How A Pair Of Microwave Engineers Broke Music
HTML-код
- Опубликовано: 12 сен 2019
- Try 2 months of Skillshare absolutely free! skl.sh/12tone18
There's lots of strange and beautiful scales out there, each with their own unique sounds, origins, and constructions, but for my money, there's none stranger or more beautiful than the Bohlen-Pierce Scale. It starts with an incredibly simple question: What if the octave just... didn't exist? What would we do then? Could we make music without it? Well, that's what Heinz Bohlen and John Robinson Pierce set out to discover. Not together, mind you: They only spoke once and it was about microwaves. But both of them stumbled on this problem, and they both arrived at roughly the same solution. (As did Kees Van Prooijen but he's not in the name for some reason.) So how does it work? Ummmm... it's complicated.
Patreon: / 12tonevideos
Merch: standard.tv/12tone
Discord: / discord
Mailing List: eepurl.com/bCTDaj
Facebook: / 12tonevideos
Twitter: / 12tonevideos
Instagram: / 12tonevideos
Email: 12tonevideos@gmail.com
Last: • Understanding Under Pr...
Stick Men: ziaspace.com/ZIA/mp3s/StickMen...
Script: docs.google.com/document/d/1a...
SOURCES:
www.huygens-fokker.org/bpsite/
ziaspace.com/NYU/BP-Scale_rese...
Huge thanks to our Elephant of the Month Club members:
Susan Jones
Jill Jones
Ron Jones
Howard Levine
Duck
Brian Etheredge
Gabi Ghita
Elaine Pratt
Ken Arnold
Khristofor Saraga
Len Lanphar
Paul Ward
Benjamin DeLillo
Mitchell Fund
William (Bill) Boston
Susan Lingenfelter
Owen Campbell-Moore
Anton Smyk
Chris Prentice
Jack Carlson
Dov Zazkis
James Treacy Bagshaw
Christopher Lucas
Hendrik Payer
Andrew Beals
Thomas Morley
Jacob Helwig
Duncan Dempsey
Patrick James Morley
Tyler Leite
Paul Grieselhuber
Ben in RI
Thomas Linevitch
Braum Meakes
And thanks as well to Corvi, Henry Reich, Gene Lushtak, Eugene Bulkin, Logan Jones, Abram Thiessen, Anna Work, Oliver, Jc Bq, Adam Neely, nico, Michael Fieseler, Rick Lees, Ben LaRose, Justin Donnell, rhandhom1, Dave Mayer, Thomás, Davis Sprague, Paul Quine, Alex, Harold Gonzales, CodenaCrow, Nikolay Semyonov, Marc Himmelberger, Chris Borland, Arnas, Sarah Spath, Skylar J Eckdahl, Daniel Gilchrist, Caroline Simpson, billy roberts, Elliot Burke, Alex Atanasyan, Alex Knauth, Michael Alan Dorman, Greg Borenstein, Tim S., David Tocknell, Elias Simon, Nathan Petchell, Blake Boyd, Trevor, Michael McCormick, Lilith Dawn, Jonathan Beck, Dmitry Jemerov, Ian Seymour, Charles Gaskell, Luke Rihn, Rob Holton, Jerry D. Brown, Elliot Jay O'Neill, Elliot Winkler, Payden Nissen, Tom Evans, Fabian, Ohad Lutzky, Kurtis Commanda, James A. Thornton, Benjamin Cooper, Kevin, Ken Bauso, Brian Dinger, Max Wanderman, Stefan Strohmaier, Adam Wurstmann, Kelsey Freese, Shadow Kat, Adam Kent, Hape Company, Lee Rennie, Richard T. Anderson, Angela Flierman, Mark Feaver, Kevin Johnson, Brian McCue, Stephan Broek, JH, Jake Lizzio, David Conrad, ml cohen, Sylvain Chevalier, Darzzr, Roger Grosse, Rodrigo Roman, Francois LaPlante, Jeremy Zolner, Rowan Fox, Paper Coelacanth, Britt Ratliff, Eddie O'Rourke, Ryan, Jon Bauman, John July, Volker Wegert, Danny, Matthew Kallend, Patrick Callier, Joshua Gleitze, Emilio Assteves, Alex Keeny, Alexey Fedotov, Charles Hill, Valentin Lupachev, Joshua La Macchia, John Paul Welsh, DSM, Chris Chapin, Gary Butterfield, Niko Albertus, Luke Wever, Elizabeth von Teig, Steve Brand, Rene Miklas, Connor Shannon, max thomas, Jamie Price, Kennedy Morrison, Red Uncle, Darrell Milton, Kirk Natoza, Doug Nottingham, Scott Howarth, Barendo, Smackdab, Nicholas Wolf, Ben Phillips, Todd Davidson, Alex Larking, Paul Guziewski, Scott Nystrom, Douglas Anderson, Greg Hodgdon, ZagOnEm, Robert Beach, veleum, Kevin Boyce, Peter Leventis, Greg, Aaron Zhu Freedman, Hexa Midine, Nicholas Steicke, John Polgreen, Tuna, Mathew Wolak, Mark Sibly, Killian Hackenschmidt, Lamadesbois, Eric J Amorelli, T, Lincoln Mendell, Vincent Engler, Noam Fields-Meyer, Luke, Blake White, Michal Mikolaj Maslowski, Cattus_ex_Machina, Todd Hauser, Phillip D Neal, Aaron Epstein, Chris Connett, Scott Frazer, salman karout, Carsten Lechte, Sam Rezek, Lucas Augusto, Matt McKegg, Dominic Montanez, Marcus Doyle, Beth Martyn, Caitlin Olsen, and Taylor Martin! Your support helps make 12tone even better!
