octaves and partials,(was I tuned my piano)

> ***I never learned "stretched octaves" when I learned piano tuning
> way back in the 1970's... Presumably this is a newer practice by
> tuners, I guess... ??
> J. Pehrson
>
>
Wally writes:
>it's not that new. piano tuners are taught to tune octaves by
> aligning certain pairs of partials, ranging from "2:1" in the high
> register all the way to "10:5" or even "12:6" in the lowest register.
> it's easy if you know which pitch to listen for beating partials at.

Greetings,
Interesting how octaves are regarded. Some people claim "pure" octaves,
others claim stretched.
On a piano, there is no such thing as a pure octave. Piano octaves can
only align one set of coincident partials at a time. If you have the first
partial exactly like the upper notes fundamental, you have a pure 2:1 octave, but
there will be beating higher up. Due to inharmonicity, the wider the octave,
the higher the Just common partials.
A 6:3 octave is too wide for the temperament area, it would produce an
objectionable beating in the middle of the piano, (as well as some pretty fast
ET thirds), but it would be a logical result near the top of a piano that had
the bearings laid in the middle with a slightly expanded 2:1 (but not quite a
4:2) octave. That amount of beginning stretch will often allow a fine sounding
temperament, though for concerto work, a slightly wider beginning allows a lot
of aggressive brilliance in the top of the instrument, (really sharp last
octave)
Tight bass octaves for country sessions,(which keeps the Korg equipped
bass player happy), tends to create some low-end beating with double octaves, but
if they are kept to under 1 bps, don't call attention to themselves. Wider
octaves for live rock and roll, as well as jazz allow the higher partials from
the low bass to align with the fundamentals of the middle range and gives a
greater resonance. It should go without saying, that different pianos require
different rates of expansion.
If you have a series of 2:1 octaves, you quickly find that your triple
or double octaves begin to sound really flat. If you have tuned so that your
double octave is perfectly Just, your single octave is definitely stretched,
etc. If you allow the fifths to determine the rate, and you tune pure fifths
from the 5th octave upwards, you will be seeing perhaps 8:4 octaves near the
top. That gives a pretty stimulative tuning which will cut through with a trio
in a loud bar, but is a little tense for general usage.
So, there is no really "pure" octave, unless one qualifies it by saying
"pure" at what partial. The near simplest interval can be as complex as any of
them! And the unison....... it's more complex than almost any.

Ed Foote RPT
www.uk-piano.org/edfoote/
www.uk-piano.org/edfoote/well_tempered_piano.html
<A HREF="http://artists.mp3s.com/artists/399/six_degrees_of_tonality.html">
MP3.com: Six Degrees of Tonality</A>

--- In tuning@yahoogroups.com, a440a@a... wrote:

/tuning/topicId_44102.html#44102

> A 6:3 octave is too wide for the temperament area, it would
produce an objectionable beating in the middle of the piano, (as well
as some pretty fast ET thirds), but it would be a logical result near
the top of a piano that had the bearings laid in the middle with a
slightly expanded 2:1 (but not quite a 4:2) octave.

***Hello Ed, and others. Just to confirm that I'm understanding
this... do you mean that in the "stretched" octave, you're actually
listening to the partials the "next octave" up, i.e. 4:2 rather than
2:1. It seems like that's what your saying...

Why aren't those lined up exactly with the octave harmonics below??

(Or am I missing something... :)

Thanks!

J. Pehrson

--- In tuning@yahoogroups.com, "Joseph Pehrson" <jpehrson@r...>
wrote:

> ***Hello Ed, and others. Just to confirm that I'm understanding
> this... do you mean that in the "stretched" octave, you're actually
> listening to the partials the "next octave" up, i.e. 4:2 rather
than
> 2:1. It seems like that's what your saying...

yup!

> Why aren't those lined up exactly with the octave harmonics below??
>
> (Or am I missing something... :)

the inharmonic series of piano strings are not "uniformly
stretched" -- the stretching increases as you go up. so if you tune
the lower string so that its second partial is aligned with the
fundamental of the higher string, the fourth partial of the lower
string won't be aligned with, but will be higher than, the second
partial of the higher string. you'd have to widen the "2:1" octave
further to make it a "4:2" octave, even further to be "6:3", etc.

for example, pretend that, for all the strings, the second partial is
1202 cents, the third partial is 1706 cents, the fourth partial is
2406 cents, etc. (each successive partial is 2 more cents higher than
where it "should" be) . . . then a 2:1 octave will be 1202 cents,
while a 4:2 octave will be 2406 - 1202 = 1204 cents, etc.

Greetings,
I wrote:
>A 6:3 octave is too wide for the temperament area, it would
>produce an objectionable beating in the middle of the piano, (as well
>as some pretty fast ET thirds), but it would be a logical result near
>the top of a piano that had the bearings laid in the middle with a
>slightly expanded 2:1 (but not quite a 4:2) octave.

