I have watched this video several times, but I have some doubts about it: Could be the possibility that Mersenne refers that there are two optios to use the pendulum? One by using each single swing and the other by subdividing each single swing? I say that because it refers to the heart beat, and systole and diastole beat very quickly and we only feel one beat (but two movements). If the two movements of the pendulum seem to be the systole and diastole It would be 30 beats per minute and not 60. It is the reason for my question, so I think that he wants to say that in every single swing, you can do the two movements. Also I think that by naming the two parts of the full cycle as the two movements of the heart beat is just an example and not a real comparison of the actual systole and diastole of a heart. It only uses that comparison for understanding the binary unit of pulse. And when other authors refer to the pendulum, they say that the back and forward movements last 1 second. It could be possible that they refer to the back forward last 1 second and the forward another second? It summarizes that by saying the back and forward movements last 1 second... I have these questions. I really do not understand correctly... Could you answer me? I would appreciate that. Thank you and have a nice day. God bless you.
This answered a whole lot of questions for me, thank you! I'm afraid some people will be able to brush this off due to the complexity of the argument, but those "Sekundenpendel" descriptions are more powerful than they appear. Great work.
I think that Wim has clearly proved with this and his other videos that the Double Beat Theory for the time period under discussion is correct, and I agree with it. But, I think there is another factor that has to be accounted for when it comes to the performance and "experience" of these pieces of music. I think the original period performances it terms of tempo (using the metronome indication), the tone/timber (using period instruments and skilled musicians), and the venue (using period buildings), can be very closely approximated. But, music is very much a "psychological" experience, and our psychology is significantly determined by factors such as the time period we live, our particular culture, exposure to information, technology, pace of life, environment, and life experiences, etc. I don't think the "psychological" effect on a person living and hearing the music of Beethoven "at that time" at the Double Beat Theory tempo is the same or even close to how a person "living now" might experience it. I listen to many of the same pieces played at different tempos. Sometimes it sounds painfully slow or ridiculously and laughably fast. I don't think the Composers had/have that in mind. I think they wanted/want to convey the experience of the music they composed to produced a certain emotional and psychological response/experience in the listener. I think that a tempo suitable to the current time period must account for that. Otherwise, it is merely an acoustic shadow of what the Composer actually intended back then, instead of the complete authentic "musical experience" intended by the Composer. I think that the amazing historical work that Wim has done on tempo research is invaluable, as it helps determine the music tempo at that time in history. But, it does not determine the appropriate tempo for a "musical experience" for all time. That is a different question, and the one I ultimately find more important. I want to "experience" what the Composer experienced, and tried to capture on a sheet of paper. What the Composer experienced as thrilling, haunting, sorrowful, amazing, etc. should strike me same in the best of all possible performances.
In my opinion, we have been accelerated by a cultural paradigm, one of productivity. To even connect emotionally with this music, we have to step out of it, and then we should be the same as they were two centuries ago. We're still the same physiologically.
Correct assuming the weight at the end of the pendulum is about equal to or greater than 50 times the mass of the entire pendulum from attach point to the centre of the weight. For example, if your string weight 2 grams, the weight at the end must weigh more than 100g, or it becomes more of a physical pendulum. The "simple pendulum" so called does meet these requirements by definition; and therefore, only the length matters. Great question.
Well, I have an elyptical machine at home. It counts steps per minute. Can you guess? How does it count them? That's right, Double-Steps 😀. So if you think this whole thing is unintuitive... it's still in use, for everything that happens to have a left & right, an up & down, or any other.
Did you know we have no exact formula for the circumference of an ellipse? Kepler was amazing to come so close, yet he was light-years away from an accurate number, but it was good enough. :D
It strikes me when Mersenne in escence says that 2 swings (i.e. back and forth) IS 1 second, people mistake the is in that sentence to be descriptive when its actually prescriptive. It makes total sense if you accept that he's defining the second into existence on his own terms purely within the confines of this treatise. As a former mathematics i personally would be much more explicit in defining my terms to be used, and probably not choose a word that could be confused as something else, but in principle there's nothing wrong in doing what he's doing assuming that it's internally consistent when using that newly defined object.
