Get 26% off CuriosityStream and a free Nebula account: www.curiositystream.com/12tone and use promo code "12tone" Some additional thoughts/corrections: 1) First and foremost, I'd like to formalize apologize to the Jabberjaw fans out there. I'm sure at least some of you exist. 2) Will the xenharmonic crowd get mad at me for calling just intonation "a popular idea in Baroque-era European music"? Yeah, probably. Am I ok with that? Also yeah, probably. 3) If you're wondering why my list of primary intervals didn't include the perfect 4th, it's because you can build its ratio, 3:4, by going up an octave, then down a perfect 5th, so a system that has those two intervals gets the 4th for free. We don't have to worry about it separately. Likewise, the minor 3rd, or 5:6, can be built by going up a perfect 5th, then down a major 3rd, so we don't need to include it either. 4) Werckmeister tunings are actually numbered in two different ways. I went with the easier one, but you may find the thing I called Werckmeister I referred to as Werckmeister III and the thing I called Werckmeister III as Werckmeister V. It's kind of a mess, sorry about that, historical tuning systems are complicated. 5) If the major 3rd that I said was really sharp didn't sound bad to you, don't worry, your ears aren't broken, it's just that equal temperament also uses a fairly sharp major 3rd, so you're already used to it. To someone more familiar with meantone, though, it would've sounded pretty out of tune. 6) One thing I couldn't really fit in the flow of the script is that the most common meantone tuning shrinks all its fifths by 1/4th of a pythagorean comma, so in the loop doodle system, even the flattest 5ths are wider than many listeners would be used to. (And, as such, all the 3rds are slightly sharp as well, although some more than others.) 7) Bach was known to enjoy cryptograms and puzzles, so it is possible that the doodles were meaningful and he just chose not to tell his students about it, but a) Lehman's historical theory relies on the idea that the doodle was a known teaching aid, and b) if wasn't communicating his intent then he was likely prepared for the possibility that people wouldn't follow it. 8) One of the most interesting approaches I've seen on this is going through the entire Clavier and counting which specific major 3rds he uses most often. According to the sources I've found, there do appear to be biases toward certain ones across keys, which implies his tuning system likely made those 3rds sound particularly good, but I couldn't find any straight-up list to examine myself so I'm not entirely sure which ones.
@bayaryan34003 жыл бұрын
Why do you draw backwards Ike manga
@stephenspackman55733 жыл бұрын
So … in these days of data science … what are we lacking to treat this-assuming that Bach was no fool-as just a joint optimisation problem? Tantacrul (to name someone completely at random…!) would be able to pluck out all the relevant intervals in seconds, with a script, I should-in my ignorance-imagine! Sevish-surely-must have the necessary solver for this ready to hand!
@chiju3 жыл бұрын
@@bayaryan3400 It's probably because he's left-handed. If he drew from left to right, his hand would constantly be covering the last thing he drew.
@flirora3 жыл бұрын
1/4 of a syntonic comma, not a Pythagorean comma.
@RobertSlover3 жыл бұрын
this video is a waste of time.....
@e3498-v7l3 жыл бұрын
Printed score of this piece is literally less than a meter away from me right now on a music stand. You've got my attention.
@e3498-v7l3 жыл бұрын
15 minutes later I have no idea how to apply anything from the video to the guitar. Oh well...
@virtua_t46953 жыл бұрын
Same!
@cgibbard3 жыл бұрын
@@e3498-v7l You'll need a saw, and some fret wire...
@xinterest90293 жыл бұрын
"Less than a meter" heh, unintentional pun
@mortenwintherolsson32373 жыл бұрын
Less than 3.1415… FEET away, you mean! A foot is a divine measure, if tuned correctly, as 432 cm, which is what the Divine Being intended, before the Evil Networking Club that controls all the sheeple who refuse to see, started listening!
@pentalarclikesit8223 жыл бұрын
Time Traveller: Mr. Bach, how should I tune my clavier? Bach: Tune it until you like the way it sounds. Time Traveller: Oh. . .
@libsteve3 жыл бұрын
That would definitely explain why his students wrote different scribbles on their manuscripts. Each one has a different opinion of what “sounded good”.
@Overxpossed3 жыл бұрын
If he had a good ear, and it sems he has it; then Bach was right.
@arthurverlaine64343 жыл бұрын
@@chrismiller5198 Did bach speck?
@GregBrownsWorldORacing3 жыл бұрын
@@chrismiller5198 I'm sure he said Oktober.
@GizzyDillespee4 ай бұрын
Bach: "ughh... this is the last time I'm hiring a tech from the temp agency..."
@Melaheidi3 жыл бұрын
Bach: *scribbles a bit to make sure the ink is good* Theorists hundreds of years later: "WHAT DOES IT MEAN?!?!?"
@NeverDoubtTheWorm3 жыл бұрын
Ahahahahaha Ahahahahaha lol 😂🤣
@wiesorix3 жыл бұрын
I wouldn't read too much into it. He was probably just bored while on the phone and started drawing some lines on whatever was closest on his desk.
@MaggaraMarine3 жыл бұрын
There are people who read way too much into Bach's music and try to find some secret messages from it. I remember my music history teacher mentioning them, and the stuff he described reminded me of those "illuminati confirmed" parody videos. Unfortunately, I don't remember exactly what kind of messages they were trying to find from the music, and how exactly they found those messages, but I do remember that it didn't necessarily have much to do with listening to the music, and had more to do with looking at the score. (Like "oh, the way this passage is notated is clearly communicating this religious message".) To me, this (the overanalysis of a scribble) seems to fall into that same category.
@OdaKa3 жыл бұрын
That's hilarious
@orb37963 жыл бұрын
@@MaggaraMarine While I agree that overanalyzing is possible for any and all art that exists, do you really think that someone as obsessive about symbolism as J.S. Bach wouldn't employ it a lot?
@toblexson50203 жыл бұрын
I don't know anything about Bach as a person, but if he was so invested into tuning his instruments himself maybe he passed that onto his students. Maybe his rather cryptic illustration was an attempt to show the tuning in a way that only his students would understand, and maybe he encouraged his students to work on their own systems that suited their own ears. This is just the first thing that came to mind when you mentioned that his students had different styles of his doodle.