J.P. asks:
> Just to confirm that I'm understanding
>this... do you mean that in the "stretched" octave, you're actually
>listening to the partials the "next octave" up, i.e. 4:2 rather than
>2:1. It seems like that's what your saying...

Yes. Tuners think in terms of what partials are actually being tuned Just.
The higher they are, the wider the octave. "Stretch" is the cumulative
sharpening that results. Since the widening of the octave becomes progressively more
pronounced as you reach the ends of the piano's span, we think more in terms
of how stretched the tuning is rather than how stretched any one octave is
going to be.

>Why aren't those lined up exactly with the octave harmonics below??

Inharmonicity! The partials of a vibrating, struck, string are not exact
multiples of the fundamental, they are all sharp, and progressively so. The
higher the partials being tuned to pure coincidence, the farther apart the
fundamentals become.
Considering a single octave, if the 2nd partial of the lower note and the
fundamental of the upper note are exactly just,(a 2:1 octave) the 6th partial
of the lower note will be sharper than the 3rd partial of the upper note. If
you widen the octave, it begins to agree at the 6:3 but the 2:1 relationship
begins to beat.
Notes that are two octaves apart require that the upper note's
fundamental be aligned with the lower notes's 4th partial. That partial will be more
than four times the fundamental, thus if the double octave is pure, the two
singles in between are both slightly wide.
Regards,
Ed Foote RPT
www.uk-piano.org/edfoote/
www.uk-piano.org/edfoote/well_tempered_piano.html
<A HREF="http://artists.mp3s.com/artists/399/six_degrees_of_tonality.html">
MP3.com: Six Degrees of Tonality</A>

For interest on Werckmeister and hearing beats in tuning octave, this is from
"Short Lesson and Addition, how one can tune and temper well a clavier,"
translated by Ellen Jane Archambault.

"Since one consonance stands against another a little too high or too low,
one calls it a vibration. This name comes namely from the organ builders, for
when they tune two pipes together, and they are almost pure, then such pipes,
when they are simultaneously sustained with each other, make a tremor, or
trembling. The closer the tuning is, the slower the tremor. When they are,
however, finally tuned together, then the tremor, or shaking, is no longer heard,
and two such pipes often sound as if they were one. This tremor, or shaking, is
called vibration by the organ builders. It is also twofold, as when the
higher pitch is too high against the other, one says that it vibrates too high; if
it is too low, one says it vibrates low, or vice versa. If the higher pitch
is too high against the lower, one says that the lower vibrates low; and thus
the tail hangs on the dog, and the dog can hang on the tail."

best, Johnny Reinhard

it sounds like werckmeister was tuning by eliminating beats -- thus
he would have ended up with 1200 cent octaves on the organ, but wider
on the harpsichord.

--- In tuning@yahoogroups.com, Afmmjr@a... wrote:
> For interest on Werckmeister and hearing beats in tuning octave,
this is from
> "Short Lesson and Addition, how one can tune and temper well a
clavier,"
> translated by Ellen Jane Archambault.
>
> "Since one consonance stands against another a little too high or
too low,
> one calls it a vibration. This name comes namely from the organ
builders, for
> when they tune two pipes together, and they are almost pure, then
such pipes,
> when they are simultaneously sustained with each other, make a
tremor, or
> trembling. The closer the tuning is, the slower the tremor. When
they are,
> however, finally tuned together, then the tremor, or shaking, is no
longer heard,
> and two such pipes often sound as if they were one. This tremor,
or shaking, is
> called vibration by the organ builders. It is also twofold, as
when the
> higher pitch is too high against the other, one says that it
vibrates too high; if
> it is too low, one says it vibrates low, or vice versa. If the
higher pitch
> is too high against the lower, one says that the lower vibrates
low; and thus
> the tail hangs on the dog, and the dog can hang on the tail."
>
> best, Johnny Reinhard

In a message dated 6/4/03 3:28:19 PM Eastern Daylight Time,
wallyesterpaulrus@yahoo.com writes:

> , but wider
> on the harpsichord.
>
>

Werckmeister didn't think so.

Johnny

--- In tuning@yahoogroups.com, Afmmjr@a... wrote:
> In a message dated 6/4/03 3:28:19 PM Eastern Daylight Time,
> wallyesterpaulrus@y... writes:
>
>
> > , but wider
> > on the harpsichord.
> >
> >
>
> Werckmeister didn't think so.
>
> Johnny

not surprising, since the understanding of inharmonicity was still
many years away.

on 6/4/03 1:40 PM, wallyesterpaulrus <wallyesterpaulrus@yahoo.com> wrote:

> --- In tuning@yahoogroups.com, Afmmjr@a... wrote:
>> In a message dated 6/4/03 3:28:19 PM Eastern Daylight Time,
>> wallyesterpaulrus@y... writes:
>>
>>
>>> , but wider
>>> on the harpsichord.
>>>
>>>
>>
>> Werckmeister didn't think so.

The operative words being "think so". Chances are good he was doing it
without noticing, no?

