Why It's Impossible to Tune a Piano

[@3blue1brown]

This also gives a nice explanation for why it is natural to have 12 notes in a chromatic scale, and not some other number: powers of the twelfth root of two have a tendency to be surprisingly close to simple rational numbers. For instance it's fifth power is strangely close to 4/3, it's seventh power is close to 3/2, it's 4th power is close to 4/5, etc. Powers of, say, the 11th root of 2 would not play so nicely. Great video!

[@ofarrillSP2]

You should do a video about it! Yours are noticeably better than Minute Physics (more thorough and accurate... And interesting). I await with excitement for your next video. Greetings from Mexico!

[@3blue1brown]

Actually, my next video will also have a little something to do with this :)

[@ofarrillSP2]

+3Blue1Brown you answered! Awesome haha I found your videos about 3 days ago, so it was a cool coincidence to find your comment on this video. I am a math fan, and your different way of explaining complicated problems is like a fresh breeze in a rather straight forward field. Keep up the good work! I'll keep recommending your channel to others like us who appreciate the beauty of mathematics. Cheers!

[@theskv21]

I have made music where the notes are all based on the eleventh root of two, and the harmonies are really odd I must say. None of them are harmonise in as simple of a ratio as in 12ET.

[@coopergates9680]

Now try the fifty third root of two, or f = 1.013164143... f^31 = 1.49994... ~= 3/2 f^22 = 1.3333858... ~= 4/3 f^17 = 1.24898... ~= 5/4 f^14 = 1.200929.... ~= 6/5 f^9 = 1.124911... ~= 9/8 Of course, the issue there is that 53 is prime, so you would have to use a digital device that could re-tune itself each time you changed keys. Otherwise the spacing would be inconsistent.

[@ofirshukrun449]

Minute physics is actually an "Hour physics" when after every 2 sentences you find yourself reading a new content in Wikipedia.

[@karleppo9043]

THIS IS ME RIGHT NOW

[@jamieeccleston2988]

This is one of the best ways to incite students to study and should be the aim of any course that wants to cover difficult material requiring self study: Provide an explanation that explains well the overarching structure of a difficult concept, giving it great context, and thus incite your students to put the details together for the next week out of curiosity and satisfaction, as opposed to explaining all the details and having your students struggle to see the point by... practicing the details (hek)

[@w.kelleyobrien459]

I hope KZbin videos are as inspirational to my child as they are to my middle aged self. I feel like I'd have done a lot better in school using shows like this, vsauce, Crash Course, etc., to introduce new subjects and build a foundation for the math and the busywork that followed.

[@TheRussell747]

@@w.kelleyobrien459 ya the beauty of KZbin and the internet as a whole, especially as a college student, is the immense access to knowledge. Professor is shit at explaining a topic? Well good thing theres probably 20 videos on that exact same topic online that can explain a professor's hour long lecture in 10 minutes. All it comes down to is knowing what to look up and you'll be able to find something online that explains the topic in a way that makes sense to you.

[@lonestarr1490]

@@TheRussell747 Except when you're studying math, where this method works for first and second, maybe the third semester, but afterwards never again.

[@flickering_wick]

I'm a piano tuner and I approve this message.

[@MegaSemi]

I'm a piano tuner as well (: but I found this message a bit misleading.

[@EnderElohim]

i'm a piano and what am i doing here.

[@calebjlee2685]

@@MegaSemi What about it was misleading?

[@josephbates7967]

So I'm a guitarist and I have a piano so could you just tune every not to exactly the pitch and not use harmonics or ratios like tune A to 440 so on so forth for every note or does it not work like that in application

[@darksnakenerdmaster]

Can you play il vento d'oro?

[@cjheaford]

Allow me to clear up some confusion: I’ve seen many comments below from people that think Henry got it wrong, because “obviously pianos can be tuned”. As with many armchair experts on the internet that can’t be bothered to do a modicum of research before they chime, there are doubters. I’m here to tell you Henry is spot-on correct. We are a dying breed us aural piano tuners. I can argue that there are fewer than 2,000 people on the planet today that truly know how to tune a concert piano by ear. Every single one of us is in demand like never before due to software. Software tuning is getting very good compared to what it once was, but all professional piano tuning software STILL must pIt itself against an aural judge before it is released. Aural piano tuning is a learned skill that requires years of practice- no matter how “perfect” you think your pitch is. I’m going to make several statements below about western tuning in general, and then some specific statements about the industry of piano tuning itself. Stay with me: 1) It is not possible to tune all 12 notes of the western scale simultaneously. (That’s the point of Henry’s video) 2) The history of Western composition itself is deeply rooted in the limitations of 12 notes being in tune. Until recently, composers simply avoided the out of tune notes. Right up until the late Baroque. Check out Chant to hear what 800 years of music sounded like before Josquin des Prez and the Renaissance. 3) IMPORTANT! All instruments of the (professional) modern orchestra or choir constantly alter pitch flat or sharp as they perform so as to be in tune at any given moment. They talk and teach amongst themselves as to how to be in tune when they play any interval at any moment. This is the price of 12 note equal temperament. It’s the reason why skilled youth orchestras are always out of tune. Position and embouchure are only learned with experience. And don’t you dare argue me percussion section that has some pitched bells and stuff. Those instruments are out of tune and it’s not your fault. 4) Pianos are a unique exception from #3. Pianos are the ONLY instrument in the orchestra who’s pitch is fixed. As a pianist, you are stuck with the notes the tuner gives you and that’s it. You can’t alter pitch as a pianist. Everybody else can. 5) Pianos are almost impossible to a physicist. High notes are played by small instruments such as the piccolo for a reason. Low notes are played by big instruments such as a bass. Here the problem: “I want one instrument that plays higher that a piccolo and lower than any bass at the same time. Plus everything in the middle must also be in tune always.” 6) Pianos have an incredible disadvantage that most instruments don’t. It’s called Inharmonicity. Henry didn’t delve here in this video, but it’s only because he must limit his scope of a short video. 7) Pianos are never, ever, EVER, tuned by pitch. That’s the barrier to you musicians that think you know how to tune. Whether or not you tune pianos by ear or software, you simply don’t care about the fundamental (note). You only match coincident partials and forget about the note. Always. 8). There is no such thing as a perfectly tuned piano for all scenarios. I am called in to tune the same piano 4 days in a row because a solo piano tuning is different that a chamber tuning that is different from a pop recording that is different from jazz. None of this is a secret- it’s simply what pros know.

[@shireenakter4409]

Ok

[@soundacademy6286]

This is so insightful thank you so much! You helped me a lot.

[@ahmedsalim3453]

My God!

[@Charles.Wright]

7) can you please elaborate?? For example, i was thinking of gettinga tuning kit off of Amazon. Then just use a tuning app and tune each string of each note to... Well, it's correct pitch?? What is wrong with that?

[@non-toxic7227]

k

[@TheHoaxHotel]

What about the elusive "brown note"?

[@AnstonMusic]

+The Hoax Hotel Just a myth concerning lower-than-audible frequencies.

[@TheHoaxHotel]

+Anston Music The only way to hear, or should I say feel the brown note, is to play the b, a, and g notes in rapid succession on a recorder. The notes will blend together in a perfect symphony of hertz and dreams, creating the elusive note we cherish most.

[@AnstonMusic]

The Hoax Hotel Interesting, I only know what MythBusters explained, but I guess that's not the whole story...

[@TheFlusteredCustard]

+Anston Music I'm preeeeetty sure that was a joke.

[@sts-31]

+Anston Music please don't believe that guy.

[@Paul-A01]

What ever happened to the well tested rigor of "Eh, close enough" ?

[@michaelsommers2356]

+TGGeko That's what equal temperament is all about: getting the tones close enough that the entire piano is consistent.

[@tobortine]

+TGGeko _"Close enough for jazz"_ is also a good tuning.

[@MikeJanes82]

+TGGeko Among piano tuners, the phrase is "Good enough for jazz".

[@JazzKeyboardist1]

+Mike Janes ....Good one but the phrase good enough for jazz came into being because Jazz musicians are masters of faking everything and composing and improvising on the spot?. So they don't really need to practice more than once. See the Miles Davis album Kind of Blue? Why would any classical musician want to practice the same advanced pieces hundreds of times when you can just make stuff up? lol

[@MikeJanes82]

+JazzKeyboardist1 A 10th that's beating too fast will stick out in Mozart, but tends to go unnoticed in an EbMaj7#5 chord. That's the joke.

[@TheEvertw]

Ah, tuning. I have once in my life heard music that was completely in tune. Only once. It was a recording of a small group of singers that sang a-Capella and had trained hard on singing with clear notes and in complete harmony with each other. A very rare experience.

[@Lulink013]

Sounds simpler than the string theory. Wait...

[@slbcs7131]

brah...

[@beneverhart2145]

+Jose Aldana I had an inverted erection, don't know why

[@david9075]

I was the 200th like... dunno why I just said that :-D

[@horsesandsmilesable]

Lol

[@DeuteriumTech]

Underrated comment. Lol

[@carledwardsagan8295]

I love pretending to understand these videos.

[@diamondsprince]

haha same

[@VizBizNiz]

Same

[@dogzer]

+Carl Edward Sagan Haha!