@OdaKa3 жыл бұрын
That makes a lot of sense, and sounds like something a good teacher would do
@calcapone93 жыл бұрын
yes
@stoferb8763 жыл бұрын
Sounds like a plausible theory. But it's not that Bach was particularily more invested in tuning than any other guy of his time, it's that unlike the organ or the piano most other keyboard instruments very quickly go out of tune and are also rather easy to tune as you don't need specialized equipment. So tuning your own instrument was just part of playing the keyboard, just as it still is today for many other instruments. Obviously he didn't hire some guy to tune his instruments every week or something like that. Neither did his students.
@wingracer16143 жыл бұрын
Possibly but there is a problem. Music was going through some radical changes at that time and the music his students and even his very own children would go on to play and compose was radically different. JC Bach and CPE Bach have more in common with later composers like Mozart and Haydn than JS Bach.
@OdaKa3 жыл бұрын
@@wingracer1614 how exactly is this a problem?
@prodcdebeatz72053 жыл бұрын
Sees title, “You’re Playing Bach Wrong” => haha, jokes on you. I can’t play Bach.
@wingracer16143 жыл бұрын
Yes you can if you want to. Seriously, Prelude in C is quite easy and actually fun to play. It takes a little time and practice but not all that much. It's one of the first things I learned to play on piano and I think it took me just one day to pretty much get it down. And if you do, you'll find yourself now able to play a piece of music that while simple is also subtly intricate as well and surprisingly moving.
@vigilantcosmicpenguin87213 жыл бұрын
Which means you certainly aren't playing it right.
@1feloniouspunk3 жыл бұрын
@@wingracer1614 kind and supportive comment Wingracer 16, and hilarious comedic response by Vigilant Cosmic Penguin
@oscargill4233 жыл бұрын
@@wingracer1614 The cool part is, you don't have to stop at learning what's written. A while back I challenged myself to play it, but every time a major chord was played (counting inversions), I move down a semitone. And somehow, it still sounds amazing. The success of the experiment prompted me to continue searching for new experiments. And a LOT of them worked really well. So if you ever feel like it's getting boring, challenge yourself to mix it up in interesting systematic ways. You might just create a new piece of music (technically speaking).
@andrejz89543 жыл бұрын
@@oscargill423 That's so cool man! I'm playing it on a guitar (don't know how accurate the tab is tho) and to think something like that is just way too hard to even try :)
@astian_sebus3 жыл бұрын
I once had the oppertunity to tune a piano with a tuner, a very precise piano tuner. You even could tune to different tuning-systems, not only equal temperament, but all sorts of things. Of course Werckmeister and Kirnberger, even Meantone, but very exotic things like the pure Pythagorean-System. So I chose the Werckmeister III System, because it's not to far away from standard equal temperament. It took a few hours before it was finished. What did I play? This prelude, of course! It sounded warmer than usual. With equal temperament you have such a cold sound. This was gone, the sound lived. If you get the chance to try another tuning system, take it. It widens your musical horizon.
@garysmith15713 жыл бұрын
I'd like to hear a recording of that! KZbin would be a good vehicle for you..
@steveneardley75413 жыл бұрын
Piano tuner here. I have often described equal temperament as "candy-box." Some of the older temperaments, because they have more pure intervals, have a more sonorous, orchestral sound. They are much harder to tune, though. We are used to the very sharp thirds of equal temperament, but people in Bach's time thought they were vile. Of course, in the very early temperaments, they often sacrificed whole keys (F sharp and C sharp, for instance) for this purity, since they unloaded all the extra beats into the fifths of these keys. Early keyboard instruments were so unstable that performers had to be able to tune as well as play, so they could just tune the instrument to a temperament that worked with the key they were playing in.
@herrweiss25803 жыл бұрын
@@steveneardley7541 I see you are not a RPT.
@cjsm10063 жыл бұрын
Most electronic keyboards have the ability to use different tunings via the main settings menu.
@istvankocsis55073 жыл бұрын
@@cjsm1006 Yes but they only simulate real sound. Electronic keyboards are good for practicing but notes can't resonate together as real strings do. I'm using Werkmeister tuning and it's like the piano starts to rebound...
@craig48113 жыл бұрын
It would have been nice to hear the simple phrase played in a couple of the different tunings.
@femthingevelyn3 жыл бұрын
12tone "you're playing Bach wrong" me, who has never touched an instrument: oh do tell me more
@eesr2 жыл бұрын
lol
@beatrixwickson84773 жыл бұрын
Melancholy Womanliness is gonna be my new band name. Every song: Dm
@5ilver423 жыл бұрын
then you just need to name your songs and albums off classic literature, like _Crime and Punishment_ or _Anabasis_ and you'll have your audience in droves.
@subjectline3 жыл бұрын
Ikr, sounds awesome.
@SunroseStudios3 жыл бұрын
equal-tempered Dm or well-tempered Dm?
@beatrixwickson84773 жыл бұрын
@@SunroseStudios Five limit tuning or bust.
@beatrixwickson84773 жыл бұрын
@@5ilver42 I reckon an album could be called Mean Tempered.
@johnlindholm12033 жыл бұрын
My teacher always told me I played wrong, didn't believe her until watching this video Thanks 12Tone!
@19divide533 жыл бұрын
You can't play it "right" if the piano isn't tuned "correctly". Your teacher was to blame, if you're using their piano
@ejlflop3 жыл бұрын
you were probably playing it fine
@PaulDeCamp3 жыл бұрын
Call your premise "The Loopy Postulate" and beat your trolls the the punchline. I will agree that most of us were mislead, either unintentionally or not, to the notion that "well tempered" was a synonym for "even tempered". I THANK YOU for disabusing us. I have studied music informally for 58 years. It wasn't until three years ago I was made aware of all these tunings. I finally wrote a program to provide me with all the pitches needed given a proscribed middle A to produce a even tempered scale.
@OdaKa3 жыл бұрын
Just to clarify, it's not 12tone's premise. It's Bradley Lehman's
@mateuslguilherme3 жыл бұрын
Is this program posted anywhere like Github or something? I would love to see it
@MegaMech3 жыл бұрын
It's not even a good premise and barely contradicts the old one. It's called the Doctrine of the Affections. The evidence supporting it is very weak. Rather a combination of both elements makes more sense: 1) Instrument technology increased along with tuning allowing for curiosity regarding what music can do now. 2) The sound produced in different keys seemed meaningful and as such the doctrine of affections places differing feelings on the different keys. How much Bach aligned to this or not is not known afaik. Nether of these elements contradict each other. Together they provide a better argument for what Bach may have intended. 12tone is basically directly contradicting Groute and Palisca (the history textbook that all musicians use).
