On Negative Time Signatures (A Response To Adam Neely)

What's a negative time signature? Well, it's not really a thing... yet. But Adam Neely made a video about the possibility and what it could mean to write music in -4/4 time, which got me thinking about other possible answers, and I think I've come up with something I really like so I thought I'd share. Plus, a little youtube drama never hurt anyone, so why not start a fight with Adam?
Seriously, though, his answer was good too. But still. Fight!
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[@AdamNeely]

Neat idea! I do like your approach, although honestly, I think the whole thing is...not super useful in any serious way, because there are already other ways to think about the subjects we offered for a "negative time signature." That said, feuding and meme theory gets the clicks, so lets fight!!!!!

[@12tone]

Yeah, in the end I don't think there's ever going to be a serious answer that actually needs negative numbers in order to work, for basically the reasons you stated in your video. Still, though, looking at weird questions is a great way to find unusual parts of music to explore, and I'm glad I went down this rabbit hole 'cause it got me thinking about systematized backmasking, which I'd never really considered before, so thanks for the inspiration! Man, I'm really good at fights, I should get into them more often.

[@OEpistimon]

Thank goodness time is 1-dimensional, otherwise we'd have to think about imaginary time signatures as well... That would be a total mind-exploding thing on its own...

[@erikbarrett85]

What weight do you two walk around at? Let's set this thing up....

[@MalahkAngel]

Dueling banjos at dawn, good sirs

[@BradsGonnaPlay]

I’m thinking we need a musical decathlon (a la Billy Madison) between y’all.

[@Zizzily]

If you write half of your song in 4/4 and the other half in -4/4, does it cancel out and leave no song?

[@FacePomagranate]

Well you'd be reversing the -4/4 which would make it positive, so actually you'd end up with the song being twice as long.

[@keylometers6342]

It's how they wrote 4'33"

[@moondust2365]

Basically you write one song that's twice as long, but the other half's basically just the first half but in reverse, I think.

[@trajan_x0128]

Big brain

[@gabrielbennett9053]

Music is not observed as a finished product. Let me use a number line as an analogy. Technically, yes, youd be going forward 4, then backwards 4, ending on zero, leaving you with no change. But music isn't just looking at the dot on the zero. Music is watching the dot moving from the zero, to the four, and back to the zero. It's watching change over time, even if that change just gets you back to where you started.

[@MisterAppleEsq]

Oh no, the lick. Adam Neely is secretly taking over the channel.

[@warped_rider]

Next video: "12tone analyzes The Lick for 5 hours."

[@arbel1231]

+Warped rider you deserve more likes

[@Livingeidolon]

The Lick, the world's first musical virus.

[@goonyougoodthing]

+Warped Rider HAHAHAHA

[@OEpistimon]

Warped Rider OH DEAR GOD WHYYYYYYY???

[@JustB3be]

12tone: "Since it's a well known thing in the KZbin community, that the best way to get clicks is to start a fight [...]." Also 12tone: "I think Adam's answer was pretty good!" Way to start a fight LOL. This cracked me up, you're so nice!

[@iam1021]

NihilisticEntropy Excuse you?

[@nikitademodov3446]

Reminds me of Papyrus.

[@bassman9261995]

What matters isn’t “what is a negative time signature” but rather: what cool musical ideas can that phrase inspire. I think your answers are both pretty good in that respect

[@JariSatta]

♫♫♩♫‿◦ ¡ʞɔıן ǝɥʇ

[@GenericInternetter]

HOW THE I DONT EVEN

[@SleepSoul]

Wouldn't a reversed recording be negative tempo, not negative time signature? That seems more natural to me.

[@rorythewriter]

Simon The Human well, the notation says that every black note equals some positive rythmic unit, so Negative time sig*Postive rythm=Negative play speed Positive time sig*Negative rythm=Negative play speed So yeah, i think both work? Lmao

[@DampeS8N]

Have to agree. Neither idea of what a negative time signature is is very satisfying to me, though I think Neely's is more accurate as a reversal of the measure's impulse and not the whole composition. In the end, I don't think the concept is very useful either way. And I can't come up with a way it would be useful unless it had exotic contextual meaning similar to how symbols in math can mean things that have nothing to do with how they are traditionally used - they are just stolen and re-purposed.

[@jmkyarrow]

Both are extremely closely linked, but I could imagine a system in which they have different functions which are similar but slightly altered

[@12tone]

Good point! I was mainly thinking of it, though, as a polymetric device, to be used for individual parts within a larger, positive composition, in which case I think it's better viewed as a change in rhythm than a change in tempo. Not sure, though!