Also, thanks to Jareth Arnold for proofreading the script to make sure this all makes sense hopefully!
Some additional thoughts/corrections:
1) I have a merch store now! Check it out: www.standard.tv/12tone
2) I used a guitar sound instead of piano on this one because the piano's harmonic spectrum includes a very strong second harmonic, which is the octave, and given what we're doing here I figured using something with a stronger third harmonic instead was probably wise. I mean, ideally I probably should've just used a square wave synth and skipped the even harmonics altogether but I don't like using synths so hey look it's a guitar.
3) Apologies for using C major in the examples. I really hate doing that, but since I'm flipping back and forth between two different notation systems it just seemed like dealing with another key would be asking too much.
4) On the octave/tritave thing, another argument might be that tritave is the better name, since the number of notes within a space is less fundamental to its identity than the ratio that defines that space, which means we should instead change octave to something like duo in order to match. (Probably not literally duo, though, that's terrible.) I'm pretty sympathetic to that idea, honestly: Octave's not a great name for what it's describing when applied outside the narrow context of Western tonal harmony. I just feel like that ship has sailed: octave is deeply embedded in the lexicon, and general music terminology is so decentralized that any effort to change it would just result in pointlessly competing standards, whereas tritave is used only by a relatively small subset so changing the common name would only require convincing a few people.
5) Looks like I screwed up a couple of the audio samples. Sorry! I originally had the examples in A major but then decided pretty late in production that the notation made that unwieldy so I had to switch everything over to C and it looks like I missed a few. Apologies for that.
Haha yeah and H is used in place of B in some places in europe... cus we are stupid
9:04 You accidentally played high G instead of high C.
I enjoy the odds only nature of 13edt it makes sense. I do think that I have some personal changes/gripes.
1. The second chord should be 15/21/35 the minor flip of 3/5/7. Also, they don’t mention 7/9/15 ever as a third triad within there strange system.
2. The real harmonic Minima of tritave equivalents is found at 15edt and not 13edt. The octave, and by proxy the fifth, the tritave inversion, are not found here. However, the base chord is 3/4/5, the actually simplest way to voice a major chord within on octave. Allowing perfect fourths to be stacked in a manner like tritave Pythagorean Tuning. You even temper out 81/80 in 15 edt, equating 16/9 with 9/5 and 64/27, the Pythagorean minor third plus an octave with, 12/5.
Tangent still going the 3/4/5 chord is the simplest chord from the harmonic series if looked at through tritave eyes. It inverts into 4/5/9 and 5/9/12. The minor chord then being 12/15/20, with inversions 15/20/36 and 20/36/45.
Another point, western theorists have been obsessed with just intonation more or less since Pythagoras, but from a performer's POV it just isn't a practical or intuitive approach all the time. Early Music Sources video on just intonation in the renaissance is extremely good and here's a link
ruclips.net/video/XhY_7LT8eTw/видео.html
Hey, do you have any music you’d like to share and your process on writing it?
Can we appreciate the bro move on Pierces part of giving the credit to Bohlm.
Truly a rare sight in naming. The trend is to try and steal credit, as if being first was the point, rather than inventing or discovering something cool.
Yah but f*** van Prooijen that guy is the worst.
@@lydiasteinebendiksen4269 If you don't steal the credit how are you gonna stroke your ego, hmm?
Feel bad for Van Prooijen though,
@@rateeightx van-bohlen-pierce
was looking forward to finding out why it took microwave engineers to make this scale. bummer you didn't go into this.
Yeah me too! Such a letdown!
Possibly because they knew a lot about signals and systems and this led to a very mathematical approach to music. Just guessing here...
Marky Marco Microwaves are electromagnetic waves. A lot of the same physics applies, though.
@@markymarco2570 microwaves are a frequency of light lol, you dont cook with sound
The physics property that make microwaves "cook" things is that microwaves are small enough to penetrate most of the organic membranes and they make water molecules vibrate. Heat is just a vibration, therefore when water molecules vibrate they heat up.
This scale is actually easier to understand if you know clarinet. Because of the clarinet's acoustics being a closed-pipe instrument, it only plays the odd-numbered harmonics. This means that the instrument doesn't overblow the octave but the 12th. This means that if one fingers a C in the low register then that same fingering produces a G in the upper register. BP scale essentially takes this acoustic phenomenon of the clarinet and treats that as the basis of the scale rather than the octave. By doing this, a BP Clarinet would now overblow what is the "tritave" and the two registers of the instrument have the same fingerings.
Ok your explanation clarifies what the heck he was talking about :)
Bret Newton - Composer BP clarinets do exist, and music is written for them - by total coincidence I was just reading about them in the ICA’s The Clarinet. Stephen Fox makes BP clarinets, and he has some links on his site to music written for both two BP clarinets and one BP and one standard clarinet.
So... how come the saxophone overblows at the octave then? (I've always wondered!)
@@alanbarnett718 because it has a conical bore.
@@ChrisFarrell I'm friends with Steve and forwarded the video to him.
Video title: "a pair of microwave engineers broke music"
Brain's first instinct: those two from the Dire Straits video
Heh, that's the way you do it.
