6 Levels of MICROTONES (in Video Game Music)

  Рет қаралды 215,193

Cadence Hira

Cadence Hira

Күн бұрын

Пікірлер: 865
@CadenceHira
@CadenceHira 9 ай бұрын
Clarifications: 1. As a few people have pointed out, alternate 12-TET tunings (i.e. A=432) are NOT commonly considered to be microtonal! I included it in this video for 3 main reasons: a) In the context of Bloodstained, where some of tracks are in 440 and some are in 432, it is possible to hear the microtonal discrepancy in the tuning between tracks that crossfade into each other. I would consider this usage microtonal! b) People with absolute pitch are able to hear the difference between different tunings out of context, and that is at least worth addressing as the weakest example of "microtonality" (432 relative to internal sense of 440). and c) culturally in the "west", 440 is ubiquitous and is ALMOST ALWAYS bundled with 12-TET. the most common exceptions include: orchestra tunings, i.e. Japanese orchestras tune to 442 iirc, and the 432 tuning in things like Bloodstained, as well as sample rate differences for the sake of timbre (as was the case for Redbone). I felt that talking about non-440 tunings as "Level 1" was important to the context of microtonality in a cultural sense, as common western workspaces don't provide intuitive, robust ways of breaking out of the 440 12-TET frequencies. If you still disagree with 440/432/tuning being discussed in a microtonality video, that is completely ok! Discourse and discussion is music theory is GOOD and is what drives the development of the ever-changing definitions of concepts, as it's only retrospective analysis of ever-changing music and cultural contexts. 2. Arthur Morgan was NOT building that house with his buddies, it was actually John Marston. I didn't play RDR2 and instead read a brief synopsis on that part of the game, that is my bad lol.
@made.online2149
@made.online2149 9 ай бұрын
a. I would not consider that usage microtonal!
@CadenceHira
@CadenceHira 9 ай бұрын
@@made.online2149 totally fine :D
@familiarstranger9617
@familiarstranger9617 9 ай бұрын
I'm a bit sad you didn't talk about 31EDO
@CadenceHira
@CadenceHira 9 ай бұрын
@@familiarstranger9617 couldn't find any 31-EDO tunes D:
@familiarstranger9617
@familiarstranger9617 9 ай бұрын
@@CadenceHira Zheanna Erose and Levi McClain have some videos talking about it but I've not found anything about peices of music in 31EDO present throughout modren or ancient history
@g_in_garage
@g_in_garage 9 ай бұрын
actually, it isn't just k.k. cruising! all of k.k.'s whistling is sharp, in all of his songs. they changed it in new horizons to be the same as his singing and guitar, so it isn't clear if the microtonal whistling was by design, or a mistake that they corrected.
@BenthovenMusic
@BenthovenMusic 9 ай бұрын
I'm so glad I wasn't the only who could hear it through all his songs! Yay, I'm not crazy!
@Fire_Axus
@Fire_Axus 9 ай бұрын
bruh
@Jesse-ri5ud
@Jesse-ri5ud 9 ай бұрын
​@@BenthovenMusic its always driven me nuts 😅 youre not alone!
@lumigpictures
@lumigpictures 9 ай бұрын
I think it’s a very intended effect to make it sound more human (or dog?). To me, something is missing in that example she shows, where everything is in tune; it sounds artificial. Making the whistling sharp all the way through is a simple way to make it sound less perfect, the way people usually whistle. But indeed, it was maybe a bit too much for our tempered ears
@moresnqp
@moresnqp 9 ай бұрын
i would assume it was accidental, cause soundfonts/ libraries back then would be somewhat out of tune anyways. it's probably just that we're used to whistling not being quite in key
@vharmi.
@vharmi. 9 ай бұрын
All music is microtonal if you don't tune your instrument like a nerd
@willfeen
@willfeen 9 ай бұрын
my favorite type of comment
@EpicManaphyDude
@EpicManaphyDude 9 ай бұрын
ye
@Halberds8122
@Halberds8122 9 ай бұрын
Ah yes, the classic all _ is _ if you're not a nerd joke
@RandomTask678
@RandomTask678 9 ай бұрын
The sound of middle school band class. Brings a tear to my wincing eyes
@xdkristof
@xdkristof 9 ай бұрын
it's still going to be microtonal, u can't tune it to exactly 440, it will always be smth like 440.07 or 439.88
@DavidBennettPiano
@DavidBennettPiano 9 ай бұрын
Thanks for the shout out Cadence! Great video as always 😊
@brotundwasser
@brotundwasser 9 ай бұрын
It's him
@CONSUMEDBYMYYOUNGERSISTER
@CONSUMEDBYMYYOUNGERSISTER 9 ай бұрын
The man the myth the legend himself
@planetoforts
@planetoforts 9 ай бұрын
Please make a video of microtones
@brotundwasser
@brotundwasser 9 ай бұрын
@@planetoforts he did
@silask.1966
@silask.1966 9 ай бұрын
I think the k. K. whistling is a nod to whistlers not being in tune a lot. Like a lot of people whistle when they are at home and it sounds absolutely horrible
@vi64489
@vi64489 9 ай бұрын
I love whistling at home and I hope it sounds good 🥺
@Dayanto
@Dayanto 9 ай бұрын
The weird thing about whistling is that it doesn't really have any overtones, so it can't ever really be "out of tune" with itself, only relative to some other sound that does have overtones. It gets even weirder when you consider things like metallophones, which DO have overtones, but don't conform to the harmonic series. This opens the door to all sorts of weird (but consonant) music that you can't play on a piano. (even if you tune it to the same notes)
@silphv
@silphv 9 ай бұрын
​@@Dayanto I think out-of-tune whistling would mean melodically (one way to be out of tune with yourself) or harmonically like the K. K. example. It does bring up though that equal-tempered instruments, unless they're pure sine waves like whistling is (or nearly), are all timbrally out-of-tune with themselves all the time. That's why the just intonation harmony has that clear "ringing" quality, all the overtones are in tune with the fundamental harmony. I agree, pitched sounds with inharmonic overtones are really interesting. I always think of church bells. I've seen the word "xentimbres" used (by Sevish, anyway).
