Some additional thoughts/corrections: 1) You can find Newton's essay here: cudl.lib.cam.ac.uk/view/MS-ADD-04000/288 and his tuning calculations here: cudl.lib.cam.ac.uk/view/MS-ADD-04000/221 You can also find a transcription of the essay at the bottom of this paper: www.academia.edu/36141785/Isaac_Newton_and_the_mystery_of_the_major_sixth_a_transcription_of_his_manuscript_Of_Musick_with_commentary 2) If you're curious, the scale Newton thinks is just as usable as Lydian is what we would today call Aeolian Dominant, or Mixolydian b6. Melodic minor is also on his list, and it's his second-favorite of the non-Greek Mode options, but not enough that he's willing to argue for it over Lydian. 3) Typically, the breakdown of just intonation ratios goes the other way, starting with the 1:2 octave and dividing it into smaller chunks, but like I said Newton was very interested in patterns of different kinds of half-steps, so showing a bottom-up approach seemed appropriate. 4) I should note that, in practice, most music of the era was made with a compromise system called meantone tuning, not directly on just intonation. However, meantone was specifically viewed and developed _as_ a compromise, not as its own alternate philosophy of consonance: It existed specifically to solve practical issues in the implementation of the idealized principles of just intonation. Equal temperament also started that way, but I would argue that in modern practice it has genuinely developed into a self-contained philosophy in a way that, to the best of my knowledge, meantone never did.

@dibblethwaite

8 ай бұрын

12EDO was around in Europe well before Mersenne. Vincenzo Galilei, Galileo's father, talks about it in his book Della musica antica et della mederna in 1581 so I don't find it surprising that Newton was aware of it. Vincenzo was a lutenist and argued that equal temperament was the only sensible way to tune a fretted instrument. That's assuming that the frets go straight across the fingerboard I guess.

@stephenspackman5573

8 ай бұрын

@@dibblethwaite That's interesting-unless I'm confused, the invention of the logarithm is usually credited to Napier, a generation or two later. How was the maths done?

@allekassen

8 ай бұрын

@@stephenspackman5573 It wasn't, it was purely practical -- for a lutenist. Keyboards and woodwinds could have tuned to a 12-tone lute, but stuck to their own systems. And brass were tied to the overtone series, no alternatives possible. You can tune a string instrument to 12EDO by placing a fret every 17th of the length. After 12 frets, you don't arrive at the middle of the string, but you could adjust the action so that the fretted and thus tightnened string would indeed sound the octave at the twelfth fret, and all intervals along the string are equal. It follows that you also have to turn the other strings to a stopped note and not to a harmonic.

@superkillrobot

6 ай бұрын

Out of all the videos on KZread explaining Baroque music and it’s greatest composers, this has given me a much greater understanding of why Baroque music sounds the way it does. There’s usually so much emphasis on the personal lives of the composers and the world they live in yet, rarely any information on the theory they were taught, the context they were taught it in, and how it differs from what we use today. Thank you for such an unexpectedly insightful video!

@nicolenovi4619

5 ай бұрын

​@@dibblethwaitesorry dude u lost me i cant even listen to this

Euler also did some really interesting things with music. Interestingly enough, he wanted to eventually make music a sub-field of math.

As an aside, Turkish music theory actually uses an equal division of the octave into 53 units ("koma") as a measurement of interval size.

OPTICS: the only subject in school my best friend ever truly sucked at. Why? She's blind. She's literal genius and awesome at everything else, but please, anyone, try explaining colour to a friend, even a fully sighted friend. Bet you can't do it without using comparative language (i.e. dark, bright, vivid, etc.). You and I (if you're not blind) have visual context for those words, but you kind of NEED comparative language to describe colour, so if you don't know what the words mean, you CAN'T grasp colour.

@mixenne

8 ай бұрын

Off the top of my head (as a VI person): describe the emotions/feelings each color can evoke, use temperature or textures to represent different colors. Smells or sounds, too. It's difficult, but not impossible. E.g., light blue=warmer/smoother/fluffier, dark blue=colder/rougher, etc.

