A question for Joe Monzo: Tonalsoft definition of gleichschwebend

Just came across this entry in the Tonalsoft Encyclopedia of Microtonal Music Theory under "Gleichschwebende temperatur":

"German writers used the phrase "gleichschwebende Temperatur" to denote equal-beating temperament since the beginning of the 18th century. This is not to be confused with equal-temperament, and instead actually denotes certain meantones, well-temperament, and other tunings where the varying temperings of different intervals results in them having equal numbers of beats per second."

As part of a small side-product of my exhaustive study of the evolution of the meaning of the term "schweben" in German literature 1511-1890, I'm just putting the final touches on a paper I will read next year at an international conference called "Fritz, Sorge and the Myth of Equal-Beating Temperaments". I'm wondering if you still stand by the validity of the above quoted entry, i.e. can I use it in my talk as one of the examples of the persitence of this modern mythology? If yes, it would be interesting to know on what historical evidence the entry is based.

Thanks in advance,

Paul

Hello Paul,

I'm not familiar with the term "gleichschwebende Temperatur",
and I can neither confirm nor negate if it _can_ actually
refer to other tunings than 12-EDO.

However, I thought it's worth mentioning that Marpurg,
a known proponent of 12-EDO, used the term "gleichschwebende Temperatur" to refer to 12-EDO:

"Zu meinem Versuch über die Temperatur hat mir eine gewisse Entdeckung des Königl. Oberbauraths und Professoris Herrn Lambert Gelegenheit gegeben. Einer seiner Freunde, der Hr. Agricola erzählte mir eines Tages wie dieser große Geometer eine Methode erfunden, die gleichschwebende Temperatur, ohne Zuziehung eines Monochords, dem Clavier aufs Gewisseste mitzutheilen, wie diese Methode so sinnreich als simpel wäre, und wie nach selbiger sieben reine Quinten und eine reine große Terz gebrauchet würden, um eine um 1/12 Commat. pyth. unter sich schwebende Quinte hervorzubringen."

Friedrich Wilhelm Marpurg: "Versuch über die musikalische Temperatur" (1776), page V:
http://books.google.de/books?id=lVFDAAAAcAAJ

He's basically writing that he learned a method to apply
the (!) "gleichschwebende Temperatur" to a piano, and that
this method requires seven just fifths and a just major
third to generate a fifth that is lowered by 1/12 of a
pythagorean comma.

- Gedankenwelt

--- In tuning@yahoogroups.com, "Paul" <paul@...> wrote:
>
> Just came across this entry in the Tonalsoft Encyclopedia of Microtonal Music Theory under "Gleichschwebende temperatur":
>
> "German writers used the phrase "gleichschwebende Temperatur" to denote equal-beating temperament since the beginning of the 18th century. This is not to be confused with equal-temperament, and instead actually denotes certain meantones, well-temperament, and other tunings where the varying temperings of different intervals results in them having equal numbers of beats per second."
>
> As part of a small side-product of my exhaustive study of the evolution of the meaning of the term "schweben" in German literature 1511-1890, I'm just putting the final touches on a paper I will read next year at an international conference called "Fritz, Sorge and the Myth of Equal-Beating Temperaments". I'm wondering if you still stand by the validity of the above quoted entry, i.e. can I use it in my talk as one of the examples of the persitence of this modern mythology? If yes, it would be interesting to know on what historical evidence the entry is based.
>
> Thanks in advance,
>
> Paul

--- In tuning@yahoogroups.com, "gedankenwelt94" <gedankenwelt94@...> wrote:
>
> Hello Paul,
>
> I'm not familiar with the term "gleichschwebende Temperatur",
> and I can neither confirm nor negate if it _can_ actually
> refer to other tunings than 12-EDO.
>
> However, I thought it's worth mentioning that Marpurg,
> a known proponent of 12-EDO, used the term "gleichschwebende Temperatur" to refer to 12-EDO:

Funny you should mention that, as just today over lunch I was reading Marpurg's translation of Lambert's article which appeared in his Historisch-Kritische Beyträge zur Aufnahme der Musik B. 5 (1761). There he describes the trick of tuning 7 pure fifths and a pure major third to arrive at the enharmonic equivalent of a 12EDO major third above the first note. Marpurg is a gold mine for quotes proving that schweben/Schwebung = offset and not beating, but he is only one of many.