>>
>> Johnny
>
> not surprising, since the understanding of inharmonicity was still
> many years away.
>
>
>
> You do not need web access to participate. You may subscribe through
> email. Send an empty email to one of these addresses:
> tuning-subscribe@yahoogroups.com - join the tuning group.
> tuning-unsubscribe@yahoogroups.com - unsubscribe from the tuning group.
> tuning-nomail@yahoogroups.com - put your email message delivery on hold for
> the tuning group.
> tuning-digest@yahoogroups.com - change your subscription to daily digest mode.
> tuning-normal@yahoogroups.com - change your subscription to individual emails.
> tuning-help@yahoogroups.com - receive general help information.
>
>
> Your use of Yahoo! Groups is subject to http://docs.yahoo.com/info/terms/
>
>
>

In a message dated 6/4/03 5:23:57 PM Eastern Daylight Time,
kkb@breathsense.com writes:

> The operative words being "think so". Chances are good he was doing it
> without noticing, no?
>
>

Yes, I would trust his ears, inharmonicity claims by Paul, or not. A single
plucked string to a single plucked string on a harpsichord would be measurable
as an octave to me even without beats. Johnny

--- In tuning@yahoogroups.com, Kurt Bigler <kkb@b...> wrote:
> on 6/4/03 1:40 PM, wallyesterpaulrus <wallyesterpaulrus@y...> wrote:
>
> > --- In tuning@yahoogroups.com, Afmmjr@a... wrote:
> >> In a message dated 6/4/03 3:28:19 PM Eastern Daylight Time,
> >> wallyesterpaulrus@y... writes:
> >>
> >>
> >>> , but wider
> >>> on the harpsichord.
> >>>
> >>>
> >>
> >> Werckmeister didn't think so.
>
> The operative words being "think so". Chances are good he was
doing it
> without noticing, no?

yes, exactly. by eliminating beats, he would have been tuning wider-
than-1200-cent octaves on the harpsichord, without even knowing it,
as you say kurt.

--- In tuning@yahoogroups.com, a440a@a... wrote:

/tuning/topicId_44102.html#44128

>
> Inharmonicity! The partials of a vibrating, struck, string are
not exact multiples of the fundamental, they are all sharp, and
progressively so. <snip>

Ed, this is an incredibly clear explanation of what's going on.
Thanks!

J. Pehrson

--- In tuning@yahoogroups.com, a440a@a... wrote:

/tuning/topicId_44102.html#44128

> Inharmonicity! The partials of a vibrating, struck, string are
not exact multiples of the fundamental, they are all sharp, and
progressively so.

***Now the question is... (which I regrettably didn't think of before
my last post :) :

If one is tuning an "upper octave" and actually tuning its second
harmonic to the fourth harmonic of the lower one (2:4) wouldn't
the "stretching" take place *naturally* since those harmonics would
be the ones one would listen for in order to eliminate the beating??

JP

--- In tuning@yahoogroups.com, Afmmjr@a... wrote:

/tuning/topicId_44102.html#44149

> In a message dated 6/4/03 5:23:57 PM Eastern Daylight Time,
> kkb@b... writes:
>
>
> > The operative words being "think so". Chances are good he was
doing it
> > without noticing, no?
> >
> >
>
> Yes, I would trust his ears, inharmonicity claims by Paul, or not.
A single
> plucked string to a single plucked string on a harpsichord would be
measurable
> as an octave to me even without beats. Johnny

***It's true that there isn't enough sustain there to perceive
beats... so does that mean the "inharmonicity" and the 4:2 overtone
alignment for the higher octaves wouldn't pertain to the harpsichord??

JP

on 6/4/03 4:24 PM, Joseph Pehrson <jpehrson@rcn.com> wrote:

> ***Now the question is... (which I regrettably didn't think of before
> my last post :) :
>
> If one is tuning an "upper octave" and actually tuning its second
> harmonic to the fourth harmonic of the lower one (2:4) wouldn't
> the "stretching" take place *naturally* since those harmonics would
> be the ones one would listen for in order to eliminate the beating??
>
> JP

Yes, that's exactly what I've said 3 or 4 times now! :) And that is what
wallyesterpaulrus was saying regarding Werkmeister a couple of hours ago.
You _might_ just want to go back and reread the whole thread since now you
may have a better understanding of a couple of issues.