[@vincentnydam]

Bone Machine by The Pixies sounds to me like the drums are in -4/4 while the vocals are in 4/4. I hear Adam Neely's 'reverse of the accent pattern'-or rather a differing accent pattern-between the drums and vocals. The drums accent beats 1&3 while the vocals accent beats 2&4. To me the verse is in -4/4, the refrain combines -4/4 rhythm section with 4/4 vocals, and chorus is in 4/4. Whadyu think? kzbin.info/www/bejne/r3uwZmpslJaIjpY

[@lolvalle]

Jeez... Just binge watched all content on your channel and just applied to resume my studies in musical theory. You just kicked me out of a five year (+) depression!

[@pubcollize]

Negative 4/4 is the rhythm that happens before the composition begins, such as a metronome, clearing your throat, blowing your nose, reaching for some tissues.

[@tulsatrash]

My favorite kind of KZbin fight.

[@charlesrosenbauer3135]

Now do imaginary or complex time signatures! Or quaternion or octonion time signatures! /s

[@Scigatt]

For imaginary time signatures, take the Fourier transform as your waveform.

[@scottblair8261]

My major concern with imaginary time signatures is that there is no way of multiplying time signatures. You can add them, and multiply by scalars, but time signatures are not scalars. You can't multiply 2/4 by 4/4. At least there is no clear way to do this. I disagree with the solution in the video because it doesn't comply by time signature arithmetic 4/4-2/4 is not 2/4 by this definition.

[@anonymousloner4480]

Wait if that's the case then i know what a negative time signature is!!! It just means play every beat Except for 4/4 or whatever shows the time signature following the negative sign is

[@appa609]

Must be played by a cylindrical speaker

[@djjjjjjjjjjjjjjjjjjjj]

My favourite one is 7.6π/-i to be honest

[@Ice_Karma]

I have no idea what a negative time signature should be, but I enjoy and appreciate both of your attempts to describe what it might be! ♥

[@Nyhilo]

If you haven't heard it, Miracle Musical's "The Mind Electric" is a song that's played backwards first, then forwards, lyrics and all. It's interesting because while you're listening to the first part you get a sense of this musical theme that's going on, as well as a theme in the lyrics - then those themes resolve when it switches to playing forwards. It's really good.

[@DougerArt]

We all know this is because of what he said on your analysis of Africa! Let the fighting begin!

[@NinjaWahlrusMC]

This is great! What’s really cool about it in my opinion is that this style of composition could be used in a lot of modern genres... Rather I’m actually surprised it hasn’t been used as much. Great video!

[@AndriyVasylenko]

I happened to transcribe reversed pieces of music (such as Metallica's Damage Inc and Blackened intros, or my Gone Too Far's outro), and it was a tricky thing to do. Simply writing them forward and leaving a note "play it in reverse" didn't satisfy me. Perhaps, 12tone's interpretation of negative time signature could make that more accurate in a way. Anyway, I may not judge you guys, since I suck at music theory)))

[@YTSPoster]

KoolAid same man lol when 12Tone was talking about reversing harmonies and melodies my brain just screamed "Blackened!" haha.

[@theploymaker]

That gear system you drew at the end can't move, and that's really the main problem with your thesis. (kidding, kidding. But it still bugs me)

[@12tone]

That was intentional! It was an example of something pointless, to go along with the narration.

[@ZipplyZane]

I knew it! I assumed it was intentional. It fit too well.

[@mememem]

If negative numbers aren't real then explain my bank account

[@Richard.Atkinson]

Another less-famous musical palindrome (something that is the same backward and forward) is the minuet of Haydn's 47th Symphony in G major: kzbin.info/www/bejne/r5alkIKepdigbJYm45s

[@AidanMmusic96]

Richard Atkinson The one I knew first! Cool piece indeed.

[@rojachi7847]

Richard Atkinson I seem to remember hearing that Samuel Barber's Adagio for Strings was also palindromic in some way. But I would have to look it up to confirm.

[@MasonIshida]

Didn’t you write palindrome variations?

[@ThisIsTeeKay]

Completely random lick 😉

[@AlanKey86]

Awesome video 12tone. My objection to the scheme proposed by Adam is that it doesn't follow arithmetic rules. Namely, a bar of 4/4 followed by a bar of 2/4 could be notated as a single bar of 6/4. But a bar of 4/4 followed by one bar of -2/4 does not equal a bar of 2/4. Like any of the worst critics, I raise this objection without having a constructive response of my own. The only vauge thought I had was the idea of inverting a waveform and playing it at the same time as the non-inverted waveform so that they cancel out. But even this isn't subtracting time in the way that I think negative time signatures ought to do.

