Math, Music & Metric Modulation
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- Опубліковано 15 лип 2022
- Metric Modulations are famous for being for the mathematically minded music-nerd only, but they have loads of interesting and cool uses, I take a look at a few.
#metricmodulation #mathematics #music
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Research:
The Evolution of Metric Modulation Nick Hartland
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The Minack Theatre:
www.minack.com/whats-on/firew...
A few more excerpts from The Firework-Maker's Daughter
• Firework-Maker's Daugh...
Elliot Carter String Quartet no.1
• Elliott Carter - Strin...
Dream Theatre Mirror
• Mike Portnoy - The Mir...
Wynton Marsalis Autumn Leaves
• Wynton Marsalis - Autu...
• Autumn Leaves - Wynton...
Lionel Richee Say You Say Me (original)
• Lionel Richie - Say Yo...
(Philip Arabit Cover)
• Lionel Richie-Say you ...
Tigran Hamasyan Drip (Berklee Middle East Fushion Ensemble)
• Tigran Hamasyan - Drip...
Transcription
• Drip - Tigran Hamasyan...
Adam Neely This BPM Is Trash, Here's Why
• This BPM is trash, and...
This channel has really helped make music more accessible for me. Thanks for the content and for helping me appreciate music more
Can't agree more!
@kibbleofdoom just out of curiosity what did you major in in college if you went?
@@claydoub dropped out of an anthropology degree, joined the navy, and am now back in college for history.
A tip for avoiding the decimal point: start out (in your case) with a tempo that divides by 9. If the initial tempo is 99 bpm, not 100, the modulations will produce 132 bpm and then 176 bpm exactly.
Smrt
I just wanted to comment a similar thing.
But... your mileage may vary for this, but for me as a musician this is even more cringe. Because instead of starting with one of the most common tempos of 100 you are doing higly unusual things just to make the math look good on paper without any added musical value.
The math should serve the music, not the other way around...
@@Posiman Right you are! But, so long as just marking the modulation itself has not become common practice among performing musicians in orchestra (as it has become in Jazz by now, I think), you have to choose the lesser of two (or more) cringes. Pick your poison :-)
Otoh, you can probably just round down to 133, having the exact decimal doesn’t really matter for human performers
@@nathan2743 but then you'll be off by 1/400! 😉
David felt bad about Adam dissing decimal tempi so made a very instructive video about how composers end up using them and even suggests alternative ways of using metric modulation without resorting to deicmals. I wish the world was full of Davids.
Yes, but the video actually misses the point of Adam's video, so it is a non-response trying to pretend to be a response. I find it unfortunate. David's video could have been much better had he simply said the video was about metric modulation, and was not pretending to be a response to Adam's video. Because the reality is, while the video is definitely very informative, as a response video specifically, it does a rather bad job.
I like that you know we're Online enough here that you can mention Numberphile, Jacob Collier, and Sungazer in the first few minutes of this video :)
The examples from Lionel Ritchie, Marsalis, and Tigran Hamasyan all led nicely into the points you were making about The Firework Maker's Daughter-great video!!
the awkwardness of the bpm only stems from how the decimal system works, or counting systems in general; relationships like 4/3 are, in pure math, quite simple but in the way we write numbers it starts looking cringe, but as a tempo it’s neither impractical nor unnecessary, unlike the ones adam neely was talking about; because the tempo isn’t defined by the 177,77 per minute but as 4/3 of the old tempo.
like there was a time as a kid where i thought 1/3 was an irrational number which is so dumb, it just looks so complicated because we try to write it in decimal, which is not suited for a number of the definition 1/3
There's a reason why jan Misali favours the seximal number system. (Their videos are strange, wonderful, and varied.)
Yes indeed. I believe Neely's point was that the precision decimal bpm's suggest is just not realistic or important. But the way you phrase it makes a lot of sense, it really is 4/3 of the original tempo, not precisely 177.77...
If David Bruce had started the original tempo with 99 bpm instead of 100, then the modulations would’ve led to an even 132 bpm and 176 bpm that don’t have decimals points. The only reason the decimal points are there is because 100 isn’t divisible by 3. However, 99 is divisible by 9, so both new tempos look neat
Multiples of 12 would be very useful fo things like this because it has so many factors (1, 2, 3, 4, 6). 60 is even better (1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30). This means that dividing them, or multiples of them, by any of those numbers results in whole numbers. 144 is the square of 12 so if you started there, 4/3 would be 192. If that's a bit fast, you could _start_ with 108 and then go up to 144. Or start with 96 and go up to 128.
