Proportional beating and pianos

I'm not sure to what extent Wendell's or others' temperaments would
succeed in producing synchronous/proportional beating on a modern
piano, since the overtones are fairly inharmonic. Beat rate
calculations based on the exact harmonic series wouldn't correspond
very closely with what the instrument actually produced.

Of course, this doesn't rule out the temperament sounding good for
reasons other than integer ratios of beats.

~~~T~~~

--- In tuning@yahoogroups.com, "Tom Dent" <stringph@g...> wrote:
>
> I'm not sure to what extent Wendell's or others' temperaments would
> succeed in producing synchronous/proportional beating on a modern
> piano, since the overtones are fairly inharmonic.

They succeed, since the inharmonicity is pretty uniform and the
resulting corrections to the tuning are only second-order.

> Beat rate
> calculations based on the exact harmonic series wouldn't correspond
> very closely with what the instrument actually produced.

But most of the errors involved cancel each other out in the course of
the calculation, for these particular applications.

> > I'm not sure to what extent Wendell's or others' temperaments
> > would succeed in producing synchronous/proportional beating on
> > a modern piano, since the overtones are fairly inharmonic.
>
> They succeed, since the inharmonicity is pretty uniform and the
> resulting corrections to the tuning are only second-order.

That's true only for well-maintained instruments, in the middle
of the keyboard. Inharmonicity varies widely between instruments
in the bass, even on very high quality instruments. For spinets,
my experience is that between partials is often louder than beating
between fundamentals, even very near the middle octave.

> > Beat rate calculations based on the exact harmonic series
> > wouldn't correspond very closely with what the instrument
> > actually produced.
>
> But most of the errors involved cancel each other out in the
> course of the calculation, for these particular applications.

Have you ever used an electronic tuner and then checked beat
rates? It's why the Verituner has a tune-by-beats mode...

http://veritune.com/veritune.asp?id=10

-Carl

--- In tuning@yahoogroups.com, "Carl Lumma" <clumma@y...> wrote:
> > > I'm not sure to what extent Wendell's or others' temperaments
> > > would succeed in producing synchronous/proportional beating on
> > > a modern piano, since the overtones are fairly inharmonic.
> >
> > They succeed, since the inharmonicity is pretty uniform and the
> > resulting corrections to the tuning are only second-order.
>
> That's true only for well-maintained instruments, in the middle
> of the keyboard. Inharmonicity varies widely between instruments
> in the bass, even on very high quality instruments.

But Wendell's beat rate ratios are for relatively tiny intervals on a
single instrument!

> For spinets,
> my experience is that between partials is often louder than beating
> between fundamentals, even very near the middle octave.

So? What does that have to do inharmonicity, let alone with the
corrections to Bob Wendell's calculations that result from it?

> > > Beat rate calculations based on the exact harmonic series
> > > wouldn't correspond very closely with what the instrument
> > > actually produced.
> >
> > But most of the errors involved cancel each other out in the
> > course of the calculation, for these particular applications.
>
> Have you ever used an electronic tuner and then checked beat
> rates?

Yes.

> It's why the Verituner has a tune-by-beats mode...
>
> http://veritune.com/veritune.asp?id=10

If inharmonicity does indeed spoil Wendell's calculation, you'll
never be able to realize all the specified beat rates at once.

> > > > I'm not sure to what extent Wendell's or others' temperaments
> > > > would succeed in producing synchronous/proportional beating
> > > > on a modern piano, since the overtones are fairly inharmonic.
> > >
> > > They succeed, since the inharmonicity is pretty uniform and the
> > > resulting corrections to the tuning are only second-order.
> >
> > That's true only for well-maintained instruments, in the middle
> > of the keyboard. Inharmonicity varies widely between instruments
> > in the bass, even on very high quality instruments.
>
> But Wendell's beat rate ratios are for relatively tiny intervals
> on a single instrument!

If one distributes a scale as a bunch of cents values, he or she
presumably intends it to be applied to any number of instruments
beyond his or her control. Further, one implies that an
electronic tuning device will be used that most likely will not
correctly take inharmonicity on a particular instrument into
acount.

Bob presented his beat ratios as being significant for octave
displacements of the close-position triads.

> > For spinets, my experience is that between partials is often
> > louder than beating between fundamentals, even very near the
> > middle octave.