[@12tone]

That's a great point, and it's one my solution doesn't really address either! There's not really a clean way in my system for a part to switch from a positive to a negative time at all, so it doesn't directly create those sorts of contradictions like Adam's does, but there's no real equivalence to the arithmetic relationships that real positive and negative numbers have. Although... If I had a part written in, say, 4/4, and I inserted a bar of -2/4 at some point, it would make sense to, in editing, take that section and reverse it back through the bar before it, so that it ended on beat 3 of the previous bar. That creates some problems with the next forwards component, which would then overlap the original, but you could use that to create layering, like an ensemble produced out of one voice that snakes back and forth through time... Neat!

[@Livingeidolon]

But arithmetically speaking a negative sign simply means the opposite of. The opposite of having one thing isn't not having a thing, it's owing a thing, right? So, mathematics would say that your example of 4/4 followed by - 2/4 would indeed be felt as 2/4. The reason why that's nonsensical is that time signature doesn't work like math. 4/4 followed by 2/4 could feel like any number of subdivisions of six pulses divided into quarters. Man I don't feel like that's clear, but my break is over.

[@TheViolaBuddy]

On the other hand, a bar of 2/4 followed by a bar of 6/8 might not feel like a bar of 10/8; it might instead feel like a bar of 4/4 but subdivided as triplets in the latter half (it depends on if there's the "♩ = ♩." marking or not). And in general something like 3/4 does not feel the same as 6/8 even though they're the same fraction. Heck, 6/8 doesn't even feel like six beats; it feels like two. So there are already some oddities about time signatures.

[@yoverale]

Good point, then we should answer first what is a 0 (zero) time signature in a musical context. 4/4 bar = 1 = a whole note -4/4 bar = -1= a negative whole note (?) Then 4/4 - 4/4 = 0 bar ... does it have any meaning to you?

[@Livingeidolon]

Ale Lloveras see that's where I got stuck on at first. But the negative sign doesn't change the number, per se, it changes the concept attached. That's when I started thinking that - 4/4 would mean change the rule from four pulses and a quarter note to anything but that.

[@TheDamasada]

2:20 OH SHIT I'M FEELING IT

[@Karmy.]

Charlie Brown's Parents by Dishwalla instantly comes to mind for me with a 9-8-7-6-5-4-3 guitar riff leading into the chorus

[@StefanoPapaleo-TS]

The real question is: since Marty McFly travelled back in time from 1985 to 1955 and played Johnny B. Good. was that an example of negative time signature or simply disproved time travels in only one direction, and thus destroyed both your theories, or was he a tachion? But most of all... how many sheets of music paper do you use per video?:))

[@UndecimeBeatitudo]

Takyon? You say Takyon?! OH SHIT, I'M FEELING IT!!!

[@matthewjamestaylor]

Did your last line suggest that I shouldn't continue to rock, or that I've always been rockin' and you are retroactively its source? Cheers.

[@einarabelc5]

Adam talks a lot and he's sometimes helpful but this was pure mathematics. Well done sir.

[@pocarski]

But what about complex signatures? 4i 4 anyone?

[@keyboardwarrior6296]

6/8^2=6/64 Have fun.

[@BenjaminKassel]

2:32 “This completely random lick...” Well done to both you and Adam. Additionally, the bit on backmasking reminded me of the intro to the Electric Light Orchestra’s “Fire On High” from their Face the Music album. There’s a backmasked message where Bev Bevan says, “The music is reversible, but time... is not. Turn back! Turn back!...” It’s an interesting message, especially in the context of this video.

[@yoverale]

I have another mathematical music topic to philosophize about. If we have additive meter (i.e. 3+2+3/8), could we also have subtractive meter? (3+2-3)/8 would be the same that 2/8? Just wondering

[@frtzkng]

One example of this backmasking, that immediately came to my mind is a song used in soome Vsauce videos; 145 (Poodles) by Jake Chudnow. Its base melody is the reverse melody played on a piano, recorded, and played in reverse. Essentially playing that piano melody in -4/4.

[@OnlyARide]

Adenosine Breakdown/Adenosine Buildup, two tracks by Blotted Science that are the same composition played backwards. It's some of the nuttiest stuff Ive ever heard.

[@pvanukoff]

YES!

[@Cloudkusanagui]

Up, Jarzombek should be cited in this subject for sure!

[@AidanMmusic96]

Many thanks for introducing me to a new band! :D My mind has been truly frazzled for many days!

[@aykutaydogdu269]

This is the most prestigious and high quality fight I have ever seen on KZbin.

[@jraluark]

"Ma Fin Est Mon Commencement" composed by Guillaume de Machaut is an earlier example of reversible music from the 14th century. It is 3 lines of vocal music. The second line is the retrograde of the first line, and the third line is the retrograde of itself. Just an extra factoid about music in reverse. Great video.