Ultimately, though, you're right the depiction of the tempo in decimal is mostly unimportant to the music.
Great video, David! So glad you found my metric modulation paper interesting, thanks for featuring it 🙂
I had to relisten to that "Autumn Leaves" part a couple of times that was so cool.
Also, is that a young Jean Batiste on piano?
yeah I noticed that too!
Instant recognition!
The best tempo marking in this case would be to express it as a rational (i.e. 4:3), as opposed to a scalar. This is precisely how you explained it in this video. It would then be understood as "in relation to the master tempo" ; which then makes complete sense, as our brains are better with ratios than with scalars (Weber's Law).
Metric modulations are very common in folk music where they go from jigs (6/8) to reels (8/8) (or sometimes slipjigs, 9/8) in a tunes set
It's also common within the same tune in metis fiddle music and French Canadian music. The fiddle tunes are called "crooked" because they add extra beats to some measures.
Watched this when it premiered 5 minutes ago before I slept, it still had something like "Metric Modulation" or "How math made music" or something like that in its title.
Woke up, and now the title chose violence.
The pivot is a rhythmical double entendre…
Excellent, 30 years ago I had a similar experience, I was walking and listening to music with my Walkman and when I arrived at a crossroads from inside a house another music came out that was incredibly in the same key but they were two different styles and tempos, I remember standing by the window surprised, it was like what you composed, now I understand why!!
My brain totally heard that autumn leaves part as increasing the subdivision factor by one each measure within the same tempo. I think some drummers (I recall at least Marco Minnemann) call that type of trick a 'pyramid pattern'. Cool to see it actually is metric modulation in this case!
That’s actually a smarter way to look at it, if you ask me
That's also how I feel it, and I'm just an amateur choir singer without formal training. I'm pretty certain that our conductor has strongly influenced me in this way, because several times he made a point of having us try to feel the whole "bar" (what is currently transcribed as a bar, even if there were no proper, written bars in that musical period) as one pulse, instead of each quarter note as its own pulse. It actually made a difference to think of it that way: phrasing became more fluid and there was less general dragging after that exercise.
Both are equally good analyses, but I'd say I feel it more as increasing subdivisions
As an american I have come to the conclusion that the brits are correct in their spelling/pronunciation of "math" as "maths". My thinking is that both "math" and "maths" are short for "mathematics (note the 's' at the end). We do not say, "I am studying mathematic". Rather, we say, "I am studying mathematics". Thus, the more appropriate shorthand version, IMO, is indeed "maths".
That's always been my thinking.
I think americans should also say "Physic" and "Mechanic" rather than "Physics" and "Mechanics" to be consistent.
@@nuberiffic Physic and Mechanic don't end in "th", so that would be inconsistent anyway.
@@MNbenMN ...neither does mathematics you peanut
If "mathematics" -> "maths", why isn't a "television" -> "telen" or "administrator"->"admir"? Seems odd to me that the last letter of a singular noun thay happens to end in "s" should retain that letter. It would be clear cut to retain the "s" when a plural is being abbreviated, but Mathematics is a singular area of study, after all.
@@MNbenMN ...no dude.
Mathematics is plural.
It's the field of study of many mathematical ideas
I hope very much for an in-person hearing of your opera one day, David. The snatches you've shared thus far are so tantalizing.
I've mostly felt that Metric mods are more "challenging" back in my playing days. But once I started playing in a "Latin" band where the horn section is v often required to play percussion the practically of playing complex rhythms made almost any metric transition easy for me. Also it made it easy for me to make a living for a couple of years playing drums in a pop/rock band.
I'm super thankful for this channel, David! It helps me and challenges my creativity as a composer, and I watch each of your videos as they come out!
Nice to see Dream Theater making an appearance, they have lots of songs with metric modulations - simple ones, in general, but they always give such a refreshing feel to the songs
Really like the bits from your opera. Expect to listen on line soon. I'll share a related idea that I had--or heard--decades ago that I called simply rhythmic modulation. I was turned on to jazz much later than to classical, when I was 19 and a friend played LPs for me of ''Kind of Blue" and "My Favorite Things." Around the same time Brubeck's "Time Out" was popular and I heard it often and liked it a lot. The following year, 1962, I attended the Monterey Jazz Festival, and heard a performance by Brubeck's quartet. In one piece I heard him gradually extend the time interval by which [what I'll call, for want of a better term] the secondary or "swing" beat played by one hand preceded the main beat, maintained by the other hand. As this interval increased it changed the whole rhythmic feel of the passage. Then he closed down the interval, bringing it back to where it had been, just a small bit ahead of the main beat. If I'd ever heard this before in jazz I hadn't noticed. Indeed I've heard such a thing a few times since, but far less marked; on this occasion I was very excited by my realization of a rhythmic possibility in jazz, or any music, that I'd never thought of.