-Kurt

--- In tuning@yahoogroups.com, Kurt Bigler <kkb@b...> wrote:

/tuning/topicId_44102.html#44168

> on 6/4/03 4:24 PM, Joseph Pehrson <jpehrson@r...> wrote:
>
> > ***Now the question is... (which I regrettably didn't think of
before
> > my last post :) :
> >
> > If one is tuning an "upper octave" and actually tuning its second
> > harmonic to the fourth harmonic of the lower one (2:4) wouldn't
> > the "stretching" take place *naturally* since those harmonics
would
> > be the ones one would listen for in order to eliminate the
beating??
> >
> > JP
>
> Yes, that's exactly what I've said 3 or 4 times now! :) And that
is what
> wallyesterpaulrus was saying regarding Werkmeister a couple of
hours ago.
> You _might_ just want to go back and reread the whole thread since
now you
> may have a better understanding of a couple of issues.
>
> -Kurt

***Thanks, Kurt. Got it! (Finally...)

JP

on 6/4/03 4:33 PM, Joseph Pehrson <jpehrson@rcn.com> wrote:

> --- In tuning@yahoogroups.com, Afmmjr@a... wrote:
>
> /tuning/topicId_44102.html#44149
>
>> In a message dated 6/4/03 5:23:57 PM Eastern Daylight Time,
>> kkb@b... writes:
>>
>>
>>> The operative words being "think so". Chances are good he was
> doing it
>>> without noticing, no?
>>>
>>>
>>
>> Yes, I would trust his ears, inharmonicity claims by Paul, or not.
> A single
>> plucked string to a single plucked string on a harpsichord would be
> measurable
>> as an octave to me even without beats. Johnny
>
>
> ***It's true that there isn't enough sustain there to perceive
> beats... so does that mean the "inharmonicity" and the 4:2 overtone
> alignment for the higher octaves wouldn't pertain to the harpsichord??

Yes, the decay makes it less of an issue than on the piano, and even on the
piano it is much less of an issue than it is on the organ. Possibly also
because (correct me if I'm wrong) harpsichords never have wound strings, so
perhaps the inharmonicity is not as bad, though the different string tension
that the harpsichord (vs piano) uses at the same pitch would have an effect
also, and I don't know how that figures in. I think lower tension means
that the string displaces (bends) more for a given energy level, which makes
for more nonlinearities (and therefore greater inharmonicity) at a given
amplitude.

I have read that the decay on the piano is one reason why 12et is relatively
less objectionable on the piano, even when used with an orchestra. (Sorry
about my incessant lack of good references. Eventually I'll embarass myself
enough to have these things at hand.)

Decay aside, I wonder how the inharmonicity of the harpsichord really
compares to the piano. My impression is that the harpsichord is cleaner in
some way but I also have the impression that I am hearing more
inharmonicity.

-Kurt

>
> JP
>
>
>
>
> You do not need web access to participate. You may subscribe through
> email. Send an empty email to one of these addresses:
> tuning-subscribe@yahoogroups.com - join the tuning group.
> tuning-unsubscribe@yahoogroups.com - unsubscribe from the tuning group.
> tuning-nomail@yahoogroups.com - put your email message delivery on hold for
> the tuning group.
> tuning-digest@yahoogroups.com - change your subscription to daily digest mode.
> tuning-normal@yahoogroups.com - change your subscription to individual emails.
> tuning-help@yahoogroups.com - receive general help information.
>
>
> Your use of Yahoo! Groups is subject to http://docs.yahoo.com/info/terms/
>
>
>

--- In tuning@yahoogroups.com, "Joseph Pehrson" <jpehrson@r...> wrote:
> --- In tuning@yahoogroups.com, a440a@a... wrote:
>
> /tuning/topicId_44102.html#44128
>
> > Inharmonicity! The partials of a vibrating, struck, string
are
> not exact multiples of the fundamental, they are all sharp, and
> progressively so.
>
> ***Now the question is... (which I regrettably didn't think of
before
> my last post :) :
>
> If one is tuning an "upper octave" and actually tuning its second
> harmonic to the fourth harmonic of the lower one (2:4) wouldn't
> the "stretching" take place *naturally* since those harmonics would
> be the ones one would listen for in order to eliminate the beating??
>
> JP

"2:4" is only one possibility. other possibilities
include "1:2", "3:6", "4:8", etc. all are slightly different
intervals, but all are wider than 1200 cents.

--- In tuning@yahoogroups.com, Kurt Bigler <kkb@b...> wrote:
> on 6/4/03 4:33 PM, Joseph Pehrson <jpehrson@r...> wrote:
>
> > --- In tuning@yahoogroups.com, Afmmjr@a... wrote:
> >
> > /tuning/topicId_44102.html#44149
> >
> >> In a message dated 6/4/03 5:23:57 PM Eastern Daylight Time,
> >> kkb@b... writes:
> >>
> >>
> >>> The operative words being "think so". Chances are good he was
> > doing it
> >>> without noticing, no?
> >>>
> >>>
> >>
> >> Yes, I would trust his ears, inharmonicity claims by Paul, or
not.
> > A single
> >> plucked string to a single plucked string on a harpsichord would
be
> > measurable
> >> as an octave to me even without beats. Johnny
> >
> >
> > ***It's true that there isn't enough sustain there to perceive
> > beats... so does that mean the "inharmonicity" and the 4:2
overtone
> > alignment for the higher octaves wouldn't pertain to the
harpsichord??
>
> Yes, the decay makes it less of an issue than on the piano, and
even on the
> piano it is much less of an issue than it is on the organ.

but on the organ there is no inharmonicity.