I must add another equivalent to this excellent upload of yours: after forcing my husband to see, hear and understand the WBMP (he is not a musician but loves physics) as clearly shown here with Mersenne's examples, I asked him to make us coffee, which he agreed, but being a little lazy, he said to me: "but please, you bring the 2 cups" - to which I've answered: "Oh no! 2 'swings', one action - you'll do the whole operation!". Come to think of it, I could have asked him to do "triple"... :)
Dr. Lewin is awesome, and this video is one of the best to prove "Conservation of Energy", which has very serious real-world applications which I won't go into here because they are not necessarily musical although I could whittle my way around to it, make no mistake ... :D Yes, we have had several different "time systems" on earth, and in some cultures, the watch on your wrist is set to "a" certain time, but read some hours differently - even today. Measuring pendulums, we've had Rhen. in., Imperial in., and even the French metric metre. Thomas Jefferson proposed using a staff (with uniform mass throughout as a physical pendulum) of exactly 1.49 metres long to _BE_ the new measuring stick or "metre" because swinging it would always be set to the second in the Colonies. Thomas Jefferson was no stranger to clocks and motion works. In fact, prior to my knowing that he did this, I had already designed a clock that as it released the weight drving force could also be used to tell the day of the week. He did this at Montecello. Now, on to music. The idea of a pendulum to regulate was perfect. It was worldwide "sufficiently" accurate for the needs of descening and recarding tempi, and the only drawback was the "One if by Land; Two if by Sea" ordeal that we deal with today. In your coffee, the hardest decision, I think is "one lump or two" ... we are surrounded on earth with duplicity (double entendre) , and at the end of the day (which is also a hotly debated topic since Biblical times), do you take one tick or two for the M.M.? Is it musical? Is it authentically from the time? What other corroborating evidence do we have to merit one or the other? Within what span of time (ouch that word again) do we take a one beat or a two beat? On with the shew! :D
Search out the Quadrivium. A musician should be educated. This little apparent deviation will open the mind that often gets neglected but is absolutely essential in music. Bravo to Wim and Father Gadient! 💓
@@thomashughes4859 I really appreciate the quote on quadrivium! And trivium also. That is, in a way, the key for many other things. We totally lost that way to knowledge. Bravo Tom!
That is exciting to see! I'm very interested in this, for us, strange concept. So if in the nineteenth century the metrical second was quite well accepted, does this also mean that we should reassess the descriptions by Maelzel of beats per minute? Metrical seconds implies metrical minutes, could Maelzel have used metrical minutes in his concept of the metronome? I don't think he is explicit in that. That will mean that even WBMP has to be reshaped and redefined! Lots of discoveries to be made!
Are you going to cover Loulie and his Chronometre in your book? There are troubling things in there, like the way he beats time. For instance a "Mesure a quatre Temps" is marked with two "Frappers" and two "Levers" and not with four "Frappers/Levers" as you would expect if you assume the pendulum matched the way measure was beaten. If I understand Loulie correctly, he implies that your hand starts from some kind of mid-point and beats first down twice (2 "Frappers") then up twice (2 "Levers") which almost calls for a SBT reading of the pendulum. But later on he mentions the "Vibration" of the pendulum which brings us back to WBT.
Although Louis-Leon Pajot (1678-1754) describes a "Vibration" more like the swing (right to left or left to right) of the pendulum than the frequency and says they last 1 second with this pendulum, so back to SBT. It looks like there has been some interesting research done on tempi of the French baroque (Beverly Jerold) easily accessible online.