I've been aware of this for some time. It's a fascinating subject and I use Metric Modulation frequently in my own compositions. Here is a sequence of Tempo markings that relate to one another without producing decimals. 36, 45, 48, 60, 63, 75, 80, 84, 100, 105, 112, 140, 147, 175, 196 and 245. They do not all relate to one another but rather produce a network of possible relationships based on 3:4, 3:5, 3:7, 4:5, 4:7 and 5:7 and the reverse 7:3, 7: 4 etc.
Thanks for posting this easy to understand video on a valuable musical technique.
It's always good to look at both perspectives of something before you make your own decisions. I watched Adam Neely's video and then this one. I honestly agree with both of you because I can see the viability and pliability of both methods. This was very informative and well made. Thank you.
The Minack Theatre is amazing! I am so impressed that your work is being performed there!
This is also one of the reason I adore Hamasyan's solo album 'An Ancient Observer.' While the metric modulations in his ensemble work do still sound great, there's something about doing it in a solo environment that, even when composed, have this unique feeling of spontaneity that I adore. I guess, because of the complexity of metric modulations, when you do it in an ensemble, it pretty much has to be planned out, whereas a solo performer could hypothetically improvise a metric modulation at any moment.
I did something like this in one of my pieces: It consists of two parts, the first one is a rather slow 4/4, the second one a driving 6/8. The transition goes something like this: At the very end of the first part, there is a riterdando that slows the 4/4 down so much that 16th triplets in the 4/4 become the new 8th of the 6/8. This leads to the etfect that the drums at the end of the first part starts to slow down into a classic jazz swing feel just to be taken over by the pumping 6/8th for the second part. I like to play around with the listener's expectations and metric modulation is a good way to do something like that. And yes, it took me a while to figure out how to calculate the bpm I had to write over both parts of the piece, but it took me even longer to figure out how to communicate what i had in mind to reader of my partition...
Suggestion, instead of 100 -> 133.333 -> 177.777, you could instead go with 99 -> 132 -> 176 which still adheres to the n/3*4 ratio and is very close to the original BPM.
You could even do 90 -> 120 -> 160 but you'd be affecting the tempo at that point
I’d say 100->132 because we can’t distinguish in a range of 2 after 100bpm (there are research papers). So, we can say 99 but write 100 and vice versa.
@@antonselitskii8351 That might be enough precision in most cases, unless one have a recorded track in 100 BPM which will also be used in 132 BPM section, lets say, some percussive sound. Then it will end up more and more out of sync the longer it plays. But, this scenario I describe seem to be such rare use-case, as in most cases 100 -> 132 will be fine. But, I really do not see any problem with using 99 instead of 100 but for the preference of numbers evenly divisible with 10 (base 10 bias most of us have in western culture).
@@FatLingon I see now, thank you for the clarification! I tried to fit the metronome notation for the convenience of the performer.
@@antonselitskii8351 I personally can't distinguish at all in a range of 2 regardless of starting tempo, whether it's really slow or really fast. 3-4 bpm feels to me like rubato and not true tempo change, if I even notice it. 5 bpm is my threshold for feeling that a true tempo change is happening.
Funny that you mention a marketplace since that's the name of the movement of Carl Nielsen's Aladdin Suite where he also uses overlapping melodies to convey a crowded scene. Though he used four separate ensembles playing over each other
Very thorough. Your channel provides a nice contrast to all of the jazz theory videos I watch! Thanks for all of the great content David.
Organ Farmer (King Gizzard) has my favorite metric modulation I think. It instantly becomes a banger.
Such a cool concept! Thanks for such a wonderful presentation of it :) I look forward to going through all the examples...
Loved the way you explained every details of this really cool concept.
Really cool concept. Thank you for this video, I'll definitely keep Metric Modulations in my back pocket for when I want to throw someone for a loop.
OK. So now I understand it a bit better. I've certainly heard metric modulation before but didn't know what it was. I think I will need to watch this again at least twice to get all the salient points. Very interesting. I love learning new approaches to music.