> Decay aside, I wonder how the inharmonicity of the harpsichord
really
> compares to the piano. My impression is that the harpsichord is
cleaner in
> some way but I also have the impression that I am hearing more
> inharmonicity.

i think you're correct in that the authentic harpsichord has less
*systematic* inharmonicity (that is, stretching), but more "random"
inharmonicity due to the sharp attack transient and due to the lower
uniformity of authentically constructed strings.

on a slightly different note, anyone truly interested in this
discussion should read the following on how inharmonicity affects
pitch perception:

http://lib.hut.fi/Diss/2003/isbn9512263149/article4.pdf

--- In tuning@yahoogroups.com, Kurt Bigler <kkb@b...> wrote:
> on 6/4/03 4:24 PM, Joseph Pehrson <jpehrson@r...> wrote:
>
> > ***Now the question is... (which I regrettably didn't think of
before
> > my last post :) :
> >
> > If one is tuning an "upper octave" and actually tuning its second
> > harmonic to the fourth harmonic of the lower one (2:4) wouldn't
> > the "stretching" take place *naturally* since those harmonics
would
> > be the ones one would listen for in order to eliminate the
beating??
> >
> > JP
>
> Yes, that's exactly what I've said 3 or 4 times now! :) And that
is what
> wallyesterpaulrus was saying regarding Werkmeister a couple of
hours ago.
> You _might_ just want to go back and reread the whole thread since
now you
> may have a better understanding of a couple of issues.
>
> -Kurt

actually, kurt, the answer to joseph's question is "no". 2:4 would
not necessarily be the harmonics one would listen for in order to
eliminate the beating. one could instead listen for 1:2, or for 3:6,
or for 4:8. each of these procedures will lead to a different tuning
for the octave, though normally all of them are wider than 1200
cents. the general idea, as ed foote pointed out, is to minimize the
beating of the partials which lie in the frequency range where most
of the harmonic activity takes place in keyboard music -- generally
the middlish register. so one would generally tune 1:2s in the middle
and 5:10s or 6:12s in the low bass. therefore, even if the
*fundamentals* of the bass notes are really flat, its *partials* will
be generally be in tune with the chords you're playing, which matters
more. also, as you can read in the link i just posted, the
fundamental is not even that important in determining what pitch is
heard for the bass note -- all the partials play a role.

on 6/5/03 1:26 PM, wallyesterpaulrus <wallyesterpaulrus@yahoo.com> wrote:

> --- In tuning@yahoogroups.com, Kurt Bigler <kkb@b...> wrote:
>> on 6/4/03 4:24 PM, Joseph Pehrson <jpehrson@r...> wrote:
>>
>>> ***Now the question is... (which I regrettably didn't think of
> before
>>> my last post :) :
>>>
>>> If one is tuning an "upper octave" and actually tuning its second
>>> harmonic to the fourth harmonic of the lower one (2:4) wouldn't
>>> the "stretching" take place *naturally* since those harmonics
> would
>>> be the ones one would listen for in order to eliminate the
> beating??
>>>
>>> JP
>>
>> Yes, that's exactly what I've said 3 or 4 times now! :) And that
> is what
>> wallyesterpaulrus was saying regarding Werkmeister a couple of
> hours ago.
>> You _might_ just want to go back and reread the whole thread since
> now you
>> may have a better understanding of a couple of issues.
>>
>> -Kurt
>
> actually, kurt, the answer to joseph's question is "no". 2:4 would
> not necessarily be the harmonics one would listen for in order to
> eliminate the beating. one could instead listen for 1:2, or for 3:6,
> or for 4:8. each of these procedures will lead to a different tuning
> for the octave, though normally all of them are wider than 1200
> cents. the general idea, as ed foote pointed out, is to minimize the
> beating of the partials which lie in the frequency range where most
> of the harmonic activity takes place in keyboard music -- generally
> the middlish register. so one would generally tune 1:2s in the middle
> and 5:10s or 6:12s in the low bass. therefore, even if the
> *fundamentals* of the bass notes are really flat, its *partials* will
> be generally be in tune with the chords you're playing, which matters
> more. also, as you can read in the link i just posted, the
> fundamental is not even that important in determining what pitch is
> heard for the bass note -- all the partials play a role.

Ah, yes. I was being sloppy in reading what joseph was saying. So to
clarify, if the question were less specific and didn't mention 2:4, as in
this edit (which is basically what I read into what joseph wrote):

If one is tuning an octave against another wouldn't the "stretching"
take place *naturally* since the harmonics one would most likely hear
spontaneously would be the same ones one would need to listen for in
order to eliminate the beating??

then wouldn't the answer be yes? (Though perhaps it sounds like it is
reduced to a tautology that would be missing the point.)