[@seaden0000]

+Carl Edward Sagan nice one

[@jaimesantos809]

+Carl Edward Sagan laughed harder at your picture, priceless

[@te0nani]

Irrational Numbers. So we met again...

[@ThePizzabrothersGaming]

at least they're still real...

[@CsBence98]

_i_ know right?

[@ThePizzabrothersGaming]

CsBence98 _j_, someone gets me

[@CsBence98]

_k_ I didn't expect to be counter-mathed.

[@ThePizzabrothersGaming]

CsBence98 can _i_ _x_ your something? _y_ do we even use imaginary numbers?

[@aghanr]

"man physics is difficult, i'll just be a musician, there's no way there's gonna be physics and math right?" "shit"

[@harambo88]

music is just a subclass of math. pythagoras wasnt looking for nice sound when he invented the intervalls.

[@vjc5920]

@@harambo88 *confuse in electronic music*

[@whatislife459]

I had the same thing but with programming. Hahaha I made an alien dance on Alice I hope I never have to use equations math, science to do anything. Shit

[@gordonshing4707]

I play piano and guitar and work with math too, I can say for sure piano / guitar are as hard as maths. It‘s just that with lots and lots and lots of practice, piano/guitar/mathematics all look “easy”

[@Maddolis]

The hardest question for a musician isn't physics or maths, it's economics. "How do I make money doing this?"

[@PrincessFelicie]

Is mayonnaise an instrument?

[@PianoHaiku]

+Ryoga Hibiki Yes, check out Mayones guitars. It's a very good brand.

[@Appletank8]

+PianoHaiku Patrick has finally found his spirit instrument.

[@Godtierlee]

+Ryoga Hibiki No Ryoga, mayonnaise is not an instrument.

[@BenjaminDod]

Horseradish is not an instrument either

[@Mornys]

+Ryoga Hibiki Yes it's a percussion instrument. First it makes a _slap sound_, then it makes _people yelling at you sound_ and then it makes the _men in white coats coming to get you sound_. It's also always horribly out of tune.

[@Shilag]

That was extremely interesting. I've played the piano for years and years but I didn't know tuning wasn't based on harmonics.

[@uztre6789]

+Shilag It is though. Have you watched the video?

[@GregoMorgan]

+uztre6789 Have you ?

[@Shilag]

+uztre6789 Well, one of us clearly misunderstood the video. I'm not sure I understood everything he said but what I gathered was that pianos can't be tuned based on harmonics because it won't add up cleanly to an octave with twice the frequency of the last one, no matter what harmonics you base it on. Therefore we just tune it based on even mathematical intervals instead.

[@uztre6789]

Shilag Harmonics still matter because why care what an octave is when you don't base it on harmonics.

[@GregoMorgan]

uztre6789 Fair point.

[@primeirrational]

What's wrong with irrationals?

[@primeirrational]

Evi1M4chine touché

[@0ArthurKirkland]

As a dumb person, I support this message.

[@alanhilder1883]

I will stick to the square root of -1. It's unreal.

[@NoorquackerInd]

I am the square root of -1!

[@teovinokur9362]

because 7 8 9

[@PuckishAngeI]

When you finish physics, music and math in school

[@monochromeart7311]

and have a drunk anime girl as a pfp

[@sammyboy447]

And also a hint of health class

[@oblivion2755]

And it's a master.

[@michelchaman6495]

IKR people always ask... so... why?

[@tinman1955]

I'm gonna tell my tuner I want my money back.

[@blueschase11]

Good idea lol

[@rusianalf]

+Tin Man and he'll tell you to go flat yourself

[@13lackk9]

+Tin Man Or you can drop your piano down a mine shaft. You'll get A Flat Minor.

[@ariak9858]

+Disgruntled Solly HAH

[@PrincessJayseff]

+Tin Man try getting to college to study music and finding this out 2 years in from your sight singing instructor...

[@ToddHowar.d]

He mentioned viola! WE'VE BEEN RECOGNIZED

[@ExternusArmy]

+monks9098 Violas > Upright Bass > Cellos > Violins. That's an actual fact.

[@alec8182]

+monks9098 MELODY BELONGS TO FIRST VIOLINS ONLY! AWAY WITH YOU VIOLAS! lel

[@heartseed478]

+ExternusArmy whatever... I play them all wahahaha

[@ExternusArmy]

***** You're a god amongst men.

[@therealzilch]

+monks9098 Time for some viola jokes, then. What do you do with a dead violist? Move him back one stand. What's the difference between a violin and a viola? A viola burns longer. Why is the viola called "bratsche" in German? Because that's the sound it makes when you sit on it.

[@toastedclubsandwich]

I watched this video 4 years ago when it came out and I didn't understand it at all. Well, it took 4 years, but I've finally returned and now I can confidently say that I still do not understand anything.

[@kirjian]

Had to detune this video to A 432 to prevent mind control, carry on

[@rogueanuerz]

lol conspiracy hoaxer

[@barrygeistwhite3474]

I don't get this, so I'm going to assume that it's really clever.

[@GeorgeSPAMTindle]

@Shallex 432Hz is the resonant frequency of a tinfoil hat full of Koolaid.

[@SchiferlED]

You can tune a tuna but you can't fish a piano.

[@TheMiracleMatter]

+SchiferlED I laughed way too much at this...

[@Laikadaisical]

but you sure can play on its scales

[@TheMiracleMatter]

Space Admiral Laika ba dum tsssss...

[@JazzKeyboardist1]

You hooked me

[@GenericInternetter]

+SchiferlED "you can tune a piano but you cant tuna fish." you're welcome.

[@Modo942000]

i have no idea what you said in this video

[@TheCh0senOne]

+Modo942000 Yeah, he had to add music terms, too... like my struggle with physics wasn't enough

[@Modo942000]

TheCh0senOne1 my struggle is with music not physics :D. i really don't know what tuning is since i never took music class in school

[@seaman83]

Me too

[@clearwaterlakota8405]

+InSilentSpaces -Please post the actual title of her video on tuning, I'm not seeing specifically which one you're referring to. But thanks for turning me on to her, she's brilliant!

[@luvsYuri]

Me too I don't understand anything lol

[@EmdrGreg]

Not to be obnoxiously picky, but it isn't impossible to tune a piano-- it is just impossible to tune one without stretching most intervals. The topic is very well presented.

[@MusicalRaichu]

+Greg Scott Even with natural tuning, you can pick any key and tune your piano such that the three major chords and two minor chords are perfectly in tune, or two major chords and three minor chords are perfectly in tune. Everything else and every other key will be out. E.g., in C major, you can tune it so that C, G, F major and E and A minor are OK but D minor will be out. Alternatively you can tune D minor but F major will be out. So it's impossible for all 6 main chords to work with a perfect pitch keyboard.

[@EmdrGreg]

MusicalRaichu ...of course, MR. This is well known among people with any knowledge of piano tuning. There were many methods that were common in centuries past for tuning of harpsichords and clavichords; these methods allowed musicians to play the music of the day adequately. There are many different schemes for tuning keyboards. No one takes the methods you suggest seriously for standard piano tuning, but many people do use specialized methods for specialty recitals or recordings. The tuning scheme used in Chopin's day, for example, is different from equal temperament and in some cases really highlights the beauty of Chopin's harmonies. All of this illustrates that there is no one perfect method for tuning the piano; that is impossible. We're running the risk of getting way too picky here; the idea is that mathematics itself prevents a piano from being tuned in such a way that every chord in every key is perfect. There MUST be compromise somewhere.

[@MusicalRaichu]

Greg Scott yep that's what I was trying to say. didn't know that it was different in chopin's day though. guess that shows how music is an evolving art.

[@EmdrGreg]

MusicalRaichu Yeah-- the history of tuning is more complicated than meets the eye... or, ear. You're probably aware that Bach famously endorsed well temperament as used in The Well-Tempered Clavier, and many people confuse that system with modern equal tempering. In fact, well tempering was an attempt to compromise in a few ways so that you could indeed play in every key, but some keys had intervals that were a little farther out than others. A musician would not be able to play all the pieces of TWTC on a keyboard tuned in the conventional method prior to well tempering. There were different approaches to temperament throughout Europe, including different standard pitches. It was only within the last century or so (I think) that A=440 was accepted as standard pitch. In Chopin's day, they didn't use equal temperament, but something a little closer to Bach's well tempering. So some of Chopin's music sounded different to Chopin himself than it does to us on modern equal tempered pianos. It's very interesting stuff if you're into that kind of thing.

[@MusicalRaichu]

Greg Scott Actually, to me, a modern piano sounds different in different keys. Flat keys sound mellow while sharps are brassy. Is that's my imagination, or is modern tuning a bit biased in some way?

[@admiralcapn]

Bach's Theory of Relativity: E = Fb

[@GeorgeSPAMTindle]

B = Cb in the key of Gb, or F = E# if you want to call the key F#. It's in that pesky area of the circle of fifths where you whether you pick to have six sharps or six flats you are going to have to step out of accepted naming convention one way or the other.

[@jfly609]

admiralcapn well done

[@EsperantistoVolulo]

(F double sharp)oo(E double flat) jok(F flat).