Why not use ratios? I would find 4/3×100 as a new meter after a 100 meter so much easier to read than 133.3 (or even worse 133) - but admittedly I am an engineer ;)
I usually write both-- the ratio shows what the change is doing and that it's a modulation and not just "going faster/slower", while the bpm number helps the musician practice and figure out the speed of that section without having to do math
You did a great job explaining this. I wish I had this information several months ago for a piece I was writing at the time. But now I have it stored away for the future. 😁 Thank you.
The Minack theater is always absolutely stunning.
Another cool example of a simple metric modulation from a typically-not-theory-heavy band. "Mole" by the Mountain Goats revolves around a 3:2 polyrhythm in 4/4, which transitions into 6/8 for the bridge :)
Amazing! Now I know how to call something I’ve been trying unsuccessfully to craft in my music for a while ✌🏼
Keep on the great work, Bruce!
I once dived into the analogy between metric and harmonic modulation, and discovered that the decimal number problem we struggle with metric modulation is basically the same we struggle with tuning systems, excepts that our ears (thank god!) won't feel any difference between 133.33 and 133. But basically the 3:4 ratio is the same as a just perfect fourth, and if you were to apply the same metric modulation over and over for twelve times you would get back to the starting point, only with LOTS of decimal numbers... Just like the Pythagorean comma in the circle of fifths! I never actually found any musical value in this "circle of 3:4 metric modulation" though. I feel like there are much more possibilities available than those which are actually usable in metric modulations, same as polyrhythm. The ones in the video are much musical though!
Do you have any papers, links, or resources about this by chance? Thanks!
@@jg0r I could upload my messy papers, but I would first check out if there are other resources online, I don't think that nobody has ever thought about it, there must be something out there.
Great stuff! Learned a bunch and ill definitely look into metri modulation for my future compositions 😁
David, Bravo! What an exciting and intriguing exploration of something so important in today’s music! Thank you! Might I take issue with one aspect of the terminology used? I’ve always tried to be as clear as possible with definitions of terms in music because so many terms are thrown around without much care that the result is obfuscation rather than clarity. In this current post you have adopted the commonly used definitions of meter, modulation, and tempo used today almost as a vernacular among composers, theorists, and musicologists. I find the need to pick nits or split hairs here. If you please, the term beat simply means a regular pulse in time (yes, we can have rubato, ritard, etc. within the accepted practice, but still “the clock” continues to tick). Fine, no problem there. Tempo is defined as the speed (frequency) of that beat. Again, no problem. Meter is defined as a grouping of those beats at a given tempo. Once again, no issues with that. However, the waters become a bit murky if we then use the term “Metric Modulation” when we are (sometimes) talking about altering tempo along with meter. Let me explain. The simple change of time signature from say, 4/4 to 5/4 is technically all that is required to affect a metric modulation - we have in fact changed meter, No? If we then change the temporal length of the pulse by for example stipulating the new quarter note as being derived from the prior dotted quarter note, we have in fact affected a change in tempo. If we were to go from a meter determined by the pulse being a dotted quarter note (say in 12/8) to a pulse represented by the new quarter note (say in 4/4) we have affected a temporal modulation, NOT a change in meter (as we have redefined the pulse timing (tempo), not the grouping of the beats (4 in this case) (Meter.). Do you see the problem of using the term metric modulation when we are really describing a Temporal Modulation. Granted, these two different things OFTEN happen together, but again, in the interest of clarity…. I mean for example it is possible for us (adopting the analogy to pitch) to change Key in a piece from say C major to Eb minor. It would be customary when describing this modulation to refer to it colloquially as a “change of key” when we are really changing tonality from a C centered tonality to an Eb tonality AND changing from a major (or Ionian) modality to a minor modality at the same time. This is a clear and accurate description of the attributes of pitch organization that have actually changed. Since what we are discussing here is NEW STUFF I feel it necessary to raise my hand to encourage our lingo to be more clear on this. I have written pieces that were polytemporal - imagine two choirs with two conductors performing in two different, unrelated tempi. How it’s notated is another issue but suffice it to say that it is metered in a way that makes sense for the performers but bar lines do not line up in the score. Hey, thanks for listening. I salute you, your determination, your ability to finish pieces (something I have huge issues with!) and for the balls to write as freely as you do. Thanks again. - Steve
Thank you for the interesting remark on the definitions!