@ActiveAdvocate1

8 ай бұрын

@@mixenne , I'm also VI, though not totally blind, and that ONLY works in terms of synesthesia, which is the describing of one sense by way of another (i.e. "Your orange shirt is very loud"). It still can't give her an impression of what the colour LOOKS like. And yes we have tried that route.

@GrimAxel

8 ай бұрын

@@ActiveAdvocate1 Yeah, I can only really see that working in terms of "This place has more infrared radiation going on than anywhere else" or similar because there it's *literally* warmer than somewhere else. It's a way to describe "brightness" in terms of feelability, but it's experienced in such a way that only the most *massive* of differences would be understandable. And it doesn't even cover how things can feel bright in different ways.

@mevinkoser8446

8 ай бұрын

A chakra chart would be a great reference. 7 Chakras are assigned their respective, affirmations, colors, emotions, music notes, elements, crystals, ect.

@ActiveAdvocate1

8 ай бұрын

@@mevinkoser8446, yes, and I can tell her that the Muladhara Chakra is red and relates to the Earth, to survival instinct, and to fear as its primary blocker, but she still couldn't visualize red, you know what I mean? PS: I got all A's in Eastern Philosophy in university. So I agree with you, and I LOVE that stuff, though I especially hate the New the appropriation of already marginalized religions by was of Capitalist colonialism.

So much great creativity can come from lockdowns. But Newton's Annus Mirabilis and Bo Burnham's Inside are the top two IMO.

@cartilagehead6326

8 ай бұрын

yes tell us more about Newton’s annus…

@beatrixwickson8477

8 ай бұрын

@@cartilagehead6326 Well, Newton thought it was "Great!" because he had his most creative burst of inspiration. It's when he invented the Great Plague of London and the Great Fire of London. Which do sound pretty great. No wonder he thought it was a great year. Or maybe he liked it because 1666 is the only year to contain each Roman numeral once in descending order (1000(M)+500(D)+100(C)+50(L)+10(X)+5(V)+1(I) = 1666).

@micp4130

8 ай бұрын

Mary Shelley's Frankenstein should also be included on that list.

@treyebillups8602

8 ай бұрын

@@beatrixwickson8477 i think cartilagehead was making a joke about how "annus" looks like "anus"

@beatrixwickson8477

8 ай бұрын

@@treyebillups8602 yes, that was my interpretation also. Purposely failing to acknowledge it while talking nonsense about Newton inventing the plague etc was my joke. Though it is true about the Roman numeral thing, it's just part of the joke also. Now, as Mark Twain compared it to a frog dissection, this dissected joke has now been killed in the process.

Im a programmer and love math. It is interesting how much applies to music. Math and music are deeply connected

Well, we've established that 12tone has watched both The Prisoner (4:10) and Rocky & Bullwinkle (5:47)

@annamatic85

8 ай бұрын

And Phineas and Ferb 😊

@slolerner7349

8 ай бұрын

A true renaissance man!

really lovely how you say "an instrument" and drew a theremin at 0:57. that puppy is definitely An Instrument

A lot of the folk music in Newton's day probably used the mixolydian scale (ionian and dorian being very common also, aeolian probably less so), so whatever abstract reasons he had for preferring it, he was also justifying a preference for something familiar.

This was really insightful. It's a bit different from the usual videos, but I really enjoyed it. I'd love to see more like this.

The grid pattern Newton put the notes into is an example of a "tonnetz", which is a word that can be searched on to bring up all sorts of interesting resources.

Recall that the modern music theory of Turkish makam uses a system of 53 equal-temperament. While I don't think Western music would have arrived at the same makam/scales, could you imagine if history took another path and Western music theory used the same underlying framework of tuning?

I love how the drawing of the doubt face resembles Cilian Murphy's role as Oppenheimer.

Thank you for putting so much thought and effort into this- so worth it for us!

I always learn so much from your videos. Also, I love that you used the T-Shirt shape when you referenced patterns :)

12:00 I think he means that the half step between the 6 and b7 is equally spaced between the fifth and the octave, instead of having it be next to the fifth (b6) or next to the octave (major 7th).