So interesting as Einstein claim time is relative. I think time and dynamics come from the soul. By the way I loved your analysis on the Beethoven moonlight sonata 3rd movement. Thank you for everything you do for music
Here's a heuristic argument to show why these sources saying that 2 seconds are actually just 1 second. Let's assume there's 30 treatises that say that the double swing oscillation lasts 1 second instead of 2. And let's say that the chances that an author made this mistake with a probability of 0.5, so that is to say, there's a 50% chance of writing 1 in stead of 2 is a misprint or a miscalculation or whatever. (Personally I think it would be closer to 1%, but let's be as generous as saying it's a 50:50 chance it should have been a 2 instead of a 1.) And then let's assume that these 30 treatises can be seen as independent (That might not be the safest assumption since I could easily see these being written as redactions of earlier treatises, so for example maybe Mersenne was used as a source to copy from thus meaning it's not really independent. But for the sake of argument let's assume independence) The the probability that all of these authors were wrong in writing 1 second when they should've written 2 seconds thus would be (0.5)^30 And that roughly equals 0.000000000931 Which is about a 1 in a billion chance that they're all wrong regarding this issue. (So approximately a 99.9999999% chance that at least one of them is accurate in trying to mean what is written and thus not to be dismissed)
Hello Wim, great video as always. This particular one got me quite excited as you started adding more and more detailed pieces of information! It didn't feel as 30 minutes at all! :) I have one extra point to add to this paradox... I was just wondering, has anyone already mentioned the simple fact that second (or its Latin origin secundus) is literally the ordinal number for 2? I think that JUST even that word is implying something already. :P (I have a feeling I am onto something maybe hahaha)
@@JérémyPresle I looked it up and it derives from "sequitur" which means "to follow". That makes sense, because in order to feel a second, it needs to "follow" another one... :o
Yeah, case closed ;) I'm still curious about any musicians after Beethoven indicating somehow that a piece must be played in single beat, is there a video on transitioning or overlapping practices w regard to mm more recently??? 👏
@Kingshuk Chakravorty Thanks for playing! The answer is _The Pendulum_ . See as the pendulum "slows" (the speed literally slows as the angles become less), the time period "increases" as we reach the smallest angles of displacement. Were this pendulum nestled between two cycloidal cheeks - as Huygens tried to do three and a half centuries ago - this little riddle wouldn't work. :D
@Kingshuk Chakravorty This is a fascinating world. Look up "Snell's Law" and find out why something in the water isn't where you think it is as the light bends. This is the same concept but related to gravity and time. :D
Why do you guys delete all questions concerning Maelzel and the metrical minute? Because you know your theory is BS right and you just want to feed your flock all your nonsense?
Out of interest are there any sources from the time of these treatises such as reviews or comments in which people said something like "This pendulum treatise is so useful. It's perfect and accurate in every way" ? Since if there is something like that, it would strike me as much harder to suggest the author has made an error given someone at the time is saying how it doesn't have any errors in it. And thus you wouldn't need an explicit confirmation of comparing the metrical second against the second of a watch to infer that claim that 1 second = 2 seconds is a genuine one that needs consideration. Just thinking out loud tbh.
Wim... We are musicians (in the best case), not physicians! Do you really expect anybody to understand this? 😂😂😂😂 Music theory world is not lead anymore by personalities like Mersenne or Young............
@@massimilianomiani9927 You're not going to believe this, but even doctors used pendulums to check the pulse rate in inches. The doctor would get the pendulum swinging and check the heart beat that way.
You've answered a question I've had for years: why are Joplin's metronome numbers so high, yet writes "NOT FAST"? Enlightening, thank you.
I have watched this video several times, but I have some doubts about it: Could be the possibility that Mersenne refers that there are two optios to use the pendulum? One by using each single swing and the other by subdividing each single swing?
I say that because it refers to the heart beat, and systole and diastole beat very quickly and we only feel one beat (but two movements). If the two movements of the pendulum seem to be the systole and diastole It would be 30 beats per minute and not 60.
It is the reason for my question, so I think that he wants to say that in every single swing, you can do the two movements.
Also I think that by naming the two parts of the full cycle as the two movements of the heart beat is just an example and not a real comparison of the actual systole and diastole of a heart. It only uses that comparison for understanding the binary unit of pulse.
And when other authors refer to the pendulum, they say that the back and forward movements last 1 second. It could be possible that they refer to the back forward last 1 second and the forward another second? It summarizes that by saying the back and forward movements last 1 second...