[@GeorgeSPAMTindle]

@No one cares The conventional thing to do is to call it Gb because all other keys are either Natural or Flat, but F# is an equally valid name. Your suggestion is the best approach.

[@GeorgeSPAMTindle]

@No one cares I'm sure that there are 11 others.

[@groszak1]

There is a compromise between equal temperament (any song playable) and harmonics (nice sounds), it's called *well temperament* . The notes are tuned for example like this: C: 1/1 C#: 200/189 D: 9/8 D#: 32/27 E: 81/64 F: 4/3 F#: 625/441 G: 3/2 G#: 128/81 A: 27/16 A#: 16/9 B: 189/100 C: 2/1 You still preserve 8 of the fourths as 4/3, while 3 of them will be 75/56 and one of them 83349/62500 (3/2, 112/75 and 12500/83349 for fifths). But they are only off by a few cents, while Pythagorean tuning and meantone have one _horrible_ fifth. Other intervals are nice too. Edit: This tuning is better: C: 1/1 C#: 256/243 D: 28/25 D#: 32/27 E: 5/4 F: 4/3 F#: 45/32 G: 3/2 G#: 128/81 A: 375/224 A#: 16/9 B: 15/8 C: 2/1

[@groszak1]

***** Actually there are many variations of well temperament, with no standard one. I just created one myself by using 75/56 together with 4/3.

[@groszak1]

If you want to use a well temperament with fraction ratios, I recommend to use this instead: C: 1/1 C#: 256/243 D: 28/25 D#: 32/27 E: 5/4 F: 4/3 F#: 45/32 G: 3/2 G#: 128/81 A: 375/224 A#: 16/9 B: 15/8 C: 2/1 C-E and G-B major thirds are pure, as well as E-G minor third. C-G, E-B, B-F#, C#-G#, G#-D#, D#-A#, A#-F and F-C fifths are all perfect. G-D, D-A and A-E fifths are slightly flat, while the F#-C# fifth is indistinguishable from a perfect fifth. In short, *you will be able to play C-E-G perfectly, and G-B-D quite good*. *Here is why equal temperament is used now:* Tuning began with *Pythagorean tuning*, which tunes a fifth to 3/2, and stacks them. Octave (2/1) is also used. However, major/minor thirds were impure (81/64 and 32/27 respectively) so *mean-tone* was invented. It flattens the size of fifth to be flatted, so that major and minor thirds would be closer to 5/4 and 6/5. The problem with Pythagorean and mean-tone tunings is that the circle of fifths could not close to octave, so one of the fifths was a wolf fifth (There is a maximum of 8 major thirds or 9 minor thirds because of that). *Modified mean-tone* spreads the wolf fifth into 2 or more parts, so that wolf fifth would be more acceptable and to get more than 8 acceptable thirds. *Well temperament* makes all 12 thirds usable. This is done by spreading the comma on Pythagorean tuning instead of mean-tone, so that the worst third would be Pythagorean fifth. More often used fifths are flatted to achieve better thirds. Most well temperaments don't have *pure* thirds, but have some close-to-pure thirds. However, music started to switch between different fifths/thirds more quickly, and in well temperament, C-E for example sounded differently from F#-A#. So *Victorian well temperament* was used which makes different fifths and thirds closer to each other, though the more often used ones were still purer. Because of the difference between these was still a problem (though reduced) finally all fifths/thirds were equalized, resulting in *equal temperament*. _I don't know why they considered switching between fifths/thirds more important than making more often used fifths/thirds better._

[@groszak1]

***** The reason for switching from well to equal temperament is that music has started to change keys quickly, instead of gradually (C major, G major, D major, A major, ...) and abrupt changes in color of thirds/fifths was bad.

[@Iendyil]

There was never any tuning system called "well temperament" you're referring to the system used by Bach in "the Well tempered clavier"this was just one tempered system. There were many different systems of temperament, "well temperament" is just a phrase to describe a system where you could play in all keys. and whilst a convincing case has been made by Lehman for the system you've described its contested whether this is what the squiggles on the top of that page by Bach actually mean.

[@groszak1]

***** I just designed one well temperament. Well temperament was used in many forms, depending on the composer.

[@EvanC0912]

? ? ? These harmonics caused disharmony in my brain... Maybe I should learn theory of musics

[@FernieCanto]

+EC912 It's worth it. Once it starts making sense, it's pretty fun.

[@mikedavino2400]

+EC912 use 432Hz sacred solfeggio instead of J Goebbels muddy 440hz

[@orfeasliossatos]

don't don't don't it's a waste of time.

[@mikedavino2400]

I'm a music theorist and a jazz piano player

[@FernieCanto]

Mike Davino So what? Musicians can be wrong too. A432 is an outlandish conspiracy theory with no historical or music basis whatsoever. If you can demonstrate you're right, I'd really appreciate it if you did so.

[@TheDeuceofSpades]

You forgot to factor in inharmonicity, which further complicates the problem of tuning equal temperament. Basically, the stiffness of the physical string doesn't create a perfect harmonic. Those harmonics resonate octaves above their fundamental note, but due to stiffness, they resonate slightly sharp of the theoretical frequency they should sound like. Tuners must factor this in as well in order to make playing notes several octaves apart continue to sound pleasant to us. Mathematical tuning will not optimize harmony in a piano. Uprights have the worst of it, because the string length is already being compromised from its ideal length/fundamental pitch ratio to an extreme.

[@cjheaford]

David Marley You are 100% correct about inharmonicity. Good explanation. I’m sure Henry knows this too, but it was beyond the scope of this video.

[@amitailavi9512]

Me: your intonation is terrible Friend: how? I am playing the piano *Pushes up glasses *

[@Tschoii90]

Hah. I didn't understand a word. 10/10 I love your channel.

[@danielonenut1864]

same here xD

[@shaantubes]

This cracked me up 😂

[@AzhadCom]

*aah, the sound of shaking animal intestines*

[@feel.s1304]

Azhad Its usually steel or nylon, not many people use gut strings.

[@mytasteinmusicisyourface3020]

I mean strings which are traditionally made out of cat gut but regardless of what is made out of when a string of vibrates it does so with the ends fixed to the instrument this means that it can only vibrate in certain ways sign waves like a jump rope with one bump or 2 bumps or 3 or 4 or some combination of these bumps the more bumps the higher the pitch and the faster the street has to vibrate in fact the frequency of a string's vibration is exactly equal to the number of bumps times the string's fundamental frequency that is the frequency of vibrations for a single bump and since most melodious instruments use either strings or air vibrating pipes which has the same sinusoidal behavior it won't surprise you to hear that musicians have different names for the different ratios between these pictures in the traditional western scale 1 to 2 bumps is called an octave 2 to three is a perfect 5th 3 to 4 is a perfect 4th then a major third minor third some other things that arent in the scale and 8 to 9 bumps is a major 2nd or whole step if you play a few of these notes together you get the nice sound of perfect harmony, hence the name for this pattern of pitches, harmonics! In fact the sound that matches one of the harmonics of a string can cause that string to start vibrating on its own with a resident ringing sound. And a bugle playing taps its only the note in a single series of harmonics which is part of why the melody of taps rings out so purely and why you can play taps with the harmonics of a single gutair string harmonics can also be used to tune string instruments, for example, on a violin Viola cello the third harmonic on one sting should be equal to the second harmonic on the next tree up. Bassists and guitarists configure the 4th harmonic to the third harmonic on the next string up But then we come to the piano or historicly the harpsichord or calivicord, either way, the problem is this, it has too many strings there is sting for each semi tone of the western scale times 7, if you wanted to, to tune these strings using harmonics, you could, for example, try using whole steps of example you could tune the 9th harmonic on one key to the 8th harmonic two keys up but if you do it 6 times, you'll get to what's supposed to be the original note on octave up which should have twice the frequency except that our harmonic tuning method multiply the frequency by a factor of 9 8hs each time And 9 over 6th is not 2 it's 2.027286529541, etc. If you tried harmonicly tuning a piano using major thirds instead you'd multiply the frequency by 5 4ths 3 times or 1.953125 still not close. using fourths you get 1.973 not 2 5th gifts 2.0277 again and don't even by using half steps you'll be off by almost 10 percent and this is the problem. It's mathematically impossible to tune a piano consistently across all keys using perfect beautiful harmonics. So we don't most pianos these days use what's called equal tempered tuning where the frequency of each key is the 12th root of 2 times the frequentcy of the key below it. The 12th root of 2 is and irrational number something you'll never get your ratio loft harmonic tuning benefit is that once you go up 12 keys, but a benefit is that you end up with exactly the 12th root of 2 to 12 wich is twice the frequency. On a Perfect octave, however, the octave is the only perfect interval on a equal tuned piano 5th. Are slightly flat, forth slightly sharp. Major thirds are sharp minor third are flat and so on. You can hear kind of wah wah wah wah wah effect in this equal tempered chord which goes away using harmonic tuning. But if you tune an instrument using the 12th root of 2 as most pains digital tuners and computers instrument are you can play any song in any key and they will all be equally and just slightly out of tune. This minute physics video is brought some to you in part by audible.com the leading provider of audio books across all types of literature, including fiction nonfiction and periodicals if you go to audible.com/minutephysics , you can try a couple out by downloading a free audiobook of your choice. I just read the name of the wound by patric roffus it's a fantasy novel with a very music and scientifically oriented protagonist and I Thoughouly enjoyed it. You can download this audio book or a free audio book of you choice at aubible.com/minutephysics and i'd like to thank audible for helping me continue to make these videos. Why I'd I do that? Because I'm bored.