@althealligator1467

8 ай бұрын

Except that's the case for both dorian and mixolydian as they both en with 5-6-b7-1, so it wouldn't explain why he prefers mixolydian over dorian. It does seem that he was talking about the semitone in the first part of the scale, between 1 and 5.

Love the 'phenomenon' Mahna Mahna joke

new anxiety unlocked, my half-written drafts becoming subject to being analysed in future

@bluesmcgroove

8 ай бұрын

I don’t have that worry because I’d have to somehow be famous for that to matter XD

@Fire_Axus

8 ай бұрын

@@bluesmcgroove same, they are just too sensitive

@kaitlyn__L

8 ай бұрын

I love how he’s got “elaborate on later” and “I’ll fill in the rest some other time” sections

HE USED THE HAT FOR “is consistent with the overall pattern” (what a nerd)

@rmdodsonbills

8 ай бұрын

The Easter Eggs is one of my favorite parts and yes, they indicated a deep nerdery that I appreciate and identify with :) Like the Ma-na-ma-na muppet to go with the word "phenomenon."

Fabulous stuff. I knew of Newton's musical dabblings, but I didn't know the details! So, thank you for giving them the 12tone rundown. A pity there wasn't a second plague to squeeze out his ideas on how to change scales mid song! And as for 11:33...It could be that by "the half step being more central", he means more central to the scale/ to the octave (not the root and fifth). And by "greater distance from it", the 'it' could mean the root (not the fifth). But I'm just trying to make it work, and it absolutely sounds like a confusing contradiction, exactly how you interpreted it! (and contrary to his other thought patterns/ justifications/ values, ie regarding the importance of how things relate to the fifth)

For my final quarterly project in science we get to make a project about any one of our interests, with the idea being for us to do something we're passionate about at the end of the year. The only other criterions are that we 1. connect it back to science in some way, and 2. do a presentation with literally anything other than a slide show. For my topic, I chose to talk about tuning and temperament, more specifically the evolution of it. I found this video a while back but just stumbled upon it again while looking at one of your other videos about temperament, and I wanted to say thank you for giving me another source to talk about music with. I really enjoy your videos in general, and have been watching them for a while at this point, and the fact that I now get to use your video as an additional source for my project is really cool. It also means I get to tie in both Pythagorean AND Einstein, which will at least be familiar names to the non-musicians in my class that have to hear this, lmao.

For the inconsistencies and stuff, all I know is that when I was in college, if I had to write an essay about something outside of my area of interest/expertise, it would definitely be kinda poorly scrapped together with a healthy dose of bs-ing. Heck even on things I cared about there still would be things that aren’t actually correct

this video answers every music theory question i didnt know i had

i love you 12 tone youve taught me so much

This was a fascinating video! Newtons musings mirror my own in some ways which is gratifying. Thanks for your work!

Isaac "M.F." Newton. One of my favorite historical wizards. The more i learn about him the more impossible his life feels.

Oh, do I know the temptation of having a nice play with THAT. I'm not surprised he moved on, but it's nice to see someone good at that messing about with it the same way I did, only badly. And no, I got nowhere near as far as him, I don't have that relationship with math or music.

"Overall pattern"... well played!

(*puts on PhD opinionated hat) I think that if you want to see what musical thought in the mid 17th century looks like, you'd look to the Norths. Francis North wrote and published a book on acoustics, and Roger North wrote extensively about music in his diaries from the 1680s or so up until the 1730s. But what a fun video! I was expecting the answer to be "Newton didn't write about acoustics, he mostly looked at optics" but it being an unpublished plague-year diversion absolutely makes sense.

The original apple music

@TriplicateTrey

8 ай бұрын

heh

Non-mathematician here, just wanted to express my appreciation for the monotile at 3:55 😀

At 14:48, when you say “Newton himself”… is that Kazuki Tomokawa you drew there? If so, awesome!

9:53 The middle of the two scales reminds me of the Ballad of the Wind Fish from Link's Awakening

Love it! I really like this approach of systematically building everything up from the fundamentals rather than taking the Major scale for granted as the starting point for everything. Maybe that's Newton, maybe it's his time period, I don't know. Can anybody point me towards good music theory resources that do it this way? Thanks for a great vid 12Tone!