I have these questions. I really do not understand correctly...
Could you answer me? I would appreciate that.
Thank you and have a nice day. God bless you.
This answered a whole lot of questions for me, thank you! I'm afraid some people will be able to brush this off due to the complexity of the argument, but those "Sekundenpendel" descriptions are more powerful than they appear. Great work.
My lord... I always found the metronome to be a fascinating tool, but I never imagined it could generate so much discussion!
I think that Wim has clearly proved with this and his other videos that the Double Beat Theory for the time period under discussion is correct, and I agree with it. But, I think there is another factor that has to be accounted for when it comes to the performance and "experience" of these pieces of music. I think the original period performances it terms of tempo (using the metronome indication), the tone/timber (using period instruments and skilled musicians), and the venue (using period buildings), can be very closely approximated. But, music is very much a "psychological" experience, and our psychology is significantly determined by factors such as the time period we live, our particular culture, exposure to information, technology, pace of life, environment, and life experiences, etc.
I don't think the "psychological" effect on a person living and hearing the music of Beethoven "at that time" at the Double Beat Theory tempo is the same or even close to how a person "living now" might experience it. I listen to many of the same pieces played at different tempos. Sometimes it sounds painfully slow or ridiculously and laughably fast. I don't think the Composers had/have that in mind. I think they wanted/want to convey the experience of the music they composed to produced a certain emotional and psychological response/experience in the listener. I think that a tempo suitable to the current time period must account for that. Otherwise, it is merely an acoustic shadow of what the Composer actually intended back then, instead of the complete authentic "musical experience" intended by the Composer.
I think that the amazing historical work that Wim has done on tempo research is invaluable, as it helps determine the music tempo at that time in history. But, it does not determine the appropriate tempo for a "musical experience" for all time. That is a different question, and the one I ultimately find more important. I want to "experience" what the Composer experienced, and tried to capture on a sheet of paper. What the Composer experienced as thrilling, haunting, sorrowful, amazing, etc. should strike me same in the best of all possible performances.
In my opinion, we have been accelerated by a cultural paradigm, one of productivity. To even connect emotionally with this music, we have to step out of it, and then we should be the same as they were two centuries ago. We're still the same physiologically.
I really really appreciate the sources you quoted near the end of the video. This is what it's all about. Thank you Wim.
Just for clarification, speed of pendulum depends on length of arm only, not on weight on the end or speed it is pushed.
Correct assuming the weight at the end of the pendulum is about equal to or greater than 50 times the mass of the entire pendulum from attach point to the centre of the weight. For example, if your string weight 2 grams, the weight at the end must weigh more than 100g, or it becomes more of a physical pendulum. The "simple pendulum" so called does meet these requirements by definition; and therefore, only the length matters. Great question.
Well, I have an elyptical machine at home. It counts steps per minute.
Can you guess? How does it count them? That's right, Double-Steps 😀.
So if you think this whole thing is unintuitive... it's still in use, for everything that happens to have a left & right, an up & down, or any other.
Did you know we have no exact formula for the circumference of an ellipse? Kepler was amazing to come so close, yet he was light-years away from an accurate number, but it was good enough. :D
It strikes me when Mersenne in escence says that 2 swings (i.e. back and forth) IS 1 second, people mistake the is in that sentence to be descriptive when its actually prescriptive. It makes total sense if you accept that he's defining the second into existence on his own terms purely within the confines of this treatise. As a former mathematics i personally would be much more explicit in defining my terms to be used, and probably not choose a word that could be confused as something else, but in principle there's nothing wrong in doing what he's doing assuming that it's internally consistent when using that newly defined object.
I must add another equivalent to this excellent upload of yours: after forcing my husband to see, hear and understand the WBMP (he is not a musician but loves physics) as clearly shown here with Mersenne's examples, I asked him to make us coffee, which he agreed, but being a little lazy, he said to me: "but please, you bring the 2 cups" - to which I've answered: "Oh no! 2 'swings', one action - you'll do the whole operation!". Come to think of it, I could have asked him to do "triple"... :)
I can tell that these thumbnails are a highlight of your week 😂
Watch Lewin's video to see where this came from - it's classic on so many levels in physics!