@@worldf1re41 money for nothing and your chicks for free
That ain't working
@@antiloompa8338 That's the way you do it
Would a Bohlen-Pierce Scale sound more natural if arranged using electronic instruments based on square waves?
Our traditional instrumentation -- the human voice, vibrating strings, and resonating tubes -- all feature a strong second harmonic. That could form the basis of our affinity for the octave, since a frequency-doubled note is in exact harmony with the first overtone of its lower counterpart.
But with the square wave and a few other such constructions (such as the ramp), the even harmonics are completely absent. A tritive equivalency is now the natural harmonization with the first (present) overtone.
Just don't try singing to it.
Clarinets have pretty quiet second harmonics, so that might work.
xenontesla122 BP composers are already ahead of both of you, but it's great you realized this. There's a fair bit of BP clarinet stuff out there!
True, but we get "really pure square waves" very easily with electronic generation. The NES sound system, for example, provided two square-wave channels and a triangle-wave channel -- all of which provide just odd harmonics of the fundamental. (The triangle wave is the integral of a square wave, and it does not introduce new harmonics.)
Matthew Morycinski Keep in mind that "odd harmonics only" is just a suggestion for BP. The important even harmonics to omit are the ones closest to the fundamental, as well as all the octaves. Beyond harmonic 12 or so, it's basically just texture and won't clash too badly with the non-octave structure.
@@Majromax we get close approximations of a square wave in the signal, where we can transition between the two voltages quickly, but then what happens when you try to play that through any sort of speaker to actually produce the sound? That "purity" starts to go out the window. The mechanical inertia and momentum of the drivers is going to soften up that waveform a lot, and start introducing the overtones whether you want them or not. The closest you could get would be electrostatic drivers at higher volumes, since the mass of the voice element is so low in electrostatic systems.
Heyo! I study classical composition in kuwait, and along with western music theory, we study arabic music theory. As far as i can tell, we don't treat the octave the same way everyone else does. Essentially, every note, including the same note with accidentals, has it's own individual name. An example being middle C being called rast, C# zirkola, and C an octave up from middle C kurdan. There's a big list of all the note names, and it's super convoluted, so I feel like we might not treat octaves the same way it's treated in western theory!
Saleh Hayati From What I’ve noticed in my listening, it’s treated as similar but different.
@@xbird532 it might be a regional thing as well. Traditional kuwaiti music is vastly different than moroccan music or egyptian even. Hit me up with who you've been listening to I'm actually really curious!
The note names are a holdover from historical theory and Ottoman influence, I think, because they have something similar.
Also hi from Qatar!
@@MisterManDuck that is true! A lot of my peers that have studied with turkish musicians tell me that the note naming system comes from the ottomans, and if I'm not mistaken, are the only other people that use this system anymore. Salute from kuwait!
@@Ibanezlover1221 Yes and no? It's hard to tell. I'm in contact with one Turkish Maqam expert (Eric Ederer) who's familiar with the history of it, but I don't know exactly how common it is.
The other thing is that the naming system is a mess. Like. Rast is considered the root mode for everything, but Yekah is a fourth lower because at some point they decided the Rast root and Yekah should be different to extend the range.
But Dugah and Segah etc are the same relative to Rast anyways!
*insert rant here*
Threw me for about fifteen loops.
3:20
Says it's a C major scale.
*plays A major*
IKR!?!??!?
God it annoyed me so much
My thoughts, exactly.
Nice ear mate
I feel like he did that on purpose
There's no octave equivalency in byzantine liturgical music. The scales repeat by tetrachords, which means it repeats by perfect fifths in the soft-diatonic, hard-chromatic, and soft-chromatic modal genres, and by perfect fourths in the enharmonic (also known as hard diatonic) modal genre. Octaves are entirely unimportant in any case.
Anastasios Iraniن neither is in old russian chants
I won't say Arabic/Turkish/etc Maqam is necessarily a counter example to the octave equivalency principle, but it's not treated as a *necessarily* universal rule.
Since in theory Maqamat are built by stacking Genera (typically spanning a perfect fourth or fifth, sometimes a major ir minor third), you can stack them in such a way that you can miss the octave note entirely and it's still considered valid.
The most commonly known example is Maqam Saba.
Some scholars like to play this up to say Maqamat are impossible to codify fully. I disagree, given that octave equivalent scalar structures are still built into Maqamat like this, but that's a whooooooooooooooooooooole other discussion.
There is also the fact that a root note and it's octave are still treated as tonally different, in a way.
Maqams are sometimes implicitly defined by where they start, so you'd start at the octave and work your way down as opposed to starting on the root.
MisterManDuck Also a similar situation with the Persian system! Dastgâh-e-Šur, for example, doesn’t end up with a clean octave - it’s off by around 60 cents, if I remember correctly.
@@archkde
Good point, and worth a mention!
Generally when I talk about Maqamic stuff I also implicitly mean Dastgah (not the same, but the Dastgah concept as is has shared historical roots), it's just if I were to list every related tradition I'd spend a long time typing.
I feel like this scale could totally work as the soundtrack to an alien planet in a sci-fi story.
