G Sharp and A Flat Are Not The Same Note

That's right. They're two different notes! Today we learn a little bit of the history of tuning systems, and how G Sharp and A Flat are not the same note. We'll talk about Pythagorean Tuning, Just Intonation, and Equal Temperament, and what is good and bad about each system.
This is the 3rd Video in the Acoustics Series:
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[@garysharp7871]

My name is Gary Sharp and since 6th grade music class my nickname is A flat. And I'm not changing it

[@DatOneGamer9870]

Gary Sharp. Rival to jazz composer Chris Sharp. A duel will commence shortly

[@themadgamer4571]

Well met Aaron Flat

[@d4rkm4g1c-brawlstars3]

Gary Sharp wow weird name. Why isn’t ur nickname g snap?

[@VisualDrone12]

You were a G Sharp minor at the time

[@justinsievers2756]

VisualDrone12 AHHHHHHHHHHHHHH

[@finnrock5558]

As an engineer who never learned to play an instrument, this is exactly the kind of explanation I needed. Thank you very much.

[@shahnewazmanto4798]

Do you mix audio ?

[@RightAway87]

I'm a good musician that plays multiple instruments and I absolutely suck at math. I'm so right brained that I still have to count on my fingers to do simple addition, and I'm 34. When it comes to writing, or languages or making music I have no problem, but I couldn't be mathematical to save my life lol!

[@freshman1212]

The fact that it's so ingrained in common now is exactly why I'm now looking into microtonality to find new types of melody and harmony.

[@twominutemusictheory]

There are so many different colors and Sonorities to be found outside of the 12TET box!

[@simonsanchezkumrich8489]

Listen to microtonal banana by king gizzard

[@granttomlinson164]

this is more than 2 minutes lol

[@ipsurvivor]

😀 Good catch... But it could be said that his “tempered long time” on the video is about what’s recommended to develop a message or point that has a lot of moving parts. Around 7 minutes... Less than that and the point can’t be made in full and more than that and people’s attention starts to wane.

[@chaplainmattsanders4884]

😂

[@michaelbauers8800]

The difference between the actual length vs. the 2 min lie, is called the "youtube comma", in video length theory.

[@ganaraminukshuk0]

Vid: G# and Ab are not the same note. Me, an intellectual: E and Fb are not the same note either.

[@katelijnhovestad8382]

😂😂

[@robertajoestar4636]

😂😂😂😂😂💫

[@Kassiusday]

Well then the key playing Gsharp is not the same as the one playing Aflat ... : ( quantum music )

[@johnsmith-ch7fg]

I assume that's a joke but actually there is a perfectly rational case for that; it is only a joke if your using 12tone equal temperament the current mainstream tuning solution

[@lassehoffmann625]

Im here with g double sharp is not a flat

[@stevonico]

I was okay with equal temperament until I heard the glorious beauty of a justly tuned major 3rd...

[@ryanotte6737]

Ah, then it is settled. We will require pianos to be built/tuned as are harmonicas. Get a different piano for every key you want to play. 😜

[@fernwehn5925]

@@ryanotte6737 Ever heard of Well-temperament?

[@FernieCanto]

My mind was blown when I first heard a comparison between just intonation and equal temperament. One was absolutely, perfectly in tune, while the other sounded like a bizarre mess. ... except, as it turned out, the "bizarre mess" was just intonation. My ears are so accustomed to equal temperament that the *other* systems sound weird to me. So, I realised, I don't care about tuning systems. I care about MUSIC. Tuning is something we use in order to listen to music, not the other way around.

[@mitchelledels9762]

Tuning a different way is good as long as it sounds good .

[@johnsmith-ch7fg]

Steven C go find your self a harmonic 7th then

[@kevinskogg2179]

Why is TWO MINUTE MUSIC THEORY 7 minutes long?

[@feelfactory9118]

there are three music theory....and 1 minute intro.....#save_Tamilnadu_from_tamils....

[@kevinskogg2179]

@@feelfactory9118 Not really, it is one concept.

[@feelfactory9118]

@@kevinskogg2179 im kidding,, i wanna help from you..

[@onionvlogs5222]

@First Last biggest bruh comment

[@JamesMulvale]

It's 2 minutes Equal Temperament

[@jamesbachreeves]

In a conducting seminar at Amherst, we were studying a difficult contemporary opera which was going to be performed that night. The professor, referring to a less-than-stellar student soprano and a challenging high note, said "She's not going to get to that high b. She's going to be flat...." We all groaned, and he leaned back and said, "That WAS a-sharp remark, wasn't it?..." We all threw up, and then I said, "If I made a pun like that I'd pretend it was accidental."