[@pinkajou656]

Translation; My End Is My Beginning. Just thought that was cool :)

[@JMnyJohns]

Absolutely great. The practicality of an answer is a temporal judgement - just because no one can figure out the utility of something now doesn't mean they won't in the future (history of: contact lenses, solar cells, etc). Plus 'out-rigoring' Adam is good for him - gives him a reason to raise his (already formidable) game. ;-) I never would have thought I'd enjoy music theory so much - thanks to you and the whole KZbin MT posse. :-)

[@tearlach47]

2:32 I see what you did there. Nice.

[@Quellification]

Can anyone explain what he did there?

[@lucascisneros8147]

Reşat Yıldırım its one of the most famous licks among the jazz community

[@pmnt_]

more importantly, it's the most famous lick among adam's community

[@chuckbrown7590]

It’s literally called “the lick”

[@roygbiv1122]

It was on Adam's T-shirt (in the same key) in the original 'negative time signatures' video.

[@whitex4652]

Math teachrr here. Of course you can have minus three elephants. If you owe someone three elephants. You also can have negative money. It's called debt. So...

[@TheViolaBuddy]

"[I figured I'd try] to start a a fight. (...) So first of all, I think Adam's answer was pretty good." You might want to work on your fight-starting skills there. Anyway, I definitely do think your response is a better more accurate way of having a negative time signature than Adam's. His is not "really" negative in any sense. Consider, for example, a regular 6/8 beat. You have / ˘ ˘ / ˘ ˘ with two offbeats. Which offbeat would you make the new downbeat in the chords? You have two options, ˘ / ˘ ˘ / ˘ and ˘ ˘ / ˘ ˘ /. That's not very negative-like though; -1 * -1 = 1, not some third thing. We want some sort of operation like multiplying by -1, except that you can do it three times before you cycle instead of just two, where / ˘ ˘ / ˘ ˘ leads to ˘ / ˘ ˘ / ˘ leads to ˘ ˘ / ˘ ˘ / leads back to / ˘ ˘ / ˘ ˘. But you know what does act like that, giving three different "states" when you multiply it? e^(120° i). That's a scary way of writing "120° around the unit circle in the complex plane" which is in turn a scary way of writing "a 120° rotation, expressed as a complex number." We get three numbers out of this rotation: 1, e^(120° i), and e^(240° i) (which replaces the 1 and -1 in the duple rhythm case); we can then multiply it by the normal positive time signatures 6/8 to get three related time signatures: 6/8, e^(120° i)*6/8, and e^(240° i)*6/8. So if we take Adam's definition of negative time signatures, then we can actually extend this idea into the complex plane in this way. But anyway, that tangent aside, I'm not sure if I entirely buy that definition to begin with. It doesn't really seem to map out any sort of real time, which I feel like is what the time signature is saying. And besides, why are there only two markers of accents? There are probably other characteristics of accents that can be separated out (loudness, pitch, chord changes, intensity of vibrato, and probably other weird ones we don't even think about as we perform); why don't we separate out these other aspects? Instead, directly manipulating time seems like a better way to interpret messing with that top number of the time signature. Reversing recordings is really the only way we have as universely beings to do so, so I think it's a fair way to work with that. Also, what happens if we mess with the bottom number of the time signature? In math, the fractions (-4)/4 and 4/(-4) are the same thing, but in music, the "numerator" and "denominator" have very different roles. Playing -4 beats, with each beat being a quarter note long, isn't necessarily the same thing as playing +4 beats, each beat being a "negative quarter note" long... depending on how we define a "negative quarter note." Though "messing with time" is reminiscent of special relativity (and general relativity, but that's even weirder). Reversing recordings is actually not our only way of messing with time (though it's probably our only way of reversing it); we can also travel super quickly (or near black holes, but again, let's ignore general relativity). How would we talk about a piece of music wherein one musician is on a spaceship traveling at half the speed of light relative to another, and both are moving relative to the audience? Would that change our time signature? That'd be an interesting exercise in polytonality, since the musicians both think they're playing in the same tempo and same time signature, but experience the other's playing as stretched out in time. ...Relativity is weird. Though come to think of it (though this is no longer about time signatures), even if the musicians are moving at a more reasonable speed, say on a train, and we're on the ground, we would hear their pitch shifting thanks to the Doppler effect. What if there's a long line of musicians on that train, each of whom suddenly drops in pitch as he/she passes us. Then the way the music sounds to an audience member depends on both what the musicians are playing and where along the tracks that particular audience member is, since the different musicians pass us at different times and therefore jump in pitch at different times. And what if every musician is on a different train? What if the train accelerates and decelerates repeatedly? In fact, the musicians could each be on a different train, and they all play the same note for the whole concert, and depend purely on the train's speed and the Doppler effect to change the pitch. That'd make for an interesting concert environment, if nothing else. (Also as a practical matter we might not hear anything other than the screeching of the train wheels.) ...Uh, I should probably stop thinking about this now.