What I am interested in is any source whatsoever for this idea that there ever was such a thing as an "equal-beating" temperament, at least until Jorgenson. I'm up to about 135 original texts before 1890, and I've yet to find even one. Every time I try to pin this myth down it evaporates into thin air, nobody can provide any evidence. It's sort of the tempeament equivalent of the poodle in the microwave.

;-)

Ciao,

P

hi Paul,

there exisit an source (in German) about the history of "equal-beating" tunings:

http://www.wegscheider.eu/img/Juergen.pdf
including some relevant references about the origin in that way of tempering,

especially for instance about triads with same amount of detuning of PC^(1/5)
within the 5ths versus 3rds.

Are you aware about that?

bye
Andy

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

Just came across this entry in the Tonalsoft Encyclopedia of Microtonal Music Theory under "Gleichschwebende temperatur":

"German writers used the phrase "gleichschwebende Temperatur" to denote equal-beating temperament since the beginning of the 18th century. This is not to be confused with equal-temperament, and instead actually denotes certain meantones, well-temperament, and other tunings where the varying temperings of different intervals results in them having equal numbers of beats per second."

As part of a small side-product of my exhaustive study of the evolution of the meaning of the term "schweben" in German literature 1511-1890, I'm just putting the final touches on a paper I will read next year at an international conference called "Fritz, Sorge and the Myth of Equal-Beating Temperaments". I'm wondering if you still stand by the validity of the above quoted entry, i.e. can I use it in my talk as one of the examples of the persitence of this modern mythology? If yes, it would be interesting to know on what historical evidence the entry is based.

Thanks in advance,

Paul

I will have to find the time to amend my webpage .. I do very little work on my website these days, and also hardly ever check in on this list anymore.

Anyway, Marpurg's method of tuning 7 3:2 perfect-5ths and 1 5:4 major-3rd to find a very good approximation of 12-edo is indeed very ingenious .. but the interval found this way is very close to a 12-edo tempered perfect-4th, not 3rd.

2,3,5-monzo | -13 7, 1> = 10935:8192 ratio ~= 499.99872 cents

-monz

---In tuning@yahoogroups.com, <a_sparschuh@...> wrote:

hi Paul,

there exisit an source (in German) about the history of "equal-beating" tunings:

http://www.wegscheider.eu/img/Juergen.pdf
including some relevant references about the origin in that way of tempering,

especially for instance about triads with same amount of detuning of PC^(1/5)
within the 5ths versus 3rds.

Are you aware about that?

bye
Andy

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

Just came across this entry in the Tonalsoft Encyclopedia of Microtonal Music Theory under "Gleichschwebende temperatur":

"German writers used the phrase "gleichschwebende Temperatur" to denote equal-beating temperament since the beginning of the 18th century. This is not to be confused with equal-temperament, and instead actually denotes certain meantones, well-temperament, and other tunings where the varying temperings of different intervals results in them having equal numbers of beats per second."

As part of a small side-product of my exhaustive study of the evolution of the meaning of the term "schweben" in German literature 1511-1890, I'm just putting the final touches on a paper I will read next year at an international conference called "Fritz, Sorge and the Myth of Equal-Beating Temperaments". I'm wondering if you still stand by the validity of the above quoted entry, i.e. can I use it in my talk as one of the examples of the persitence of this modern mythology? If yes, it would be interesting to know on what historical evidence the entry is based.

Thanks in advance,

Paul

You are right of course, Joe, but note that Gedankenwelt didn't say "3rd" (but he did say "5th" which is still not strictly correct but closer in a sense).

---In tuning@yahoogroups.com, <joemonz@...> wrote:

I will have to find the time to amend my webpage .. I do very little work on my website these days, and also hardly ever check in on this list anymore.

Anyway, Marpurg's method of tuning 7 3:2 perfect-5ths and 1 5:4 major-3rd to find a very good approximation of 12-edo is indeed very ingenious .. but the interval found this way is very close to a 12-edo tempered perfect-4th, not 3rd.