[@anirishpotato4427]

Rocket science: At least it's not music theory

[@karhukivi]

To try to clear up the confusion, a piano could be tuned perfectly to one key, e.g. "C" but would sound slightly off-tune in another key. Instead, a compromise tuning is done to allow the piano to play more or less correctly in all keys. Most of the time it isn't noticeable except to the most discerning ears!

[@rezneba101]

Title isn't quite right. Correct title: "Why It's Impossible to Tune a Piano using only harmonics"

[@leejared]

+rezneba101 If you watched the video you'll see that there is no tuning method that will tune every single note perfectly across multiple octaves. You have to compromise between tuning every note an octave higher perfectly or every note within a single octave perfectly, but you can't have both. Title is accurate.

[@rezneba101]

***** I did watch the video, again. All examples refer to harmonic tuning. Except the last explanation, which, seems to me, fails to demonstrate why the same problem doesn't apply to all other instruments.

[@leejared]

+rezneba101 because the piano has more than one octave worth of strings. There's too many strings. A violin for example can play more than an octave worth of notes but only has four strings.

[@rezneba101]

***** I find that argument unsatisfactory.

[@willferrous8677]

+rezneba101 your face is unsatisfactory =D

[@QuirtemGames]

I had to duck while watching this video, because all of it went over my head.

[@Jay-rj8uc]

Edgy!

[@Thrna_1]

I do too.

[@legofan431]

I have no idea what you just said in the last 4 minutes

[@Olivia-qb8vm]

Same..😕😑😖😛

[@soda_gt.]

+legofan431 you guys didnt have music class in elementary ,k

[@Neclony]

+legofan431 He just said that a piano is always out of tune. xD

[@asd0l5]

+legofan431 The only thin I understood, was the catgut part :o

[@asd0l5]

+waynetraub3 so did mine

[@jarrahtree5130]

Hearing all these people not understanding anything being said makes me feel like my music degree is perhaps worth at least something.

[@williamkrause5831]

Jarrah tree yeah its worth the thousands of dollars u spent on getting it lol

[@ynsmdd8678]

Not really, I took a physics class on waves and we studied how instruments work. I'd say a physicist would understand this video better than someone with a music degree.

[@xisotopex]

you should have instead gotten a degree in actuarial science, then you could do music in your spare time and teach yourself the same things you went to school for, except you would making a 6 figure income.

[@MegamagRC]

@@xisotopex Right, do YOU make a six figure income?

[@xisotopex]

@@MegamagRC no I got a degree in music theory and performance...

[@bradhintz2901]

0:07 **sees screen** **stops petting cat**

[@LittleCorns]

Next video: Why life is mathematically impossible

[@ZER0--]

+ConWolf You do realise you comment is a paradox.

[@templare251993]

That was incredible! It mix Music and Math, two of my favourite passions! Thank you very much for sharing this knowledge!

[@ScenicDepot]

I've been doing occasional piano tuning since the 1970s, and always used the old method of stretching the fourths (+ 1 beat per second), compressing the fifths (- 3 beats in five seconds), and double-checking the process with the major thirds. This approximates the twelfth-root method. Then you have to start stretching the octave once you get to two Cs above middle C by a factor of two beats per second because it will sound flat to the ear otherwise, even if tuned to the perfect frequency. Most electronic keyboards that I have heard do not take this into consideration and they sound a little flat to me in the upper treble section. Some strings on some cheaper pianos will have false beats, meaning they will wah-wah-wah no matter what you do. Piano tuning involves some major compromises and is a bit of an art.

[@physioweng]

I'm a complicated man, I see a video I don't understand, I press like.

[@9000fail]

I have now mastered music

[@KainYusanagi]

+MrOrder67 Anyone who says that they don't take practice hasn't actually played them.

[@SOCOM955555]

+MrOrder67 Ouch, I personally am a marimba player but come on. Any musical instrument takes time, effort, and love to learn and play properly. It is just kinda rude and not fair to say the Tuba, Flugelhorn, and Trumpet don't take any practice. Even more so with wind instruments where breath control is a factor, if you really want an instrument that requires no practice then try the snare drum, even an untrained person can play a basic note on a snare, but it takes a master to make that drum sound amazing.

[@General12th]

+MrOrder67 Yep. Trumpets require no thought at all. There's no difficulty in playing it. None at all. Anyone can do it proficiently. **walks away whistling**

[@purewaterruler]

+MrOrder67 You have no idea how difficult they can be. You haven't played any of them have you...

[@samuelhodil1458]

+MrOrder67 What are you even talking about. All of those instruments are hard to learn. I can't even start playing them because I can't hold enough air in my lungs to blow through a tuba. It takes so much time to learn.

[@awesomeariados6501]

I hate my piano teacher's piano. It's been seven years of "That was a wrong note. Play that again." No, it WAS the right note, you just need to TUNE YOUR PIANO, GURLFRIEND! IT'S BEEN YEARS! As an experienced pianist, I can tell you that piano tunings are a mess.

[@matthewwright57]

Digital Pianos for the win!

[@TheZALGOisCOMING]

Why the fuck did you stay with that teacher for 7 years then?

[@gensoumusic2145]

maybe they mean wrong key, I don't see how they heard the wrong note being played if their piano is out of tune.

[@Richardyu678]

Digital Pianos SUCK. On one, it is literally impossible to play with emotion.

[@diegoteclas]

maybe you didn't tried a modern clavinova digital piano, fully based in 32 bits stereo samples n 16 layers of faded samples conrolled by 2 cpus. using weighted keys and graduated hammer effect depending on the keyboard zone. try an advanced CASIO privia model, you will be surprised

[@paulhoward5703]

And this, my friends, is why barbershop music is so good and pure. Voices, when properly trained, can actually figure these Harmonics out; thus, overtones!

[@PianoMastR64]

What if there was an electric piano that dynamically adapts the tuning of each note depending on which multiple notes are being pressed simultaneously to force them to have perfect harmony but in such a subtle way that we wouldn't notice while we're playing unless we're listening for it?

[@PaulMagnusSrensenClark]

+PianoMastR64 Very interesting suggestion. I'm sure that would be possible to make. I wouldn't be surprised if it already exists.

[@PianoMastR64]

I have a keyboard and I know a bit of C#. If I can learn how to work with midi signals, then I might be able to make a program that can do this.

[@Vladythebest96]

+PianoMastR64 m8..

[@Leo1239150]

+PianoMastR64 I too know a bit of C#. C# F G#

[@PianoMastR64]

I know both C# and Db. Yeah.

[@HaniiPuppy]

But you can tune a fish.

[@Jawz4Lyfe]

Leave.

[@MRLegendPiano]

GET OUT

[@ujiltromm7358]

No, but a tin can.

[@charliedajoob2246]

shanghai?

[@livedandletdie]

You deserve a single clap of my hands.

[@thedevildances]

Is Wawawa-effect a correct term? ^^

[@joez6235]

+Earl Ofargyll It's called oscillation

[@linguaphilly]

And the psychological term (for the sound your mind actually perceives) is "binaural beats"

[@IamGrimalkin]

Isn't it called "beating"?

[@minecraftermad]

+Jose lol no

[@minecraftermad]

+Jose oscilation is just a wave... VERY basically

[@Bean41]

I’ll just have to take your word that there was a wawawa sound... I couldn’t here it.

[@ejoomf]

Bean 41 he also said there was a chord and that was a single note lmao

[@KnakuanaRka]

I had to put in the headphones and turn the volume way up to hear it at all, but it’s there. Doesn’t help that he gives you very little time to hear it without him talking over it.

[@lucaselting2946]

@@ejoomf no man it was a chord

[@Syckxpack]

@@lucaselting2946 or an interval? Gr. Terz oder quarte...

[@lopata_of_death6894]

it's called acoustic beats.

[@geoffstockton]

From a music educator of 15 years and author on the topic, great job! This is the best short video I've seen regarding temperament! I'm subscribing. The channel name tells me I'll enjoy it.

[@wickett7078]

+Geoff Stockton My band directors first name is Geoff...

[@jorgepeterbarton]

Oh ok. That wasn't the answer. Equal temperament is considered 'in tune' since a lot of the other instruments you mentioned also exhibit this. Its nothing to do with string number, its to do with fixed pitches. You can play a violin in tune to harmonics, but not a guitar, as it has frets. Likewise a trumpet actually plays harmonics and the keys merely adjust the key they are in for more notes, whilst a clarinet has equal tempered keys- although its registers are harmonically related. Pianos aren't tuned to equal temperament. They use stretched tuning. Not just because of 'it sounds nice'. The strings on a piano are not perfect strings in a maths eqution. They exhibit harmonics that lie slightly off what the perfect string is. The string also lowers in pitch as the note decays in time, differently across the whole keyboard. causing the string to sound detuned when really the fundamental is perfectly in tune. So even if you tuned to only harmonics, it would still be off between the lowest A and highest A. This needs compensating as its imperfect, so really a perfectly professionally tuned piano, the fundamentals are not in tune-to anything- its merely a compromise between both perfect tuning, and the fact that strings aren't making perfect notes in the first place!