I agree completely. If only movie studios were gutsy enough to actually have alien sounding music rather than just non-western music.
ruclips.net/video/jo54v85xeNE/видео.html
There is a vocal music traditional to Georgia (the country) using equivalency of fifths rather than octaves
I was about to rite a very similar comment! The major ninth therefore becomes the equivalent of the (double) octave
Sevish Not to mention that it is roughly divided into equidistant quarters, resulting in something akin to the stretched 7-EDO (sort of) of Thai classical music but without the actual octaves and more rounding back to 11-limit just intervals like 11/10 and 11/9. Oh, and it sounds absolutely gorgeous! Honestly that's probably the really important part.
Imma have to counter to all of you by saying you're all kinda right.
Depending on the source I've dug up they'll flit between 7ed*/2 and 4ed*3/2. There's one interesting study I dug up that shows a not very fixed step size that can range from 155ish cents to about 204ish cents.
I was wondering if you'd show up in the comments 😂
I love this thread because I live in Thailand and hear classical 7-note music and singing quite often, and I was recently in Georgia and heard the fantastic harmonic singing of the Svan people in Mestia.
Nothing beats Bohlen-Anders scale. Such gems as "You're my heart, you're my soul" and "Brother Louie" are written using that collaborative masterpiece.
lmao
Flashbacks intensify
Some time ago watching one of your scale videos I was wondering "is there a scale that repeats not in octaves, but in some other way" and now I finally know the answer, thanks!
Bohlen-Pierce is just one of a number of such scales, although most of the others don't use tritave equivalence (A12 does).
en.wikipedia.org/wiki/Category:Non%E2%80%93octave-repeating_scales
About the octave equivilancy: I stumbled over some studies and it seems like that humans and even monkeys are hard-wired to perceive octaves as equivalent.
- Braun, M., & Chaloupka, V. (2005). Carbamazepine induced pitch shift and octave space representation. Hearing research, 210(1-2), 85-92.
- Braun, M. (2006). A retrospective study of the spectral probability of spontaneous otoacoustic emissions: rise of octave shifted second mode after infancy. Hearing research, 215(1-2), 39-46.
- Wright, A. A., Rivera, J. J., Hulse, S. H., Shyan, M., & Neiworth, J. J. (2000). Music perception and octave generalization in rhesus monkeys. Journal of Experimental Psychology: General, 129(3), 291.
yes, thank you. tritave equivalence makes sense just as much as minor third equivalence
Thank you. I like weird theory, but octave equivalency is rooted in our physiology (and apparently monkeys' as well). Why is beyond me, but some of the most musically ignorant individuals can recognize a tune played in one octave versus another. Its no coincidence that it transcends cultures.
The octave is the first harmonic, and usually the strongest. I’d suggest that plays a big role into why we hear octaves as different parts of the same sound source when played at the same time.
Edit: When I say usually I mean in nature and my point was our hears have evolved to recognise that if we hear octave harmony, chances are they are coming from the same source and it’s not two things that just happened to be in tune.
I guess a another consequence of this theory, is that - since the third harmonic is the 1:3 ratio this video talks about right? the tritove- maybe that is why tritove can feel somewhat equivalent but not as much
@@calinguga The video below is a pretty good experiment that kind of shows that tritave equivalence definitely makes more sense than minor third equivalence. Not maybe as much sense as octave equivalence, but definitely more than minor third equivalence.
ruclips.net/video/9rIVPtcYgMU/видео.html
The first harmonic is the first octave, 1/2 the wavelength of the tone. The next octave is 1/4 the wavelength. The octave after that is 1/8 the wavelength. And so on. There is a basic math behind the physiological process that creates the psychological experience of equivalence of octaves.
I listened to Stick Men and it's... Surprising. It sounds "right" in a way and is incredibly uncomfortable at the same time. The harmony was making me think about anguish. Which is a feeling that a movie or video game score could use. :)
Stick Men? can you direct me?
it’s very interesting for sure
sounds very scifi to me. Like "folk" music from a civilization who uses different physics
@@atn_holdingsexactly this, it felt marvelously alien
"Don't worry, you'l probably never have to sightread any Bohlen-Pierce music. Hopefully."
I don't know why that's as funny to me as it is.
Yes u do You just can’t elucidate it
The fact that you have GROKED it means that you do know :-)
I laughed out loud. Hours later I played this for my husband and laughed again. 😆
Isn't the reason we hear octaves as "similar" or "versions of the same tone" across cultures simply physics? The nodes (parts of the air column or string that doesn't move) of a lower octave is contained in any higher octave as well. So the part of our inner ear that analyses frequency gets excited in a similar pattern.
So a couple months ago this video sent me down a rabbit-hole... yesterday I finally finished a rock song written entirely in Bohlen-Pierce (and with an electric guitar refretted in BP)!
It's really hard to make this scale sound "natural" or comfortable, but putting it into an analog instrument you're familiar with (guitar, in my case) really opened it up and made it less alien sounding. If anyone's interested, I put the full song and BP guitar build tutorial up on my channel, would mean a lot if you check it out!
I wonder how H and J would be named in German since the American B is named H here. So every C major scale already contains an H
They have Ä tho haha
Ң maybe? It's technically pronounced as guttural n but looks like H with a twist xD
Same in Poland, the Western system is much superior imho though
I would consider that it would be J and K🤷♂️ or German theorist give al notes numbers und use this instead of letters🤷♂️
Lena Interestingly, Bohlen is himself German, and has done a lot of other weird stuff with scales in his own right (such as using phi as a period rather than 2 or 3), although I'm not sure which of the fellows who stumbled upon this set of ideas actually came up with the naming system.