-Kurt

--- In tuning@yahoogroups.com, Kurt Bigler <kkb@b...> wrote:

> If one is tuning an octave against another wouldn't
the "stretching"
> take place *naturally* since the harmonics one would most
likely hear
> spontaneously would be the same ones one would need to listen
for in
> order to eliminate the beating??
>
> then wouldn't the answer be yes?

the only problem is, people tend not to hear harmonics spontaneously,
and pretty much need to consciously entrain their listening to a
particular pitch, so that one can hear the harmonics there and
whether they are beating or not. a low piano octave is fiendishly
difficult to tune unless you consciously focus on the higher pitch of
one (and only one) of the harmonics and eliminate beating there.

on 6/5/03 3:29 PM, wallyesterpaulrus <wallyesterpaulrus@yahoo.com> wrote:

> --- In tuning@yahoogroups.com, Kurt Bigler <kkb@b...> wrote:
>
>> If one is tuning an octave against another wouldn't
> the "stretching"
>> take place *naturally* since the harmonics one would most
> likely hear
>> spontaneously would be the same ones one would need to listen
> for in
>> order to eliminate the beating??
>>
>> then wouldn't the answer be yes?
>
> the only problem is, people tend not to hear harmonics spontaneously,
> and pretty much need to consciously entrain their listening to a
> particular pitch, so that one can hear the harmonics there and
> whether they are beating or not. a low piano octave is fiendishly
> difficult to tune unless you consciously focus on the higher pitch of
> one (and only one) of the harmonics and eliminate beating there.

Fiendishly difficult, but not impossible, right? Lacking today's science
and technology (and going back to Werkmeister for example) musicians may
have lacked also some kinds of technical language for describing their
experiences, but this didn't prevent them from finding ways to describe
their experiences, nor from having their experiences in the first place.

I make this point because we can rely too much on how technical knowledge
meshes with our experience, and as a result miss too much of the fruit of
what lies in experience itself. Knowledge is all too likely to keep the
seed of the unknown from sprouting. Take your knowledge of partials away,
and what would you hear? Maybe less, and maybe more.

-Kurt

on 6/5/03 1:03 PM, wallyesterpaulrus <wallyesterpaulrus@yahoo.com> wrote:

> --- In tuning@yahoogroups.com, Kurt Bigler <kkb@b...> wrote:
>> on 6/4/03 4:33 PM, Joseph Pehrson <jpehrson@r...> wrote:
>>
>>> --- In tuning@yahoogroups.com, Afmmjr@a... wrote:
>>>
>>> /tuning/topicId_44102.html#44149
>>>
>>>> In a message dated 6/4/03 5:23:57 PM Eastern Daylight Time,
>>>> kkb@b... writes:
>>>>
>>>>> The operative words being "think so". Chances are good he was doing it
>>>>> without noticing, no?
>>>>>
>>>> Yes, I would trust his ears, inharmonicity claims by Paul, or not.
>>>> A single plucked string to a single plucked string on a harpsichord would
>>>> be measurable as an octave to me even without beats. Johnny
>>>
>>> ***It's true that there isn't enough sustain there to perceive
>>> beats... so does that mean the "inharmonicity" and the 4:2 overtone
>>> alignment for the higher octaves wouldn't pertain to the harpsichord??
>>
>> Yes, the decay makes it less of an issue than on the piano, and even on the
>> piano it is much less of an issue than it is on the organ.
>
> but on the organ there is no inharmonicity.

I have been thinking of tunings for organ a lot, so that sort of leaked in.
The point being that *beats* resulting from the tuning are more of an issue
for the organ. So there _is_ that kind of inharmonicity, the kind related
to the tuning, in keeping with your use of "systematic inharmonicity" below.

In spite of the problems with tuning an organ, or keeping it in tune, the
organ itself is inherently more capable of being tuned exactly, because
inexact tuning is ever-so detectable by the ear becuse of the sustained
notes.

It was very interesting to hear how the organ sounded when tuned to MUCH
BETTER than within one cent, even though such a tuning would not persist for
even a few days, and in spite of the fact that at the time I was putting a
12et tuning on the thing. There was a lot of consonance there which could
be taken advantage of by emphasizing octaves and fifths.

>> Decay aside, I wonder how the inharmonicity of the harpsichord really
>> compares to the piano. My impression is that the harpsichord is cleaner in
>> some way but I also have the impression that I am hearing more inharmonicity.
>
> i think you're correct in that the authentic harpsichord has less
> *systematic* inharmonicity (that is, stretching), but more "random"
> inharmonicity due to the sharp attack transient and due to the lower
> uniformity of authentically constructed strings.