[@syrup128]

scrolled till i found this +1

[@MegaSemi]

Exactly!

[@thisisawsome34253212]

Here's an idea for future computer instruments and sample piano recordings. Use micro-tonal tuning to get multiple frequencies for every semitone. As a result when your stacking the chords you can pick the right version of each note to stack against the root and everything will be in tune. What do you guys think?

[@groszak1]

You mean something like 53edo, which splits the octave into 53 equal parts instead of 12?

[@avavav1232]

Someone has already done it: kzbin.info/www/bejne/jaGah514qbR9bZY

[@avavav1232]

every interval here is just (sort of)

[@drakep271]

I'm pretty sure that's actually what they do for lo-fi hip-hop. Adam Neely made a video called The 7 Levels of Jazz or something like that and talked about it towards the end

[@jack_papel]

Look up Benedetti's puzzle. Actually, Adam Neely has a great video on it. It's the reason why that wouldn't necessarily be so great

[@martymodus7205]

I'll never forget teaching this concept many years ago when one of my wonderfully bright, perfectionist, string players got seriously upset as she started understanding it and declared passionately to the whole class, "This REALLY makes me mad!" I pointed out that ET is a really elegant solution to avoid the much worse intonation issues that arise without it, but that didn't help. It's like learning that Santa isn't real. Takes a while to get over it.

[@somatia350]

Marty Modus just tell them about the wolf 5th Blows their mind out

[@xisotopex]

it can also be comforting... when I learned about 12 tet I finally realized why certain chords on guitar always sound a little bit off, even when its 2000$ martin.

[@adamkubiak1933]

xisotopex funny thing is, though, that when you play a guitar with frets built to accommodate for this characteristic and guitar plays in tune, wel... you guessed it.. it doesn’t sound like a guitar. 😉

[@xisotopex]

I dont mind a chorused effect, but most guitars just sound bad in certain positions...I would love to play a guitar that was perfectly in tune in any tuning in any position

[@martymodus7205]

@@adamkubiak1933 If the frets aren't equal temperament, then they can only be just temperament relative to certain chords, so I'm not sure what you mean about the adjustment of the frets. Regardless, it's physically impossible to make any instrument "in tune" relative to all natural harmonic series/ratios. We all must compromise one way or another.

[@douggwyn9656]

There is a lot more to piano tuning. The modern default tuning "standard" is higher-pitched than the norm centuries ago, and is "equal-tempered" (uniformly spaced logarithmic scale), so that octaves are exact and every other ratio is only approximate. In Bach's day, it was common for pianos to be tuned for best results (most exact ratios of small integers) in only one particular key, called "well-tempering". His "Well-tempered Clavier" exploits its properties; W. Carlos of "Switched-On Bach" fame put out at least one record album using well-tempering. As somebody else mentioned, common practice for the multiple-wire notes is to spread out the spectrum slightly so that resonances are improved, and piano tuners iteratively tweak the tuning for best overall sound in the most frequently used keys.

[@barristanselmy2758]

There's a glitch in the matrix.

[@RubenHogenhout]

Yes I know that.My piano teachter a long time ago spoke to me that not all keys were the same in older days. That the E b was a bit more heroic for example. And that also the E flat was a bit higer then the D sharp ( Am I right? ) But now on the piano they tunes everything the same a bit out of tune. So you can pay in all keys and that this was in earlier times not possible. At the same time it can also be a bit of a pitty. A bit different keys can also be interesting and give charater to a piece of music. All the same can also be boring. Or am I wrong?

[@BobPlody]

This is a great video, but actually the harmonic tuning method is also fundamentally flawed. The harmonics on stringed instruments don't actually create perfect integers of the fundamental frequency. Due to the strings being physical things with tension, a phenomenon called inharmonicity occurs. This means that the harmonic frequencies actually slighty increase with each integer. For example, if the fundamental frequency is 100 Hz, then the 1st harmonic may be 200.02 Hz and the 20th harmonic may be 2034 Hz. This means that when tuning a piano, using the equal temperament system, the higher keys will be sharp and the lower keys will be flat. Interestingly, this is still how we tune pianos and when keyboards have been produced with "perfect" tuning, musicians and sound engineers have preferred the "imperfect" tuning. Perfectly tuned pianos sound wrong to us.

[@SillyPutty125]

+Banjo Bob Perfectly tuned pianos sound wrong to us for the reasons discussed in this video. When you play a 5th on a piano, it doesn't sound in tune because to our ears, it sounds in tune when the ratio of frequencies is exactly 1.5 but a well tempered tuning makes it 1.4983, which is 0.1% off. For comparison, the difference between 200Hz and 200.02 Hz is 0.01%, which is 10 times as hard to perceive. You can even hear the beats ("Wahwah") when you play a 5th on the piano. The inharmonicity doesn't affect a piano's tuning because they aren't tuned with harmonics. if one 'A' is tuned to 440 Hz, then the one an octave above it is tuned to 880 Hz, not 880.09 Hz. High and low keys usually sound bad on a piano because they are the first to go "out of tune," meaning you just need to tune the piano more often.

[@Howard_Wright]

+SillyPutty125 The inharmonicity is actually the main cause of piano tuning problems. Notes that appear to be an octave apart on the piano are deliberately tuned to be slightly further apart than an octave, hence the term "stretch tuning". So if one note is tuned with a fundamental of 440Hz, the same note one octave higher up on the keyboard will be tuned higher than 880 Hz. This is the way almost all piano tuners tune pianos, to get the best-sounding compromise which deals with the effects of inharmonicity. It's disappointing that the video didn't mention this at all, but it's in all the musical acoustic textbooks.

[@SillyPutty125]

+Howard Wright Oh I get it now. I didn't realize that it doesn't sound "in tune" to us unless our octaves are stretched because it sounds in tune when the harmonics line up. Do you have any online references on how/why perfectly tuned pianos (with no inharmonicity) sound wrong to us? Does that mean our brains are just used to inharmonicity, and if you take it away it sounds strange?

[@Howard_Wright]

+SillyPutty125 I think we are conditioned by what we grow up hearing, and as all real strings are inharmonic (steel strings more so, gut/nylon less so) then yes our brains get used to slightly inharmonic or "stretched" string harmonics as being "normal". Not sure what you mean exactly by perfectly tuned pianos with no inharmonicity. All piano strings will have harmonics that are not exact multiples of the fundamental, but are sharp - i.e. inharmonic. This is the case however the piano is tuned. But as you say, if the harmonics of one string are not lined up (in terms of frequency) with other strings, this gives an out-of-tune feeling. So the stretched octaves of piano tuning minimises the mismatch between the frequencies of different harmonics of different strings, and gives the best overall result. Tuning is always about compromise, it's just that the piano effects make it a much messier compromise than other instruments!

[@SillyPutty125]

+Howard Wright By "no inharmonicity" I mean when a violin played with a bow (it doesn't exhibit inharmonicity due to "mode-locking") or electronic instruments, which have no need for inharmonicity. You mentioned in your OP: >>Interestingly, this is still how we tune pianos and when keyboards have >>been produced with "perfect" tuning, musicians and sound engineers have >>preferred the "imperfect" tuning. Perfectly tuned pianos sound wrong to >>us. I was wondering if you know of any references on this topic.

[@JoeJulien93]

Especially with synthesizers it is very popular to add detune to a sound to make it seem broader, warmer, etc. I think that's why it doesn't matter that much if it's not 100% fitting to the tuning of other instruments. :)

[@RubenHogenhout]

I agree it is a bit boring everything sound the same. They should experiment a bit more.

[@chinossynthesizer705]

​@@RubenHogenhout. For subtractive analog synths and wavetable synths. But with fm synthesis and addictive synthesis ifs much harder.

[@archdukebigdogkoopa3821]

1:04 I love the part right here.

[@Hedwyns]

Your explanation is interesting and well done, but even though it is correct that's not really specific to piano. Actually you explained what equal temperament is, but your statement can be applied to any instrument tuned in equal temperament. The issue with the piano is that it can not be tuned perfectly even in equal temperament. That comes from the string rigidity; an ideal string should keep its shape after beeing twisted, which is obviously not the case in real life. Because of that, the harmonics are not perfect integers(f,2f,3f,4f...) of the fundamental frequency; for example, the second harmonic of an A 440 Hz has not exactly a frequency of 880 Hz. That means than if you play this A and the one one octave higher, assuming your the octave is pure, the second harmonic of the low A will clash with the high A(because there's a difference of a few Hz). To minimize this, the piano is somehow tuned wrong deliberately, and there is no perfect solution to that. It's only a matter of compromise.

[@RipleySawzen]

Simply change the tension and length of the string then. You can get any frequency you like by doing this. A piano is THE MOST tunable instrument because you have a true "infinite" range of tensions and lengths.

[@MegaSemi]

Exactly. Also, inharmonicity aside, it should be noted that equal temperament is not the only solution to the problem this video presents.

[@aaronmueller1560]

Tuning it perfectly in tune is good, but as soon as you play in a different key, it sounds far off from how it should sound. The point of equal temperament is to make every step equal, so it is close enough to in tune for every single key. Otherwise you have to re-tune the entire piano every time you change key.

