MARIN MERSENNE : FIRST SOURCE ON PENDULUM NOTATIONS
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- Опубліковано 3 жов 2024
- "Some really believe I'm nuts", Lorenz said to me, "some - believe me - know very well this metrical approach is legitimate, but they will never even consider to discuss the matter openly, although they could make all the difference. In stead, they just keep feeding this mantra that this all has been rejected many years ago. That's in fact their main counter-argument. And perhaps the only one too."
We sat outside at his new home in Ingolstadt, where Lorenz Gadient just recently was appointed community priest. The sun was shining, and when he said the word "nuts", he pointed his finger to his forehead. "Wait", I replied, 'that would make a great picture for a thumbnail!", never expecting that he, immediately, with no hesitation, took the same pose when I took my camera.
And there you have it: the thumbnail for the first 'small talks' with Lorenz Gadient, author of the ground breaking book "Takt und Pendelsschlag", perhaps one of the most important and certainly fascinating books on music written over the past decades, but, strangely enough (or is it a sign of our time) almost unread. One would hesitate to take the word 'censured' in his mouth. Lorenz is right in that regard that one, over and over, reads the reply "It all has been proven wrong thirty years ago, so why would we even consider reading this". People really seem to believe the theory that tells them to take the metronome numbers literally, while a vast majority of them are practically unplayable. Strange, not?
Time to do something about that, since what that book is about, brings us very close to what I learned from a totally different angle, coming out of the class of Jacques van Oortmerssen (1950-2015). Jacques submerged his students with close looks to notation, and what Lorenz writes about the metrical readings of speed indications, comes so incredible close to what the 17th/18th century notation, still so much connected to the tempo ordinario, teaches us...
So here you have the man behind the double beat understanding. We (Anja and the kids were also "on holiday 🙂 ) took a trip to Ingolstadt, where this incredible amiable musicologists - priest lives. So extremely calm in his research and patient for its outcome, he talked with me two days, recording no less than 17 interviews. All topics, one by one, right from his memory.
In this first episode, the father of the metrical time measurement, Marin Mersenne (1588-1648) is discussed. In his 'Harmonie Universelle', Mersenne explains, with the use of the pendulum swinging in seconds, how two such swings are representing the duration of one second. It cannot be clearer than this.
In the next episode, to be released on Saturday 27th of May, 5PM CEST, I will be asking the question to Lorenz why his outcome of this source is the opposite of e.g. Klaus Miehling. That question leads to a new and interesting explanation of the same source, but first, his primary take on Mersenne.
Publication dates of these interviews: every other Saturday at 5PM CEST
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Fascinating. The Pendulum was the precursor of the metronome and hence metronome numbers had to be interpreted according to the general musical speed of the piece in accordance with principles of the pendulum.
Eureka! I finally understand. The more realistic way of reading a MM marking is to take the PERIOD of the note at the mark stated. For example, if Beethoven wanted the crotchet at 168 for the Waldstein (if I remember it was 168 and later a 176 edition emerged - no matter), then the two quavers that make up the crotchet took the "highest points" on the pendulum swing (I made a pendulum at 21 degs N lat. at 1800 metres AMSL that required 1005 mm for the length of the string holding the weight, and it was perfectly in time with my computer MM at 60 bpm for the high points). The MM is a pendulum that makes use of a wound spring and catchment to counteract gravity. So the PERIOD at 168 to the crotchet means that each quaver takes the two high points (each audible "CLICK") on the pendulum swing. This would be consistent with the early 19th century understanding of the MM.
See: www.roma1.infn.it/~dagos/history/sm/node3.html for a written account of this idea. I hope it makes sense to the rest of the people.
Listen to your heart!
Dear Professors Winter & Gadient: This discussion is academically very interesting and perhaps important, but it boils down, methodologically, to establishing the equivalence of the modern metronome with the historical ones. If Mersenne's pendulum is a pillar of your theory, you still have to establish a link between that pendulum and the historical metronomes. In practice, though, it is a completely moot point. As several commentators have noted (see below), actual performance tempo is a function of several factors: mood (the audience's as well as the performer's), the instrument, the acoustics, etc. Beethoven himself, realizing this, abandoned the idea of indicating the metronomy of his own compositions. I have personally witnessed my father playing his signature encore, Mendelssohn's Song w/o Words, "Lost Illusions," at significantly different tempos. This can be verified in his live recordings. Schnabel's Beethoven Sonatas were significantly faster than my father's or, for example Rubinstein's or Serkin's. How unutterably boring it would be if every great musician played at the same tempo, with the same phrasing, the same dynamics, the same everything! Is that what music is? Prof. Winter, you are clearly a very able pianist: why would you perform the Waldstein at the tempo at which you have recorded it? Here is a good experiment (but, please, for your sake, don't do it!):: play the Waldstein at that tempo in public, and count how many listeners are still in the hall at the end! I know I couldn't take it. Why do such a disservice to yourself and your own artistry? With best wishes, Peter Gimpel
Thanks Lorenz for your hospitality. Looking forward to the videos !
great interview. im waiting much more from mr Lorenz!