@realraven20003 жыл бұрын
@@mateuslguilherme Pianoteq would be a great program that provides plenty of running systems even in its basic version
@candysue42603 жыл бұрын
@@MegaMech The well tempered clavier refering to well temperament instead of equal temperament just makes sense. Well temperament is unequal so the keys actually do sound different and all keys are still playable.
@rmanami3 жыл бұрын
Its interesting that the damn title of the book explicitly states how its intended to be tuned and yet not only does it not give a lot to work with, but also nowadays we just more or less interpret it to be like "Oh thats a nice adjective bach put for his cute pieces", when the entire point of the book was that each key sounds different - the exact opposite to how we tune today
@nomansland51133 жыл бұрын
If you paid attention, no, we don’t know what Bach intended with that word, we just don’t. Don’t get me wrong, I’m the type of nerd that loves historically informed performances. But this looking down on equal temperament and alleged fidelity to “true” Bach is just… silly, and sooooo pretentious
@dianamccandless70943 жыл бұрын
Bach be like: "Get a Korg electronic tuner off Amazon and tune your G 3 cents sharp."
@克立张3 жыл бұрын
@@nomansland5113 If we can perform Bach as he would have heard it, why shouldn’t we?
@karlrovey3 жыл бұрын
There are several different well-tempered tuning systems. There are papers regarding tuning instructions being derived via artwork on the cover of the Well-Tempered Clavier.
@montybanana3 жыл бұрын
If most tuning systems prior to Bach were characteristically out of tune when playing in different keys, would it not make sense that the point of the compositions was to demonstrate how they the different keys could actually sound the same with a tuning system closed to equal temperament?
@shiragoldmusic3 жыл бұрын
12tone: You're playing Bach wrong Also 12tone: Bach's dead, he doesn't care.
@mortimermacmanus89653 жыл бұрын
Way to play all the notes at once.
@subjectline3 жыл бұрын
Digital pianos usually have a choice of these different tuning systems and you can change the frequency of your concert A in seconds. It's fun to try different combinations.
@dianamccandless70943 жыл бұрын
Wow! Good to know! I've been really wanting to get a keyboard, now there's another reason.
@subjectline3 жыл бұрын
@@dianamccandless7094 Mine is a Yamaha P255 (now obsolete) and you can select Pythagorean, Meantone, Werckmeister, Kirnberger, Pure Major and Pure Minor. You give a reference pitch - the key you want to sound most I tune. It's a fairly high end digital piano and maybe the cheaper ones don't have this, but you can check in the manual.
@istvankocsis55073 жыл бұрын
Real strings giving real sounds... Everybody should try well tempered grand piano. I'm learning and practicing on digital but playing on grand piano tuned to Werkmeister III. For me this is the ultimate sound experience. :)
@istvankocsis5507 Жыл бұрын
@@everydaytenor8862 Thank you I will try it! :) Young I. or II. ? Wich temperament do you suggest for an upright piano from cca. 1900? I'm using free Instrument tuner wich have cca 5 styles of equal temperament Broadwood perhaps equal to perfect octave + fifth?
@istvankocsis5507 Жыл бұрын
@@everydaytenor8862 Thank you for your advise! :)
@hawtaro29163 жыл бұрын
I’ve always wondered how Bach would sound with his well tempered system so this video is amazing to me. Great work!
@jaj1453 жыл бұрын
this video contains the most subtle spinal tap reference i've EVER experienced my my entire life. great vid.
@dianamccandless70943 жыл бұрын
And what was it?
@JWolfe-nq7nq3 жыл бұрын
@@dianamccandless7094 tuning to 11?
@S00NERD0G3 жыл бұрын
@@dianamccandless7094 D minor, which is the saddest of all keys
@RockStarOscarStern6343 жыл бұрын
Quite alot of lost information is being recovered. The Pedal Harpsichord & Pedal Piano are great for playing Organ pieces right off the bat.
@VladdViever3 жыл бұрын
Love the collaboration with Tim. Always cool to hear different creators voices.
@fariesz67863 жыл бұрын
ah, good to know i identified the voice correctly
@feasible3 жыл бұрын
I always love your videos, but this one is especially pertinent to me: I'm a professional public historian, and I really appreciate how you illustrate (literally and figuratively) how historic research and rigour works. Both the fun and frustrating parts of it. Love the reference to the "past is another country", but this quote at the end is poignant and well-said: "The answer is just an answer; the fun part is asking the questions." That's how I feel about history. Thank you so much.
@DanielEMacKay3 жыл бұрын
OMG FINALLY!! I have wanted this video FOREVER. I have been trying to explain to people that in Bach's time, the keys had personalities and really they do not now, and I just get blank looks. FINALLY a thorough exploration of it. THANK YOU THANK YOU.
@Alomoes3 жыл бұрын
Bach once got into a fight over tuning, and pulled a knife on someone else. Unfortunately the only one to know how Bach played his music for sure as of now is Bach.
@Wind-nj5xz3 жыл бұрын
In the beginning i thought this was going to be a pun about Bach's knife being "sharp" in the same sense that some notes in his tuning would be sharp
@rumar4u3 жыл бұрын
@@Wind-nj5xz I believed he did, except he didn’t had to because we all know how it ended.
@daltorb87393 жыл бұрын
I'm not sure he got into a fight over tuning - I've only ever read that he pulled a saber on his bassoonist, but I'm not sure if that's what you were referring to. Could you clarify?
@vigilantcosmicpenguin87213 жыл бұрын
Bach is going to rise from the grave to annihilate everyone who plays with the wrong tuning.
@dianamccandless70943 жыл бұрын
@@Wind-nj5xz so did I! esp because the artist draws a knife to symbolize sharp
@bradleylehman43272 жыл бұрын
My newest article about this Bach tuning is from 2021-22, and published by the Riemenschneider Institute in November 2022. I explained further how it comes from 17th and 18th century practices of tuning "temperament ordinaire": setting up the naturals (C major scale) first, and adjusting all the sharps and flats to fit the gaps. The tuning process by ear is a listening skill, not math. Free PDF copies of this article are at my websites.
@bradleylehman43272 жыл бұрын
The new article goes again through the mountain of direct evidence that people disregarded, both over the past 300 years and over the most recent 17 years that it was in my first article. (Time index 12:40 of your video, asserting that there isn't enough.) The evidence is Bach's music requiring flats and sharps at the same time, viewed against the models of scale structure in use at the time. Plus, there are plenty of clues from theorists and teachers whom I've cited: showing how to tune by ear, and showing how musicians other than keyboardists grappled with problems of flats being different from sharps.
