tuning string pairs

Dear clavichord and tuning experts

After owning a clavichord for a few years, and tuning it mainly via the  help of computer programs such as WinTemper (which I thoroughly recommend), I am still baffled by one aspect of tuning:
The two strings of every string pair must be tuned to almost, but not quite, the same frequency, becauseIf they are tuned to the exact same frequency, then the two sounds interfere with each other and they "cancel out" one another. (With grateful acknowledgment to Peter Bavington's book "Clavichord tuning and maintenance").
So, in the vicinity of this point where the two strings are identical in frequency, you have a zone where the further apart the two frequencies, the louder the combined sound.But, if you go too far, the combined sound begins to sound inharmonious and
"vulgar".My problem is that I find it difficult to determine how much is enough in "detuning" the concordance of the two strings. If I aim for "loudness", I find myself going too far as in 4. If I aim for needle-sharp precision, I find myself choking off the sound as in 2. If I try to do it "by ear", I frequently find myself with some notes sounding one way and others sounding the other way. Obviously it is a matter of taste and practice - but surely it should be possible to quantify this?

So here is my question:
Does anyone care to give an opinion on what the difference in pitch should be (in cents, or whatever) between the two strings of a pair? Alternatively, has anybody measured this value in a "well-tuned" instrument?
Second question:
Is this interval constant, or does it vary from the bass registers to the treble?Third
question:
Do the same principles apply for other instruments with string pairs, such as a lute or mandolin? (As far as I know, a harpsichord is tuned identically to a clavichord... but I am not so sure about pianos). What about organs - does this problem occur with them as well?

Best regards to all

Gerard Vila

Hi Gerard,

> So here is my question:
> Does anyone care to give an opinion on what the difference in
> pitch should be (in cents, or whatever) between the two strings
> of a pair?

My answer: as little as needed to avoid the cancellation. :)

> Alternatively, has anybody measured this value in a "well-tuned"
> instrument?

Not to my knowledge.

> Do the same principles apply for other instruments with
> string pairs, such as a lute or mandolin? (As far as I know,
> a harpsichord is tuned identically to a clavichord... but I
> am not so sure about pianos). What about organs - does this
> problem occur with them as well?

I don't know about organs or lutes. I've tuned a number of
harpsichords quite carefully and have never noticed the issue.
On the piano I also prefer my unisons as near as possible.
Some piano tuners prefer their unisons detuned, but they don't
seem to agree on the amount of detuning or their reasons for
wanting it.

In a harpsichord, no two strings will be plucked at precisely
the same moment. In a clavichord they will, since they are
struck by a single fret. It also occurs to me that the
clavichord is unique in imparting energy to its strings at
the fundamental node -- an impossibility in an ideal system.
Probably the coupling is very strong through the fret...

Sorry I am not of more help,

-Carl

--- In tuning@yahoogroups.com, Gerard Vila <fluffychien@...> wrote:

> Does anyone care to give an opinion on what the difference
> in pitch should be (in cents, or whatever)
> between the two strings of a pair?
> Alternatively, has anybody measured this value
> in a "well-tuned" > instrument?

Hi Gerad,
there are many opinions about how much the strings should deviate from unsion, for example see:
http://www.opscience.iop.org/0031-9120/25/1/003/pdf/0031-9120_25_1_003.pdf
Quote:
"...The often-cited piece of research (Kirk 1959), on the tuning of unisons reports thatlisteners, all with some musical trainig, prefer
tunings with 1 to 2 cents spread among the strings of a unison group..."

Also see:
http://www.speech.kth.se/music/5_lectures/weinreic/mistuned.html
attend especiall there 'fig. 8':
"
Calculated vertical force on the soundboard when driven by two strings with different "mistuning" ( f). In this example beats occur only when the "mistuning" is larger than 0.3 Hz, illustrated by the curve for f = 0.64 Hz. For smaller values the strings lock to a common frequency, and the effect of the "mistuning" is to control the level of the aftersound (cf. the curves for f = 0.22 Hz and 0.06 Hz).
"
as also referred in:
http://www.forum-pianoteq.com/viewtopic.php?id=777

bye
Andy

--- In tuning@yahoogroups.com, Gerard Vila <fluffychien@...> wrote:

> 1. Does anyone care to give an opinion on what the difference in
> pitch should be (in cents, or whatever) between the two strings of > a pair?