I tried to summarize this, using more mathematics.
Mersenne gives 3.5 feet, which is around 1.07 m, for the string he used for a "1 second" period. Using the equation for Period (in modern definition, the time it takes for the weight to travel back to its original position) = 2π√(L/g), L being the length (1.07 m) and g being the acceleration of gravity (9.81 ms^-2), this gives 2.08 seconds as the period.
However, since Mersenne says that this length gives 1 second as the "period", we can safely say that he defined "period" as one swing forwards, which is 1/2 of the modern period.
It only remains to be shown whether this usage was carried forwards to Beethoven/Mozart's time, and when/where the transition happened.
However, the heartbeat analogy seems rather strange, as the average resting heart rate is around 60 bpm (bpm defined as one systole & diastole, or one "lub-dub") which means that one period (modern definition) would be 1s, or in "Mersenn-ese", 0.5 s.
But he says here that it corresponds to 1 sec. However, 1 sec in the purported Mersenne understanding above would be 30 bpm, which is usually rare and only found in resting endurance athletes or people with heart block, and probably not in a 17th century mathematician. What does Lorentz make of this inconsistency?
Note: Galileo was known for his research on pendulums. Are there any sources on how Galileo defined "period"? He was probably more famous/controversial than Mersenne. I highly doubt that the above equation was derived by Galileo, since he only knew that there was a acceleration constant, but it was Henry Cavendish who found 9.81 ms^-2 by measuring the density of earth with (guess what) lead pendulums. But I think looking into Cavendish (living at the same time of Mozart/Beethoven) might be more relevant.
Hi Andy, interesting questions, but as you say, the system is not used to -as with a stopwatch- measure duration, but to indicate time. Take a football and bounce it and count. See what is easier, count as we all do (so 1 every 2 bounces) or every bounce; And imagine than that that would be your speed indicator, which system would you use? Here from the latest mail of Lorenz, a Portuguese source talking about the same in 1820 (and Lorenz has 30 similar sources now as we speak, reaching to machinery and astronomy:
zwar besitze ich schon seit Jahren das Buch "Principios da Musica" von Rodrigo da Costa von 1820. Aber da es auf Portugiesisch geschrieben ist, befasste ich mich kaum damit. Nun bekam ich die Hilfe von einer deutschstämmigen, Portugiesisch sprechenden Frau, die mir half, einige mir für die Tempofrage einschlägig scheinende Passagen zu übersetzen.
Ein besonders wichtiger Satz steht auf S. 78, formuliert als rhetorische Frage:
"Quanto nao he facil formar um pendulo graduado,
(was ist leichter, als ein graduiertes Pendel einzurichten,)
cujas oscillacoes marcando meia batuta do compasso,
(dessen (einfache) Schwingungen (je) einen halben Taktschlag markieren,)
a batuta inteira, ou duas pancadas,
(einen ganzen Schlag oder zwei Pendelschläge,)
dirijao os Executores no principio de cada peca?"
((die) den Ausführenden den Takt angeben am Anfang jedes Musikstückes?)
Aus dieser Bemerkung schließe ich Folgendes:
1) die einzelnen Pendelschläge markieren je eine Hälfte des Taktschlages;
2) zwei Einzelschläge markieren einen ganzen oder vollen Taktschlag;
3) mit "vollem Taktschlag" (batuta inteira) ist der Dirigierschlag gemeint, worauf das Verb "dirijao" hinweist, und nicht "ganzer Takt" (im Sinne von "Zeitraum zwischen zwei Taktstrichen");
4) die Taktteile, die in der Dirigierbewegung markiert werden, werden vom (Metronom-)Pendel als Doppelschlag-Einheiten angezeigt.
Das möchte ich auf eine andere Bemerkung auf S. 73 beziehen:
dort bezeichnet da Costa die MM-Angabe "Viertel=25" (identisch mit Achtel=50), deren "mathematischer Ausdruck" 1/25 Minuten sei oder "2 Sekunden und 24 Terzen", als "batuta do compasso" von "2 1/2 minutos segundos proximamente".
Eine "batuta do compasso" ist definitionsgemäß eine Doppelschlag-Einheit (thesis-arsis) und wird, wie oben erwähnt, als "batuta inteira" mit einem Ab- und einen Aufschlag dirigiert.
Da die MM-Angabe Viertel=25 als "batuta de compasso" von "nahezu 2 1/2 Sekunden Dauer" bezeichnet wird, folgt daraus, dass dieser Autor eine MM-Angabe grundsätzlich als Anzeige einer Doppelschlag-Einheit versteht.