[@chobyriley417]

This was beautiful

[@paulski7307]

In 'like spinning plates' by Radiohead Thom wrote the vocal melody, learned it, recorded him singing the backwards melody then reversed that to get the effect of singing backwards forwards in a way. The whole thing is also over a reversed backing track from what would become 'i will'. Hopefully this provides some inspirational insight. Love these thought experiments!

[@MultiAwesomered]

If you owe three elephants you have negative three elephants :/

[@MuzikBike]

but is the "negative elephant" corporeal? is that even a requirement?

[@OnlyARide]

Good thing there are -3 people in the world who owe 3 elephants

[@MultiAwesomered]

If you have the elephants to pay back they add to the total, meaning you'd have more than negative 3

[@tonybates7870]

The crucial yet puzzlingly obscure musical concept of negative elephants is finally being acknowledged. About time. (Actually, this video is about time, isn't it? See what I did there?)

[@davidwuhrer6704]

I'd say if you have -3 elephants, you are missing three elephants, or you have three elephants missing, or you are three elephants short. The point is: You can count negative elephants.

[@Yet_another_placeholder]

On the topic of backmasking, I do recall one particular song, where if the backmasked part is missing, the song loses what makes it sound interesting to my ears. That song is "Pushing Me Away" by Linkin Park. The backmasked part playing mixed in with the pre-chorus is Mike Shinoda rapping "Everything falls apart, even the people who never frown eventually break down. Everything has to end, we'll soon find we're out of time left to watch it all unwind." In the Reanimation-version of the song, they turned changed it from a hard rock song to a ballad, and let Mike's lines in the pre-chorus remain non-backmasked, that is, played as originally recorded, and honestly, it doesn't really have the same ominous effect. I recall hearing the Reanimation-version played live once, however, where the rap-part was kept backmasked, and suddenly, the entire song had an even darker, more ominous feel to it than it did originally. So in short, there are songs that have been written, even if unintentional, where backmasking is a big part of the sound and feel of the song

[@martijnvanweele6204]

Does that mean that the Ballad of the Goddess from The Legend of Zelda: Skyward Sword is Zelda's Lullaby in -4/4?

[@markedone6667]

Playing recordings backwards can be really cool. Just found out about a week ago that the intro of metallicas blackened is actually the reversed recording of what they played. I think it has a cool sound to it, kinda like definitly an electric guitar, but not actually sounds the instrument could make on its own.

[@Dinos4urFour]

I wrote a short metal track that plays forwards and backwards, called it 'Mirror Song', this video made me want to revisit it!

[@erikbarrett85]

Dinos4urFour link?

[@Dinos4urFour]

here you go, quickly bounced out of GuitarPro 5 so hope you can stand the audio haha soundcloud.com/user-272978224/mirror-song

[@igloo_igloo]

Hmm... interesting! I think it kinda sounds like game(?) music

[@erikbarrett85]

Dinos4urFour I like it too actually. Was it all instrument, or guitar and all midi?

[@InfinityPotato97]

Dinos4urFour Reminds me of BtBaM 😀

[@everestjarvik5502]

Honestly I just feel the need to point out that a lot of EDM or ambient electronic producers often have entire reversed instrument parts in their songs: the the large-scale use of your version of negative time is not entirely uncommon. Great video though, I love your take on it!

[@Mezurashii5]

If 1 + -1 gives us 0, then a whole note in 4/4 followed by a whole note in -4/4 should give us no sound. What two notes give us no sound? Phase reversed notes! So negative signatures could just be a "flip phase" indicator

[@martinkrauser4029]

on recordings only, though phase flipping doesn't get you silence in meatspace

[@HollowDesert]

Mezurashii5 But I didn't think time signatures were mathematical. That's why 6/8 isn't the same as 3/4.

[@Anonymous-df8it]

@@martinkrauser4029 Except it does work irl. It's literally how noise cancelling headphones work!

[@mcol3]

I like the subtlety at 5:00 when you say "multiplied by -1" and you draw e^{\pi i}!