@perhir013 жыл бұрын
Fun fact: in Sweden, A = 442 Hz is quite common among classical musicians while most pop/rock people I've met use A = 440 Hz.
@dcarbs29793 жыл бұрын
A lot of Baroque music is thought to have been written for A=432hz. It's a much more naturally harmonious frequency to humans than 440. Probably why I prefer the era to more modern classical.
@anter1763 жыл бұрын
Carbs, go look up some of Adam Neelys A 432 hz videos
@OdaKa3 жыл бұрын
@@dcarbs2979 Um, did you watch the video at all? Where he talks about how tunings of the instruments varied wildly? Harmony has nothing to do with what specific frequency A is tuned to, everything to do with the relationships of frequencies to one another. And ... The likelihood of the recordings or performances of Baroque music you've heard in your life being played in A=432Hz is very low. It's more likely to have been played at A=415Hz. So how are you measuring your appreciation of the music based on Hz? Do you only like when people perform the music in 432Hz tuning, and dislike it if it's anything else despite the fact that it's Baroque music? And humans likely have a relatively wide range of audio frequency preferences per individual, which vary throughout their lives as their hearing changes. Have you considered that you just really like the composition of Baroque music because your life experiences have shaped your preferences? You may want to research more deeply into the real history of tuning standards before coming to conclusions based on such claims.
@dcarbs29793 жыл бұрын
@@OdaKa I have not only watched this video, but also several others on both the 432hz phenomenon, and on historic tuning (to varying conclusions). Not to mention first hand performances (I play it myself), not just listening to recordings or even live for that matter. If it's a coincidence, it's a very strong one. There are two clear facts: I tend to prefer Baroque. Baroque has a different tuning frequency to 19th century onwards. Being exactly 432 vs 440 is unlikely, but being different is a certainty, even between instruments playing the same piece. Most performances I have no idea of the tuning. You feel it, but not necessarily hear it or get told about it. It may be the individual performance or instrument. Nothing is exact. On recordings it could even be the frequency responce of the mics or reflections from the room. Far too many variables to be sure.
@OdaKa3 жыл бұрын
@@dcarbs2979 Okay cool. So long as facts are facts.
@qpSubZeroqp3 жыл бұрын
So, what did those examples actually sound like? Talking about tuning and knowing the theory is great. I just wish that at least at the end those examples were included if it's not copywrited
@kleinesfilmroellchen3 жыл бұрын
After hearing you on hellofutureme, I shouldn't be surprised to hear Tim here. But still!
@carlstenger58933 жыл бұрын
Excellent video! Your arguments are interesting. The delightful thing about Bach is that no matter what instrument you play his work on, it always sounds like Bach. I've been a subscriber for several years. I always find your videos interesting. Thanks so much!
@delyar3 жыл бұрын
Standardized pitch=A is a very recent thing. “The story of A” by Bruce Haynes starts you out on this journey
@miketate34452 жыл бұрын
11:00 Battletoads. Battletoads is your doodle for "difficult". Dude, you're the best.
@SmartHobbies3 жыл бұрын
I live with someone who likes to play this on our piano. I got totally hooked on what you were saying and love all the historical references. Thanks for sharing this.
@MrPSaun3 жыл бұрын
I remember sitting down to analyze this piece and being baffled by measure 23 in my Schirmer edition (the Schwencke measure). I am definitely someone who would be considered an amateur in the classic sense of the word, I'm completely self-taught and have little formal training, but I remember coming across this measure after reading W. A. Mathieu's "Harmonic Experiance" and thinking "Bach did not write this". There are very some interesting, but not unheard of, harmonic devices used in Prelude no.1, especially in terms of inter-modal relationships, but measure 23 defied analysis. The movement of the F# to the Ab in the bassline that occurs if you remove the Schwencke measure is definitely a bold choice, but the harmonic direction is still toward and related to V7, where the domimant pedal begins, so can be seen as a prolongation of tension, whereas the CmM7 chord in second inversion, of the Schwencke measure, is not only very out of place in a piece from the High Baroque Era but also ruins the dramatic approach to the dominant pedal that itself precedes a tonic pedal and the end of the piece. The entire piece is just a masterclass in Major mode writing. I love it so much. Thanks again for the lovely video!
@aimilios4393 жыл бұрын
I really hate that measure is considered by many original. Bach was bold and we are lucky about that.
@MrPSaun3 жыл бұрын
@@aimilios439 Absolutely!
@hugobouma3 жыл бұрын
also, Gounod's Ave Maria is based on the version with the added measure which is just another strike against that piece ;)
@reverbscherzo78503 жыл бұрын
Interesting. My copy has that extra measure as a footnote, saying it “has become generally accepted despite its non-authenticity”, so I’ve been including it when I play this piece. Now I will happily leave it out.
@jasminethenoob10803 жыл бұрын
I think censoring "sh*t" with the wolf fifth is comedy gold, 10/10
@AnthonySmith-sc4zs2 жыл бұрын
I know it’s overplayed but I love this song so much. It’s got so much feeling and flow. The feeling of the chord progression just works so well.
@SomniRespiratoryFlux3 жыл бұрын
"...and your understanding of what's going on in the piece will suffer for it." *draws the bicycle from The Prisoner* nice
@quarkrahm3 жыл бұрын
Refreshing to see some content on classical music again! I get that talking pop and chord loops is en vogue, but I always loved your content on classical music and theory.
@seth_piano3 жыл бұрын
Just imagine 300 years from now and all the current music (pop, EDM, video game music, etc.) has all been destroyed except for the MIDI files, and historians trying to figure out what our music sounded like from just that. All the audio is gone, just a bunch of dots in the piano roll. That's us trying to figure out what the heck Baroque music actually sounded like. Not practical, I know, but an interesting thought experiment. :)
@cgibbard3 жыл бұрын
Imagine trying to figure out that a piece of music was using midi note numbers 0 through 42 to represent the pitches of 43edo and that different channel numbers were mapped to octaves.
@seth_piano3 жыл бұрын
@@cgibbard Yes exactly! That's sounds horrible and hilarious at the same time.
@torydavis102 жыл бұрын
My take on this, given Bach's affinity for leaving some 'exercises for the reader' in his compositions, is that the title 'well-tempered clavier' was meant as a challenge. If your clavier can play this and sound good, it is well-tempered.