@ismailgharbiyeh7743
@ismailgharbiyeh7743 5 ай бұрын
%{@%{-N3 [-085NQ512Q [5T8NESDY 8RFANS _{)%*@% __-3NQ 5[-02NM5 1[5 -20N 21[5 -28QN15 21]Q-[85 NTSRFY F8NSFR WN{ _)*n%@% _-_*_-)N35 [-2Q815 N12Q5RT-_**_ [ESAUD FRAWS 9{ )_***%@n}-38 N5]2-[20N5 N1Q5 ESU NRF9WAS N[_)*n%@"{}_ *N53[]2 572N135 [-20Q RNTEASDY FGNSDE A[P)_n*%@)_n %-0N3 25[21N[ T2-]Q385 NYESD FRNBW P9NR5[23 85NM12[5 2N1Q5[20Q8- R[-8SE0R NWAS []_ *n%@{ **_%*n3[- 50N215 _**_-2105[ NE[S]F -R8NA {})-_**- %_@m% u9N3MW 5RTN3[5 UN21[Q580 NM5125-** 0[R8SNM F7RUAWZN 9n {_)%*&n! %32[5- 2N15[2058- NMREYAS98RFNWAS [P09N {_)%*n_**_______________** n598032N5[ 208N5M 215[ ]8ESND FRAW[-0 N %*_@)n%]23[ 08N21 Y5R89WEN RF90N &()%@ N32
@silask.1966
@silask.1966 5 ай бұрын
@@ismailgharbiyeh7743 no way!!!
@northstarjakobs
@northstarjakobs 9 ай бұрын
I didn't know that just intonation was the reason why barbershop sounds the way it does, but it's super cool. One thing I wish you'd touched on in the video was how the historical use of just intonation led to the idea of different keys having their own character and feeling, which was a result of certain keys feeling more or less "in tune" because of the way that just intonation works, which just doesn't exist in the same way with modern equal temperament tunings.
@Veepee92
@Veepee92 9 ай бұрын
It wasn't necessarily just intonation that led to the idea of key colour - which itself was apparently a somewhat disputed concept in its time - but rather it was meantone tuning principles, where the syntonic comma of 81:80 was split across the 12 keys in various ways, depending on the tuning system. Interestingly enough, in contemporary microtonal theory the varieties of meantone tunings - quarter-comme, third-comma, sixth-comma etc. - have been generalised as a concept known as "diamond tradeoff", as they rightly are a microtonal idea in and of themselves.
@The_SOB_II
@The_SOB_II 9 ай бұрын
I think you're thinking of other tuning systems. Well temperaments (as in The Well-Tempered Clavier), and before that meantone, had that property. In JI, esp as used in choral music, people do their best to transpose intervals perfectly afaik, but I'm not a professional chorister
@killedbycrit
@killedbycrit 9 ай бұрын
14:34 the single measure of 1/8 had me DYING
@AlbySilly
@AlbySilly 8 ай бұрын
My headcannon is that the person who made the song added one too many notes by accident, making it a measure of 9/8 instead of 4/4
@TorutheRedFox
@TorutheRedFox 7 ай бұрын
you should see the score for gerald barry's piano quartet no. 1 then
@man_in_space
@man_in_space 3 ай бұрын
It was the crit that your username reports killed you.
@jmuspup
@jmuspup 9 ай бұрын
Wow...... its crazy that you notated all of that. I can just imagine myself going insane trying to hear 48TET intervals.......
@Penningtonac
@Penningtonac Ай бұрын
It’s seriously next level talent… I want to contact about lessons once I am done being starstruck 😭
@sirstephington8869
@sirstephington8869 9 ай бұрын
15:39 My parents had a candle that played happy birthday when you twisted it. I learned that if you twisted it slightly, it would play flat, and the high notes were even flatter, as if it was struggling to hit the high notes. So, I tormented my perfect pitch gifted brother with it on his birthday for years, until it inevitably stopped working.
@iexist_nt
@iexist_nt 6 ай бұрын
why did your brother hate it I love it when stuff is slightly off tune
@nuggetangel103
@nuggetangel103 Ай бұрын
​@@iexist_nt Perfectionism probably
@iexist_nt
@iexist_nt Ай бұрын
@@nuggetangel103 guess there's two types of us "NOOOOO IT'S 0.0425 CENTS OFF AAAHHH" "this is like 40 or so cents sharp. i like it"
@fuhua765
@fuhua765 18 күн бұрын
@@iexist_nt He has perfect pitch, according to OP, and being able to notice when things are very out of tune can be quite irritating with perfect pitch.
@_XRMissie
@_XRMissie 9 ай бұрын
For all you maths nerds out there, N-TET can be defined as 2^(n/m) where n is the note number relative to whatever key centre you've chosen, and m is the number of notes in the octave. 12-TET then is 2^(n/12), and 1¢ is 2^(1/1200). Just to show how this works, assume A=440Hz, moving 12 notes in 12-TET you have a ratio of 2^(12/12):1 which is just 2:1. To get E (the 5th of A), it's 2^(7/12):1 ≈ 1.4983:1, _not quite_ the 3:2 (or ratio/factor of 1.5) of just intonation and results in E ≈ 659.255Hz. You can also calculate the ¢ difference between any 2 notes with 1200*log2(f2/f1), where f is the frequency OR the ratio/factor, so if the 5th in just intonation is 1.5 and a 5th in 12-TET is 1.4983, 1200×log2(1.5/1.4983) ≈ 1.955¢ Disclaimer: This was written at 4am, so pls forgive me if everything is totally wrong and completely unintelligible lmao Also, I'm leaving out ridiculous amounts of decimal places for obvious reasons 💃🏽
@quinoa759
@quinoa759 9 ай бұрын
2:56 I think it's important to mention that a plausible reason why 12-EDO was favored is because it approximates the first few harmonics pretty well. Intervals using the 2nd, 3rd, 4th, 5th, 6th, 8th, 9th, and 15th all match pretty closely to 12-EDO, something that not all tuning systems can do. Imo the biggest disadvantage of 12-EDO is that the 7th 11th and 13th harmonics aren't approximated very well so we have some completely valid tonalities missing from our system.
@Dayanto
@Dayanto 8 ай бұрын
It's worth noting that the 5th harmonic is 15¢ out of tune, which carries over into the 10th and 15th harmonics, and shows up in a number of common intervals such as the major and minor thirds (5/4, and 6/5), major and minor sixths (5/3, 8/5), as well as some more unusual ratios such as 9/5, and 10/9. All of these are relatively simple 5-limit intervals, so it's not just the higher harmonics that are a problem.