I've used this scale on a touch sensitive screen synth. When playing alone in a 'trance' state I made sooooper cool music. I've never used it with others tho.
david bruce talks in his 12 shades of grey video about the tuning of central african xylophones, where what matters most is that neighboring notes are 200, 240 or 280 cents apart (with some additional constraints), even if that stacking ends up missing the octave.
Călin Guga I was thinking of bringing that up! There is often some degree of octave equivalency in the overall music played with those instruments and accompanying voices, but the melodic structure frequently does ignore this in something akin to the way that (as others here have noted) the genera-based maqamat sometimes do.
I think the near-universality of octave equivalency can just be chalked up to the fact that, because the frequency ratio is 1:2, the ear sends an extremely similar signal to the brain.
I was thinking similar - if note A is sending 1:2:4:8:16, and you jump up an octive, you're sending 2:4:8:16, right?
Allen Gould I’ve tried using synths with really prominent harmonics at powers of three and you can sort of get tritave equivalence.
Tbh its more due to the nature of harmonics
Yeah, I would think that it is because the most dominant sound (other than the note played) is the second harmonic, which is the octave
Use a square wave for BP. There is no second harmonic there, but there's a strong third.
On consonance: seems like the most likely source for the perception of consonance is at root a function of how sound stimuli is transduced. Frequencies are basically mapped linearly to the surface of the cochlea, and from there, the individual receptor cells' signals are then kind of bundled together into overlapping receptive fields (spectro-temporal receptor fields, if you want the ten cent name), which then bounce things further down the line.
Briefly, neurons, assuming nothing is acting on them, fire at a specific rate (called the resting rate). They can fire faster (this state is called being excited) or slower (called being inhibited). Different things can cause different changes in receptor cells firing rates because they can be "tuned" differently. A given freq can cause no change in one, faster in another, and slower in yet another. These are grouped into receptive fields that overlap each other and because of the different tunings, different locations, and the way that they are grouped, a running ton of information about the stimuli can be delivered to the brain for deciphering, but a very important part (imo) for sound is the physical relationship between the spacial relationships of the receptor cells. Like if you unroll a cochlea (pls ask nicely first), the hair cells on one end are tuned to low frequencies, the other end high frequencies, with the rest spanning the spectrum in between. Knowing that typical hearing can range from around 20 Hz to 20 kHz and that the wider side is the lower frequency side, you could do a pretty good job of pointing out what frequencies are detected where.
Think about what this means in terms of the physics of sound, of how say three harmonics would be mapped versus a pure tone. These relationships are hardwired into us at the most basic levels of the auditory system. There's no having to process (at least in the way of something like conscious thought) that two sounds are say inharmonic because they don't activate the same receptors. Or that they are harmonic because they do hit at least one of the same group of receptors.
I think that you'd probably be pretty happy if you got your hands on a college Sensation and Perception text. You mainly will need to just read the first bit that talks about how exactly neurons work (hint: a lot like penises, unironically) then just jump into the auditory system. It's a very approachable topic in those books.
Would you be so kind as to refer me to some source material or divulgation text? Cheers
@@GuzmanMPetit look for university texts on "sensation and perception". They usually contain all of the cellular level stuff at the beginning (so you can understand how neurons work, things like receptive fields, the difference between transduction and encoding, etc.), then they go through each sensory system. The auditory system will be what's of primary interest to you, but going through all of them will help as vision, touch, and hearing all have significant parallels in their handled by the body.
I suspect there's probably also psychoacoustic texts out there that deal with these topics, but you'll be best equipped for them by going through the more general information first.
I performed Pleiades by Xenakis this summer and I believe the movement Claviers is written completely from this scale. I figured out the pattern while studying the puece, it's nice to finally understand the theory.
My take on the octave equivalency - I guess it's more physical in nature than anything else. It has to do with the frequencies. An octave means double frequency, which is easy to process since the zero points at both frequencies fall at the same time (or if they don't they are spaced at the same time intervals). That means there is no weird dissonance, no overtone or anything, there are just two perfectly locked in frequencies. That's why I think they are perceived as being the same. No other interval does that.
"You can learn tritave equivalency by cultural indoctrination"
*Aldous Huxley wants to know your location*
Hey 12Tone! Microtonality is a topic I've been "into" since ~1977 when I made 10-tone-per-octave equal-tempered guitars, then flutes, as a Science Fair project!
In your video, I think you missed an extremely important point about non-octave tunings, which I'll point out below.
I'm glad you brought up Bohlin-Pierce, and Elaine Walker! It's an absolutely fascinating tuning to say the least! I've discussed it with Heinz Bohlen in comparison with the "88CET" (88-cent [per step] equal-temperament) tuning I discovered around 1988 (just a coincidence). See soundcloud.com/mr88cet/sets/88cet-lecture-demo-gary-morrison-june-2001. 88CET is also a "non-octave tuning" -- a tuning in which no two pitches are exactly an octave apart. In fact, it turns out that these two tunings are related in another way: As Brian McLaren was prompt to point out, Bohlen-Pierce is close to every fifth step of 41-tone-per-octave equal-temperament, and 88CET is close to every third step of 41-tone-per-octave equal-temperament. (12 * 100 * 5/41 = 146.3, and 12 * 100 * 3/41 = 87.8)
Anyway, the point you may have missed about non-octave tunings:
One might imagine that proponents of non-octave tunings are “in denial” about the importance of octave-equivalence, but that's exactly *not* the case! *Octave equivalence is every bit as important to non-octave tunings as it is to octave-based tunings, but just for the opposite reason* : Octave-equivalency is valuable in octave-based tunings because they allow you to expand a harmony across a wide range of pitches. Octave-equivalency is important to non-octave-based tunings because you *do not get this effect* . Instead, you get something potentially *even more valuable* : *You get an all-new set of harmonies in each octaves' span* !