[@TheSquareOnes]

This method doesn't actually change the time signature though, which seems like a massive flaw for obvious reasons. A "negative time signature" should be something that expresses rhythm differently but here the rhythm is identical, all you've changed is the nature of the voice performing it. How is that functionally different from having the same line played with a trumpet or with a different synth setting? It isn't, which tells us that it's not useful as a concept. For what it's worth I don't think negative time signatures can be useful concepts. My version of the idea back in high school was to "start the bar" earlier by the indicated amount, if a time signature tells you the duration of a measure then a negative time signature should also tell you the duration just in the opposite direction. So if we have a passage that goes 15/16, -3/4, 7/8 the "measure of -3/4" would actually be performed starting on the 'a' of beat 1 in the measure of 15/16 in effect performing a brief polymeter. I think this is still the best answer I've heard to the question but obviously it's also completely useless since there's nothing stopping us from just writing the notes of the -3/4 in the 15/16 where they would end up anyway and ditching the superfluous notation entirely. So that's both my explanation of how it could work and also my explanation of why the concept is dumb and will probably never be useful.

[@YostPeter]

Marvel: "Infinity War is the most ambitions crossover event in history." 12Tone:

[@Haggismchaggish]

Wel Adam, your turn again ;) To be honest, two different views on the subject gives me way more information (and thus inspiration). I think there is no better answer just more information to use to come up with new music.

[@AlRoderick]

There's actually a clever example of backwards music in The Legend of Zelda Skyward Sword, the games main theme is a time reversed version of Zelda's Lullaby, a famous piece used throughout the series.

[@luccaburgess]

My favorite time signature: π/4

[@keyboardwarrior6296]

It would just sound like 3/4 but with mistakes.

[@Mathhead2000]

Break it down to definitions in group theory. -4/4 is what ever you have to add to 4/4 to get the additive identity. So before answering what -4/4 is, we need to find some way to "add" time signatures, and then we use that to figure out what the identity time signature would be. My vote for defining time signature addition is composition, just playing one measure after the next, in which case a measure of -4/4 next to a measure of 4/4 would mean play no music. Or at least that no notes could exist in the combine measure. Which mean we need a sort of negative note. We could use destructive interference for this perhaps. Just some ideas.

[@ryanbusse5374]

Stone Roses have a song that’s just another reversed

[@pr000n000bie]

Your explanation brings the intro from Metallicas "Blackened" to my mind. It doesn't matter if you listen to it forward or in reverse, it still sounds the same.

[@brandon-cs7fw]

2:21 *_I'M FEELIN' IT_*

[@whatsstandard]

One aspect that I haven't really seen yet (but I am also late to this particular party) is what we describe as music. If music is defined as sound ordered through time, it would follow that Time Signatures are a meaningful measure of that sound. If we also follow the mathematical relationship between positive and negative integers being that they are "opposite" or cancel each other out, the only observable musical equivalent that springs to mind is Silence as the antithesis of sound. In my mind Negative Time Signatures would operate in such a way as to render Silence the governor of said time, not sound. But then we get into Cage-ian rabbit holes, and I don't even know how I would go about doing that. I'll have to play around with the idea. It's also interesting to me that the sound played in reverse comes literally from nothing: That is to say the perceived pitch begins with a decay and ends with the articulation, which is not physically possible on any wind, string, or percussive instrument. Again just coming from the perspective that in Negative Time, Silence is the driving force-not sound.

[@icelingbolt]

**12 Tones version of "fighting":** "I agree to most things you said, but here's a logical addition to your statement and a pinpoint on where our statements diverge to reduce confusion" **Other youtubers** *Pay 15 bucks to see a staged match from a staged perspective formed by a staged set of videos staged to agro one another* Be like 12tone.

[@legoharry100]

Yeah yeah but TONEWOOD

[@T_hatsil]

BLACKENED INTRO BY METALLICA! the absolute most legendary -4/4 music piece

[@The_Rising_Dragon]

Please analyze Hey Brother by Avicii. R. I. P.

[@JJJthebest]

Not much to analize, RIP but the song is shit

[@Skiptracer1981]

So he's a dead communist? Best kind of communist.

[@123unknownsoldier126]

“Like Spinning Plates” and “I will” by Radiohead

[@Zendryon]

Rip Avicii

[@brynnhill8848]

I mean, there's the Vihart video where she plays music backwards and calls it reversing time. I was thinking about that while watching Mr. Neely's video. Nice

[@astrocrowbeats]

Ayyy

[@althealligator1467]

4:28 actually The Beatles' I'm Only Sleeping from the Revolver album has a backwards electric guitar in it, so that's also in "negative time."

[@badtrinket]

This has probably already been mentioned in the comments (though I can't see it) but the concept of a song that is playable and makes sense both forwards and backwards was also explored by Danish rock band Mew on the first track of their 2009 album "No More Stories...". The opening track "New Terrain" has an entire other composition backmasked through the whole recording called "Nervous" with a whole set of new lyrics!