@Buriaku
@Buriaku 7 ай бұрын
​​@@Dayanto Exactly! Calling anything, but the 2nd and 3rd prime harmonic in tune in 12EDO does not get the point. 12EDO is a 3-limit temperament plain and simple. The "horrible" thirds are the main reason people are interested in other systems😮. There are reasons that mean tone systems (ie 5-limit tuning) were common before the piano got ubiquitous.
@godwin972
@godwin972 9 ай бұрын
the Pikachu exploding jumpscare into microtonal Megalovania around the 16-minute mark is a true combo
@philb2972
@philb2972 9 ай бұрын
pleaseeee help me out here, what was that tune that pikachu was playing?
@jebi-sensei497
@jebi-sensei497 9 ай бұрын
@@philb2972Pretty sure it was “Under the Sea” from The Little Mermaid
@kvn_la
@kvn_la 9 ай бұрын
As someone with perfect pitch, I actually love when the tuning of an entire song is off. It makes it sound so alien. Miss me with songs that have been transposed though.
@spencerbell8386
@spencerbell8386 9 ай бұрын
Just saw one of my fav bands on their 20 year tour. All their songs were transposed down to make to singable. It was almost unbearable for me.
@asukalangleysoryu6695
@asukalangleysoryu6695 9 ай бұрын
Get help guys. This is why people say perfect pitch is a mental illness :D
@glue2222
@glue2222 9 ай бұрын
@@asukalangleysoryu6695 i'd like to think anyone would notice their favourite songs being in an entirely different key thooo
@simplylight4916
@simplylight4916 9 ай бұрын
@@glue2222 yes. i intentionally transpose songs when i get bored, because it gives them new flavor every time i do
@kvn_la
@kvn_la 9 ай бұрын
@@asukalangleysoryu6695When people are envious of my perfect pitch, I tell them they really shouldn't be. It's way more detrimental than it is helpful.
@rozelia_the_octo06
@rozelia_the_octo06 9 ай бұрын
Me waiting for the section about every toby fox song
@DangerNoodle68
@DangerNoodle68 7 ай бұрын
ME TOO 😭
@nirgunawish
@nirgunawish 5 ай бұрын
plz
@skythealmighty2826
@skythealmighty2826 Ай бұрын
ESPECIALLY Fallen Down and Undertale pleaseee those are not a = 440
@leppycolon3
@leppycolon3 Ай бұрын
even if they're not A = 440, they're not really "microtonal" per se, since the actual relationships between the notes don't change . it's like transposing a song
@Grozione
@Grozione Ай бұрын
The guy is a genius, but people really inflate everything he does...
@Sevish
@Sevish 9 ай бұрын
Re: Help with Microtones Hi Cadence, Yes, 22-EDO all day long! Sincerely, Wil Wheaton
@CadenceHira
@CadenceHira 9 ай бұрын
LOL hi sevish
@nomad_0036
@nomad_0036 9 ай бұрын
mwah, i love you sevish
@RainbowLayer92
@RainbowLayer92 8 ай бұрын
You are my favorite! ❤ love from USA
@Vrila_X3
@Vrila_X3 8 ай бұрын
We love you! Sevish!
@ellaalexeisdaughter2636
@ellaalexeisdaughter2636 7 ай бұрын
Your music is like an exotic beverage that you get addicted to and spend all your cash on /pos
@saturnkodiak
@saturnkodiak 9 ай бұрын
For anyone curious about those Gizzard Wizards and their microtonality, i'd recommend Honey from their album KG, or Rattlesnake from their Flying Microtonal Banana.
@GANONdork123
@GANONdork123 9 ай бұрын
Flying Microtonal Banana is just full of bangers in general.
@goffikgurl666
@goffikgurl666 7 ай бұрын
Microtonal banana FTW
@oliverascher213
@oliverascher213 4 ай бұрын
I think Sleep Drifter is the best song for people new to microtonal music because the intro is a scale, which makes it easier to identify and appreciate the microtones. Also, as much as I love Rattlednake, it is admittedly really repetitive.
@WadWizard
@WadWizard 9 ай бұрын
Im into microtonality but i still want to say 12edo isnt exactly arbitrary, it just achieves one specific goal. When you stack 3/2 and reduce the ratios you get from that to be within 2/1 first you get... well technically first you get a 2:3:4, after that you get something akin to the familiar pentatonic scale, then diatonic(with the major third tuned sharp and minor third flat, and fifth exact), and after that you get a 12 note scale(mind you these are just the sizes at which there are only two step sizes and theres only one unusual fifth[generator more broadly, you could stack anything], its called a MOS but that is a whole bag of worms) this would be pythagorean tuning. If you flatten the fifth you can get the thirds closer to 5/4 and 6/5 and this is generally what various tunings of meantone do. These are systems that were used in western music long before 12edo became standard and the main goal is/was essentially to get 4:5:6, 12edo does this quite well for its size, of course theres issues with the major third being quite sharp but you would have to go up to 19edo to fix that and then the fifth would be flat, 31edo seems to be the most common alternative but now you have 31 notes to deal with compared to 12. 17edo goes the other way and the fifth is even sharper along with the major third which some think of more like a 9/7 or 14/11, but it does give you a neutral third(which may be one of the types of intervals that blue notes are aiming for) You could also stack alternating 5/4 and 6/5 to get whats called zarlino or ptolemys intense diatonic, this also extends to 17 notes(with 3 step sizes this time) but doesnt have a pentatonic form(though you can find one in it) Some alternative things you could use that can still reach semi familiar territory in an unfamiliar structures are porcupine in which you stack something in between one third of 4/3 and half of a minor third of your choice such as 6/5 or something nearby which gives you 7 and 8 note scales(and 15), theres also mothra or gorgo(maybe also called slendric) which is basically stacking something like 8/7 or a third of a fifth (im fond of 25/22) to make a 5 note scale and an 11 note scale which can get you close to having 3 4:5:6:7 or in sharper tunings more like a 6:7:9(idk what the seventh would be), both of these coincedentally have nice tunings in 37edo Also personally i dont think of alternate fundamentals as microtonal, it is something people should take advantage of but it doesnt actually give you any new intervals all the relationships are the same within the tuning. That all said i don't spend much time with these simpler ratios, ive spent a long time wrestling with 16edo along with mavila/antidiatonic which is shaped kinda like diatonic except the fifth is so flat that it generates a minor third before the major third and so all the major thirds and minor thirds are swapped but if thats all it was it wouldnt be much to wrestle with, the semitones become supermajor wholetones(like 8/7[the inversion of 7/4] but probably something rougher) which means the minor seventh is something like 7/4, and the wholetones become neutral seconds like 12/11 which also means the major seventh is replaced with a neutral seventh and the major ninth is also neutral instead, which certainly takes some getting used to(well some people seem to take to it quicker) i like the seventh and ninth better than the second personally but its growing on me. You can get this by stacking something like 40/27 or 28/19.