Had to stop and listen to that dance beat example twice, it was so slick. I'm definitely gonna be trying to incorporate that
Awesome video as always!
10:44 optional stick swirl as opposed to a mandatory stick swirl. it's in the sheet music dude you gotta do it
This is what I was thinking when I watched Adam’s video! I’m so glad you made this!
15:50 hahah i love the "omg what have you written for the love of God" face
The bottom line for me is that a minute is an arbitrary length of time in the first place, back in my day we had analogue metronomes that were so analogue we approximated, and thirdly I enjoy music for the music that it is, which is an expression a work of art, so David on with the show.
i’m trying to find my dads youtube channel but you have the same name as him so now i’m here and i’m enjoying it
I must revisit my Frank Zappa collection. I'm sure I've heard every example here buried in Frank's work somewhere!
As an improvising bassist in Jazz and non-european musics I have done this for decades with no idea how to notate or conceptualize it as a composer (2 sides of my brain I guess)Thank you!!
love this channel
love the editing
Check out the track Heartsease by the band Spiro on their album Pole Star for a great example of a recontextual metric modulation where the initial context seems to come entirely from the listener's expectations. It starts with the accordion playing what sounds like a fast 3-beat rhythm (or maybe slow 6) but then the fiddle seems to come in completely off the beat. Eventually you readjust to hear the true slow 3-beat rhythm that was actually there all along. It's an interesting challenge to then play it from the start and hear the slow 3-beat rhythm, with the accordion actually starting on a tied upbeat and the fiddle coming in right on the beat.
Man… right from the start of this video, I thought I need to point you to DT „The Mirror“. I literally jumped off my seat when it showed up after 10 minutes! 👍👍👍
It’s nice to see some opera presented in a really relatable way so people who may never have been exposed to it might hear it here and find something interesting or enjoyable in it. Cheers mate!
That's the best explanation of a meter that I've ever seen. One thing is to feel a groove, another is to rationalize it, and for me it's much easier to rationalize stuff visually and hierarchically.
If I remember rightly, Carter’s Asko Concerto uses modulations that would result in decimals, but the decimals are left off.
Yay! A new DB video! Thanks!
I once borrowed the score for Stockhausen's Zeitmaße from the library of Sibelius Academy in Helsinki. At one point, I remember there being a metric modulation, a 3/16 bar of silence and a new metric modulation.
There were quite heavy bite marks on that page of the score.
Often being compromising when it comes to the time signature can help us to avoid the decimal point if we want to do that. For example, I wrote a piece which was mostly at crotchet equals 65, but then I wanted to have a section where a semiquaver in section B is equal to a sextuplet semiquaver in section A. If I had stuck with crotchets as the unit of duration I would've ended up with a decimal. As it happened, I went for dotted crotchet equals 65 and set the time signature to a combination of 3/4 and 6/8. If you choose a number that has a lot of factors as the tempo marking you can figure out lots of ways of making it work.
Exceptional! 👏🏼👏🏼👏🏼
Peter Schickele once commented that the most obvious metric modulation is the transition from "Carry that Weight" to "The End" on side two of _Abbey Road_. The 12 note transition is like a teacher showing you what to do.
There's an argentine jazz band called Fernández 4 which a song of their repertoire is called "Hack or Shack", and the entire song plays with polyrhythms and metric modulations. It blew my mind the first time I heard the song, and made me be interested in this subject:
ua-cam.com/video/Xc8DQSjbS8c/v-deo.html
Thanks. I assumed they played 14 doted eighth notes, so the drummer plays 4/4 + 4/4 + 5/8.
14 x 3 = 42 sixteenth notes 16 + 16 + 10 = 42 Entonces, it must be correct.
That's what I found, perhaps they wrote it differently. They play this Avishai's stuff in Argentina ?
I thought you guys were playing salsa like the rest of America latina !
@@ofdrumsandchords hahaha no, actually, even Salsa for us seems a little distant for us. Chamamé, Zamba, or even Tango are more traditional styles than Salsa (Argentina was, generally speaking) musically different than the rest of Latinamerica. About Jazz, we had an interesting development in jazz since the legendary show that Duke Ellington gave in 1968. Artists like Chivo Borraro, Walter Malosetti, Gato Barbieri; or even now, with Javier Malosetti (Walter's son, and labeled as the Argentinian Jaco Pastorius), Pipi Piazzolla (the grandson of Ástor Piazzolla) or Lucio Balduini (a very versatile guitarrist). Check out their latest release. At least for the argentine scene, are very interesting (I went to a Fernández 4 show, and it blew my mind).