@Userminusone3 жыл бұрын
I always enjoy it when you get into tuning theory, 12tone! Do you think you might be able to make a video analyzing various microtonal equal temperaments such as 17edo, 19edo, 22edo, or even weirder ones such as 14edo and 15edo? (I know you've already done something like that in "tet for tat: why do we use 12 notes?", but in that case it seems that you just briefly described the different equal temperaments rather than talking about JI approximation, commas, scales, and other elements of different equal temperaments)
@TheHunterGracchus3 жыл бұрын
Microtonal temperaments that achieved better equal-tempered fifths by finer divisions of the octave were popular among Renaissance-era theoreticians. Some composers, especially Gesualdo, are thought to have made use of these systems.
@Userminusone3 жыл бұрын
@@TheHunterGracchus Interesting
@SidewaysThinking2 жыл бұрын
Much of what Bach did, as described in this video, is above me. However, I picked up learning the cello after being a pianist because, after some years, I couldn't stand the sound my piano with intervals tuned to equal temperament. I then tried tuning to the Bach Lehman temperament, which I though basically tightened some of the fifth intervals (this I noticed when tuning the cello to Bach Lehman). I enjoyed the results on different instruments. The difference is subtle but now I enjoy playing the piano more, while I don't think at all of the temperament I am in. I think it may be hard to tune to the Bach Lehman precisely for piano tuners, and so cause an off sound. They are not used to it. I cannot tune so well by ear, listening to beats between notes. What I do is tune by using an app which tells me each perfect note - this, after programing the intervals of the Bach Lehman temperament into the app. Any subjective internal confusion on the tuners part, however professional or experienced, is bypassed, resulting in a natural sounding and comfortable temperament within which to play. I tried the other temperaments of Bach's time and prefer the Bach Lehman.
@StaticR3 жыл бұрын
I'd kinda love to hear pieces in just intonation where the slight drift in pitch over time is an intended part of it.
@Chord_The_Seeker3 жыл бұрын
A lot of this goes over my music theory 101 understanding of music, but it’s still fascinating, and your rapid fire presentations make my little brain struggle to keep up. Thanks for all of the amazing videos. I love this channel.
@TheMister1233 жыл бұрын
2:04 - I thought it was called the "pianoforte", not the other way around. Was I taught wrong?
@AlexKnauth3 жыл бұрын
IIRC they are 2 different instruments. The Fortepiano came first, with hammers striking strings instead of plucking them, but it was still a bit rough around the edges of its range. Then the Pianoforte came later as a significant improvement to it with greater consistency and expressiveness, I think. Keyboards aren't my instrument though and I don't know for sure
@TheMister1233 жыл бұрын
@@AlexKnauth Thanks!
@DaedalusYoung3 жыл бұрын
Gravicembalo col piano e forte
@deebles40823 жыл бұрын
I never thought I would hear Hello Future Mes voice in a 12tone video but here we are I guess.
@nefdsnet3 жыл бұрын
There was an arrow on one elephant's head and multiple Fire Nation logos in this and the last video. Are you really surprised he showed up? 😃
@AlexKnauth3 жыл бұрын
I also heard 12Tone's voice in a recent Hello Future Me video too (edit: Hello Future Me's most recent released video "The Power of Abandoned Places" around the 10 minute mark)
@wiesorix3 жыл бұрын
I feel like these different tuning systems can really add to the musical experience. Compared to equal temperament, the better intonated chords can be much more satisfying, much fuller, stronger. Too bad I didn't choose an instrument that allows for experimentation with tuning systems.
@davidweihe60523 жыл бұрын
Which? Trombones, violins of whatever size, violas of whatever size (assuming that you can make one other than the alto viola), and guitar/lutes without frets are all that I know can be tuned continuously. Oh, and synthesizers, of course.
@gerardvila46853 жыл бұрын
There's another category of people who are interested in this stuff: the harpsichord players and clavichord players (they do exist), who have to tune their instruments every few weeks, and who very often do it themselves. The trouble is, if you own one of these instruments you may well want to play Bach and his contemporaries, but also 16th and 17th century composers, who used mostly mean-tone tuning - if so you will need to chop and change. (I was at a Gustav Leonhardt concert once - first half was little-known French "Petits Maîtres" - Little Masters - and the second half was Bach. The harpsichord was re-tuned during the interval.) Plus there are the historical pianoforte players, who typically want to sound like the pianos in Mozart and Haydn's day, which were tuned a bit closer to equal temperament but still "Well Tempered" as far as we know. And the icing on the cake is, before frequency meters were invented, everything was done by ear - for all we know, people might have thought they were using equal temperament, but actually been out a bit. (It might even be the case that Bach himself tuned so many instruments, one way or another, that it became completely instinctive for him, the way you drive a car after 20 or 30 years, so that he himself had forgotten exactly how he did it by the time people got around to asking him. But don't quote me on this, I'm just an amateur.)
@Loweene_Ancalimon3 жыл бұрын
....harpsichord and clavichord players tune their instruments every few weeks ? More like three times a day, not sure who you're talking about
@1feloniouspunk3 жыл бұрын
brilliant! thank you! loved every 1/12 second of it
@AndromedaCripps3 жыл бұрын
I am an HPP enthusiast and was delighted to see not only how well you handled some of the more technical questions of HPP, not only the novel and relevant topic of the Well-Tempered Clavier (they always taught me in school that Well-Tempered WAS Equal-Tempered, and that the whole point was to showcase the strengths of that system by writing in every key), but ALSO to hear you so succinctly and eloquently lay out the defense for HPP to the masses who claim it is unnecessary, strict, unknowable, etc. As with all manners of cultural history which we interpret in the modern day, such as historical fashion and cuisine, there is absolutely merit in criticizing, questioning, and investigating every aspect of the history and our interpretation of it. Even if we cannot know the answers, exploring all options and engaging in the discourse of it allows us to have a broader and more comprehensive understating of the past.
@DeGuerre3 жыл бұрын
"You're playing Bach wrong" Snippet of WTC1 C major prelude played on a pianoforte with the sostenuto pedal held down for every bar. Me, knowing not only that Bach had probably not seen a pianoforte, but that the sostenuto pedal hadn't been invented yet: "I know what this is about!"
@batner3 жыл бұрын
which one is the sostenuto pedal and when do i press it?
@DeGuerre3 жыл бұрын
@@batner It's the one on the right, and you press it when you want notes held or strings to resonate sympathetically.
@batner3 жыл бұрын
@@DeGuerre Its the sustain or damper, not sostenuto.