@IsaacMyers1
@IsaacMyers1 9 ай бұрын
exactly. basically its no tuning has better fifths until you get into the 40’s.
@WadWizard
@WadWizard 9 ай бұрын
@@IsaacMyers1 29edo has one thats slightly closer but a little sharp, but not closer by much
@theemiii_
@theemiii_ 9 ай бұрын
As some who understands literally NOTHING about music other than on a piano middle C is in the middle, this was delightful to read
@LxE9799
@LxE9799 9 ай бұрын
Damn, after reading this, I wonder how good your grades in Math are lol (mine aren't 🥲)
@Starshine777
@Starshine777 9 ай бұрын
Wad this is the part where you realize you just wrote an entire script for a video and should make a video reply instead of leaving an essay in the comments >__
@partylikeits1066
@partylikeits1066 9 ай бұрын
Cadence, your videos are some of the absolute best on this site. Not only are you really great at making these concepts understandable and easy to follow for people with limited knowledge of music theory, your asides and jokes are actually genuinely funny and charming. Such an awesome and underrated channel!
@radiak488
@radiak488 9 ай бұрын
probably my favorite example of level 3 or “micro-polytonality” in vgm is the song “mysterious trap”from kirby triple deluxe, it’s mostly in standard tuning but uses a bunch of detuned instruments to create a really strange and unique atmosphere. awesome video btw!
@mardkam_triplesh
@mardkam_triplesh 8 ай бұрын
that microtonal cheap ass disney plushie but unlocked a memory i didnt know i had. awesome video!!
@andretits
@andretits 6 ай бұрын
Having perfect pitch, OH MY GOD YOU HAVE GIVEN ME SUCH A PASSION FOR MICROTONES THEY SOUND SO GOOD JUST BECAUSE THEYRE DIFFERENT AND NEW! THEY SCRATCH THIS ITCH IN MY BRAIN AND YOU DID SUCH A GOOD JOB EXPLAINING IT
@TJ-hg6op
@TJ-hg6op Ай бұрын
I have imperfect pitch
@henrikljungstrand2036
@henrikljungstrand2036 5 күн бұрын
Since you have perfect pitch, i would advice you to check out both Just Intonation pure intervals = relative frequencies, in at least the 13-prime-limit, 16-integer-limit; and the cymatics standing waves (eigen-frequencies) produced by various absolute frequencies in certain materials, such as water, in various containers, in order to find out which absolute tunings are natural enough!
@zarath5411
@zarath5411 9 ай бұрын
microtonality (especially poly-microtonality) is so cool. I feel like people should experiment much more with these inside more pop-oriented genres. It seems like the majority of it is contained in contemporary classical/experimental music in the west:(
@cosmicspacething3474
@cosmicspacething3474 9 ай бұрын
I think modern pop music is even more restrained than classical music. Classical music at least takes full advantage of its tonal system.
@unknown6390
@unknown6390 9 ай бұрын
​​@@cosmicspacething3474op is saying the opposite. They agree, just reiterating that they want to hear pop incorporate microtonality. Or, make it less restrained. Op should have said contained instead to be more clear
@Fire_Axus
@Fire_Axus 9 ай бұрын
your feelings are irrational
@zarath5411
@zarath5411 9 ай бұрын
​@@unknown6390 just saw it. That's correct
@iexist_nt
@iexist_nt 6 ай бұрын
​​​@@Fire_Axusno, I think it would be interesting to hear
@DaviFelizardoVieira
@DaviFelizardoVieira 9 ай бұрын
yippe just intonation Also the microtonal "Sadness and Sorrow" at the end made me laugh so hard 🤣🤣🤣
@indyfan9845
@indyfan9845 9 ай бұрын
As someone studying ethnomusicology (the study of music as it pertains to culture, particularly music outside of Western classical music), knowing about different ways of tuning or dividing the octave. I'm a composer for a Skryim mod team that's set in a non-Western region of Nirn, and we're trying to incorporate traditional tunings systems from the real-world cultures being drawn from into our soundtrack. It's a ton of fun! I can't share anything, yet. Hopefully soon.
@SchemingGoldberg
@SchemingGoldberg 7 ай бұрын
Europeans are an indigenous ethnic group, they are just as valid and important as every other ethnic group. Using the term "ethnic" to mean "not European" is wrong and racist, because it promotes the idea of "European vs non-European".
@indyfan9845
@indyfan9845 7 ай бұрын
@@SchemingGoldberg I never said anything about ethnic groups. That's just the name of the field.
@itaraaah
@itaraaah 5 ай бұрын
@@SchemingGoldberg The field of ethnomusicology studies how music pertains to its societal and cultural context. It does not exclude Western music but actually is an inclusive field of study that removes the "european vs. non-european" lens. I think what indyfan was trying to say is that they study sub-topics of ethnomusicology that focus on non-Western countries. But ethnomusicology is not *just* non-Western music. I think what you're thinking of is the term "world music," which yes, has very racist origins in trying to group a ton of rich histories and cultures outside of non-Western countries into one misleading, grossly defined genre of music.
@thefancyotter6432
@thefancyotter6432 9 ай бұрын
How are these videos so high quality without you being wildly popular. You are actually immaculate.
@gamhacked
@gamhacked 8 ай бұрын
Niche-ass topic
@blideojames7310
@blideojames7310 9 ай бұрын
trees in the depth of the earth mentioned pog love your videos! the pacing and lil easter eggs everywhere are a treat for my tiktok brain. yippee just intonation!!
@Fire_Axus
@Fire_Axus 9 ай бұрын
your feelings are irrational
@The_SOB_II
@The_SOB_II 9 ай бұрын
​@@Fire_Axusyour ration is overflowing
@andretits
@andretits 6 ай бұрын
Having perfect pitch, OH MY GOD YOU HAVE GIVEN ME SUCH A PASSION FOR MICROTONES THEY SOUND SO GOOD JUST BECAUSE THEYRE DIFFERENT AND NEW! THEY SCRATCH THIS ITCH IN MY BRAIN AND YOU DID SUCH A GOOD JOB EXPLAINING IT!!!