@@federicozabatta1612 Thanks. I was joking, of course. I listened to Gato Barbieri, and Astor Piazzolla is well known in France but besides these guys I don't have the slightest idea of what's happening in Argentina.
I play with columbians, so I'm vaguely aware that there is a life outside of Cuba ! So far, I studied brasilian and cuban music. Being not a genius, I had to make a choice between the two, and I decided to learn spanish.
More gainful than speaking portuguese. And Barcelona is not far from where I live. Three hours of highway.
Currently, I study cumbia. I don't want to hurt my fellow musicians. But basically, I'm crazy about the clave.
So much to learn, and so little time. All the eastern Africa is rythmically fascinating. I'm done with 37/16.
I didn't go any further on the Fernandez 4, I only spent a few minutes, perhaps the drummer's logic is in 7.
I guess I get why my comment was deleted, but my track Dancing yourself to Death does have fine metric modulations and is worth tracking down and listening to if your into rhythmic finesse as laid out in the video above. Great video, Mr Bruce.
Along with John Baptiste playing with Marsalis, I also recognized the singer-songwriter MARO in the Berklee Middle Eastern Fusion Ensemble. She toured with Jacob Collier and this past year won the song contest for Portugal to represent them in Eurovision.
Interesting, I'll check her out, thanks!
A friend of mine performs with modular. I wanted to add to his track, but wanted it to be on the grid so my effects would be in time with him. Since his performance was live, I had to adjust the tempo to the thousandths to get things to line up correctly.
10:17 I'm no guitarist but i think the work your looking for is Djentle, Butt Chugging is also fitting for the genre.
The opening music to Marvel films, whilst the logo is being shown, has a metric modulation. Have never worked out what it is properly but I think it’s in 6/8 then the dotted quaver becomes the new crotchet in 3/4 then it returns back to 6/8
Good example for cool Metric modulation is the "Fake Five" cover of Take five from Panzerballet. It works liek this: original is 5/4 bar in 8th-triplets (15 pulses per bar). They change the tempo so that the triplets become 16th and they change the bar length to 4/4 (16 pulses per bar). The original "loops" 4 bars -> 60 pulses. The new 4/4 bar in 16th has to be played 3 times (48 pulses) and the 4th bar is a 3/4 (12 pulses) so it fits again to the original melody length. :)
Unless we’re working with synced audio or video, it’s kinda a Wibbly wobbly point
This was great - examples, animated explanation, everything. The Mirror by Dream Theatre (well corrected :D) was the first example to come to my mind and it was a lovely surprise to see it included.
I'd say Adam's still right about 114.57 in particular, and decimals generally. 114.57 has no apparent correspondence to a ratio. Even if it was the end result of many different rational modulations accumulated through the piece, one would have required some fraction with a 67 in to end up here from an integer because that's one of the prime factors of the numerator. The high accuracy is meaningless here, except if you want to communicate the ratio with it: I could look at your clean 100 to 133 and go "ok, 1/3 faster" but in the general case, that's a very opaque way to write it when fractions exist. Even then, you might have to turn back several pages to find what the previous number was and do some thinking to get the critical idea.
I'm not sure "[note] = [note]" on its own is any clearer. The = symbol very often means 'assign right to left' in programming languages, but many people would read it as "this old note's length is now written as this new note" because the layout of the bar is old on the left, new on the right. Or it could just look like 'equals' which is a reflexive operator (a=b is the same as b=a) and then it doesn't make any sense to use for this. With all that in mind, in the animation glitch at 10:39 where these tempo markings get jumbled and become the same, I really have to think to figure out which of them was incorrect. The arrows pointing backward and forward (e.g. at 11:58) do help to indicate that you have old note length on the left being assigned to new note length on the right.
Thank you!
Definitely would have been cool to mention Sibelius. I know his Violin Concerto and 7th Symphony have moments where (essentially) the same music is played but in drastically different tempi. Unlike in the examples you point out in this video, it is done in such a way that the transition between the tempi/metrics is stretched out over much longer stretches of time and hence not as noticeable.
That Tigran Hamasian piece sounds like something Fripp did. From 'Starless and Bible Black'.
One could use nomenclature such as '⁴/³ A Tempo'.
@9:08 You can see the bassist looking at the drummer and him laughing off the "cheat" david's talking about... what's not to love about the rhythm section?