@PutItAway1013 жыл бұрын
Even if the sustain pedal had existed, we would know he didn't intend it for this piece because of the way it's written with the low notes held and the high notes short, which is meaningless if the pedal is down
@batner3 жыл бұрын
@@PutItAway101 What do you say, high notes are legato or non legato? I play with sustain.
@Cross_Contam3 жыл бұрын
It would be nice to hear a familiar piece performed in each tuning. I imagine having the qualities of the notes varying by some degree depending on the octave could have its advantages for a cinematic composer.
@JoshuaWillis893 жыл бұрын
It would have been nice if you had mentioned that there actually are plenty of musicians who study this stuff in-depth and make serious attempts to use historically accurate performance practices, maybe even shout some of them out.
@pavaomrazek Жыл бұрын
2:03 Little mistake there. A fortepiano (and even a modern piano) doesn't respond to how hard or soft you touch the keys, but rather how fast or slow you touch the keys.
@migadepancito3 жыл бұрын
I love how most drawings he makes make sense but every once in a while there's a random ass drawing that's unrelated to everything else
@dzuschin3 жыл бұрын
The organs in Bach's very first church jobs at Arndstadt and Mühlhausen were both well-tempered - probably one of the Werckmeister tunings. For more info see "The Organs of J.S. Bach: A Handbook" by Christoph Wolff, Markus Zepf, Lynn Edwards Butler. (Bach owned a copy of Werckmeister's treatise btw)
@pyrokinetikrlz3 жыл бұрын
Bach tuned his keyboards in 15 minutes?!?!?! damn!
@batner3 жыл бұрын
I can re-tune mine in 7sec. It's under Settings->Tuning and AdvancedSettings->Temperment
@aBachwardsfellow3 жыл бұрын
- only 1 string per key, only 56 keys = 56 strings ( piano - 88 keys, 200-plus strings)
@bradleylehman43273 жыл бұрын
Yes, it's easy enough to do that on harpsichord with practice. Weather changes make us get plenty of practice. I'm usually around 8 or 9 minutes for a single-8 register with this temperament, by ear.
@karlrovey3 жыл бұрын
@@aBachwardsfellow What about the possibility of a two manual harpsichord?
@aBachwardsfellow3 жыл бұрын
@@karlrovey I think Bradley Lehman could probably answer that better than I. I'm not sure where we are getting the fact that "Bach tuned his keyboards in 15 minutes" from, or how well grounded/substantiated that claim is. Bradley seems to think it's reasonable for a single register harpsichord. It also seems that different temperaments may be easier to tune due to the presence of more consonant (i.e. beat-less) intervals.
@therealzilch5 ай бұрын
Very well done, thanks. As a tuning freak myself, I've gotten to the point where I don't think about the exact ratios, but rather tune more fifthy or thirdy, depending. cheers from sunny Vienna, Scott
@bluedragon79253 жыл бұрын
Music is the only subject needed in school. Just about everything else somehow gets included!
@ButWhyMe...3 жыл бұрын
I know right.
@TheAndersJames3 жыл бұрын
I would like to congratulate you as this video prompted me to set up my MIDI keyboard, boot up Waveform, and scrawl through my libraries and plugins to set up a proper clavier sound for Bach. Of course, now I have to go find a decent Scala file and wait for this 74 MB sound library to finish its download.
@zperk133 жыл бұрын
"you know that bach piece? the one that goes ..." i was literally just playing it yesterday...
@AstrosElectronicsLab3 жыл бұрын
Bach*
@zperk133 жыл бұрын
@@AstrosElectronicsLab whoops! thanks!
@jdmitchell65593 жыл бұрын
O well, you were playing it wrong (says some guy who didn't hear it), I played it a couple of years ago in a recital at my church on a virtual harpsichord. I expect I played it wrong too. It's great to be wrong, one is in such good company. I find 12tone's scribbling strangely sinister, BTW. Interesting video.
@Jinkaza18823 жыл бұрын
Temperament and period performance. Great stuff. Ty for the vid.
@pocojoyo3 жыл бұрын
It is strange that the focus is on tuning and relative tuning in general and no mention on dynamics and/or tempo, the arpegii pattern to sustain the sound of the chord vs the necessity or not of the sustain pedal. Maybe in Part 2: "You are still playing Bach wrong" .
@reverbscherzo78503 жыл бұрын
This. I second this proposal!
@pocojoyo2 жыл бұрын
@@redcuillin what would Bach think of us mortals bothered by such details ?
@Acoustic-Rabbit-Hole Жыл бұрын
"The truth is that Bach went into a trance and channeled the Akashic records. Wrote it all down, but forgot about it the next day." - Thus spake The Acoustic Rabbit Hole
@upinsmokeproductions64713 жыл бұрын
I always tell my friends, one of the greatest tragedies in my life is never hearing classical pieces by the original artists. I always wonder what flourishes or improv they would toss in just to show off, much like guitarists extending a solo when the song never had it before.
@EleneDOM3 жыл бұрын
Sometimes we have evidence, for example, variations of certain passages that Chopin wrote out for his students.
@teucer9153 жыл бұрын
As soon as I heard you play the clavier, I knew where this was going. Bach's work in equal temperament is a beautiful thing, but there's something magic about hearing it just right.
@the-selfish-meme75853 жыл бұрын
Spinal Tap guitarist and songwriter, Nigel Tuffnel famously agrees - D minor is the saddest of all keys. In fact, he wrote the 'Tap classic...
@inf0phreak3 жыл бұрын
"Lick My Love Pump" - a kind of Mach piece...
@Michael_______3 жыл бұрын
the editing and sense of timing here good job fluid with your narration
@connorlarkinbass3 жыл бұрын
I thought you were gonna talk about the missing bar in this piece. Not sure if you know about that. regardless...great video!
@tylerbreisacher58413 жыл бұрын
Wait what? Are there any good videos about this missing bar?
@LesterBrunt2 жыл бұрын
Well I think you can say that even in equal temperament keys have different characters. there is a cutoff point on the bottom and top of the audible register. The lowest possible D will sound different than a G. The lowest D on a piano still sounds acceptable but the G below that is almost indistinguishable because it is on the limit of perception. So the lowest G is a fourth above the lowest D which makes it give a different character. And similarly for the highest registers.
@4kassis3 жыл бұрын
I was kind of hoping there would be a performance of how that piece would sound with the tuning that Bach may or may not have liked...
@travisrainey11713 жыл бұрын
Yeah, with all that build up I expected to hear an example at the end.