Using 88CET as an example, since I personally am more familiar with it: Within a single octave, 88CET has no major nor minor thirds. It instead gives you three thirds: Sub-minor (7:6), Neutral (11:9), and Supermajor (9:7). However, in 88CET tuning, while you don't have major nor minor thirds, *you do have quite traditional major and minor 10ths* ! In my SoundCloud demo above, I demonstrated even fairly-chromatic renderings of traditional harmony in 88CET tuning. You just have to voice them in the correct inversion! Definitely recommend you check it out!
This scale sounds like it would work great for someone trying to do Lovecraftian mad piping hahaha.
Or just alien music in general.
Octaves are inherent to frequency. Look at their waves and you see that every other peak of the higher note lines up with every peak of the lower note, and this is why it sounds so resonant that the notes are basically the same. When you do the same with Tritaves only a single peak or trough lines up and it sounds dissonant because of how weak the synchronization is. As you said in the video, if you're going to base music on simple ratios because those ratios sound good, why would you base it on an inherently more complicated ratio?
EDIT: I forgot to say that in an octave, the second peak of the higher note lines up with the trough, so there are 2 points of resonance. This is the main difference between the two ratios the way I see it.
Yeah seems like the whole thing is a thought experiment by non-musicians attempting do the equivalent of reinventing the wheel by making its circumference greater than its diameter times pi. Sure it makes a thing that has a peculiar and unique feel to it, and it's worth doing for sake of discussion, but it's ultimately a case of pushing somethings boundaries so far that it not functional anymore.
@Matthew Morycinski That synchronization (or the lack thereof) is what makes dissonant or consonant sound. The worbling you listen for when tuning an instrument is actually the waves being slightly out of sync with each other. You actually are hearing the difference of the two frequencies, which isn't possible with octaves because that difference is simply the lower note when the ratio is 2:1.
It‘s kinda like numeral Systems with different bases, like the decimal and hexadecimal numeral system. It’s really confusing at first, because it is so unfamiliar, but once you grasp the basic concept, it really makes sense. Here, it‘s like our normal system is based on the 7, and then we have to rethink everything to the base of 9. Right?
I think the reason people tend to hear octaves as the same is because the frequencies of two adjacent octaves have a ratio of 2:1. That’s about the simplest way to compare frequencies for our ears and brains.
woah that stick men song is so cool, and really really interesting. It sounds so 80s pop-tune like, but at the same time, it sounds like a modern avant garde microtonal song, which I guess it is when you think about it critically. Thanks for the song link, it's opened my ears a bit more to the wackiness of microtonality.
So what I learned from this is
The Joke in Red Dwarf about Holly inventing two new notes -H and J is actually very accurate.
Triangles will have four sides, pianos will be the length of zebra crossings...
@@AdamKnappDoesMovies course, women will have to be banned from playing the cello.
Yo, I've been watching your channel for a while, and I'm proud of you for two reasons! I'm proud that you finally achieved this goal of yours, and also the fact that this video had the best transition into a sponsor shoutout yet.
When you drew the Battle Toad for "the hardest thing" I lost my shit.
And now I'm a subscriber.
Excellent! I recently got a quantiser module that has a Bohlen-Pearce option along with several other alternative tunings, and I’ve done a bit of reading and listening about it, but your explanations are always clear and inspiring. Now I really need to start exploring it in my own music!
10:49 the hardest thing I've ever learned *draws the Battletoads logo*
Young 12tone: *exists*
2 microwave bois: imma end this mans whole career.
this is so cool it has inspired me to make a song in this scale
and just like get
_real weird with it_
I don’t know how many years I got left in this earth
Got a link?
@@rickstevens1167 not yet
Ique how about now?
While I was listening to Stick Men I imagined opening my eyes to see a bright light and then someone whispers in my ear “welcome back to life and to the year 2352”.
I want to seriously thank you.. your videos go a very long way not in teaching music but teaching people how to think about music.. and that's a rare thing
I was most curious about why 2 different microwave engineers independently made/found the same crappy musical scale.
Yeh that needed some comment or explanation. If there is one.
Im glad im not the only who thought it sounded wayy too wack to be enjoyable.
Probably because frequency and harmonic analysis is a keystone of RF engineering. A disproportionate number of microwave engineers also seem to be music nerds so it’s not hard to imagine a bored RF engineer tooling around with a ten input frequency mixer and thinking “hey, what if we built a scale from ten frequencies”.
@@OnboardG1 Can confirm as electrical engineering student. There are a lot of current / former musicians. Pretty much everything we learn past the basic maths/physics/computer coursework has to do with frequencies. There are alot of weird theoretical types as well.
Louis Stubbolo Digital Hardware here. At least half of the EEs at my office are also musicians.
Subscribed after watching the whole video, but you had me intrigued at the beginning from the notion of a twice-identified-by-physicists scale that has taken you-despite your background in music theory-4 YEARS to become comfortable describing this in a concise video.