It's a notational problem. But I'm still with Adam here. When you have to do a metric modulation you should show your intent in the score: the absolute BPM is not interesting for the performer, it's the ratio in relation to the previous tempo (like, for example 4/3). The nice thing is, since metric modulation is practically bound to the ratio of two integers, you don't even need the decimal point. Just show the ratio. Imagine having a tempo at 97 BPM. Now the next tempo is at 124.71429 BPM. You cannot guess the ratio by just seeing these two numbers. The ratio is 9/7 in this case. And the statement "124.71429 BPM" would be even essentially wrong, because the real value is not representable in the decimal system in that case.
You're right, when the piece is being performed. But when it is being practiced, or during a rehearsal it isn't so convenient to always find that new tempo. Say, you have the new tempo at bar 100. You don't always want to go from bar 98 to get the new tempo right. So the conductor will probably do the maths and write down the new tempo rounded. So be nice, and help the guys with writing down both. The ratio for the performance, and the rounded BPM in brackets to help practising it.
@@andrasfoldesi5409 I didn't say: don't write the tempo down in BPM. I only said it doesn't make sense to write the tempo to the Nth decimal digit (as the video suggested). It's probably ok to write something like 9/7 ~125 BPM. That way the conductor doesn't need a calculator ;) My point is that an anouncement like "124.71429 BPM" still isn't exact AND doesn't make sense in musical terms.
@@agemans_stuff Oh, OK then. I'm happy, we agree. :D
It's also a useful tool in thinking about giving unity to performances of multi-movement pieces in general. Example: I always thought that Glenn Gould's 1982 Goldberg Variations felt a lot more whole than any other recording I listened to-- and it turns out the reason for that is Gould thought of the tempo of every individual movement as a metric modulation of the adjacent movements. Just found out recently from an interview he gave, which he seemed bashful about the process perhaps seeming too "mathematical and unmusical"-- but the proof is in the pudding.
So basically its the ancestor of electronic dance music or build up/drop assemble in House or Techno related genres
I had this same concern with that Adam video. I think it's a stupid arbitration of how us humans measure, but it makes sense why we have it dictated that way. I think it also compares to how we treat Pitch standard, where one would say a=430 is cringe. In my opinion, it's smart for us to set a pitch standard, but that shouldn't necessarily rule out the use of others.
BTW that section of Drip earlier appears on Corrupt, off of Tigrans Red Hail album. If you haven't listened to that album, I highly suggest it, quite a jam!.
I don't remember exactly which piece it was in, but I remember being surprised that C.P.E. Bach played around with something like metric modulation. What I remember is how he used it to completely blur the transition from a fast movement into a slow movement so that the listener couldn't really tell when it happened.
I use 6s because it's a result of an old musical notation format. Gives me TONS of options with 2/3 divisible. Also this is really common in minimal electronic music. Check out guys like Nathan Fake. Idk how you would even transcribe the beat shifting over a period of minutes in relation to the melody...
If you really wanna stress your transcription abilities, check a genre literally called "fucked-up beat".
I love this clear explanation of metric modulation with excellent examples. Concerning the issue of BPM - I wanted to say the same thing to Adam when I watched his BPM video. There is nothing special in tempo about whole numbers in the same way there's nothing special about a minute.
See, but that is false, and Adam actually explained why it is false in the very video you are talking about. BPM is not something you take into consideration in a vacuum. When you write BPM in a music sheet, you are trying to communicate something to the performers reading the sheet. As such, it very much matters how easy the BPM is to read off in the first place. I feel as though David completely failed to understand that point within this video, and just ignored all of Adam's explanations. It is bad logic.
@@angelmendez-rivera351 I agree when you say "When you write BPM in a music sheet, you are trying to communicate something to the performers reading the sheet." That doesn't disagree with my point at all.
@@mstalcup But it does
Technical problem: At 10:39 the metronome/tempo marks are right, but then at 10:41 the upper one has changed incorrectly. (...and, poor me - I paused exactly on this frame:) )
Just showing the metric modulation would be a lot more effective if you ask me. The point isn't to go exactly to 133, but to play something that is 4/3 times as fast. There may be situations where 133 gets that across, but I can't easily think of any where that would be clearer than showing the modulation.
Another reason you might want finer bpm differences... You can use wider intervals of bpm as rough ideas of what you want, but for example, if you notice it's a bit too dense and busy, you could try lowering the bpm just a bit for that touch more breath, it can make a good difference in context. A single bpm won't make an important difference, but sometimes I notice with blind testing I prefer 127 over 128 just a bit, while 126 hits the spot, and every bpm lower it seems to get gradually sluggish.