[@ninjaboy1098]

Hello I am the only not smart one in this comment thread

[@The-Stitch]

@@ninjaboy1098 No im stupid

[@VoicesofMusic]

You definitely can't tune a guitar with harmonics, owing to the syntonic comma: the octaves will be out of tune. And strings aren't made with catgut, although some violinists, folk musicians and players of early music use sheep gut. In addition, vibrating strings may not be in tune with their own harmonics, owing to stiffness of the strings at the end points. Equal temperament is just a starting point for the art of tuning in a system that is not trying to be "just temperament" or some imaginary perfect temperament.

[@oldaccountthatidontuseanymore]

Catgut can be made with any animal's intestines, like a sheep. It's a bit misleading when the word cat is in the name...

[@DragonWinter36]

clank I mean, the “cat” in catgut comes from an Old English word for sheep

[@videopeaberry]

@@DragonWinter36 "Catgut" strings come from sheep intestines made in Catalina, at least those were the most sought after strings before wire dominated.

[@GeorgeSPAMTindle]

Try paying attention when you watch videos, you'll learn a lot more.

[@Greg_Bal]

Thаt's weird. I've seen people tune а guitаr with hаrmonics quite а few times.

[@MPSpecial]

Keep also in mind there are three strings per key (two for the bass ones), and these strings are slightly detuned from eachother. The same mess happens with harps, with only one string per note and pedals for the sharps and flats. It feels so nice to play brass.

[@boptillyouflop]

All solid objects with some symmetry will also naturally have pairs of overlapping harmonics that are very slightly out of tune - for instance a harmonic on a guitar string vibrating vertically vs vibrating horizontally... A vibration pattern on a timpani and a version rotated 90°, or a deformation pattern on a tubular bell and the same pattern rotated 90°... In other words, plucked strings and chromatic percussion are slightly detuned from *themselves* (which is why they sound so good). :3

[@onceupon4t442]

Thanks man, now ill live with the joy of knowing all instruments are out of tune :D

[@spadeofalltrades1321]

Didn't need science to tell me me and my band's outta tune...got the audience for that😉

[@gaymerjerry]

Actually this video is about only how the piano is out of tune the problem is pianos acant adjust tune on the spot every time you play it whatever the notes are tuned to is how its tuned. Most instruments can control air flow or make micro adjustments to change whats known as embouchure. This allows them to make micro adjustments while playing and thats also why they only need to tune to 1 note not every individual note on their instrument. The problem is the 12 tone system we use now is designed for those instruments and not pianos or harpsicord or celestas or xylophones or any of those instruments

[@saboo_tage]

I'd love more videos about music! (Preferrably some that I'd understand)

[@classicmartini]

saboo Try Rick Beato's channel.

[@johannes914]

The "well tempered" method is now the general rule. But you can still find some old instruments like organs that are tuned on different scales.

[@minecraftermad]

+johannes914 suomi perkele!

[@michaelsommers2356]

+johannes914 What is your evidence for that? Everything I have read (admittedly not much) says that equal temperament is virtually universal today in western music.

[@powck]

+Michael Sommers Yeah but classical music has a real hard time of letting go of old habits, for example cembalos are often harmonically tuned.

[@michaelsommers2356]

powck What is your reference for that? I would expect that how you tune your harpsichord would depend on what kind of music you are playing (more specifically, what era the music was written in), and I don't think harmonic tuning was ever used.

[@ohooper]

+Michael Sommers You're correct. A lot of Harpsichord other baroque instrumentation based concerts are played in other temperaments because that was the norm at the time. Certain pieces were written for different temperaments as different chords and keys had a different feeling, this is why you may hear certain keys referred to as having characteristics. Search 'temperaments' on youtube and you'll find a load of interesting videos explaining further.

[@RacecarsAndRicefish]

everything made perfect sense until math started happening like 2 minutes in

[@ZER0--]

+waawamellon at least you can count up to two.

[@blueschewsmith]

+waawamellon Very simple math! Thats part of what makes it beautiful.

[@RacecarsAndRicefish]

***** where does the 9/8 come from?

[@hi-tech6261]

I've seen u NOTHING IMPOSSIBLE

[@RacecarsAndRicefish]

***** alrighty so 1 half step is the smallest interval between 2 notes that we use in western music, and a whole step is 2 half steps an octave is made up of 12 steps, meaning it takes 12 of these intervals to get from one note to the same note but with twice the frequency (half the wavelength) a major scale has 7 notes (8 including the first one but an octave up), and the intervals between the notes are whole step, whole step, half step, whole step, whole step, whole step, half step if you add those up (1 whole = 2 half steps) you'll find that that's 12 half steps a fifth is the interval from a note to the 5th note in the original note's major scale this means whole step + whole step + half step + whole step, or seven half steps fifths are a very important musical interval and are used all the time in twinkle twinkle little star, the interval between the notes you sing when you say the first two 'twinkle's is a perfect fifth

[@jakesinclair7452]

Loved it! Alittle over my head but think I got the gist of it as I am now trying to tune my piano myself. Thank you!

[@GoodVolition]

The standing waves in both wind and string instruments can be fairly complex without thourough testing. The acoustics within the piano are even more difficult. What is important to factor in is that the piano was not necessarily made to obey harmonics. Biology also limits the change in pitch that a human is able to hear. This allows the piano to be tuned, despite not actually being in tune.

[@SamuelEstenlund]

I've heard that a reason to why there are several strings on each (or most) keys, is that the strings will not be tuned exactly the same. So when you're playing a chord looking for a certain harmony, physics will make the string that happens to coincide best with that harmony be amplified, while the other strings are damped. So a key will sound with a slightly different pitch depending on which other keys it's combined with.

[@michaelsommers2356]

+Samuel Estenlund I think it has more to do with getting more volume.

[@volespam]

+Michael Sommers And a richer sound.

[@jamacalexander]

Actually, having the strings tuned slightly different from each other creates a chorus effect which gives it a richer sound. Perfect is not always best as a "perfectly" tuned piano can sound dead flat - no life. (I used to tune pianos)

[@MattStormage]

doesn't this mean that every instrument is tuned incorrectly? like the first 12 frets of a guitar, are they also 2^(1/12) apart in pitch or not

[@Pedun42]

yes. every instrument tuned to Western musical Theory is slightly out of Tune because it is even tempered. wind instruments like the trumpet or a saxophone have their own difficulties when trying to tune.

[@MattStormage]

why was your comment removed pete? i didnt even see it until now

[@whatdyathink]

most ensembles that do not play with fixed pitched instruments (i.e. guitar,piano, marimba,etc) play using "just intonation" which is a style of tuning in which you try and make the least amount of dissonances in a chord ex: in a major chord you would raise the 5th by 2 cents and drop the 3rd by 13 cents. Makes for a much more lovely and pure sound. However, being humans, we're not able to really do just intonation perfectly which some could say is a good thing as it throws off some aspects. If you were to, say in F major, go around a diatonic circle of 5ths then the F you started on wouldn't be the same F you ended up at and would definitely get more and more distant from the original as you went on

[@LatchezarDimitrov]

What about the inperfection of the human ear??? We disscut too much math and not enought music here, imo...

[@bampfibus5773]

Latchezar Dimitrov the thing is, while you cannot really recognize if a single tone is slightly off the scale (btw basing our scales on the a at 440hz is also a quite recent thing to do. before that they took like 432hz as their a and before that everybody tuned their instrument as they wanted to, which is kind of unpractical for orchestras etc), you still can hear that "wahwah"-effect with two tones of the tempered scale played together as demonstrated at 3:26 in the Video. i especially notice that when tuning the guitar by ear, as i can hear the point of perfekt harmony, but have to tune it slightly off anyway.

[@Science__Politics]

I've played piano for years and I did not know about this, but it all makes so much sense to me now. Thank you

[@LnPPersonified]

Finally, something in math I fully understand.

[@PutItAway101]

It's not true to say that a piano is tuned to equal temperament and a guitar isn't. Tuning the open strings using harmonics is a red herring, the fret distances on a guitar are based on equal temperament even if you tuned the open strings based on harmonics, it's all equal-temperament from there up the rest of the neck. And in fact virtually everyone tunes their open strings to the equal-tempered pitches, usually with a tuner. One of the few exceptions is Eddie Van Halen, who sometimes tunes the B string slightly flat, so it makes an ideal major third with the G string, that way you can play A-shape major chords with distortion that sound as solid as power chords without that muzzy intermodulation jangle you get with an equal-tempered third. Think "Runnin' with the Devil"... Of course the problem then is that while those major thirds sound fantastic slightly flat, every other note of the scale sounds worse slightly flat, and you find yourself doing slight bends on the B string all the time to bring them up to pitch...