@@thomashughes4859 Oh, I know the video 😂 Faith in knowledge!
And I just watched it again, what a showman...
@@surgeeo1406 He's great!
Dr. Lewin is awesome, and this video is one of the best to prove "Conservation of Energy", which has very serious real-world applications which I won't go into here because they are not necessarily musical although I could whittle my way around to it, make no mistake ... :D
Yes, we have had several different "time systems" on earth, and in some cultures, the watch on your wrist is set to "a" certain time, but read some hours differently - even today.
Measuring pendulums, we've had Rhen. in., Imperial in., and even the French metric metre. Thomas Jefferson proposed using a staff (with uniform mass throughout as a physical pendulum) of exactly 1.49 metres long to _BE_ the new measuring stick or "metre" because swinging it would always be set to the second in the Colonies. Thomas Jefferson was no stranger to clocks and motion works. In fact, prior to my knowing that he did this, I had already designed a clock that as it released the weight drving force could also be used to tell the day of the week. He did this at Montecello.
Now, on to music. The idea of a pendulum to regulate was perfect. It was worldwide "sufficiently" accurate for the needs of descening and recarding tempi, and the only drawback was the "One if by Land; Two if by Sea" ordeal that we deal with today. In your coffee, the hardest decision, I think is "one lump or two" ... we are surrounded on earth with duplicity (double entendre) , and at the end of the day (which is also a hotly debated topic since Biblical times), do you take one tick or two for the M.M.? Is it musical? Is it authentically from the time? What other corroborating evidence do we have to merit one or the other? Within what span of time (ouch that word again) do we take a one beat or a two beat?
On with the shew! :D
Search out the Quadrivium. A musician should be educated. This little apparent deviation will open the mind that often gets neglected but is absolutely essential in music. Bravo to Wim and Father Gadient! 💓
@@thomashughes4859 I really appreciate the quote on quadrivium! And trivium also. That is, in a way, the key for many other things. We totally lost that way to knowledge. Bravo Tom!
@@massimilianomiani9927 Thanks, Massimiliano! It was what Newton, Galileo, et al. studied and why there were so much smarter than the people today.
Thank you! Such a good and convincing explaination.
That is exciting to see! I'm very interested in this, for us, strange concept. So if in the nineteenth century the metrical second was quite well accepted, does this also mean that we should reassess the descriptions by Maelzel of beats per minute? Metrical seconds implies metrical minutes, could Maelzel have used metrical minutes in his concept of the metronome? I don't think he is explicit in that. That will mean that even WBMP has to be reshaped and redefined! Lots of discoveries to be made!
Are you going to cover Loulie and his Chronometre in your book? There are troubling things in there, like the way he beats time. For instance a "Mesure a quatre Temps" is marked with two "Frappers" and two "Levers" and not with four "Frappers/Levers" as you would expect if you assume the pendulum matched the way measure was beaten. If I understand Loulie correctly, he implies that your hand starts from some kind of mid-point and beats first down twice (2 "Frappers") then up twice (2 "Levers") which almost calls for a SBT reading of the pendulum. But later on he mentions the "Vibration" of the pendulum which brings us back to WBT.
Although Louis-Leon Pajot (1678-1754) describes a "Vibration" more like the swing (right to left or left to right) of the pendulum than the frequency and says they last 1 second with this pendulum, so back to SBT. It looks like there has been some interesting research done on tempi of the French baroque (Beverly Jerold) easily accessible online.
Bravo!
Ahh. Clavichord + Sweelinck = :)
Good video. I'm looking forward to the book.
So interesting as Einstein claim time is relative. I think time and dynamics come from the soul. By the way I loved your analysis on the Beethoven moonlight sonata 3rd movement. Thank you for everything you do for music
Thank you!
Finally a video on the grotesque double second!