Cheers. Looking forward to checking out your other videos!! 🎵👍👍🎶
I love your attempt at pronouncing Kees van Prooijen 😂 For an English-speaker, it was a pretty good attempt though ;)
If you're curious: it's kinda like Case vahn Pro-yen
Oh man I love this and I'm glad you did a video on it
So many of the 2 note intervals sound really good but a lot of the times a third note is added it gets really dissonant
I think that's because you aren't used to it. I think they sound great, but I've been exposed to a lot of supposedly dissonant music from a young age.
@@finnkenyon1289 Indeed. I don't think I've ever listened to this scale before but I'm listening to Stick Men right now and it sounds a lot less dissonant than some other stuff I like such as Scriabin. But then I also thought that inversion example he showed actually did sound like the same chord to me so I may be weird.
Probably because a tritone with the ratio 7:5 appears in most of the 3-note chords
William Sethares' "Tuning Spectrum Scale" is a good read regarding octave equivalency. He argues that the phenomenon is due to overtone structure using Balinese Gamelan as a jumping off point. Definitely worth checking out!
I've been waiting for you to do a video on this
It would make sense to me that the octave (or something similar) would be universal. Since it is ~ a doubling (or halving) of the Hz, starting and ending on the same note feels a lot like a complete revolution
When I started listening to that song it immediately made me think of Björk.
Dazzyls except it wasn’t beautiful
what song?
Omg thanks for turning me on to Elaine Walker and Stick Men! This is some seriously awesome stuff!
you say so concisely and well stated correctly as I see it. Thank you alot.
I quit relating intervals to the major scale a long time ago. It's much more easy to see what's really going on when you relate directly to the chromatic scale rather than cross-referencing through the major which is the standard practice for all who still read music and are familiar with its over-complicated antiquated theory.
Super duper awesome! Thanks for sharing!
I believe you forgot a word in the title
technically a letter but also a word
What word are you thinking of?
... sorry...
"of"
I have enough to work with inside equal temperment... however, this is really interesting- will have to watch a few more times before I might be able to really grasp it. thanks!
I hope to see the day when music becomes so boundless that we have over a 1000 different tones
your little drawings that illustrate what you’re saying...so amusing!
Now Playing: Concerto for Microwave and Orchestra in J-narrow, by Bohlen and Pierce.
in terms of inversion, I think it's equally valid to take the otonal/utonal approach to retain chord size equivalence between "major" and "minor".
4:5:6 becomes 1/4 : 1/5 : 1/6
3:5:7 becomes 1/3 : 1/5 : 1/7
The latter of both being divided in the opposite direction (forward instead of backwards) to represent the ratios of each interval in decimal. This also parallels 12tet in that all you're doing to build a minor chord on a note instead of a major chord is flatting the third.
Can you do a video on how different “music cultures” notate music? Because that seems like it would be incredibly interesting
Lots of things I love about this channel, but today I'm going to focus on the geeky easter eggs in the drawnings. Like the Periodic Table entry for technetium when something is rare. Today it was the canopied penny farthing bicycle to represent the number 6. The only reason I get that reference is because that bicycle shows up on the GURPS Prisoner worldbook for the SJGames roleplaying game. I saw the original series but never noticed the bicycle, so for me, this is a very deep cut and so I get a big kick out of it. Thanks!
I can’t tell if Stickman sounds so eerie because of the tritave scale or because it’s a strange song to begin with. Would love to hear an example of a different style with this scale. Cool concept though.
It sounds so amazing and beautiful
That song is the most unsettling song I’ve ever heard. I definitely want to find a way to use this at some point in the future
This is over my head. I will be back in four years.
I've never been formally trained in music theory, but I actually mostly understood most of what you said here! Either you're really good at explaining this stuff, or I'm just naturally a music genius..... Eh it's probably just you :P
Also, as a chemistry nerd, I love how you used hydrogen when you said "most common". Little things like that really add a lot to these videos
Are we sure Stick Men isn't using some octaves in the drones? If not, I may like this scale more than I thought during the 12tone video. It may be some harmonics, or my ears filling in octaves, of course, but that's half the fun.
I love that you used The Prisoner's penny-farthing when you said 6!
i am a jazz and classical composition student, and i have absolutely no idea what is happening in this video. you are a genius
I gotta admit, when I first listened to Stick Men, the first thing that popped into mind was some of Bjork's music.
I really love BP i made like, lots of things and its like, really beautiful ♥️
I experimented with scales based on the tritave when I was younger. This was before MIDI, but I managed to make a PC play a sample of this scale. And when I heard it ... it was hideous! Then and there, I put aside my calculations and gave up on the tritave.
Fm6 and Dø7 are differentiated only by inversion, I think that lends itself to the argument that inversions as the same chord is somewhat enculturated
What a great video (as usual) - thank you! A few thoughts on octave equivalency from the perspectives of physics and psychology:
I would argue there's a really good mathematical/physical reason for octave equivalency. It's about the nature of wave phenomena and modes (of a vibrating medium) - stable phenomena and repeating patterns occur when you have integer multiples of wavelengths or frequencies (meaning this holds true both in the "higher" and the "lower" direction for any given frequency or wavelength). There is something that "stays the same" with integer multiples of a frequency or wavelength which doesn't stay the same when you have non-integer multiples/fractions. An integer multiple of an audio frequency is a higher octave of that tone, an integer multiple of an audio wavelength is a lower octave.