@bradleylehman43272 жыл бұрын
An hour of music in that tuning is here: m.kzbin.info/aero/PLgqUCA7I97rpRCfPsN32DyGrCQLPE9BgY
@bradleylehman43272 жыл бұрын
And this prelude is here, including a better explanation of the tuning: m.kzbin.info/www/bejne/eGOTknaGbJypbpY&noapp=1
@MegaMech3 жыл бұрын
Cristofori's piano was not really called a fortepiano (interchangeably, pianoforte) rather something like 'clavicembalo con forte e morbido' (harpsichord with loud and soft). There's no doubt that Bach meant The Well Tempered Clavier to be played by any keyboard instrument. Certain pieces are definitely 'orchestrated' for organ while others appear to be more for clavichord. German harpsichords were not really used as solo instruments. It's likely the entirety of WTC was composed on clavichord. afaik Bach never wrote in stop changes and rarely wrote in tempo changes. 12tone likely sources his information from Wikipedia and as such gets the fundamentals of the Baroque era completely incorrect instead going on a tangent that has little or no relevance to WTC. Also, citing two arguments that don't contradict each other but when considered together provides an interesting perspective of how Bach and other musicians approached their musics. In the Baroque era musicians played according to their experience. Bach wrote in a generic style without providing musical directions because that's up to the performer. Whether you play with stops, without stops, change them halfway through, add decorations, remove decorations, change notes, improvise endings, etc. Beverly Jerold's articles on Numbers and Tempo is super enlightening as well as "Good Taste in the Art of Music." Historic instrument for Beethoven's works are much more significant than Bach's. Bach was basically like "Here's a cool experiment I did, where I exhaust every possible idea I can while also implementing the peak counterpoint, have fun." Play it at any tempo, on any instrument, with any changes you want (within reason). As long as your performance is unique and musical, then you're playing according to what Bach wanted. At least, as far as the evidence shows this is the best answer and you won't find a better one. Cookie cutter performances is certainly not what Bach intended... In any of his music. Today, playing Debussy in a cookie cutter style would be desired because he was super intentional about his musical directions. Another shakily researched video from 12tone..
@Nebulous-393 жыл бұрын
I love the Kipo reference at ~8:07 haha
@bazingacurta25672 ай бұрын
Very well researched video. Please keep on doing this!
@DomenBremecXCVI3 жыл бұрын
Wait, Bach's dead? I wanted to see him live so badly...
@DaedalusYoung3 жыл бұрын
I hope I can get a refund of these tickets.
@AstrosElectronicsLab3 жыл бұрын
Bach's dead. He doesn't care.
@jamesm49703 жыл бұрын
*cues up The Residents' "Bach is Dead"*
@wingracer16143 жыл бұрын
But I just saw him a few days ago. He still belts out I Remember You like god.
@Quim1441 Жыл бұрын
This video is really good! Really precise and accurate and yet well sintesized. Good job!
@123Joack3 жыл бұрын
This is proof for the whole beat theory, which means the metronome used to be read at 50% speed, counting each full swing. Explains away countless problems with period performance, falls in place with the documented speeding up through the 19 hundreds. And of course, fingerings as well.
@19divide533 жыл бұрын
Will:
@bernatrosello43753 жыл бұрын
The issue was, actually, that metronomes were just popping up and since not everyone knew how they worked exactly Bach read the bpm number under the pendulum weight instead of above it. He might have considered the weight's shape looked kind of like a down facing arrow and gone with that.
@123Joack3 жыл бұрын
@@bernatrosello4375 Thats a baseless theory, made to explain the unrealistic speeds. All evidence indicates the metronome was a toll specifically designed to be exact, as opposed to the vague tempo words
@bernatrosello43753 жыл бұрын
@@123Joack it's actually not, though I did get it wrong, it's known that Beethoven did this, most notably, I'm not sure about Bach. kzbin.info/www/bejne/fHabeYScpryHisk
@alicewyan3 жыл бұрын
@@bernatrosello4375 The explanation that Beethoven read the wrong side of the metronome weight is the most convincing one I've heard so far for the discrepancy in his tempos vs what sounds good. But Beethoven was essentially beta testing the metronome, it didn't exist yet while Bach was alive.
@agranero610 ай бұрын
The first time Bach saw a piano was in the palace of Friederich II of Prussia invited by him through his son Carl Philip Emanuel. A rule of thumb is the older the music is the higher the A is (not counting on the non equal temperament way to tune it), but is more complex than that as Bach usually messed the the organ all the time filing pipes, etc for each composition (he was Kapellmeister). We probably will never know how he tuned it.
@aelfrice3 жыл бұрын
There are hundreds of videos on KZbin of amateurs and tinkerers playing these beloved pieces in all manner of non equal temperaments. . The novelty wears off rather quick. This is because keyboard temperament issues are an illusion, are inherent to fixed-pitch instruments vis a vis the tonal series, and are beside the point. The point is music. . For centuries, keyboard instruments were not used to accompany singers due to the fact that singers don't sing in equal temperament. Special keyboards were used for vocal ensembles to better approximate the purer thirds and sixths and better adapt to modulating key centers. . This subject is far too contingent on historical musicological exposure to warrant this video. It's cool to appreciate the harmony of the spheres, but those things are secondary to the actual fact of man's musical awareness--a sort of synthesis of physics and the human mind. (reposted from reply) But I love your videos and please keep them coming!
@bradleylehman43273 жыл бұрын
Colleagues and I have been using this temperament in our concerts, church services, and CDs for 17 years. It lets the music sound more beautiful without drawing attention to itself.
@GillAndBurtTheCop3 жыл бұрын
You couldn’t include a corrected end rendition of the song? Thanks..
@zkingsalsa3 жыл бұрын
"bach's dead. he doesn't care" bach: >:(
@AstrosElectronicsLab3 жыл бұрын
He doesn't, lol. He doesn't exist to care.
@davidweihe60523 жыл бұрын
Which Bach? All of them, including distaff side descendants? He had a big family (several of whom had better reputations as composers in their lifetime than "Old Bach" did), several of whom had big families, and beyond that I don't know, but I doubt that they all went celibate. Not to mention upstream family. There is probably a Bach alive, today, even if they have no idea that they were related. He/she may even be musical.
@zkingsalsa3 жыл бұрын
@@davidweihe6052 yes
@OmnipresentPotato2 жыл бұрын
There are two contradictory statements here: 1) Bach assumed he did not need to specify the tuning as he thought it was obvious. 2) Bach made his own tuning system. If statement two is correct, that means he can't have assumed it would be pointless to write it down. Since it's obvious that statement one is correct, I think that negates statement two.