HAHA! 😁👍
Here's a heuristic argument to show why these sources saying that 2 seconds are actually just 1 second.
Let's assume there's 30 treatises that say that the double swing oscillation lasts 1 second instead of 2.
And let's say that the chances that an author made this mistake with a probability of 0.5, so that is to say, there's a 50% chance of writing 1 in stead of 2 is a misprint or a miscalculation or whatever. (Personally I think it would be closer to 1%, but let's be as generous as saying it's a 50:50 chance it should have been a 2 instead of a 1.)
And then let's assume that these 30 treatises can be seen as independent (That might not be the safest assumption since I could easily see these being written as redactions of earlier treatises, so for example maybe Mersenne was used as a source to copy from thus meaning it's not really independent. But for the sake of argument let's assume independence)
The the probability that all of these authors were wrong in writing 1 second when they should've written 2 seconds thus would be (0.5)^30
And that roughly equals 0.000000000931
Which is about a 1 in a billion chance that they're all wrong regarding this issue. (So approximately a 99.9999999% chance that at least one of them is accurate in trying to mean what is written and thus not to be dismissed)
Hello Wim, great video as always. This particular one got me quite excited as you started adding more and more detailed pieces of information! It didn't feel as 30 minutes at all! :)
I have one extra point to add to this paradox... I was just wondering, has anyone already mentioned the simple fact that second (or its Latin origin secundus) is literally the ordinal number for 2? I think that JUST even that word is implying something already. :P (I have a feeling I am onto something maybe hahaha)
@@JérémyPresle I looked it up and it derives from "sequitur" which means "to follow". That makes sense, because in order to feel a second, it needs to "follow" another one... :o
@@JérémyPresle Yes.
Yeah, case closed ;) I'm still curious about any musicians after Beethoven indicating somehow that a piece must be played in single beat, is there a video on transitioning or overlapping practices w regard to mm more recently??? 👏
You're really good! I listened to _Exvot_ très intéressant.
No. Case closed.
22:38 - Genesis 1:5. Yes!
Perfect.
Pop Quiz!
Q: What goes faster the slower it goes?
A: ... ???
@Kingshuk Chakravorty Thanks for playing! The answer is _The Pendulum_ .
See as the pendulum "slows" (the speed literally slows as the angles become less), the time period "increases" as we reach the smallest angles of displacement. Were this pendulum nestled between two cycloidal cheeks - as Huygens tried to do three and a half centuries ago - this little riddle wouldn't work. :D
@Kingshuk Chakravorty This is a fascinating world. Look up "Snell's Law" and find out why something in the water isn't where you think it is as the light bends. This is the same concept but related to gravity and time. :D
@Kingshuk Chakravorty The brachistochrone comes from that law. :D
Why do you guys delete all questions concerning Maelzel and the metrical minute? Because you know your theory is BS right and you just want to feed your flock all your nonsense?
Out of interest are there any sources from the time of these treatises such as reviews or comments in which people said something like "This pendulum treatise is so useful. It's perfect and accurate in every way" ?
Since if there is something like that, it would strike me as much harder to suggest the author has made an error given someone at the time is saying how it doesn't have any errors in it. And thus you wouldn't need an explicit confirmation of comparing the metrical second against the second of a watch to infer that claim that 1 second = 2 seconds is a genuine one that needs consideration.
Just thinking out loud tbh.
Wim... We are musicians (in the best case), not physicians! Do you really expect anybody to understand this? 😂😂😂😂
Music theory world is not lead anymore by personalities like Mersenne or Young............
Did you know that music is a branch of physics? Not that it changes anything of what you know in physics, but just to let you know.
@@roberacevedo8232 long story, from Pitagora, to the seven medioeval arts...
Actually, I am a physicist, so Ill be able to spot any mistakes if there's any.
@Classical Pianist thanks a lot! Anyway, who knows... Maybr there will be something also for doctors... 😂
@@massimilianomiani9927 You're not going to believe this, but even doctors used pendulums to check the pulse rate in inches. The doctor would get the pendulum swinging and check the heart beat that way.