-Kurt

--- In tuning@yahoogroups.com, "wallyesterpaulrus"

/tuning/topicId_44102.html#44208

<wallyesterpaulrus@y...> wrote:
> --- In tuning@yahoogroups.com, "Joseph Pehrson" <jpehrson@r...>
wrote:
> > --- In tuning@yahoogroups.com, a440a@a... wrote:
> >
> > /tuning/topicId_44102.html#44128
> >
> > > Inharmonicity! The partials of a vibrating, struck, string
> are
> > not exact multiples of the fundamental, they are all sharp, and
> > progressively so.
> >
> > ***Now the question is... (which I regrettably didn't think of
> before
> > my last post :) :
> >
> > If one is tuning an "upper octave" and actually tuning its second
> > harmonic to the fourth harmonic of the lower one (2:4) wouldn't
> > the "stretching" take place *naturally* since those harmonics
would
> > be the ones one would listen for in order to eliminate the
beating??
> >
> > JP
>
> "2:4" is only one possibility. other possibilities
> include "1:2", "3:6", "4:8", etc. all are slightly different
> intervals, but all are wider than 1200 cents.

***Thanks, Paul! Yes, I think I finally got that part...

JP

--- In tuning@yahoogroups.com, Kurt Bigler <kkb@b...> wrote:
> on 6/5/03 1:03 PM, wallyesterpaulrus <wallyesterpaulrus@y...> wrote:
>
> > --- In tuning@yahoogroups.com, Kurt Bigler <kkb@b...> wrote:
> >> on 6/4/03 4:33 PM, Joseph Pehrson <jpehrson@r...> wrote:
> >>
> >>> --- In tuning@yahoogroups.com, Afmmjr@a... wrote:
> >>>
> >>> /tuning/topicId_44102.html#44149
> >>>
> >>>> In a message dated 6/4/03 5:23:57 PM Eastern Daylight Time,
> >>>> kkb@b... writes:
> >>>>
> >>>>> The operative words being "think so". Chances are good he
was doing it
> >>>>> without noticing, no?
> >>>>>
> >>>> Yes, I would trust his ears, inharmonicity claims by Paul, or
not.
> >>>> A single plucked string to a single plucked string on a
harpsichord would
> >>>> be measurable as an octave to me even without beats. Johnny
> >>>
> >>> ***It's true that there isn't enough sustain there to perceive
> >>> beats... so does that mean the "inharmonicity" and the 4:2
overtone
> >>> alignment for the higher octaves wouldn't pertain to the
harpsichord??
> >>
> >> Yes, the decay makes it less of an issue than on the piano, and
even on the
> >> piano it is much less of an issue than it is on the organ.
> >
> > but on the organ there is no inharmonicity.
>
> I have been thinking of tunings for organ a lot, so that sort of
leaked in.
> The point being that *beats* resulting from the tuning are more of
an issue
> for the organ. So there _is_ that kind of inharmonicity, the kind
related
> to the tuning, in keeping with your use of "systematic
inharmonicity" below.

i don't get it. there is no inharmonicity in the organ, systematic or
otherwise. beats are of course a huge issue for tuning the organ. so
you're saying . . . ?

> In spite of the problems with tuning an organ, or keeping it in
tune, the
> organ itself is inherently more capable of being tuned exactly,
because
> inexact tuning is ever-so detectable by the ear becuse of the
sustained
> notes.

and because there's only *one* place where the beating stops for a
given intended ratio, unlike the case with inharmonic instruments.

on 6/6/03 1:56 PM, wallyesterpaulrus <wallyesterpaulrus@yahoo.com> wrote:

> i don't get it. there is no inharmonicity in the organ, systematic or
> otherwise. beats are of course a huge issue for tuning the organ. so
> you're saying . . . ?

[removes foot]

[catches breath]

Ok, so I better stop using the term "systematic inharmonicity" which after
all I never heard of until yesterday.

I guessed wrong in how I interpreted your use of "systematic inharmonicity",
when you said:
> i think you're correct in that the authentic harpsichord has less
> *systematic* inharmonicity (that is, stretching)

So I thought that "systematic inharmonicity" could refer to inharmonicity
involving more than one (separately tuned) notes, i.e. that it actually
referred partly to the stretch itself, as opposed to the pattern that
results in the "need" for the stretch. But now I think you mean that
systematic inharmonicity simply refers to the latter, which makes total
sense.

So I was basically going off-topic onto the issue of beats and tunings
alone. Beats are less of an issue on the harpsichord than on the piano,
because of the faster decay, and in turn beats are less of an issue on the
piano than on the organ. The pattern of relationships between the chosen
12-tone tuning and the harmonics on the organ create a complex web of
relationships in a perhaps more "fussy" way on the organ than on the piano
(because of the prominence of the beats in the long-sustained notes). I was
thinking of this web of relationships as a global structured kind of
harmonicity/inharmonicity (determined by the tuning and the harmonics
present), and confusing that with the meaning of systematic inharmonicity as
I was temporarily understanding it.

That's all! Sorry for the confusion.