Quite often you do wanna make more noticeable jumps in bpm to really make room for an arrangement or give it the desired momentum, just like how you often want to exaggerate expressions etc., but not always. I almost always do my tempo by ear anyway, and am not concerned with DJ's playing my stuff, a lot of ugly decimals that don't matter.
Do you have a link to the music that's played at around 14:50 ? Also thank you for the video
The impression I have is that having decimal points in bpm might be important if the relationship between the tempo of the piece and the frequencies of the notes or particular timbres of the notes is important (and if you need to have particular tuning of the notes as well), or something like that...
Something like a kind of rhythm of a timbre lining up in a certain way with a particular bpm
But I guess at that point, for notation for performers, it might be easier to just explain that relationship and have a performer use that relationship to get an understanding of the bpm instead of relying only on the bpm
If you look closely at 9:09 you can see that the bass player recognizes that the drummer snuck an extra beat in there. And the drummer smiles and does this little shrug as if to say "yeah well, it was easier that way".
Maths and music, and rhythm specifically? Have you had a look at Godfried Toussaint's "Euclidean rhythms" en.wikipedia.org/wiki/Euclidean_rhythm work?
Old School DT with Portnoy! An unexpected nostalgia trip.
Where's Brotherly's "System"? Such a cool modulation though.
Great video! In Argentinean Folkclore is very common to change in between 6/8 and 3/4... would that be a recontextualization?
That use occurred to me, as well. I'm not sure how a musicologist would classify it, though.
Adam Neely: "hmm I want to make a video talking about the recent popular trend of random transcription videos and how sometimes too much detail can actually be useless to performers, how do I clickbait this hmmm..."
*THIS BPM IS TRASH*
David Bruce: "hmmm I want to make a video about metric modulations how do I clickbait this"
*HEY ADAM NEELY YOU'RE WRONG NOOB DO YOU EVEN KNOW MUSIC BRUH*
Exactly.
@@DBruce xd
Thanks for including the Dream Theater example! I always thought that “The Mirror” had some cool rhythmic tricks. (BTW, the band is American, so their name is Dream Theater, not the English spelling of Dream Theatre).
Guess it depends on if it's "A Theater for Dreaming" or a "Theatre production of Dreams"?
@@kjdude8765 since it's the band's official name, there's only one acceptable spelling, which is Theater. I know this irks British people, but insisting on the British spelling is like someone insisting that my name be spelled Arron.
Mmm don’t really get the dotted 8th pattern to transform the meter. To have that pattern looping continuously like you show you would have a time sig of 15/16 as the starting time sig not 4/4 ?
Amazing video, thank you! Is it possible to listen to Firework-Maker's Daughter Opera anywhere online?
If it's being played with a click-track/other tracks, then the computer will need that perfectly accurate metric modulation (133.3333333333333333333), but if it's just humans following the groove, then you could get away with writing 133, and the musicians will most likely make the transition perfectly. Technically, they might start out about 102 instead of 100, but then they'll also adjust the ending tempo accordingly. Human brains are subconsciously mathematical experts and make micro-adjustments to account for such small differentials.
You could mark 100*4/3 as 133.(3) which means that the 3 after the point repeats itself ad infinitum
Good explanation of metric modulation and why it might produce some weird-looking BPM notations. Still, you acknowledged at the end of the video that you "settled for leaving off the decimal point," which is perfectly reasonable, given that your music is being played by humans who wouldn't be able to be that precise. So, yes, BPM notations beyond the decimal *are* cringe. If one wanted to be mathematically correct, one could show the metric modulation itself and then use ≈ (wavy equals sign) to indicate that the modulation is approximately a particular (whole number) BPM. That way someone conducting or practicing would have a reference beat to use if rehearsing a particular section in the middle of the piece.
@@JossWainwright your engraving for the performers and your instruction to the computer don't have to be the same. Engraving should be readable and meaningful to the human. It isn't computer code.
U introduced me to tigran hamasyan which has totally changed the way ive been creating music. I challenge you to check out the modulations in my tigran tribute called the grid ressurected. I wont be hurt if u dont check it out, but you and yogev gabey (and adam too) really broke down some musical walls for me and id like for one of you guys to hear that song because it wouldnt exist withought you guys. Thanks for everything!