Just curious, did Mersenne say that the heartbeat was 1 sec? In the metrical reading and using the "lub-dub" (Systole/Diastole), shouldn't a 60 bpm resting heart rate be 0.5 sec, in Mersenne's system?
I'll send you the excerpt by mail !
So the length of the metric unit "meter" was considered to be based on the length of a pendulum with a swing of 1 second. However, as a period is a tic-toc, we get 2 seconds. Fortunately, the metric revolution found another way to justify that meter number. The formula that relates the length of a pendulum with its period basically says that if you want to half the time you need to quarter the length. So a real "second's" pendulum is about 25cm or 0.25m. Because of fluctuations in gravity, the length of the pendulum can be adjusted in clocks based on said pendulum. In 1814, Mr. Winkel in Amsterdam invented the [musical thing], and in 1816 Mr. Maelzel patented the [musical thing] invention to himself (theft) calling it metronome. In 1817, Van Beethoven started to use the [musical thing] "numbers".
To me, a metronome is an upside down pendulum clock where the motor of a human, weight and gravity is replaced by a human and a spring in a wind-up clockwork.
Here, history clearly indicates the awareness of people in those days of the difference between tics and tocs on the one hand, and periodicity on the other.
The debate on the metronome number is interesting in the sense that a periodicity can describe the length of a single to be defined note. But, setting the metronome to a slow 4/4 meter, means you do not have beats for the fast notes. So, if as piece is full of fast and long notes, the student is helped better with more beats - without speeding up the time has more divisions. To me, the question is if composers, performers and authors were able to clearly communicate about these differences. Apparently not.
In the end of all these most interesting and really important discussions, we have to accept the fact that it all comes to terminology and relative definitions of musical-terms, which are different from time to time, different regions in Europe, different languages, etc. There is no one truth in these matters. I strongly advise to consider many components and musical-elements while coming to perform a musical piece, letting logic, good taste, physical personal abilities, the kind of instrument played on, the spiritual intention of the composer in each piece - determine the tempo for performance. We cannot decide on these compound matters only by math, science or arguing about the meaning of a paragraph which was taken out of context. Having said it, I thank both of you for this discussion and upload as a whole because it is most needed to increase our knowledge and ability to judge.
If only someone had documented how long it took [insert composer name here] in minutes to play a piece of his from start to finish.
There are but few are proven helpful, there still are 'problems' for both sides. The Liszt hammerklavier is a strong case however ua-cam.com/video/7PwoFoZTTHU/v-deo.html
A very enlightening interview. Well done!
Thank you Robin !
I think i get it now. The beat of the music is the same as the beat of your heart. That the heart beat consists of 2 beats. When the tempo is quick it is the same as saying that the heart beats quick; and has nothing to do with the sound. It could sound slow but beat quick.
Thank you very much.
Hi Wim, I have theoretical question. If tempo ordinario is 1 second systole and 1 second diastole, the it should be 30 beats per minute not 60 as you set it in previous videos?
Lieber Wim, lieber Lorenz, vielen Dank und herzlichen Glückwunsch für die gelungene Präsentation und Erklärungen! Vielleicht lassen sich zu Theoretikern des 18. Jahrhunderts ähnlich kurze und aussagekräftige Kolloquien ausführen, (z. B. zu Loulié), einfach zum besseren Verständnis der Masse der Musiker und Konzerthörer.
Übrigens hat insbesondere Lorenz' Buch "Takt und Pendelschlag" maßgeblich meine Interpretationen der Liszt'schen Opernfantasien beeinflußt.
Ich begleite Eure Forschungen und Aktivitäten (Wim's Beethoven-Interpretationen!) mit großem und musikalisch-aktivem Interesse und Vergnügen!
Thank you SO much, Wolfang and so nice to read your feedback here ! I'll pass your kind message to Lorenz as well.
all best wishes,
Wim
Very interesting, thanks for sharing
Εxtremely importand and interesting issues here, i hope you can make a video with Quantz descriptions of the various movements, chaconne , courante etc because there too the tempos seem a little too much.
Thank you for the positive comment ! Yes, Lorenz will talk on Quantz, the session has not been recorded yet, so it'll take some time, since the chat videos with him go every two weeks on Saturday. All this in the preparation for the new version of his book (we also are going to implement dance). If you are interested, i'm about to start a new series, assignments, in which we can together go through some pieces.
Fingers up! Looking desperately eager to hear on this so please keep up the good job mr Winters.
Mersenne like the Mersenne primes?
The Skooma Cat Yes!
Wow very interesting, didn't know that person was so diverse in his skillset. I've only heard about him previously because I'm fond of mathematics.
He was one of the most important scientists back than !
Intriguing questions indeed! Where in Switzerland is Mr. Gadient from? ;) Zürich, I suppose?
Ingolstadt, according to the notes under the video
Home to the monster in Frankenstein and the Illuminati :)
Lorenz lives in Ingolstadt in Germany, but indeed has the Swiss nationality. I'll ask where he comes from, !