-Kurt

--- In tuning@yahoogroups.com, Kurt Bigler <kkb@b...> wrote:
> on 6/6/03 1:56 PM, wallyesterpaulrus <wallyesterpaulrus@y...> wrote:
>
> > i don't get it. there is no inharmonicity in the organ,
systematic or
> > otherwise. beats are of course a huge issue for tuning the organ.
so
> > you're saying . . . ?
>
> [removes foot]
>
> [catches breath]
>
> Ok, so I better stop using the term "systematic inharmonicity"
which after
> all I never heard of until yesterday.

by "systematic" i meant the opposite of "random" -- the terminology
comes from the description of two kinds of measurement error in
science, for example.

on 6/6/03 8:43 PM, wallyesterpaulrus <wallyesterpaulrus@yahoo.com> wrote:

> --- In tuning@yahoogroups.com, Kurt Bigler <kkb@b...> wrote:

>> Ok, so I better stop using the term "systematic inharmonicity"
>> which after all I never heard of until yesterday.
>
> by "systematic" i meant the opposite of "random" -- the terminology
> comes from the description of two kinds of measurement error in
> science, for example.

Yes, it makes total sense to me now. I have to say I was thrown by your
equating it to stretch. Now getting brave again... Systematic
inharmonicity (even of the common "piano kind") after all does not _require_
stretch. The relationship is purely one of common practice, in spite of how
extremely common that may be, and how likely it might be for a nieve tuner
to tend that way without any knowledge of what is happening. The systematic
inharmonicity is distinct from the stretch, that's all. Don't mean to
argue, just further clarifying - after all there may still be some
interesting lurking tidbit to be gained here about why you equated it to
stretch. Sometimes I just can't resist these things (until they have been
beaten to death :). (And I have the feeling we have a little of that in
common.)

-Kurt

--- In tuning@yahoogroups.com, Kurt Bigler <kkb@b...> wrote:
> on 6/6/03 8:43 PM, wallyesterpaulrus <wallyesterpaulrus@y...> wrote:
>
> > --- In tuning@yahoogroups.com, Kurt Bigler <kkb@b...> wrote:
>
> >> Ok, so I better stop using the term "systematic inharmonicity"
> >> which after all I never heard of until yesterday.
> >
> > by "systematic" i meant the opposite of "random" -- the
terminology
> > comes from the description of two kinds of measurement error in
> > science, for example.
>
> Yes, it makes total sense to me now. I have to say I was thrown by
your
> equating it to stretch. Now getting brave again... Systematic
> inharmonicity (even of the common "piano kind") after all does not
_require_
> stretch.

exactly -- that was my whole point in this thread. certainly stretch
tuning sounds much better, especially on an upright piano like mine,
but i was quite satisfied with the result of zero stretch (everywhere
except the extreme half-octaves, which the guitar tuner would not
register).

> Don't mean to
> argue, just further clarifying - after all there may still be some
> interesting lurking tidbit to be gained here about why you equated
it to
> stretch.

i didn't -- what makes you think i did?

> Sometimes I just can't resist these things (until they have been
> beaten to death :). (And I have the feeling we have a little of
that in
> common.)

yup, i've been beating things to death on this list for over six and
half years now :) :)

on 6/7/03 2:05 PM, wallyesterpaulrus <wallyesterpaulrus@yahoo.com> wrote:

>> Don't mean to
>> argue, just further clarifying - after all there may still be some
>> interesting lurking tidbit to be gained here about why you equated
>> it [systematic inharmonicity] to stretch.
>
> i didn't -- what makes you think i did?

You probably just didn't notice the literal interpretation of what you
said...

on 6/5/03 1:03 PM, wallyesterpaulrus <wallyesterpaulrus@yahoo.com> wrote:

> i think you're correct in that the authentic harpsichord has less
> *systematic* inharmonicity (that is, stretching), but more "random"
> inharmonicity due to the sharp attack transient and due to the lower
> uniformity of authentically constructed strings.

-Kurt

--- In tuning@yahoogroups.com, "wallyesterpaulrus" <wallyesterpaulrus@y...> wrote:
> yup, i've been beating things to death on this list for over six and
> half years now :) :)

At times we thought the stench of the decaying carcasses alone would have given you pause, Paul...

Cheers,
Jon

ah. thanks kurt.

in case there's still any confusion, what i was talking about was
stretching of the harmonic series (that is, timbre) rather than
stretching of, or anything else about, the tuning.

--- In tuning@yahoogroups.com, Kurt Bigler <kkb@b...> wrote:
> on 6/7/03 2:05 PM, wallyesterpaulrus <wallyesterpaulrus@y...> wrote:
>
> >> Don't mean to
> >> argue, just further clarifying - after all there may still be
some
> >> interesting lurking tidbit to be gained here about why you
equated
> >> it [systematic inharmonicity] to stretch.
> >
> > i didn't -- what makes you think i did?
>
>
> You probably just didn't notice the literal interpretation of what
you
> said...
>
>
> on 6/5/03 1:03 PM, wallyesterpaulrus <wallyesterpaulrus@y...> wrote:
>
> > i think you're correct in that the authentic harpsichord has less
> > *systematic* inharmonicity (that is, stretching), but more
"random"
> > inharmonicity due to the sharp attack transient and due to the
lower
> > uniformity of authentically constructed strings.
>
>
> -Kurt