>
> So? What does that have to do inharmonicity, let alone with the
> corrections to Bob Wendell's calculations that result from it?

One might infer that a more faithful tuning of Bob's scale would
be to try to achieve his beat ratios for the loudest heard beats.
An electronic tuner won't necessarily do that.

> > > > Beat rate calculations based on the exact harmonic series
> > > > wouldn't correspond very closely with what the instrument
> > > > actually produced.
> > >
> > > But most of the errors involved cancel each other out in the
> > > course of the calculation, for these particular applications.
> >
> > Have you ever used an electronic tuner and then checked beat
> > rates?
>
> Yes.
>
> > It's why the Verituner has a tune-by-beats mode...
> >
> > http://veritune.com/veritune.asp?id=10
>
> If inharmonicity does indeed spoil Wendell's calculation, you'll
> never be able to realize all the specified beat rates at once.

I think it spoils the cents distribution method, not necc. the
calculation.

-Carl

--- In tuning@yahoogroups.com, "Carl Lumma" <clumma@y...> wrote:
> > > > > I'm not sure to what extent Wendell's or others'
temperaments
> > > > > would succeed in producing synchronous/proportional beating
> > > > > on a modern piano, since the overtones are fairly
inharmonic.
> > > >
> > > > They succeed, since the inharmonicity is pretty uniform and
the
> > > > resulting corrections to the tuning are only second-order.
> > >
> > > That's true only for well-maintained instruments, in the middle
> > > of the keyboard. Inharmonicity varies widely between
instruments
> > > in the bass, even on very high quality instruments.
> >
> > But Wendell's beat rate ratios are for relatively tiny intervals
> > on a single instrument!
>
> If one distributes a scale as a bunch of cents values, he or she
> presumably intends it to be applied to any number of instruments
> beyond his or her control.

Yes, but in *each case* it is applied to a single instrument -- get
it?

> Further, one implies that an
> electronic tuning device will be used that most likely will not
> correctly take inharmonicity on a particular instrument into
> acount.

I don't think it's fair to say that Bob "implied" that one would use
a poorly functioning electronic tuning device. But even that kind of
circumstance is possibly one that could be analyzed, and the
resulting effect on the beat rate ratios determined.

> Bob presented his beat ratios as being significant for octave
> displacements of the close-position triads.

Yes.

> > > For spinets, my experience is that between partials is often
> > > louder than beating between fundamentals, even very near the
> > > middle octave.
> >
> > So? What does that have to do inharmonicity, let alone with the
> > corrections to Bob Wendell's calculations that result from it?
>
> One might infer that a more faithful tuning of Bob's scale would
> be to try to achieve his beat ratios for the loudest heard beats.
> An electronic tuner won't necessarily do that.

I'll leave it to Robert Wendell to comment further.

> > > > > Beat rate calculations based on the exact harmonic series
> > > > > wouldn't correspond very closely with what the instrument
> > > > > actually produced.
> > > >
> > > > But most of the errors involved cancel each other out in the
> > > > course of the calculation, for these particular applications.
> > >
> > > Have you ever used an electronic tuner and then checked beat
> > > rates?
> >
> > Yes.
> >
> > > It's why the Verituner has a tune-by-beats mode...
> > >
> > > http://veritune.com/veritune.asp?id=10
> >
> > If inharmonicity does indeed spoil Wendell's calculation, you'll
> > never be able to realize all the specified beat rates at once.
>
> I think it spoils the cents distribution method, not necc. the
> calculation.

You mean it makes the electronic tuner give wrong results? If so, see
above.

> > I think it spoils the cents distribution method, not necc. the
> > calculation.
>
> You mean it makes the electronic tuner give wrong results? If so,
> see above.
//
> > Further, one implies that an
> > electronic tuning device will be used that most likely will not
> > correctly take inharmonicity on a particular instrument into
> > acount.
>
> I don't think it's fair to say that Bob "implied" that one would
> use a poorly functioning electronic tuning device.

He didn't say how. But that's how it's likely to get done.
I know of exactly 1 person on this list who has a Verituner, and
I tend to doubt even it listens to the beat rates when it sets
Bob's scale.

> But even that kind of circumstance is possibly one that could
> be analyzed, and the resulting effect on the beat rate ratios
> determined.

Know of an practical way to do this?

-Carl