@symply_Sym
@symply_Sym 13 күн бұрын
this has literally been mindblowing to me, especially with the Just Intonation bit. always wondered why barbershop quartets had such a distinct, almost otherworldly perfect sound. crazy stuff
@HA11EYS_COM3T
@HA11EYS_COM3T 8 ай бұрын
E half flat minor has such a different character over that standard tuning! It has to be intentional, honestly, it’s just so characterful and human. It makes sound like whistling, actual whistling, instead of what the regular tuning whistling sounds like: a synth.
@doritodog6242
@doritodog6242 8 ай бұрын
Last semester I wrote a research paper on the topic of different tuning systems, so while it was neat to be able to understand everything in this video, I really wish this video would have been posted while I was doing my research because of how informative and well researched everything was. Great job at making microtonality easily digestible :)
9 ай бұрын
Yippeeee just intonation!!! Your videos are amazing, this in particular deserves +1M views, at least I learned a lot! I will definitely support you in Patreon soon
@landman_0218
@landman_0218 8 ай бұрын
16:12 I would kill for a full microtonal cover of Megalovania
@domdude64dd
@domdude64dd 9 ай бұрын
In Ocarina Of Time/Majoras Mask you can free play the ocarina/other transform mask instruments to play quarter tones as well as bends using the control stick and other buttons. I'm certain Zelda has more microtonal examples, thinking of Skull Kid's horn from Twilight Princess, and a lot of the Twilight music in general Super cool video, looking forward to more stuff like this. Keep it up!
@TachyBunker
@TachyBunker 9 ай бұрын
I make microtonal music since 2 years now, it's a really great and informative video, but as you said, all of this isn't even merely scratching the surface of possibilities ;)
@typeswitch
@typeswitch 9 ай бұрын
Nice video. I kinda wish it also discussed other ways of dividing up the octave, like 19TET or 31TET. Ok it's probably not possible to find examples in game music, but it would be neat to discuss it a little & help dispel the idea that 12TET is anything other than what we've become accustomed to.
@AiNaKa
@AiNaKa 4 ай бұрын
i too wish that these scales were more common. personally i'm working on a soundtrack for a game with two other people and we have songs in 9TET, 16TET, 24TET and wendy carlos's alpha scale so far. I honestly hope that someday when it's done maybe my game can help influence other people to put microtonality in their soundtracks too.
@cubicinfinity2
@cubicinfinity2 9 ай бұрын
Microtonality is a very deep rabbit hole and it can be overwhelming to learn about. So, I think this is a good video because is gives the audience a little bit to consider then forget about but to scratch at the back of their mind. This was kind of what happened to me.
@ryan_1314
@ryan_1314 9 ай бұрын
One thing that I really like about microtonal music isn't the "blue notes" that make it sound dissonant, but the way it sounds consonant while subtly using non 12edo notes, so then when there's a large modal change you go from vibing to a soundscape to going "woah wait a second". I've been looking into microtonality across several genres, such as jazz where the 7th in a dominant chord is lowered significantly and 2-5-1s becomes ii submi7 -> V dom7 -> I ma7 or et cetera, and how the common modal changes become a lot more explicit. What's really suprising is microtonality is actually really common in dubstep... to an extent. Some tracks outright have microtonality like phonon - polyriddim changing tunings or barely alive - wompum being 24edo, but a lot of other songs are more subtle and have pitch bends that may be rhythmically divided, similar to the indian cooking game mentioned.
@wiegraf9009
@wiegraf9009 9 ай бұрын
Neutral chords are the most fun thing to make your brain pause in confusion for a minute.
@philjoseph6748
@philjoseph6748 9 ай бұрын
This is an incredible video! I have loved game music and microtones for years but could never find examples of the two together. Your explanation of microtonal concepts is spot on and your examples are great. Microtonal "purists" probably wouldn't consider just a deviation from A=440 to be "microtonal" but it is certainly the first step away from western tuning convention. I've been looking at heaps of microtonality in the west and although there are some great examples in pop-music the real MVPs are the modern musicians and theorists in the Microtonal / Xenharmonic communities online, who continuously pump out some incredible microtonal music and concepts! (yippee just intonation!)
@Fire_Axus
@Fire_Axus 9 ай бұрын
your feelings were irrational
@philjoseph6748
@philjoseph6748 9 ай бұрын
@@Fire_Axus Thanks! I hadn't noticed!
@JonathanBarouch
@JonathanBarouch 8 ай бұрын
Pitch-matching to the exact cent!? My ears ache just thinking about it. Thank you for your sacrifice.
@ZipplyZane
@ZipplyZane 9 ай бұрын
I've specifically done level 1 in a type of meme piece. It does the whole "in different composer's styles" thing, and I felt like the key was getting a bit old. So I tuned one of them to be closer to more common tunings at the time of the composer.
@CutieCakeClips
@CutieCakeClips 9 ай бұрын
This really shows how much pitch material there is that is overlooked. I would also like another video on different tuning systems in video games for different EDO systems.
@shucrut63
@shucrut63 9 ай бұрын
In level 5, on the comparison between the just intonation and the 12-TET F7, I found quite the opposite, the 12-TET being pretty clean while just intonation being kinda dissonant and "wobbly" as you described, hearing kind of a beating sound. Also yippee just intonation. Loved the content!
@nathanielouzana
@nathanielouzana 9 ай бұрын
The 48EDO is in fact well notated. Actually quite a standard way to do it in contemporary classical music.
@QuakeGamerROTMG
@QuakeGamerROTMG 4 ай бұрын
On the part in Kuruvi Onnu at around 24:50 my immediate thought as a guitarist is all the dive bombs and stuff we love to do with tremolo bridges. The closest thing to the part you pointed out is to do a trill while simultaneously lowering or raising pitch, a surprisingly similar effect to what is used in this song. Watching this video did inspire me a bit to mess around a little with quarter tones, played around with bending a string up just a quarter step and using those notes. Quarter step bends aren't particularly uncommon but I can't think of a song that really makes use of the quarter tone notes played on their own it's usually just bending a standard note slightly for effect and usually people wouldn't hold that quarter step bend. It makes me want to mess with a microtonal guitar that has extra frets for quarter tones (yes they exist)
@cinnamonsugarcourtney6073
@cinnamonsugarcourtney6073 9 ай бұрын
Undertale has Microtones! The song ASGORE has it pretty obviously.
@DPNack_
@DPNack_ 4 ай бұрын
Yeah, I love that D-half flat minor track
@cataclystp
@cataclystp 2 ай бұрын
it's just tuned .25 semitones up, that's not the same thing as being microtonal. it's still 12TET.