[@MarexKai]

This doesn't make any "cents".

[@MarexKai]

Andrew The joke flew over your head.

[@justinsievers2756]

Shut up lol hahaha

[@GeoffBosco]

It makes 1200 cents. Aka $12

[@kenmare16]

The math is head spinning but you got the point across very well. Excellent explanation of a complex topic. Thanks!

[@johnsontrimble7881]

"When we did this, G# and Ab became the same note"

[@littlefishbigmountain]

Technically, they didn’t. They became the same _pitch_ kzbin.info/www/bejne/roGrYY1ugt-Fm8U

[@gilbertmurillo695]

A.K.A the same note.

[@matiasvazquezm]

@@gilbertmurillo695 The same pitch, the note is the name we called that pitch, and that's depends on the harmonic context.

[@matiasvazquezm]

@@gilbertmurillo695 The same pitch, the note is the name we called that pitch, and that's depends on the harmonic context.

[@BlakleyBassoon]

I've been looking for a good explainer of temperament for a LONG time. This is the best I've seen! I would counter the idea that equal temperament imperfections are not so small that we don't mind them, but rather something we simply have gotten used to. Far too many musicians consider intonation (and temperament) an objective thing. It simply isn't the case! Intonation is subjective and a tool for expression and personal taste.

[@lekriz6190]

brilliantly explained ! Like to add my favorite saying: Never B sharp Never B flat Just B

[@mr88cet]

Hilariously, way back in high school (like 1979!), I made a T-shirt almost exactly like the icon for this video! Although mine was black on an orange background, rather than your white on red. Nerdy minds think alike!

[@frfrchopin]

When I saw the "Babe, I've changed" jokes on social media, I simply used to comment there "128:125" if you get what I am saying 🤣

[@EmdrGreg]

I'm ok with 12 tone equal temperament. It is nice though, now and then, to hear music of earlier times played using the temperaments it was written for. There are colors and harmonic textures that have been erased by the equal temperament system. This is true even for composers as recent as Chopin.

[@tomy.1846]

Each time I watch a video about this I feel like I understand a little more. Hopefully one day I will have a real breakthrough and more of it will fit together! Thanks for the information! :)

[@ZiadKreidy]

Very nice video :) In my opinion, the great advantage of Equal Temperament is that it's the same everywhere, it's standardized. Any unequal and well tempered temperament also allows to play all 24 keys.

[@michaelmiller1215]

Very informative. I remember my college Conductor and voice teacher stressing to make your half-steps in singing “higher ( than the equal temperament tuning) of the piano”.

[@BarryMagrew]

Quick correction: 81/80 is the syntonic comma, not the Pythagorean comma. The Pythagorean comma is 531441/524288, I.e., 3^12/2^19. Also, there is no tuning systems in which powers of 5/4 create all of the chromatic notes, akin to the way 3/2 generates the Pythagorean chromatic scale. As you say by the time you get to three pure major thirds, you arrive at another comma, here, the dies is, 128/125.

[@Anonymous-df8it]

"there is no tuning systems in which powers of 5/4 create all of the chromatic notes" 19TET: Am I a joke to you?

[@frfrchopin]

Yeah, exactly what I wanted to say.

[@fgk2588]

​@@frfrchopinMe too

[@mskiasu7137]

this is the exact moment when i realise that having perfect pitch is a curse.

[@electric7487]

I second this. Having "perfect pitch" locked me into 12-TET.

[@charleshudson5330]

As a physicist and pianist, I love your video. (Simon Stevin would have loved it, also.)

[@petermoomaw3400]

You might have touched on quarter comma meantone. It was used for far longer than 12 note equal temperament. Related tuning systems which are interesting are 19 note equal temperament, and 31 equal temperament. In fact 31 note equal temperament is arguable the indistinguishable from as quarter comma meantone for all practical purposes.

[@klausreinhard7775]

Hi, there is a mistake beginning at 3:10 of the video: 81/64 * 81/80 is obviously NOT 5/4 ! The mistake is, that you have to divide 81/64 by 81/80 (not multiply), because 81/64 is larger than 5/4. Thus the correct equation is: (81/64)/(81/80) = (81/64)*(80/81) = 80/64 = 5/4. Otherwise a well made video although a little too fast. Kind regards.