Fascinating. Thank you very much. What an astounding genius Newton was

It can be really interesting sometimes when mathematical and scientific rigger wander into the arts

@alisaurus4224

8 ай бұрын

Rigor?

@oscargill423

8 ай бұрын

Rigour?

@tegansutherland7299

8 ай бұрын

Music WASN'T an art at this time. It was either math (and therefore worthy studying) or a craft (and dismissible). Practical musical knowledge is manual labor; theory and acoustics requires academic study and probably Latin. (Mersennes, Descartes, and Vincenzo Galilei wrote their musical treatises in Latin, for example)

Just a dumb observation, which I’m sure I’m not the originator of, the frequency ratio between notes is 1:12th root of 2. Obviously that is related to the number of notes in an octave. I propose that it is the divisibility of 12 that makes it such a harmonically useful number of notes.

@kaitlyn__L

8 ай бұрын

Yep! You can find many conversations about which other highly divisible numbers work, because it’s not just the total number of divisions but also the prime numbers involved in those other fundamental ratios than the octave (which Newton focused on as discussed). So you want a combination of the two factors, and 12 is the smallest number which provides both. Plenty of alternatives with more exist beyond the ones Newton mentions with different harmonic priorities, but none smaller than 12 to my knowledge. I remember when I first stumbled upon those mathematical discussions about octave divisions, and realised this type of maths nerd exists in every field (and also accepted that I am one).

I kinda want to hear someone playing with 53-tone equal temperament now, Although I imagine it'd be quite hard to play with that many notes. Unless I suppose you found some way to simplify it, E.G. an instrument with only one scale playable, but that can be easily shifted into other scales somehow.

3:30 I did it before the suggestion lol Was kinda close Got 3 and 4 swapped, which in hindsight makes sense Got 7 and b7 swapped, which in hindsight makes sense

Ike Newton was definitely one of us. He was on the spectrum, and his spectral brain was a wonder. He lived in a time when alchemy, astrology, and religion were given equal footing to evidence-based science, and he relied more on theory than modern scientists would, but he was therefore free of the constraints of modern science, and free to think outside the box. Therefore, some of his ideas seem silly, but some of his ideas changed the world profoundly for the better.

Hi man! Can you do harmonic analisys, about The pink panther? Thanks! 🙂

I mean aren't the notations for calculus similiar to the music notation? Example: derivatives => F(x) f(x) f'(x) compared to music => C c c'

I really like the part where "less good" is represented with scrappy-doo. 12/12

The problem with all theories based on a consonance VS dissonance dichotomy is that this does not at all explain where the emotional pay off come from when emotion is the reason for musics existence. A whole tone is very dissonant, but sounds happy, a tritone is actually quite consonant, but sounds disturbing so there is something MORE to each interval that has absolutely nothing to do with dissonance or consonance. This is the "hard problem" of music which for centuries has been strenuously avoided by nearly all persons. We can not explain music objectively because music is about subjective experience, if we stick to objective explanations then we have no explanation by definition! That there is no explanation as explanation is unsatisfactory. Further its cowardice caste as if it were a virtue, we should not even try to explain anything from the subjective world then. Its said that subjective experience differs from person to person and is only inside the brain so can't be observed. This is said as if there were no such thing as facial expression or tone of voice or as if brain scans did not exist. If I put flame to skin the subjective response is remarkably similar person to person, or food to mouth after hunger, people in the same circumstance tend to exhibit the same facial expressions and tones of voice so it is NOT true that we can say nothing about subjective experience, which after all is the front line of our awareness including of our objective awareness, we always have subjective feelings connected with objective thoughts, its impossible to extricate one from the other.

Really cool episode.

I wish you wouldn't doodle so much but draw bigger Music Staff-Sheets. I liked your drawing of Intervals. I like when you transpose songs onto the Music Staff-Sheets I just want the Song Maps

Thank you.

0:12 sneak peak?

This might be a stupid question, but how did Newton, and the Greek philosophers 2000 years earlier for that matter, actually measure musical pitch?