@Butterfingers3
@Butterfingers3 14 күн бұрын
Woah, microtones are definitely the coolest concept I've learned so far! I never thought of coming up with songs that were out of tune from what you're normally used to!
@S.B.C-Pixi
@S.B.C-Pixi 7 күн бұрын
3:09 Someone decided mean-tone temperament and everything before it was cringe, and that the tempermant we all use today is the best compromise we could come up with. The Baroque period happened, and stuck with it since.
@stephenweigel
@stephenweigel 9 ай бұрын
GREAT video! If you ever want to notate -TET’s or -EDO’s in sheet music I know the best way to do each one through transcription and ear training practice. Also, you can notate Just Intonation with a system called “HEJI” which is used nowadays all over
@iceblock40
@iceblock40 4 ай бұрын
never seen any of your vids nor do i know anything about any of what you talked about but i really really enjoyed this video and i felt i should share it thank you very much for this and have a great day (this applies to anyone reading)
@EthanSantos
@EthanSantos 9 ай бұрын
Wheeeewwww you’re back! Great video as always. That microtonal Brazilian Naruto is a vibe🤣
@EthanSantos
@EthanSantos 9 ай бұрын
Also hi @Brandon hahaha
@mahoumofo
@mahoumofo 9 ай бұрын
wake up babe new cadence hira video just dropped
@sus-kupp
@sus-kupp 9 ай бұрын
bazinga
@funkydeaIer
@funkydeaIer 8 ай бұрын
really cool video, glad to see wario land 4 get featured. feel the need to mention i listen to all my music shifted up by 40-50 cents and i love it
@Not_mera
@Not_mera 9 ай бұрын
I'm a novice when it comes to music, but my partner played the violin through most of his childhood; so had a strong aversion to microtones. I like to listen to, among other things, contemporary jazz. And one of the first song I sent him was Mr. P by Philipp Gerschlauer. He asked me if it was a cruel joke and couldn't bear listening to it for more than 5 seconds. I'll have fun pointing this stuff out to him :)
@Testgeraeusch
@Testgeraeusch 9 ай бұрын
I recently retuned my electric organ (transistor model with 12 potentiometers or inductors inside for pitch) and decided to try quarter comma meantone. It works surprisingly well and the tuning was done in few minutes; i had my laptop giving me some reference notes with audacity and the beat matching can easily be done by ear. But now i have a wolf between g# and eb and i think i want to move than to c# ab instead, but i see why the well temperted tuning eventually took over... It's just so quick and easy to tune the fifths pure and then match the beating by ear (at least for organs).
@RidleyPhantom
@RidleyPhantom 8 ай бұрын
This topic has always been fun to explore, so I really enjoyed this video! I've noticed microtonality particularly in older Nintendo games. Just a couple I can think of on the spot: - Kimono Dance Theater theme from Pokemon Gold/Silver - Overworld theme from Super Mario Bros 2 (the last section before the loop; uses two wave channels to play the same melody but a quarter tone apart, presumably to give it the ragtime piano sound imo)
@philb2972
@philb2972 9 ай бұрын
22:08 the only example of just intonation in pop music that comes to mind (and it's a very small one at that) is that the first chord in red hot chili peppers' scar tissue is a major third in just intonation (the b string is tuned down 14 cents to achieve this), so when amateur/hobby guitar players try and play the song on their 12-tet-tuned guitars, it sounds slightly off
@matheuscastello6554
@matheuscastello6554 9 ай бұрын
ive been listening to a lot of microtonal music lately so its cool to see this drop! ive found myself a big fan of your videos recently too and this just further solidifies it :) microtonality, music theory, and video games?! heck yeah sign me up
@TheNinetySecond
@TheNinetySecond Ай бұрын
This was an absolute joy and so well produced! I consider myself somewhat familiar with microtonality, having thrown myself at Sevish, Lumatone keyboards and Tolgahan Çoğulu's microtonal guitar project, but even your reiterations of the basics were so well explained and paced out that it kept my interest. The historical and cultural context was really thoughtful (and could be a whole subject of a video as well) and the hard work put into transcribing was greatly appreciated. If you ever do a follow up, the fact that Nintendo is so open to microtonality compared to the western video game developers could make for a great analysis. Very enthusiastic new subscriber here!
@funnynamedottxt
@funnynamedottxt 9 ай бұрын
yippee just intonation (also you wrote perfectly twice in the description lol) (also great video) (also never heard of microtonality before, but it’s super interesting)
@Cephapopz
@Cephapopz 9 ай бұрын
when the tones are micro
@wiegraf9009
@wiegraf9009 9 ай бұрын
12 TET isn't "arbitrary" in the sense it has no basis in physics and math. It actually has desirable properties that make it a good compromise in being "close enough" to the sound of JI while also being able to be scaled evenly on a piano. It's totally possible to work with arbitrary scales but 12 TET is somewhere in between the intuitive sound of JI and the arbitrary weird sound of some very funky exotic scales. It's like saying the choice between a red sauce or a white sauce for your pasta is arbitrary. To some extent that's true because you made a choice, but there are probably properties of each that you would use to decide based on whether they're more or less to your taste. A red sauce will always be more acidic than a white sauce for example.
@catocall7323
@catocall7323 7 ай бұрын
I think she also didn't quite make clear that JI is the naturally harmonic intonation. Brass instruments that use overtones to reach higher octaves are naturally JI. Equal temperament deliberately sacrifices being in tune for the flexibility of being able to play in different keys and transposing music. Voice quartets don't have the limitations of keyboards and fretted instruments so they are free to use JI as the singer can adjust notes on the fly.
@itaraaah
@itaraaah 5 ай бұрын
I agree and I think what she was trying to say is that the argument that 12 TET is objectively the best tuning system and other tuning systems are more "primitive" is arbitrary, and frankly quite racist and eurocentric. 12 TET has its pros and cons just like any tuning system, similar to your analogy of choosing pasta sauces. But historically what's happened is that white sauce (no pun intended) has been hailed as the objectively best sauce and no other sauce pails in comparison to its taste, and anyone who likes red sauce is "weird," "primitive," and doesn't belong with those who like white sauce.
@wiegraf9009
@wiegraf9009 5 ай бұрын
@@itaraaah True yes!