[@twominutemusictheory]

Thanks for the correction! And my apologizes for my oversight.

[@98innocent33]

@@Hotters9060 Lmao Wikipedia, you gotta be kidding me XD

[@tvoommen4688]

@@Hotters9060 Having grown up listening to Indian music(which mostly uses just-intonation), I often find it difficult tuning guitar strings precisely. Sometimes I have to provide a minute vibrato to satisfy my ears.

[@joeeeee256]

There's also a mistake at 2:01

[@user-pp1nj1pz7j]

I think he has some mistakes also on 1:27

[@jgferreraza1173]

Thank you so much ! Finally a quick and crystal clear explanation of why us keyboard players puzzle the string instruments players by saying G sharp is the same note as A flat. Been trying to explain this for 45years. Genius !

[@josephsmith8358]

This is the first time that math has helped me understand something that is not math.... and I am so happy and I don’t know why lol.

[@Greg-om2hb]

But music IS math. Your auditory system understands the math even if your cognitive system has not pondered it.

[@josephsmith8358]

@@Greg-om2hb yea im specifically talking about me consciously using math to understand something that I dont perceive as math. Math does not make me happy or emotional. I dont use it to set atmospheres etc.... i think that music uses math as a fundamental element, but it is not itself math. Math is in a lot of things that are not music lol.

[@pablocamarasasola2770]

Thanks! It's hard to find a comprehensive answer and this video really helps

[@shamsigamer4107]

Your presentation is great, very compact and informative.

[@macbird-lt8de]

that seven minutes félt like three at most

[@kgigs_]

this was super helpful thank u so much!

[@therealzilch]

A very good short introduction to why we have equal temperament. I'm a tuning and temperament freak, and I think, as did Mao Tse-Tung (or at least he said so), that a thousand flowers should bloom Equal temperament is an amazing compromise, that makes all kinds of music, from Chopin to Conlon Nancarrow, possible in the first place. On the other hand, those thirds are really dreadful, and well nigh impossible to sing. The problem is, of course, mathematics: no power of two is also a power of three, or five. Even God can't change this, if She's logical. cheers from sunny Vienna, Scott

[@stratmanstudios4899]

Glad I watched! Thank you.

[@ZeroesandOnes]

Very succinct and neatly demonstrated.

[@slayy._.ayanna2577]

Title: Two Minute Music Theory Video: 7 minutes long Me: *visible confusion*

[@FernieCanto]

In equal temperament, 2 became equal to 7.

[@PeterACasanave]

Thank you. Including the Just Intonation System made the explanation work. The upshot is that tempering is "politics" i.e. trade-offs. I've been struggling with "explanations that don't make sense" since I was told that B to C was simultaneously a full step and a half step. This was back in the 1950's, and the teacher was a very authoritarian band master. I moved on, ignored music as best I could, and here I am at 74 trying to learn keyboard (a little) and cornet (more like singing but familiar to my old melophone memory) with more progress alone than I ever had with irrational teachers. Thanks.

[@artvandelay5565]

Amazing content, amazing channel. I really hope to see more.

[@ivanjavora710]

You got yourself a subscriber. Glad I found you. I will show this video to a few people to try to explain tuning of so called Histrian scale (if I have your consent). One more thing might improve understanding of historical development of tuning: number of simultaneously used tones in certain points in history (monody to full orchestra).

[@twominutemusictheory]

That sounds like a great idea for a video!

[@ivanjavora710]

Which one? Tuning vs harmonic multitude or Histrian scale?

[@twominutemusictheory]

Ivan Javora I was talking about the history of monody to orchestra. Also, absolutely share this video if you are so inclined. I intend for them to be educational!

[@jeremiahlyleseditor437]

Since most of the best portions of modern music, going all the way back to the great classical masters, was written with Equal Temperament, including the more modern works of "The Beatles" and similar, I would think to suggest that Equal temperament is good. But tuning to either 432 or 440 might be numerically better whilst giving the musician a few minor options.

[@acerebral_]

changing the base tuning pitch doesn't do anything to change the relationship between notes though, it's basically changing nothing in the music. also while most modern day music uses 12TET out of standardization, there's no reason it couldn't be performed or even improved in another tuning (e.g. how lots of music by "great classical masters" is played in equal temperament despite them being written for meantone.) trying to determine some sort of universally best tuning is kind of a moot point, it comes down to what use you need from it and what you find sounds good (which is mostly driven into you culturally.)