> 2. Second question:
> Is this interval constant, or does it vary from the bass registers > to the treble?

> 3. Third
> question:
> What about organs - does this problem occur with them as well?

Hi Gerard,
in organs, that desired effect ist not considered as a problem,
but rather as an demanded property of an organ-rank:

http://www.organstops.org/c/Celeste.html
"
Celeste [ English ]
Céleste [ French ]
Schwebung [ German ]
Literally translated as (beating) among 2 pipes of almost same pitch

When two pipes are tuned slightly off pitch from each other and speak together, they produce an undulating or shimmering tone, due to the beating effect produced by the result tone of the difference of the two frequencies. For example, if one pipe speaks approximately middle C at 256 hz, and another pipe speaks at 254 hz, a wavering of 2 beats per second will be heard when they speak together. This “beating” results from the interference of the two sound waves, alternately reinforcing each other and cancelling each other out. (This principle is also used by the Resultant, but for a rather different effect.)

The term celeste refers to a rank of pipes detuned slightly so as to produce this effect when combined with a normally tuned rank. It is also used to refer to a compound stop of two or more ranks in which at the ranks are detuned relative to each other. Rarely, a single rank of pipes can be made to produce a celeste all by itself; see Bifara and Ludwigtone.

The name Celeste, which in French means “heavenly” or “celestial”, is occasionally used by itself in a stoplist, but more often it is used as a modifier of some other name (see Variants listed below). On the other hand, the name Schwebung, a German word meaning “beat”, is usually found alone. (It is also used to refer to a tremulant.) While most celeste stops include the word “celeste”, not all of them do.

.......

Tuning

Celestes are tuned to beat at anywhere from 1/2 to about 7 beats per second. (For comparison, the bottom note of a 32' stop has a frequency of about 16 hz.) A single rank celeste may be tuned either sharp or flat of normal. A two-rank celeste may contain one normal rank and one sharp or flat rank, or it may contain one sharp rank and one flat rank. In addition to these combinations, a three-rank celestes may be tuned normal, sharp and very sharp, or normal, flat and very flat. Very large orchestral instruments may contain complex celestes of even more ranks.

String celestes are almost always tuned sharp. A common rule of thumb says that flute celestes are tuned flat, but in practice they are often tuned sharp. In general, sharp celestes are more common that flat celestes. The Unda Maris is almost always tuned flat. Brighter toned celestes are usually tuned to beat faster, duller toned celestes slower.

The tuning of celestes is a complicated business. There are basically two schools of thought: one school, advocated by E. M. Skinner, calls for tuning middle C of the celeste to be one beat per second sharp, then setting a temperament on the celeste rank so that it is in tune with itself. As a result, the celeste will beat twice as fast at each successive higher octave in its range. The other school calls for tuning each note of the celeste to a correponding on-pitch rank, adjusting the beats of each not according to the taste of the tuner or organist. This generally results in a celeste rank that is not in tune with itself, but since a celeste rank is never used alone, this out-of-tuneness does not, by itself, present a problem. Most people favor slower beats in the bass and faster beats in the treble; it has been observed that if the beat rate is the same throughout, the overall effect can sound like a tremulant rather than a celeste.

If a celeste rank is physically located too close to the on-pitch rank with which it sounds, the two ranks can pull each other into tune, ruining the effect of the celeste. The remedy for this is to not place the two ranks too close together. Sometimes the pipes of one rank will be given extra-long feet to raise their mouths several inches higher than the other ranks.

=================================================================

For further information, more deeper in detail,
about the individual beating-rates in the specific organ-stops
of the celeleste-type, please consult the corresponding links
in the above given page.

Further references:
http://en.wikipedia.org/wiki/Voix_c%C3%A9leste
http://fr.wikipedia.org/wiki/Voix_c%C3%A9leste

Additional remark:
Also it appears too in Balinese
http://en.wikipedia.org/wiki/Gamelan#Tuning
"
Balinese gamelan instruments are commonly played in pairs which are tuned slightly apart to produce interference beats, ideally at a consistent speed for all pairs of notes in all registers. It is thought that this contributes to the very "busy" and "shimmering" sound of gamelan ensembles. In the religious ceremonies that contain gamelan, these interference beats are meant to give the listener a feeling of a god's presence or a stepping stone to a meditative state.
"

bye
Andy