@neofaizan3 жыл бұрын
You mean there are more than 12 tones? You've betrayed me
@mokyoworks26963 жыл бұрын
If you were to tune a keyboard to a non equal temperament, there are limitations on what you could play before it sounded "bad". Which means the composer would be limited to how far from the home key they could modulate or use of chromaticism. That's what really unlocked the possibilities for composers using the equal temperament, they could modulate freely to any key in a single piece without retuning. So, in regard to the video, perhaps it might give more insight on his tuning to see how Bach modulates in the WTC. Depending on the temperament, some modulations may sound horrible, and therefore eliminate that tuning system.
@DanzelGlovington3 жыл бұрын
I hope he talks about how there's a theory nobody used their thumbs evidenced by fingering marks that omit thumbs. Playing all that without thumbs would make Bach even more epic than he already is.
@19divide533 жыл бұрын
I remember reading somewhere that Bach was one of the pioneers in the use of thumbs in piano playing
@ejlflop3 жыл бұрын
@@19divide53 It's unclear. CPE Bach mentions the "modern" thumb-using fingerings in his book, and he was of course taught by his father. But there is surviving teaching material (e.g. the Applicatio BWV 994) by JS that uses the older fingerings. Also thumbs were never *banned* in old fingering systems, just the practice of bending them under the rest of the hand when you ascend or descend the scale.
@mahryutka3 жыл бұрын
Your moving hand is maddening! I couldn’t concentrate on content!
@jonmackenzie3 жыл бұрын
"the answer is just an answer, the fun part is asking the questions" ain't that the truth
@dominiquemanchon9914 Жыл бұрын
9:54 I am deeply convinced that Bradley Lehman is right. I tune my harpsichord (and even my old Erard grand piano) that way by ear (well, 15 minutes are short for me, but 25 to 30 minutes are OK). It is even less difficult than tuning in equal temperament. All tonalities sound great: the worst major third, E-G# (pythagorean minus 1/12th pyth. comma), makes the E major tonality just mildly spicy, whereas F-A and C-E are beautifully close to pure. On the piano Bach sounds great, but also Grieg, Debussy, Lili Boulanger and Maurice Ravel. If you are dubious about turning Bach's drawing upside down, just replace flattened fifths by sharpened fourths...
@jasonremy16273 жыл бұрын
Dm, the saddest of all keys...
@macsnafu3 жыл бұрын
Yes, we forget that music and musical instruments didn't have all the modern stuff we have now. But with electronic keyboards and computers, it's easier than ever to try the different tunings. The Korg X5 had about 5 or 6 different tunings you could try. It would even let you create your own scale, if you felt so inclined. I'm sure these were far from the most popular settings on the X5, though.
@Rubrickety3 жыл бұрын
You just blurt out that Bach is dead? Have you never heard of a spoiler alert? Sheesh.
@AstrosElectronicsLab3 жыл бұрын
300 year old spoiler alert, eh?
@lysanamcmillan79723 жыл бұрын
The bottom joint of my right thumb is permanently wonky because I misplayed a Bach prelude on a mechanical level. Nobody told me I was supposed to pivot my hand as well as reach for an interval of over one octave. It wasn't your example in particular, but it still ached in memory of the weeks I spent in a brace while my slightly beleaguered teacher had me work on a one-handed piece his son composed. I also quip that my thumb has a Bach injury. I'm easily amused.
@segmentsAndCurves3 жыл бұрын
I was listening to Bach when I click the notification button. W H A T? Also: limiting interpretative liberty = no cookie.
@garygreen75523 жыл бұрын
Fabulous video. I believe that book one of the Well-Tempered Clavier contained all new compositions, that is written specifically for that collection. Book two, as I recall from long ago college classes, was compiled from existing music that Bach had written. I imagine that some of those pieces were modified or changed to better illuminate the goal. In any event his goal in both books was to demonstrate that a keyboard instrument with a tuning compromise could play in all keys. Now, with all of your information, I feel like opening a perfect fifth and having wee dram.
@TheApostleofRock3 жыл бұрын
While I love the idea of Bach making his own tuning system and wouldn't doubt it, I essentially refuse to believe that the answer lies in squiggles on top of the page. If it mattered to him for the tuning to be specified, he surely would have written it down in a clearer form. So either that document is lost or he was using a system that already existed. But hey, I'm no scholar
@Hamstray2 жыл бұрын
8:54 "the one from F# to A#" that's not a A# then, it's a Bb. you could tune the A# to a Bb and sacrifice some other intervals. A# and Bb are not the same note.
@strongbow38963 жыл бұрын
Disliked.
@djtomt6 ай бұрын
This is a very good explanation of the tuning dilemma. Thanks. I am pretty sure Bach understood the concept and the potential of the pianoforte even though he may have criticized early prototypes. I imagine he would love our modern pianos.
@biernut872310 ай бұрын
4:20 How did someone in 1880 ascertain that particular tone was 421.6 Hz?
@michaelmcgowan70993 жыл бұрын
Enjoyed the video and appreciate all the thorough explanations. Still, I don't think it matters all that much. I think the recent fascination with Baroque instruments to be mostly a curious hobby. At the time, many instruments were poorly made, were difficult to tune, and didn't maintain their tuning. Bach, no doubt, was a perfectionist, but the common listening experience wasn't so pure. Modern standards, quality instruments, quality materials, and especially modern recordings have done much to raise the consistency and quality of performances.
@EleneDOM3 жыл бұрын
Your statement that many Baroque instruments were poorly made is a bit bizarre, and I don't know what evidence you would have for it.
@j3ffn4v4rr03 жыл бұрын
It seems fair to assume if Bach didn't intend equal temperament, that he DID intend each piece to have the flavor and emotional tone that each different key offers. Can someone recommend a recording/performance of the WTC that illustrates the various key "colors" of a well-tempered tuning?
@pablojlascano83228 ай бұрын
actually the tuning system is more like a battle between the better fifths vs. the better major thirds.... (and incidentally, minor thirds)... you don't need to "hide" the Pytagorean comma, actually you don't have enough of it, at least historically, when they were favoring milder truer thirds, and didn't mind having almost Pytagorean thirds like nowadays,... the worst wolf that occurs is just because of that, you temper so much to get better thirds that you end up not being able to close the fifth loop by being short instead of being wide.