[@jaytc3218]

There is a problem sort of related to this in the guitar world. The distance between frets as you move up the fretboard comes about due to a mathematical formula. When you tune the guitar to concert pitch, (A=440 Hz), everything is great. But when you start identifying the locations of the natural harmonic notes, you rapidly discover that those fret distances don't line up with the calculated fret positions. New guitar players who discover this for the first time will start to "chase" the tuning of their strings flat or sharp. If you tune up harmonically, it will be out of tune the normal way and vice versa. You can't have it both ways. Arrgghh! There is a guy in Turkey who came up with something called a microtonal guitar to address this problem by moving the frets around but even that it has its own problems. We manage to create music and as a tool of expression, it's great. But when you start looking closely under the hood, you see that this system is far from this perfect.

[@tvoommen4688]

I have encountered this problem of tuning guitar precisely. This is because I grew up listening to Indian classical music which is totally based on just-intonation system.

[@168grhp]

Very helpful explanation!

[@mohig7273]

Excellent information in a nutshell... Thank you sir.... Love from India 🙏🇮🇳🙏🇮🇳🙏

[@anled.composition]

Hi, At 3:22, shouldn't you divide (not multiply as mentionned in the comments) by a syntonic comma, not a pythagorean comma ? Great video !

[@twominutemusictheory]

That is true! That’s what I get for working quickly and not checking for mistakes.

[@misterguy9051]

Thanks for precision at 5:51

[@MostlyIC]

anyone that thinks we've lost something by going to equal temperament hasn't bothered to listen to Ravel, Debusy, or Bill Evans, the number of different chords they use and the ways they fit them together and all the different feelings they evoke is staggering

[@Muzikman127]

Perhaps it's better to say: we've lost some things, and gained others. Any tuning system has advantages and disadvantages; Giant Steps isn't possible without equal temperament, the blues isn't possible without leaving behind equal temperament. (And any number of other examples). And without even going into rigourously define alternative temperaments/tuning systems, if you ever play any non-keyboard instrument (and that includes singing), being aware of the differences and different expressive possibilities of different intonation is worthwhile. And if you feel even more adventurous, just as Debussy couldn't have written Clair de Lune without the harmonic possibilities of 12 tone equal temperament, so too are there many other pieces of music waiting to be written that use the harmonic possibilities of other systems. (Personally I really like 31TET) Listen to Djavan Gasparian or Naseer Shamma to hear what beautiful music has been written by composers coming from other musical traditions using other sets of notes that are missing from the piano, for instance. Or Rahim Alhaq or Ben Johnston's string quartets

[@MostlyIC]

@@Muzikman127 you've reminded me of the time a work colleague mentioned that his son had perfect pitch, so I asked if his son might want to make some money by doing a bit of transcribing from a CD who's piano part I'm especially fond of, the answer came back yes so I lent him my "as serenity approaches" by Marcus Roberts with the request for a transcription of "Preach Reverend Preach". He came back a few days later and said the piece could not be transcribed because the trumpet was playing too many off-scale notes ! (I wasn't interested in the trumpet part but somehow that bit got lost). I had to run off and listen to Gasparian, Shamma, Alhaq on youtube, but had the same reaction I always have with far eastern, indian, middle eastern, and to some extent even some baltic music, which is that each of those cultures seem to have settled on a single emotion for all their music, its like if the US was still stuck on country western, its so limiting. and since I didn't grow up listening to it, its not my cup of tea. and Ben Johnston's 7'th - sounds like a whale song to me, something that only a whale could understand. I'd like to know what my Mom would have said about it, she was a professional violinist and was fond of saying "melody, harmony, rhythm, to be music takes at least two", and I think she would say Johnston doesn't. Anyway, now I've got to get back to practicing a beginner's piano version of "Lady Bird", which to my western trained and western limited ear has all three !

[@kuroshzamani1775]

That's amazing! thank you for the video ;)

[@muliercantatinecclesia5]

Thank you, it's very communicative and very interesting, but at the same time very difficult for me as well. As a singer I always end up tunning "as I feel it should sound" and I'm never sure if it's OK ;)

[@smittywerbenjagermanjensen7027]

I quite enjoy that as a classical wind player, my ensemble is constantly playing everything as in line with the harmonic series as possible. The conductor simply tunes each chord that needs tuning so that every little bit is practically indistinguishable from perfect harmony.