@tegansutherland7299

8 ай бұрын

I suspect it had to do with lengths of string. the Greek monochord was how a lot of the ratios were discovered, and Newton did experiments with sound that involved plucking strings to match the frequency of a fly buzzing, for example. Roger North discusses the "pulses" of concordant or discordant intervals, and even built into that word are strings! Also organ pipes were usually measure in feet and inches, so inches of string would be a natural comparison point too.

@cibbantwist

8 ай бұрын

@@tegansutherland7299 Thanks! That makes a lot of sense.

@wr2382

8 ай бұрын

@@cibbantwist Galileo Galilei's father was a musician and musical theorist who performed experiments relating pitch to the tension and length of of strings. This would have been about 80 years before Newton's time. I'm pretty sure his experimental set-up involved stretching strings either vertically or horizontally over a bridge and then suspending weights from the free end to change the tension on the strings. I'm pretty sure that he would not have actually measured absolute pitch but, instead, measured relative pitch by ear as he changed string length and tension. So, he would be doing things like seeing how much he had to increase the tension on a string in order to increase the pitch by a third, a fifth, an octave, etc.

@cibbantwist

8 ай бұрын

@@wr2382 Thanks! That makes a lot of sense.

We already got a Newton of music anyway: Brian May

I'm once again asking if you'd like to, one day, do the analysis of bittersweet symphony @12tone. I feel like it's not very likely you'll answer, even if it's a no...

@rmdodsonbills

8 ай бұрын

I don't see him commenting to others' comments on his videos. I can't think of a single exception, though I won't say it's never. However, I believe getting to suggest video topics is a perk of Patreon-age.

@gwennaneliezer8490

8 ай бұрын

@@rmdodsonbills ok ! Thanks ^^

@rmdodsonbills

8 ай бұрын

De nada.

@karawethan

8 ай бұрын

Why? What is there to analyze?

@gwennaneliezer8490

8 ай бұрын

@@karawethan the violin sample has a story and might use some analysis in terms of theory. And for the rest, I'm interested in what 12tone would find. For instance, I didn't expect him to analyse that much from Fast Car - Tracey Chapman, yet.... But if there's nothing to analyse, having him say no is a way to know it

babe wake up new 12tone video just dropped

@gordonstearns2232

8 ай бұрын

Is this gonna be like 'first' from 15 years ago where every video has this in the comments section?

@starlesscitiess

8 ай бұрын

@@gordonstearns2232 this one also has a first. also im just genuinely excited about 12tone posting lol

@Mr.Delirious1756

8 ай бұрын

​@@gordonstearns2232I think it'll be along side it. "First" still happens regularly

@Lishtenbird

8 ай бұрын

​@@gordonstearns2232No, no, it's different. "First" is attention-seeking through posting the most irrelevant and pointless comment but as fast as possible, so it's about establishing superiority. While this is attention-seeking through posting the most irrelevant and pointless comment but which is extremely recognizable, so it's about belonging to the herd. An absolutely vital difference, as you can see.

@d4nd31o

8 ай бұрын

​@Lishtenbird To expand on this. The second option is, if I'm not at first mistaken, the cringer of the two magnitudaly. However, the astute reader will notice, being first and mistaken inevitably guarantees another few members of the herd have >also In practical terms, better to use neither and/or nor.

Likes Mixolydian and Dorian: Newton likes jazz.

Please make a vid on iris by the goo goo dolls

I'm totally stealing the phenomenon/mahna mahna rhyme for a song someday!

It doesn't really surprise me that someone with a brain like his would have turned some level of attention to music

4:08 is this a sly "The Prisoner" reference I spy....

Cool

“Phenomenon” draws “mana mana” muppet

@akmadsen

8 ай бұрын

I was laughing so hard because I literally can't hear the word "phenomenon" without thinking about that song. Just in case someone doesn't get the reference-or just needs a good laugh-look up Sandra Bullock's appearance on the Muppet Show.

7:52 accidental Skyrim theme

4:35 yeah, he wasn't omniscient. Luckily, since Newton's time, we've become so accustomed to songs like Somewhere Over the Rainbow, that large melodic leaps to higher notes no longer aurally blind us.😭🤣🤣🤣

@SingularlyNaked

8 ай бұрын

Rainbow is a great show-off song for the musical saw because of that leap! (I'm looking at you, Mark Jaster at the Maryland Renaissance Festival.)

