Yahoo Tuning Groups Ultimate Backup tuning Schweben ≠ beating: best quote yet

As a matter of fact, I can. Meckenheuser's rejection of the terminology probably has to do with the use of the words Schweben/Schwebung(en). In its common historical usage stretching back to Old High German, schweben has nothing whatsoever to do with sound. There IS a good reason to explain why organ builders adopted it to refer to the sound produced by two slowly-beating organ pipes which has to do with psycho-acoustics, but that is too complex to explain here, and in any case, as part of my as-yet unpublished exhaustive study of the history of the use of the word, I’d rather keep it for later.

Recall that Praetorius had also voice his disapproval of the term, but said that it was so common among organ builders that it would be impossible to do away with it, and he would therefore begrudgingly use it as well, provided he could add the distinctions of “über sich” and “unter sich”. So he also might have called it “Terminus absurdus” had it he felt a Latin itch.

Even in the 19th century, after the original meaning of schweben (more on that in a moment) had become blurred to the point where it did indeed often mean “beating”, Scheibler forcefully rejected it from his earliest work (1834) as “unpassend” and used Stoß instead. The scientific literature immediately began to heed his advice, and we find a sudden and wide-spread adoption of the word Stoß. And it would have stayed that way, had Helmholtz not revived the term. But he may well have had something else in mind as well, concentrating not so much on the nature of the perceived sound as the underlying physical cause, i.e. the drifting phase relationship of the 2 wave forms, which adheres well to one the original proper meanings of the “schweben” which means to drift or float slowly.

In any event, it is almost beyond the realm of credibility to think that Meckenheuser was referring to a situation in which “gleichschwebende once [at some earlier time?] carried a connotation of equal beating”. The phrase “gleichschwebend” seems to have been coined by Neidhardt in his 1706 Beste und Leichteste Temperatur des Monochordi. If you have read Neidhardt, you will know that he consistently used both the verb schweben and noun Schwebung exclusively to refer to the degree of tempering in a proportional mathematical sense in all three of his publications (1706, 1724, and 1732), and that he always quantified schweben/Schwebung using units of 1/12th of the Pythagorean comma. So it is hard to believe that the term could have morphed from its original meaning in only 21 years.

Ciao,

---In TUNING@yahoogroups.com, <Francis@...> wrote :

Paul

In §76, at the bottom of page 53 continuing onto page 54, Meckenheuser writes:

Wenn wird denn die gleichschwebende Temperatur (Terminus absurdus) in die Welt kommen?

My question is why is the terminology absurd? Is it not because gleichschwebende once carried a connotation of equal beating? Can you propose an alternative explanation?

Kind regards
Charles

🔗Charles Francis <Francis@...>

Paul

Meckenheuser used the term Schweben elsewhere, so he can’t have considered it absurd or he would have avoided it. To clarify, my suggestion was that for him, and by implication for mathematicians at the time, Schweben carried an acoustic connotation. Hence gleichschwebende Temperatur left an impression that differing intervals beat identically, which he found absurd.

The ear can’t differentiate between wide and narrow beats, and Praetorius’ reservation in 1619 regarding Schweben (p. 151) is expressed in the context of tuning by fourths as these should beat wide rather than narrow. He accordingly proposes to quality the scalar term Schweben with either hoch or niedrig. Compare to Roger North:

‘The artists who deal much in tuning, will by the manner of the beats, judge in what distance the notes are from accord, but scarcely which of them is superior, for be it either the beats are alike.’

Note, Neidhardt in 1706 used [linear division of] the syntonic comma rather than [logarithmic proportions of] the Pythagorean. Not that it matters as he is close enough, and indeed the engineer Faulhaber had already published ET to within 0.2 cents back in 1630, which he calculated by using logarithms. The context for both, however, was the lack of a complete acoustic theory regarding Schweben, and importantly the limitations of the physical monochord. Note, Werckmeister explicitly warned against tuning from this educational device. Presumably Schweben carried a confluence of meanings for Neidhardt and others, including acoustic.

As an aside, what do you make of Meckenheuser §. 12. pp. 12-14?

Kind regards

Charles

🔗paul@...

Yes, you are right, Meckenheuser uses the term throughout his treatise. So does Praetorius, but he also found it bad. But how does Meckenheuser use it? If you can find a passage where he does not mean the proportional degree by which an interval is tempered, then please do so.

RE: your argument that Praetorius is only talking about scheben "in the context of tuning by fourths" is simply not true. The section begins by him giving the three rules, the third of with is that the FIFTHS should be tuned "schwebend". He then mentions that one can also tune by fourths. He then goes on to describe what schweben means. Half way through his commentary we find this:

Dann schweben soll so viel heissen wie unrein, das ist, entweder zu hoch oder zu niedrig gestimmet; sie derivirens aber daher: wann man in den Orgeln, sonderlich die Octaven, Quinten und Quarten einziehen und stimmen will, so schwebt der Resonanz und Klang in den Pfeiffen und schlägt gleich eim Trenttäant etliche Schläge: Je näher man es aber mit dem einstimmen zur Reinigkeit und accort bringt, je mehr verliert sich die Schwebung allmählich und werden der Schläge immer weniger, bis so lang, dass die Octava oder andere concordanten recht eintreten.

So he is talking about "concords", and "especially the octave, fifth and fourth".

You're right about Neidhardt and the syntonic comma. Never noticed that little detail before. Interesting, he like Werckmeister and Bendeler, just use "the comma", brushing aside the difference between the Pythagorean and the synotonic. Thanks for pointing that out.

RE: North. What he says doesn't reflect upon German literature nor upon German practice as best as we can glean from the literature. Nor does it offer us any indications as to what Germans meant when they used the words schweben and Schwebung as opposed to Tremoris, Bebung, or Schläge.

Basically, we can cut all this discussion of this or that passage in isolation by cutting straight to the very heart of the matter. To wit: is there anywhere any single shred of evidence that historically people thought that identically tempered intervals manifested equal beat rates? This is so counter-empirical that lacking any evidence, I think we can discount it completely. As far as I know, this whole idea was created out of whole cloth by Owen Jorgenson. If you have any evidence to the contrary, please let us know!

Thanks,

---In TUNING@yahoogroups.com, <Francis@...> wrote :

Paul

As an aside, what do you make of Meckenheuser §. 12. pp. 12-14?

Kind regards
Charles