@kinexkid
@kinexkid 2 ай бұрын
2:38 I heard the lick
@narwaffl
@narwaffl 9 ай бұрын
The combined just intonation and 12-TET is gorgeous. It feels super nostalgic, like an old twangy piano😌
@crystalAegis
@crystalAegis 9 ай бұрын
So, I am so happy to see you analyze the perspective of the entire WORLD for music theory!!! I agree in the idea that Music Theory is STALE AF and needs to really let itself become aware of literally anything outside West Europe. Anything... but it is up to us to keep Music Theory alive as a concept despite it's Eurocentric origin and homogeneity. We gotta appreciate everything by adding the ideas of cultures not explored yet and embracing non-traditional music! It is such a beautiful area of basic sound waves that needs to be appreciated so much more and not dismissed as a "primitive, and tribal" kinda thing (blech)
@ywenp
@ywenp 9 ай бұрын
Though I agree with the sentiment, the wording is a bit off, so I interject because that wording is usually what causes endless debates on the internet about the point of music theory. "Music theory" is just what it says on the label: the practise of studying and describing how a certain music works, in other words building a theory of it. It cannot be eurocentric because there are as many music theories as there are cultures who practise music. The Natya Shastra from India is music theory, so is the arabic Maqam, etc. Considering that _music theory_ is a synonym of _classical occidental music theory_ is actually what is eurocentric here.
@Jesse-ri5ud
@Jesse-ri5ud 9 ай бұрын
id never really realized that tune from kirby superstar is microtonal but that makes SO MUCH SENSE! i always knew something was odd about it, at least to my western-attuned ears, but i think because i heard it long before i started learning music, it just never really hit me, consciously, that its not in the common western 12-tet tuning! even tho it obviously isnt 😂 way cooler knowing that the tuning used in that song actually has real life historical basis! i had no idea it utilized an arabic tuning and thats SO COOL! i love your take on music theory. i just watched your video on weird time sigs and at the end you said "music theory doesnt have rules" or something similar, and i was like, DAMN. IT DOESNT! i think watching that video was the first time i really realized that music theory doesnt explain how things "should" be done, but rather how they ARE and HAVE BEEN done!! especially with your explanation earlier in that video of how time signatures are often applied retroactively... because theyre used to describe the music, not to define or restrict it! idk if thats making sense, but basically i really like how you perceive and explain music and will be watching more of your videos. thank you ❤
@BigBlueBazooka
@BigBlueBazooka 8 ай бұрын
I love your videos more than any other music theory videos I've seen. The time signature video really helped me understand that subject better for use in my own music.
@danieljimmy-fadairo3189
@danieljimmy-fadairo3189 7 ай бұрын
today, i have decided that this is the greatest youtube channel of all time.
@henryauden618
@henryauden618 9 ай бұрын
As usual, such a great video with an awesome overview of the approaches/areas list and enough depth to each of them. Bravo!
@axiomatic-z5k
@axiomatic-z5k 8 ай бұрын
This is so helpful for learning double stops on violin. My teacher can never explain why to sometimes play one string a bit flat, it just “sounds better” but this is why. Yippee just intonation!
@danielcorrigan8805
@danielcorrigan8805 9 ай бұрын
Another reason for A 432 is that string instruments in particular sound different when there is less tension on the bridge, giving a warmer sound. Some double bassists actually even do the opposite and tune up to have a brighter and more resonant sound (solo bass tuning)
@harambo88
@harambo88 8 ай бұрын
A=432 is flatearth for physical illiterates
@vivianriver6450
@vivianriver6450 9 ай бұрын
A friend introduced me to an artist who goes by "Bent" and released several eclectic albums. As best I recall, his songs are mostly in the key of C, tuned so that C is about half way between B and C with the usual toning. It definitely sounds different to me to hear songs like "Coming Back" and "Silent Life".
@remingtongagnard4442
@remingtongagnard4442 8 ай бұрын
Great videos! Just found your channel not that long ago, it needs to blow up! Really fantastic stuff 🎉
@Iggy30874
@Iggy30874 9 ай бұрын
Great video as ever! Just wanted to mention another interesting use of differing tuning systems alongside the usual 12TET in VGM - In Splatoon 3’s Soundtrack, tracks like Anarchy Rainbow, Surprise and Shine, Anarchy Poisons (Snake Mix), and Daybreaker Anthem have sections which use another tuning (though I’m unfortunately not sure of the exact one) to represent Frye’s heritage for a really cool effect.
@galactika
@galactika 9 ай бұрын
yes!!! so few people talk about this and almost all transcriptions i see of splatoon 3 music convert the maqam sections into 12TET
@CadenceHira
@CadenceHira 9 ай бұрын
THAT IS SO COOL I haven't played splatoon 3 so i haven't heard much of the soundtrack yet, but now I'm much more motivated to get it
@Iggy30874
@Iggy30874 9 ай бұрын
@@CadenceHira IT REALLY IS I hope you enjoy it when you get to it, the soundtrack of the game takes on so many different styles and genres while still sounding so unified, it’s honestly amazing.
@CalloohCalley
@CalloohCalley 8 ай бұрын
Thank you thank you thank you so much for mentioning A=432. I 100% agree with you. One thing people don't think about is that A=440 is part of the Treaty of Versailles. So that agreement is quite a legal one.
@pineapplequeen13
@pineapplequeen13 9 ай бұрын
I'm so glad to see other people acknowledging the fun and creative music in Marble Madness! I grew up playing that game with my dad and we both always loved the tracks. We always made jokes that it sounded like sometbing Emerson, Lake, and Palmer would write lol.
@Glurky
@Glurky 9 ай бұрын
I have watched a couple of your videos already and really enjoyed them! But a little while ago I discovered that you worked on some music for A Dance of Fire and Ice which is one of my favorite games ever!
@scottgray4623
@scottgray4623 6 ай бұрын
Yippee! Just intonation! If I had more time, I'd get into the story about how in high school detention, I thought I accidentally discovered that our tuning ratios were wrong LOL
@jessieoberreuter4755
@jessieoberreuter4755 9 ай бұрын
On many a retro machine, the synth chips are just dividing down a system clock, so all pitches are approximations, with the notes becoming more and more out of tune as the frequencies go up.
@ThePopDescriptivist
@ThePopDescriptivist 9 ай бұрын
That 'fusion-y composite minor scale' on Trees in the Depths of the Earth that you point out seems reminiscent to me of makam Suznak - consisting of a Rast pentachord underneath a Hicaz tetrachord. Now, in Arabic tuning (which is pretty much just 24-tet, which you seem to prefer here), the Hicaz tetrachord has a major third, not the neutral third that occurs in this song. But in Turkish makam, the Hicaz has a third that is pretty close to a neutral third (though the Rast's third is a little bit brighter, something between a major third and neutral third). Overall I think the song is meant to at least allude to makam Suznak, especially since it is one of the most common modulations when using makam Rast.