[@joeldcanfield_spinhead]

1. I almost understood Adam's explanation, and yours flew by so fast I got nothing. Making your explanation clearly more righter. 1. David Reffkin (and another guy named Dave, oddly enough) did a stellar job of playing Gar Fael Elpam, then reversing the video so they played . . . Maple Leaf Rag. kzbin.info/www/bejne/lYjWhJqwrsemkM0

[@mickeyrube6623]

If you play one voice fowards, and one backwards, the the band playing backt'wards. And wouldn't the time signature be 0/4?

[@forehand101]

Maybe I'm just dumb, but 4/4 actually means 4 beats per measure with the quarter note getting the beat. So a -4/4 time would just be negative 4 beats in a measure with the quarter still getting the beat, so like the music starts being played backwards, although this couldn't be used at the start of a composition. I think an awesome way to maybe use this would be to have a regular piece of music at first, but it then starts playing the same thing, but backwards. Like a repeat sign, but instead of going back to a point, it just plays it backwards to another point set before hand (maybe +4/4). The musician would then skip over the -4/4 like they would a repeat sign after they've already repeated once. Ex: You might even be able to add a Coda or something at +4/4 to skip to after the -4/4 after playing the -4/4 music, so you don't play the +4/4 section twice.

[@jonathandolan2669]

A lot of hardware sequencers, or the arpeggiators on synthesizers have a feature where they can play their sequence backwards when signaled, or alternate between playing the sequence forwards or backwards. Maybe a negative time signature could be useful there, especially if there is complicated modulation signals that you are trying to capture in your notation too, since those could be reversed as well as the notes. But then if there are no other changes to the modulation tracks, it might be easier to just create a symbol meaning "play the last measure (or whatever) backwards, then continue".

[@unhealthytruthseeker]

I had an idea (inspired by physics) about negative time signature, and it generalizes to complex time signatures as well. I posted this on Adam's video as well. I think we might be able to make sense of negative time by considering complex number time signatures (which someone mentioned in the comments). Complex numbers only make sense when you have both an amplitude and a phase, so they would only make sense with more than one time signature played at once, like a linear combination between times. In this way, a time of (1 + i)/2 and a time of (1 - i)/2 would both be 2/2 time, but they would be "out of phase" with each other. The only sensible interpretation would be that of a time-delay between the beats of one time signature and the beats of another. If you write the complex number as r*exp(i theta)/N, then r would be the number of beats per measure (with the Nth note getting a beat) and theta would be the offset of beat 1. So a theta of 0 would be no offset, and a non-zero theta would be offset by N*theta/(2*Pi) beats. Thus, if you had 2/2 and 2*exp(i Pi/2)/2 = 2i/2, the first beat of the second time signature would be played 2*Pi/2*1/(2 Pi) = 1/2 beat later than the first beat of 2/2. From this, we see that a positive imaginary signature gets a quarter-measure delay, so a negative time signature would simply represent a half-measure delay relative to a positive time signature. Note, this only makes sense when played against another time signature. -4/4 against 4/4 would be played 2 beats later than 4/4.

[@argenteus8314]

Hmm... The Mind Electric is played backwards before forwards, and seems to have been composed with this in mind such that it doesn't sound terrible when played backwards, so perhaps it would count as an example of your form of negative time signature?

[@mickeyrube6623]

You can have -3 elephants if you owe someone three elephants. If I gave you 5 elephants, you wouldn't have 5 elephants, you'd only have two.

[@Geert2682]

At 4:01 you say you "can't have negative three elephants", but you can! It would simply mean that you *owe* someone three elephants (and you should probably re-evaluate some life choices).

[@hydrangeajk]

My favorite band, Unlucky Morpheus just released a single called Cadaver/Revadac wich has two songs, one bring the mirror image of another and I love it because I feel is not something commonly used in popular music and took me by surprise

[@lyanporto]

Danish band Mew has a song that if you play backwards is an entire different song. Both versions (New Terrain and Nervous) are on the same album. Pretty great tbh

[@alevator606]

So my next question is, what about complex time signature, like... (4+3i)/4

[@ericasw28]

As well, Metallica's Battery is actually recorded backwards, and reversed for the album

[@SkinnyDevilMusicLab]

In addition to the classical examples others have provided (following your Bach example), both Tommy Emmanuel and Bela Fleck have explored this idea. A few others, too.....

[@urbangrouse]

"Rigorously impractical is kind of my whole thing." Love it!

[@stulora3172]

Thank you for the Feynman diagram there is only a few ways of illustrating the physical need of a time dimension with a preferred direction, and this is one of them. ps. if someone is interested, look for spontaneous symmetry breaking

[@inazuma3gou]

Negative objects can be counted! Imagine you are on a beach. You dig a hole. A pile of sand is +1, the hole is -1. Two holes = -2, 3 holes = -3. When you combine +1 (a pile) with -1 (a hole) you get zero.