2,3,5-monzo | -13 7, 1> = 10935:8192 ratio ~= 499.99872 cents

-monz

---In tuning@yahoogroups.com, <a_sparschuh@...> wrote:

hi Paul,

there exisit an source (in German) about the history of "equal-beating" tunings:

http://www.wegscheider.eu/img/Juergen.pdf
including some relevant references about the origin in that way of tempering,

especially for instance about triads with same amount of detuning of PC^(1/5)
within the 5ths versus 3rds.

Are you aware about that?

bye
Andy

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

Just came across this entry in the Tonalsoft Encyclopedia of Microtonal Music Theory under "Gleichschwebende temperatur":

"German writers used the phrase "gleichschwebende Temperatur" to denote equal-beating temperament since the beginning of the 18th century. This is not to be confused with equal-temperament, and instead actually denotes certain meantones, well-temperament, and other tunings where the varying temperings of different intervals results in them having equal numbers of beats per second."

As part of a small side-product of my exhaustive study of the evolution of the meaning of the term "schweben" in German literature 1511-1890, I'm just putting the final touches on a paper I will read next year at an international conference called "Fritz, Sorge and the Myth of Equal-Beating Temperaments". I'm wondering if you still stand by the validity of the above quoted entry, i.e. can I use it in my talk as one of the examples of the persitence of this modern mythology? If yes, it would be interesting to know on what historical evidence the entry is based.

Thanks in advance,

Paul

Yes, I wrote fifth, not third. Note that Marpurg didn't say that stacking 7 perfect fifths and
a major third upwards results in a perfect fifth; just that he uses them to generate one.

I didn't read the whole text, but he probably just means that 7 fifths and a major third downwards,
and some octaves upwards make a perfect fifth lowered by 1/12 of a pythagorean comma.

Of course this is - strictly speaking - still wrong, since it's not 1/12 of a pythagorean comma,
but a schisma, but since the difference is only a very small fraction of a cent (~0.0013 cents),
this really doesn't matter in tuning practice.

---In tuning@yahoogroups.com, <martinsj@...> wrote:

You are right of course, Joe, but note that Gedankenwelt didn't say "3rd" (but he did say "5th" which is still not strictly correct but closer in a sense).

---In tuning@yahoogroups.com, <joemonz@...> wrote:

I will have to find the time to amend my webpage .. I do very little work on my website these days, and also hardly ever check in on this list anymore.

Anyway, Marpurg's method of tuning 7 3:2 perfect-5ths and 1 5:4 major-3rd to find a very good approximation of 12-edo is indeed very ingenious .. but the interval found this way is very close to a 12-edo tempered perfect-4th, not 3rd.

2,3,5-monzo | -13 7, 1> = 10935:8192 ratio ~= 499.99872 cents

-monz

---In tuning@yahoogroups.com, <a_sparschuh@...> wrote:

hi Paul,

there exisit an source (in German) about the history of "equal-beating" tunings:

http://www.wegscheider.eu/img/Juergen.pdf
including some relevant references about the origin in that way of tempering,

especially for instance about triads with same amount of detuning of PC^(1/5)
within the 5ths versus 3rds.

Are you aware about that?

bye
Andy

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

Just came across this entry in the Tonalsoft Encyclopedia of Microtonal Music Theory under "Gleichschwebende temperatur":

"German writers used the phrase "gleichschwebende Temperatur" to denote equal-beating temperament since the beginning of the 18th century. This is not to be confused with equal-temperament, and instead actually denotes certain meantones, well-temperament, and other tunings where the varying temperings of different intervals results in them having equal numbers of beats per second."

As part of a small side-product of my exhaustive study of the evolution of the meaning of the term "schweben" in German literature 1511-1890, I'm just putting the final touches on a paper I will read next year at an international conference called "Fritz, Sorge and the Myth of Equal-Beating Temperaments". I'm wondering if you still stand by the validity of the above quoted entry, i.e. can I use it in my talk as one of the examples of the persitence of this modern mythology? If yes, it would be interesting to know on what historical evidence the entry is based.

Thanks in advance,

Paul