@Blobbbbb
@Blobbbbb 9 ай бұрын
You make great videos, that are so high quality and so informative, and you deserve so much praise. HOWEVER it’s actually john who builds a house with his friends, not arthur
@mimisaiko
@mimisaiko 8 ай бұрын
The track Fallen Down in Undertale, is tuned at A=431Hz. Not sure if it's done by sound font, or global setting in DAW, or pitch shifting the whole song. But it gave a melancholy and nostalgic feel like an old recording.
@Friendly-Neighborhood-Asexual
@Friendly-Neighborhood-Asexual 7 ай бұрын
Interesting. I always knew something was somewhat off about it, but I could never tell what. But is there a reason for 431Hz instead of 432Hz?
@Ringtail
@Ringtail 7 ай бұрын
A lot of the tracks in-game are pitched differently than they are on the soundtrack for some reason
@like_i_genuenly_dont_know
@like_i_genuenly_dont_know 16 күн бұрын
7:19 is that enter sandman in the background?
@deztruct0823
@deztruct0823 9 ай бұрын
I appreciate you taking the time to share your knowledge with us in ways that are easy to understand and taking the time to provide multiple examples, in a sea of garbage "content" its good to see thoughtful stuff still being made that is a labor of love.
@zachbrown4688
@zachbrown4688 9 ай бұрын
These are some of the most well versed accessible video essays on music theory I've ever seen!
@alifaghhi
@alifaghhi 7 ай бұрын
this was a really great watch! and delivered so digestibly. 👏🏼👏🏼👏🏼
@kangalio
@kangalio Ай бұрын
18:37 the way you presented the scales disregards the only interesting feature of just intonation - the pure intervals to the root note! Playing the keys one by one after the other on their own only exposes the ratio between consecutive keys to the ear, which is what just intonation specifically _sacrifices_ Each just intonation key should instead have been played together with the root note, to be able to hear each interval :)
@BryanLu0
@BryanLu0 8 ай бұрын
I think non A440 is microtonal only when juxtaposed against A440. Otherwise it's just a different tuning. E.g. Baroque violin isn't microtonal
@tsunderecat413
@tsunderecat413 7 ай бұрын
a lot of toby fox's music can sometimes be microtonal. a huge example of this would be "asgore," a song which has its key somewhere between d flat minor and d minor. some of his music, such as "savior of the waking world (which itself is in a key somewhere between e flat minor and e minor)," uses the piccolo instrument from the squidfont orchestral soundfont, which is detuned similarly to k.k.'s whistling and thus creates polymicrotonality. similarly, he tends to use an older version of an nes vst that's just slightly higher pitched than it ought to be. tl;dr: recreating toby's music can be such a pain sometimes.
@tsunderecat413
@tsunderecat413 7 ай бұрын
also, i have the opposite preference of that bloodstained composer, in that i think a = 448 sounds better than both a = 440 and a = 432 lol.
@gooroofigy
@gooroofigy 9 ай бұрын
Another banger video tackling complex topics and an informative, fun, and digestible way.
@eliditto8975
@eliditto8975 9 ай бұрын
wow i love this channel and these videos!!! they are so engaging and easy to watch, and i always learn so much!!! please keep making themmm!!!!!!!!
@AGBenson
@AGBenson 5 ай бұрын
15:53 is when I subscribed. Incredible work. Keep it up!
@Munggoon
@Munggoon 9 ай бұрын
props to such a high quality content
@nj8833
@nj8833 9 ай бұрын
You are gifted beyond belief!! I absolutely love the niche of video game music theory. This is one of my favorite videos ever, and your content helps me experience the things I love in a new way
@yzhkkhzy
@yzhkkhzy 9 ай бұрын
very well researched and edited
@BinglesP
@BinglesP 6 ай бұрын
As far as I know, a Level 1 example of microtonality in game music is some/most of the tracks in the Touhou album "Dolls in Pseudo Paradise". They are set at a tuning that isn't 440Hz(if I recall correctly) and that is part of what gives the album such a unique vibe compared to other instrumental game music, even other songs from Touhou. You can kind of get a direct comparison by listening to the album's version of 'U.N. Owen Was Her?' compared to the normal version of the song found in Touhou 6. Though, I'm aware the two tracks are different outside of just that, but I personally think the microtonality is the primary difference between the two since the notes are essentially the same. It's one of my favorite albums that I've ever listened to, it genuinely sounds beautiful, and it even has a short story to go with it that follows each track with each paragraph. You can read the whole thing in English alongside the album or on its own(though I should warn first that the story is pretty dark and spooky, especially if you hate killer clown/pierrot/whatever antagonists lmao) which really compliments the music and makes them feel more connected.
@_rringo
@_rringo Ай бұрын
explanation: 5:23 old game 5:30 remake of the old game
@0hhStormy
@0hhStormy 2 ай бұрын
I love microtunings, they give songs a whole new feeling. I thought my song was sounding kind of lame, I turned up the tuning around 40 cents and it had a whole new energetic feeling to it. Not enough to be in a different key but enough to really hear it.
@thelucksman
@thelucksman 9 ай бұрын
Can't believe that rude buster and other Toby fox music wasn't mentioned on here
@kinexkid
@kinexkid 2 ай бұрын
5:37 i feel bad for anyone with perfect pitch at this part
@kinexkid
@kinexkid 2 ай бұрын
But this is basically how Balinese Gamelan music works to a degree as well. But hearing two ultra pure tones together like that gives more of a cheese grater effect on my ears than a beat tone
@NT-nw9ek
@NT-nw9ek 9 ай бұрын
I really like this. One thing I wanna say tho (probably into the void): the tuning systems that closely approximate the harmonic series have a very deep and intimate relationship with the greatest unsolved problem in mathematics. In summary, there's a million dollars waiting for anyone that can show when zeta(0.5+it)=0, and the tuning systems that are close to the harmonic series are exactly those where |zeta(0.5+ln2/2pi i t)| has a peak
@Friendly-Neighborhood-Asexual
@Friendly-Neighborhood-Asexual 7 ай бұрын
So you're telling me that 12TET is related to the Riemann hypothesis? Insane. Never knew this!
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