@AlRoderick

8 ай бұрын

In a lot of ways, I think over the rainbow kind of proves Newton's point. Those big jumps are only used as a major decorative figure, they're like a big stunt, most of the song has relatively small interval jumps and little staircase figures. It takes someone like a Judy Garland to pull those off and stick the landing and even she only does it like four times in the whole piece. Although evidence from the rest of his life suggests that if Isaac Newton had been a contemporary of the wizard of Oz, he would have been a real friend of Dorothy.

Interesting.

Man, Newton was just FULL of hot takes. Maybes that's why we still talk about him.

Haha, the ranking of the other 6 modes is tedious. Modern mathematicians would say 'trivial', same vibe.

@kaitlyn__L

8 ай бұрын

Mathematician speak for “draw the rest of the (___)ing owl”

I thought he was saying that the fifth was farther from the root in Mixolydian mode but that also doesn't appear to be the case. Big old ¯\_(ツ)_/¯

100 pts for Interrupting Cow.

Damn I wish he would have annexed that discourse

Huh. I just noticed the musical number-line doesn't have a zero

Newton: It would be too tedious Also Newton: Does tedious math

Euler was more fun at parties (probably)

So, even Newton ignored Locrian … ?

Bubba Wholestep

"century"

"Not that important" *writes his logo* Come on Corey don't put yourself down like that

>Newton says Mixolydian is best INCREDIBLY BASED 17TH CENTURY MAN

idk him at all actually, never really crossed paths

No TOOL?

5 is too low.

Please do One - Metallica.

Damn, a melody consisting of nothing but octaves is bad?? Nobody tell Sam Smith.

Technically, Newton didn't figure out gravity so much as he came up with a theory that worked in a lot of circumstances. Einstein is the one that really took a bite out of the gravity cake. We still don't know exactly how it works, we just know mostly how it works.

Isaac Newton died a virgin? No, he was just gay for music.

Isaac Newton didn't figure out how gravity works. Newtonian gravity is not the currently accepted model.

@Pablo360able

8 ай бұрын

It's an accurate description on classical scales, and the principle of universal gravitation was the real breakthrough in terms of understanding celestial bodies.

@rmdodsonbills

8 ай бұрын

It's a *very* good approximation of the accepted model. Given that we can't seem to settle on whether it's a force or a consequence of geometry, I'd say we haven't figured out how gravity works either.

@SingularlyNaked

8 ай бұрын

It absolutely is *a* currently accepted model. Interplanetary spacecraft, for instance, use Newtonian gravitation to plot their courses. Remember, "All models are wrong, but some are useful."

Bro literally invented 12 tet during a pandemic and abandoned it because it was too simple for him.

Maybe he's more of "a father" of calculus, rather than "the father" of calculus.

First

@scottmatznick3140

8 ай бұрын

Better luck next time

me fost

@scottmatznick3140

8 ай бұрын

Yu forth

So conservative "music theorists" have been hating on the tritone, restricting what is "acceptable" for "proper" music, demanding major over minor at all times, and thinking of any dissonance as a problem since Newton's time. I'm sorry, but Newton's "music theory" is entirely philosophy, culture, and bending and scraping to the establishment. Why do I keep thinking of Shapiro's constant ranting against hip-hop with an appeal to musical theory to make it seems like he knows what he is talking about? (Side note: I have the same opinion on his "natural magic" vs. actual occultism.)

@dizzydaisy909

8 ай бұрын

yes, it is! it's a record of the times that this guy lived in, parroting what he learned in school and trying to apply new things to it because he was bored. nobody's saying this is some masterpiece; this is a fascinating amount of insight to this strange era, with its' strange culture, and a strange man who lived in it.

@tegansutherland7299

8 ай бұрын

@@dizzydaisy909 Its also useful because we don't have a lot of existing ENGLISH works about musical thought at this time. The great diarists (Pepys, Evelyn, and the like) will discuss it, but they didn't publish. Most of the acoustical work was coming out of continental Europe.