[@therealzilch]

+PutItAway101 Indeed- that open B string on the guitar, if tuned equal tempered, or worse yet, by harmonics, makes a really jarring major third in G. But what can you do? In fact, fretted instruments were probably the very first instruments to regularly utilize equal temperament, since they couldn't tune all their notes individually, but rather had strings tuned differently using the same fret. That's why, in the Renaissance, when all keyboard instruments were tuned to some kind of meantone tuning, you find pictures and descriptions of lutes having their frets spaced at least very close to equal temperamentt. Anything else doesn't really work with normal frets. Of course, as you mention, you can bend notes, and especially the players of bowed fretted instruments, such as the viola da gamba, regularly do this to get chords closer to just intonation. If you can't adjust your pitch on the fly to accomodate its function, you're doomed to imperfection, as soon as you have a scale of more than five steps. Even God can't change that, if She's logical.

[@PutItAway101]

***** Yep, no one can make the Pythagorean comma disappear, but "infnitely variable pitch" instruments like the violin family and the human voice have got the best chance to disguise it on a note-by-note basis.

[@therealzilch]

PutItAway101 Yep. And we do, because equal tempered thirds suck.

[@SoggyBagelz]

U wot m8¿

[@therealzilch]

***** Is that a rhetorical question?

[@NLite486]

so you can neither tune a piano nor a fish. got it

[@KycenPetersen]

"How about this!" *flips a table and jumps out a window in confusion*

[@remnant24]

I didn't know Jesse Eisenberg knew so much about music.

[@pastymccheese7866]

like........ what??

[@TheRandomizers]

like? OK

[@Sean_Coyne]

Tuning a piano is way more complicated than that, regardless of intonation. For a start, each note has three strings and they are not tuned exactly in unison; they are are given "voice" by have a slight dissonance between them. Secondly the bass and treble notes are tuned slightly sharp and flat respectively, as the human ear does not perceive pitch equally from very low or high notes. Then of course modern pianos are usually tuned to even temperament which has two notes that are very far from true or "just" intonation..(the perfect third and perfect fifth in particular are bent to fit the scale of equal intervals that allows for unlimited modulation). It is possible to use a compromise intonation like Bach's "mean tone" (often used in pipe organs) but that only allows a certain number of keys to be played in, as modulating too far away from the home keys creates unacceptable dissonance.

[@Sean_Coyne]

@@cjheaford Nice reply, although you mistake my experience for only book learning (although being a trad muso, not a classical one, some is). I made and play uilleann pipes, as well as play violin and other traditional instruments like Sitar, where just intonation or modes are used for many styles of music. My mistake on voicing all pianos though, (not my instrument, so I not sure where I picked that up). I have tuned accordions and concertinas and we definitely voice free reed instruments with unison pairs or triple reeds for the distinctive sound that produces. I'm fully aware of the variance between just intonation and temperaments, including even temperament. I was trying to simplify it and mentioned the two worse examples of the major third and sixth as standing out. As for Bach and the well tempered clavier, I have to disagree. He played church organs and there you have a conundrum, to sound well tuned they would ideally be tuned in just intonation, but there you are very limited in how far you can modulate, hence mean tone allowing a fair degree of freedom for the composer. So far as I'm aware he played mostly organs that were in mean tone. His violin playing and compositions though are another matter. I am familiar with the well tempered clavier as well, and there is no consensus if he meant it to be played on an even tempered instrument or one that was using another scheme, or even if it was to be retuned for each piece, as they don't modulated but are separate preludes and fugues (not so unusual with the clavier, spinets, virginals etc back then).

[@cjheaford]

Sean Coyne Kudos to your experience with instruments such as the beautiful Sitar. Respect. But the sitar - by its very capabilities and tradition - is NOTHING like western equal temperament. The sitar allows you to play all the notes in tune...and also the notes that western music doesn’t even acknowledge exist. You are trying to take this conversation beyond its original intended scope. And yes, Bach played organs. He was particularly famous for that. It’s just that for most of his life, he hated how organs were tuned. He could not play in all western keys at the same keyboard without stopping to re-tune. Bach cracked the equal temperament with his eponymous volume in all 12 major & minor keys. It’s a historical breakthrough, and all music changed after Bach proved the value of leaving all notes on the keyboard out of tune.

[@danielthompson5785]

No such thing as perfect third..

[@cjheaford]

A professional tuner actually does tune the 3 strings beatless. The myth of leaving slightly out of tune unisons is only told by lazy tuners who haven’t yet learned beatless unisons. ; )

[@galax574]

Pianists pretend they don't watch this video.

[@HellaMoneys]

I know music theory, play multiple instruments, and have taken a year's worth of college physics classes, and this was still a challenge for me to follow at the speed it was presented at.

[@tipyourscales4338]

that's why you watch it at 2AM, so you don't even try to understand it

[@Scubadog_]

The chirping of early birds outside is accompanying his mumbling nicely!

[@htmlguy88]

I can play 5-6 instruments my family gets me when I say I don't need/want gift and I could understand it basically it's saying you can't technically tune a piano the way the intervals tell you to because tuning that way gives you inaccurate results except for certain cases in which you can get the octave interval to work out that's why a piano is using a perfect root because then you can make it work for the octave and technically be accurate to the ratio of the frequencies of the notes involved in creating that interval.

[@777shadowdragon]

+tipyourscales dunno what u mean by that. 2AM is my peak of functionality lol

[@beneverhart2145]

I'm 13 and I understood perfectly

[@raz0rcarich99]

But can you piano a tuna?

[@Fuzzybuckitt1998]

I love these videos I always feel so smart afterwords when I'm telling my mother

[@rogermetzger7335]

The elder statesman in our family (musically speaking) was my dad’s older brother, Joseph Metzger. He learned to play the violin and tune pianos about a hundred years ago. Dad was a finish carpenter and also very good at reupholstering furniture. I started violin lessons in 1950. Uncle Joe taught Dad how to tune pianos about 1970 and Dad said it was the most difficult thing he had ever studied. Later in that decade, Dad taught me how to tune pianos. Did you ever mop a floor? If you used only one bucket of water, the part of the floor you mopped last was only as clean as the dirty water, right? Learning to temper the scale (so the piano would sound equally good in any key) was challenging but tuning a piano is similar to mopping that floor. Pianos are made partly of metal and mostly of wood. If the average pitch of the piano is significantly below standard pitch (A-440 = C-523.3) - which was the case for many of the pianos I tuned in people’s homes - tuning the hundreds of strings actually compresses the piano frame. If you start by tuning one string of each note of an octave near the middle of the piano and then tune the other hundreds of strings, the first strings that were tuned are then below the pitch to which they were first tuned. (The same thing happens when tuning a violin that is badly out of tune.) If you go dump out the dirty water and get clean water in your bucket and mop the floor a second time, the floor will be cleaner than it was when you finished mopping it the first time. But if the water is even slightly dirty after the second mopping, the part of the floor you mopped last is still slightly dirty. How many times should you repeat the process? Same with tuning a neglected piano that is measurably below standard pitch before you begin. If you tune it twice, it will be closer to standard pitch than if you tune it only once. You might think, why not raise the pitch on the first tuning a specific percentage of a semitone so the average pitch will be very close to standard pitch before you begin tuning the piano a second time? Problem: Different pianos - even different models from a given manufacturer - have different coefficients of compression of their frames as tension is added. Of the various things I have done - printing, managing a factory, etc. - piano tuning was the thing (for which I was paid) that I liked the most and did the longest but, by 2007, I couldn’t hear the pitch of the highest treble notes well enough so, when my wife and I moved away from where our son lived, I gave him my piano tuning tools to keep as keepsakes. If anyone is interested in the “theology in a piano”, let me know.

[@littlebigparardise9245]

that is really interesting, i always wondered why piano tuners always tuned their pianos multiple times. piano tuning seems like one of those things that is harder than it seems for sure

[@rogermetzger7335]

@@littlebigparardise9245 Each string has a tension of 160-200 pounds, resulting in a total string tension of about 35,000 pounds. In the U.S. in the twenty-first century, there are many people who, even if they could master the physics of the process, would not be willing to do the physical work of increasing the tension of the strings. On the other hand, there is enormous satisfaction in doing something that most people couldn't do if they would and wouldn't do if they could!

[@kevinstark1938]

3:44 hehe “B sharp”

[@snowspace24]

Friska_ lmao that’s just an e flat, my favorite one is E triple sharp

[@user-by1my7gb3o]

😂😂😂

[@Phughy]

Being a pianist for over 14 years.. this blew my mind :p I learned something

[@RubenJMorenoMusic]

+Phughy If you would like more information of this, an amazing book that explains this much better is "How Equal Temperament Ruined Harmony (and Why You Should Care)" by Ross W. Duffin.

[@ZER0--]

+Ruben Moreno "And why we shouldn't care" is correct. I can't rememver the last time some one said "That piano's 59th string is 0.001 hertz out".

[@RubenJMorenoMusic]

Paul L Well, thats not really the point, It actually has to do with the pre-equal temperament tunings (meantone). You can tweak temperaments to make a few keys sound dead on, but at the sacrifice of other keys and as a result it gave these keys their own personalities and quirks. This would affect a composers decision when it came to choosing keys and where he would modulate. But equal-temperament puts all keys out of tune, making every key sound bland and out of tune with no characters of their own. "When everyone is super, no one will be" - Syndrome And its actually much more out of tune than "0.001 hertz". In equal-temprament a major third is usually about thirteen cents (cent = 1/100 of a semi-tone/halfstep) sharper than its true harmonic. A person can usually hear a difference of about three cents. It's really fascinating stuff but much more relevant if you're a string player or a vocalist. A string quartet doest' have fixed pitches or frets and can/must adjust their temperament constantly.