So you have patterns (mathematically describable) that re-occur with octave-relations, making them stand out quite distinctly from non-octave relations ... not just for our ears - also e.g. for small granules you put on top of a plate on a speaker and anything affected by (patterns in) those waves.
Now let's think about how we come into contact with pitch(es), what's the most salient experience we have with them, starting even before we're born? - Voices. For rather obvious evolutionary reasons, we are especially sensitive to the human voice. Not only is it our major mode of inter-personal communication, we also have such a direct relationship to our voice that it allows us to *feel* pitch (the vibrations) quite distinctly and intimately, even if it isn't loud enough to shake the building you're in. We listen to voices, experiment with our own - and thus get to feel (however unconsciously) the speed (and intensity) of vibrations in pitches.
This also means that the patterns in how vocalized pitches vibrate and resonate your body will have distinct similarities for octaves that are not present with non-integer multiples of frequency / wavelength - those similarities are felt, making the mathematically/physically special octave relationship directly experienceable. Together, the objectively similar patterns created by wave phenomena with integer multiple/division relations between frequencies/wavelengths and the direct experience we are afforded of these can account for the (near?) universality of the special status of octaves across cultures.
Pedantic point: an octave is not just any integer multiple, but specifically multiplication by 2. Multiple octave jumps show up as powers of 2. Other multiples are not octaves, specifically multiplying by 3 gives you something else.
Excellent. I learned a lot
I know literally nothing about music theory but these videos are still interesting
Like 90% of these videos go right over my head but it's fine
Literally was coming up with the concept of scales that don't repeat by octaves but by other intervals. aaaaaaaaaand it's already been done.
halfway through and I'm lost. I will try this video again when I am better rested
that was a lot to take in. cool!
I had to slow the video down to half the speed so I wouldn't pause every four seconds
Yesss I'm so here for more microtonal theory videos
This felt like a vihart video
Man, now that my mind has been completely overwhelmed in a very entertaining way, I badly need me some SCHFITY-FIVE!!!
Glad to see the BP scale getting more attention. One of my personal favorite pieces in BP tuning is "I Know of No Geometry" by Richard Boulanger:
soundcloud.com/boulangerlabs/i-know-of-no-geometry-movement-3
"the first 8 notes of the C major scale"
*plays the A major scale*
Music theory reminds me of Maths in Goedel's Theorem - it can be complete or consistent, but not both.
Cultures probably develop octave equivalence due to the fact that one octave up is double the frequency. Doubling the frequency is pretty fundamental even if early cultures didnt specifically realize it. If you have a flute or pipe or something to blow into to make music, without touching any holes or anything sound forms standing waves and the only stable ones are the fundamental, double the fundamental, triple, and so on. Early cultures could have viewed these, since they are played the same, as the same note or part of some family of notes.
double the frequency could also naturally interact with our ear in a similar way as the fundamental since the waves hit our ear at the same frequency as the fundamental, just that the double then also hits it again in between the fundamental's waves. So up one octave interacts with your ear the same but with a bit more in between, that be could why the ear hears them as similar. Not to mention that instruments also often have their other harmonics at multiples of the fundamental frequency which means that even the fundamental note already teases your ear with the note that is one octave higher, so when you hear the higher note it is already familiar and associated with the lower
5:04 And now our scale is really starting to take shape. _Draws a Ditto_
A 12 tone video about a 13 step scale for teens...
Not really but I like the pun.
I listened to the song and after a little more than three minutes in, my body started to randomly wince
Octaves are primal, wired in. More people can recognize an octave than can identify any other interval.
One reason octave equivalence is so common worldwide is that most instruments’ overtones follow the harmonic series, so notes that match the harmonics of other notes are more consonant. With non-harmonic instruments, such as metallic instruments, the consonant notes don’t necessarily line up at the octave. Check out gamelan music for illustration of this, it’s non octave based, yet consonant due to the timbre of the instruments. William Sethares has written at length about this, it’s pretty interesting.
The harmonic series relates to this and why we use the intervals we do
Says the word "Sacrifice"
Draws a Pentagram with candles
LMAO
Says "model", draws a Feynman diagram
So one of the reasons octave equivalency works so well is because of harmonics. Any time you play a note on a string, a note exactly an octave up also sounds along with all of its harmonics. You also get a note an octave up from a perfect fifth, which would be the tritave. But as each higher harmonic drops in volume, it's not as pronounced as the octave. However, that's strings. On many wind instruments, odd harmonics tend to have a lot more amplitude than the even ones. Which means the tritave will be louder than the octave. So on wind instruments, tritave equivalence might actually feel more natural. So if anyone has a trombone and wants to experiment with weird scale, I'd be curious to know what came out of it
Slightly reminiscent of the Alpha, Beta, and Gamma Scales by Wendy Carlos which split the fifth into 9, 11, and 20 steps respectively but which all lack a perfect octave (I believe she uses these tunings on her Beauty In The Beast album). However these are perhaps not as mind breaking as Bohlen-Pierce as they still support traditional triads.
And I see of course you already have a video about those :D
Sticking with the model I think is the simplest
*Proceeds to draw Feynman Diagram*
my favorite note, J!
Being a musician and new Biggest Ideas In the Universe series fan- 12Tone has helped me appreciate MASERS all the more. I 12Tone has helped me understand why, in my depression 15 years ago I wanted to move music notation to "decades" 4:00. A ten unit system. Its more scientific!