[@SgtAbramovich]

This is the first time I've stumbled upon this channel, here's my first impression: You're the Vihart of music.

[@TsunamiBeefPies]

Fascinating thought experiment! I personally like your interpretation a lot, though I think Adam's is more letter-of-the-law, while you seemed to approach it almost as a flight of fancy. I'm not well-versed in music theory, but I understand your videos pretty well, and if you consider your interpretation rigorous, I'll have to take your word for it. It seemed wonderfully creative to me.

[@williambilliam5001]

There is one example that I could think of when (at least part) of a piece, when played backwards, was actually another song. The theme song for The Legend of Zelda: Skyward Sword, has a part that, when played backwards, was actually another piece, "Zelda's Lullaby". While this wasn't exactly an entire song, it does remind me of the concept that was covered here.

[@luigivercotti6410]

Again, the correct answer to this question was, is, and will always be to take a half or full bar rest and then just play in 4/4

[@hypersans6209]

4:51 Is where I think I lost it. To see euler's identity in a music video was 2 worlds colliding violently.

[@laughingdaffodils5450]

3:58 ish - I can have three elephants but I can't have negative three elephants. You are only unable to have negative three elephants because you are not currently blessed with 3 or more elephants. If you had 4, you could certainly subsequently have -3. Great video! Just discovered you and already a fan.

[@jmkyarrow]

Love Adam but I prefer your one much more. I think something fresh like this is only useful when it expresses an idea that isn't easily expressed with current notation or not even possible at all, like this. Great stuff :)

[@cyanadofai]

"Plus, a little youtube drama never hurt anyone" lmfao

[@hobg5786]

Come on 12Tone, now I'll be up all night searching for a way to write it! I hate how much I love music...

[@kevinvu5993]

On a slightly related note, Joyner Lucas released a video called "Backwards" where he raps a bunch of lines with lyrics that make sense in either forward or backwards direction. It's not exactly what you and Adam are talking about, but it's a fascinating tangent.

[@Khaztaroth]

Rob Scallon did a song backwards, as in, played it in a way that it would sound "right" when played in reverse, so I guess that was on a negative time signature

[@Matyanson]

I have 3 IDEAS. 4/4 is a time signature. It consists of 2 numbers. First defines how many beats are in a bar. Second defines which notes is a beat. 4 - quarter note; 2 - half note (is "slower"); 1 - whole note. Following this pattern there would be 0 note which would mean 0 speed / infinite long beat / no direction in time and finaly -1 which would be whole note played in backwards. (or maybe the bpm should be negative...or either of those to make it reverse. and if both are negative it is positive) Back at the First number value of the signature. Normaly you count 4/4 like this: 1 2 3 4; 1 2 3 4; ... from the number 1 to the number representing how many beats there are (per bar). that would mean: 3/4: 1 2 3; 1 2 3; 2/4: 1 2; 1 2; 1/4: 1; 1; 0/4: 1 0; 1 0; -1/4: 1 0 -1; 1 0 -1; -4/4: 1 0 -1 -2 -3 -4; 1 0 -1 -2 -3 -4; (from 1 to -4 ... that makes 6 beats) But that is weird so we would count negative from -1: 0/4: ---- -1/4: -1; -1; -4/4: -1 -2 -3 -4; -1 -2 -3 -4; And my 3rd idea. Negative means you count in reverse: 0/4: ---- -1/4: 1; 1; -4/4: 4 3 2 1; 4 3 2 1; That would reverse an order of the notes in every bar but all the bars would be arranged normally. You would play it in time running forward. disclaimer: I just learned what time signature is so I am no good with music theory (so far)

[@Matyanson]

Also puting that number in ableton or fl studio might answer your question xdd

[@genaroguerrero9228]

Negative time signatures neither can be heard: we still listen in one direction-> forward. The process of reversing what was recorded only gives a pieces of "positive time signature" music that has its attacks and envelopes backwards, in the end being just a timbre change

[@Vasharan]

Damn, I'm late to this argument (thanks, KZbin algorithm). But what happens if we reverse not just the time signature/metric accents, but chord progressions and/or melodic and tonal development? So, instead of II-V-I, chord progressions go I-V-II. You'd start the Overture 2181 with cannons, and finish off with unaccompanied cellos and violins. You'd also start every meal with dessert, what a world we live in!

[@ДаниилРабинович-б9п]

Time to think about imaginary time signatures.

[@ifer1280]

You win! Adam, you need to react to 12tone now!

[@Stray0]

-4/4 is -4 beats of 1/4th notes. -4 beats is 4 beats reversed. I agree

[@jakestewart7862]

“This completely random lick” LMAO