27/16.
But 19/15 is cool too.

----- Original Message -----
From: "Tom Dent" <stringph@gmail.com>
To: <tuning@yahoogroups.com>
Sent: 15 Haziran 2007 Cuma 21:24
Subject: [tuning] Re: practical Pythagorean tuning puzzle

>
> I certainly hope not! Allow me to believe I can distinguish between a
> perfect fourth and a Pythagorean third. Actually, following a bit of
> arithmetic, I think I had hit on 19:15 - which should now be well
> known as very close to 81:64.
>
> What would you call a tuning which had the fourth root of 19:15 as a
> generator?
>

You mean 102.3111 cents? 47 equal features such an interval. What are the
properties for this temperament, I wouldn't know.

> ~~~T~~~
>

Oz.

--- In tuning@yahoogroups.com, "Tom Dent" <stringph@...> wrote:

> What would you call a tuning which had the fourth root of 19:15 as a
> generator?

Are we talking a temperament which tempers out 1216/1215? In that case,
two generators give a 9/8.