[@RubenJMorenoMusic]

Paul L That was really long winded, sorry. I'm really bored right now.

[@RubenJMorenoMusic]

***** Equal temperament started gaining real popularity during the late 1800's and became standard when we started recording music. Beethoven definitely used a mean-tone tunings.

[@patrickbaker7014]

Instructions unclear: I ate my cat

[@CC-tl3zs]

I expected this and I am still disappointed

[@ashut0ast23]

Rip

[@thelordz33]

I'm pretty sure those were the instructions

[@ErilynOfAnachronos]

Did you cook it, fry it or bake it? Which spices did you use? And what did you serve it with? Poor kitty. 😢

[@thddgdr59]

Instructions unclear: I ate my dog

[@trinar.s.6550]

You can't tune a piano.. but you can tuna fish

[@KainYusanagi]

Holy crap, something interesting about actual physics! It's been... what, two years? More? since the last one. >_>;

[@tehalexy]

1:12 having multiple instruments nearby and all start to say "hello, im here" :D

[@barrythebee2819]

Me watching this video in front of my fake friends, "yeah, yeah" and trying to pretend understanding this.

[@Racnive]

The amazing thing is that 12th roots of 2 happen to include 2 numbers so close to the basic fractions 3/2 and (thus also) 4/3. Compare any other set of scaling roots of any small integer; 2^(7/12) and 2^(5/12) are amazingly close: 2^(7/12) is 0.1% off from 3/2, just as (by corollary) 2^(5/12) is from 4/3.

[@TopazTK]

You may hear a little "wowowowowow" but that's normal at this point.

[@Knuts_n]

heeey i got that joke

[@TopazTK]

@@Knuts_n Finally.

[@TopazTK]

@@aimless-slug Nono, Numbers ain't h a r d, numbers are *H A R D*

[@phonglove6767]

*_Numbers are hard._*

[@lynnlo]

3:26 WOAH WOAH WOAH WOAH

[@andro7862]

Well, my brain is broken.

[@jeroenstrompf5064]

Yes, you can tune a guitar or violin using harmonics, as demonstrated at the beginning of the video, but you'll get just intonated tuning, which is 1.955 cent off per string, compared to the usual equal temperament tuning

[@tomeelikee]

Came to say this 😂

[@robinleebraun7739]

Same goes for guitars. If you tune even tempered, it will often sound a little out of tune in some keys with some chords. If you tune with harmonics, it will be perfect in only one key and really off in others. So some people split the difference so you can play in multiple keys and it sounds as good as possible under the circumstances.

[@davidalbro2009]

in equal temperament, it will sound equally out of tune in all keys

[@pedrova8058]

@@davidalbro2009 not really (that´s the point of the video). in some positions, you can get an "equal" temperament. but as you go up the fingerboard (or into the piano keys) the inharmony of the strings starts to become more noticeable (and the frets on a guitar are arranged in relation to the same fixed ratio, so the harmonics of the notes are more and more displaced as you go up) Inharmony is just that phenomenon: the harmonics of a vibrating string start to become less "consonant" when that string gets shorter or much longer (as happens in the higher/lower keys of a piano.) Physically, it is defined by the relationship between the length of the string, its diameter and its weight.

[@davidalbro2009]

@@pedrova8058 That's EXACTLY the point of the video. 3:40 "In equal temperament you can play any song in any key and it will be equally and just slightly out of tune." Also, you are 100% wrong about the piano. The interval of a 4th, let's say, is the exact same ratio in any key in the 7th octave as it is in the third octave. What you are talking about might be timbre, but that is never discussed in the video.

[@pedrova8058]

@@davidalbro2009 nop, that's the theory (it can be applied to virtual instruments, even synthesizers, or simple electronic tuners) But the reality is different (in strict terms referring to the effective "percentage distance" between 2 frequencies). This is called "stretching", and occurs in all stringed instruments with a large spectrum (say, over 4 octaves; in electric guitars, for example, it can be compensated at the bridge (called "intonation"), with individual saddles at the bridge (that's why it's a more frequent problem on classical guitars)). It's done precisely to seek uniformity in the timbre of the piano in all its registers (which is achieved in a "compromised way" obviously) ... A fourth in the 6th octave is slightly "longer" o "sharper" than one in the central section of the piano (hence a simple electronic tuner has problems in the extreme ranges of the keyboard) . If we wanted to avoid "stretching", we would have to use progressively thinner strings for the higher section , but that would change the timbre, and also the actual volume of the instrument. . (for the same reason is that the old "jazz" guitars began to use steel strings, and then much thicker steel strings, they were looking for more sound volume, and for that more tension is needed (which pushes you to use strings thicker, more bridge compensation, etc)) . en.wikipedia.org/wiki/Stretched_tuning

[@pedrova8058]

btw, we are talking about small differences, which only trained musicians, technicians appreciate. (the difference is noticeable when using extreme harmonies, with chords in the low/middle section, and harmonies at the top of the keyboard)

[@BytebroUK]

I am *so* sad that my late grandmother isn't around to watch this. She had 'perfect pitch', to the extent that she allegedly went to a recital and because the players were about an eighth of a tone off concert pitch she felt it as a physical pain - no idea if that is plausible. The point is that she claimed to always know what a note was, but if they are 12th-root-of-two apart, is that even feasible?!

[@eugenelevin9809]

Of course it is. Pi is an irrational number, but you can still tell it’s greater than 3.1 and smaller than 3.2. If you search Jacob collier out of tune, on KZbin you’ll see a cool demonstration that’s likely similar to your grandmother.

[@realscapegoat592]

Absolutely it is feasible! People with perfect pitch recognize notes like we recognize color - it doesn't matter how specific the ratio between the notes is.

[@Teth47]

Huh... I guess you can't tuna piano or piano a tuna after all...

[@finlittowinit]

+Teth47 lol

[@Daniel-md8vv]

SNANS!

[@thinhho93]

what about the glue?

[@Teth47]

Thinh Ho Found the Redditor

[@lanebiddle6490]

Thinh Ho I knew you'd get stuck on that one

[@GabsARV]

Thanks for making the video. I had to use this as a part of my report on my class, I reported about tuning musical instruments and the other instruments that cannot be physically tuned. I read my book and found the piano to be a confusing and long piece of shit so I found this video and let my classmates just sit and tilt their heads and watched it. Thank you! You saved my time!

[@toddcallison8087]

Which is why you can't use harmonics to tune a guitar, either

[@Bambuskus505]

My brain has expanded in an unnecessary, yet interesting way

[@vibraphonics]

Choirs will go out of tune more in some keys than others because our brains don't account for equal temperament.

[@p__b__3749]

Being a lifelong musician, I have great appreciation for the fact that our Western tradition uses equal temperament, and that we get all sorts of great mathematical and physical explanations for how that came to be and how we implement it. But, I would LOVE to see more counterfactuals explaining alternative temperaments. One easy way to do that would be to juxtapose current instrumentation with pre-Baroque fixed-pitch instruments. Also, it would explain to a larger audience why Bach (and not, say, Haydn, Mozart, Beethoven, Schubert, etc.) was such an impactful composer in the Western tradition, which is: he was there when equal temperament became a "thing" and he was genius enough to know how to get the most out of it. Which does not at all explain why his genius regarding fugues or thematic variation was so important/compelling/enjoyable. Just that, well, hey, fortunate timing! And also the coffee :D

[@Minossko]

Why exactly is this a piano specific problem? Shouldn't the whole step problem apply to a single guitar string as well?

[@fran6b]

+Peter Mačkay Guitar is different because of the fret board. You have only 6 strings who make all the notes and the 12th fret is adjusted be the same harmonicaly and when you press your finger on that 12th position. With a piano, each note are made by different and open strings. In other word, the fret board temper the tuning of a guitar but nothing but a specefic tempered tuning can tune a piano to make all octave superposable (stackable). That how I understand it.

[@michaelsommers2356]

+Peter Mačkay I think the main issue is that a piano spans over 7 octaves, while a guitar, for all practical purposes, spans only 3. That means that the deviations from the ideal tones are less noticeable on the guitar. I would also guess that guitars generally are played in only a few keys.

[@powck]

+francis bélanger also, a guitar is always slightly out of tune in some scales, but everyone is so used to it that we don´t notice it as wrong

[@TheUglyGnome]

+Peter Mačkay In matter of fact tuning guitar with harmonics also leads to similar problem as with piano: There will always be at least one interval which is way off (usually interval between G and B strings). And because guitar is chromatic instrument with fixed selection of notes (those frets), you should tune it equally tempered anyway. If you use only very limited number of chords or scales, you can make it sound a lot better though using some harmonic method (if you know what you're doing). So, the maker of this video didn't really know what he was talking about, when it comes to guitars. The real problem is not a number of strings, but instrument capable of creating (only) chromatic scales. Violin doesn't have this problem, since it doesn't have frets.

[@michaelsommers2356]

TheUglyGnome Pianos are also chromatic; what instruments in the western tradition do more? And violins may not have frets, but they are played as if they do. That is, the fingers are placed where the frets would be if there were any.