[@glennchapman1003]

WOW. Been trying to figure this out and found your video. Done!

[@lesavdesabonnes]

It's about intention and referential, one is there for ascending and the other one for descending. Also taken alone (without other notes arround) each underlies a role just by the name itself!

[@Flopsaurus]

Without a background in music theory, this video is essentially in a different language

[@gregole6367]

Thanks--Mind blown! Okay so is there any music being made using an alternative to what we are using now like you are speaking of? I am assuming this affects us at some level. Well great there's another rabbit hole to fall in, like there wasn't enough already...LOL! Thanks for the info. Oh ya bout the whole math thing um, something about drinking whisky I got the fith part down years ago. Been playing music all my life and never under stood this stuff cause I play by ear. I dig what you are saying and I understand the concepts basically but now I want to apply it. I would like to know what I am doing first. Is there a way you could find a translator to maybe make a video to communicate this stuff to rest of us knuckle dragging apes who are still stuck on ooh ooh shiny?

[@rafexrafexowski4754]

Hello! There is a lot of music written in tunings other than equal temperament. First, there are obviously instruments that naturally play other frequencies. All brass instruments can only play in just intonation and string instruments without frets will usually change from equal temperament to just intonation while playing whenever they can. Second, a lot of non-Western classical music uses non-equal temperaments, like traditional Arabic music (it's very hard to explain how it works to the Western listener, basically there are a ton of scales called maqams that each use a completely different tuning system, but can be approximated using 24-tone equal temperament). And finally third, a lot of historically informed performances use the tunings that were used at that time. Music of Bach, Mozart, Beethoven, Chopin, Grieg and many others was all influenced by their old, non-equal tunings. Some of those tunings were meantone temperaments which tune like Pythagorean but instead of tuning with perfectly tuned fifths they use slightly out of tune fifths (this difference is called the mean, hence meantone). The mean is specifically chosen to make another interval perfect, like the extremely popular 1/4-comma meantone, which results in ideal major thirds, and 1/3-comma meantone, which perfectly tunes minor thirds. Those temperaments later turned into well temperaments, which sacrificed some of the perfect intervals to allow you to play in every key while still retaining the differences between key. Those temperaments were mostly the ones used by those famous composers I named earlier (although some like Mozart also really liked some meantones). Equal temperament was known since around the 15th century in Europe, but wasn't used because most called it souless and without character. It only became the standard because of modernism which needed to be able to modulate to every key without the change in quality. Tl;dr There is a lot of music written in non-equal temperaments, like some instruments that can only play in just intonation, music of other cultures and historically informed performances using original tunings.

[@johniielgouddi3017]

Awesome Level up!

[@jackwilloughby239]

Could you explain how to play a chromatic scale on the violin with a drone a 5th above and then with a 5th below, keeping all the intervals in tume? And also explain why the chromatic scale going up is different then going down( G# and Ab are not the same I get, but how do you know which one to play when?). None of the scale books talk about this specifically, but Sevcik kinda does in his Opus 11, The Art of Intonation. I realize this is a big question, but Violinists and their families and eventual audiences would be very grateful. Thanks!

[@ScaleAudio]

Does anybody know if there is a plugin that will let you quickly play in these different tuning systems? Seems like it could make for some really interesting soundscapes.

[@sebastiandiaz29]

Great video, I just have one question, are wind instruments tunned in just intonation?

[@reaper84]

Pythagorean and just intonation just not as obsolete as it appears here. Quite the contrary. As a violinist you apply both, all the time.

[@topnotch3944]

GUITAR PLAYER HERE....working on a blues tune in a flat /g# ......thanks 4 info

[@jb3636]

My head is about to explode. More grateful than ever that I am able to play by ear but I have a new goal to get educated on music theory. So I will watch another 10 times I guess. Thanks for the explanation!

[@philipstapert3517]

ET sounds okay until you listen to a pure M3 compared to an ET M3. Lately I've been listening to a lot of music in extended meantone with split black keys, and it sounds amazing!

[@GripoGanid]

Nice concepts but I’m going to be the geek here and say these: @1:18 when you multiply the ratio of 3:2 by 3:2, it should give you 9:4 for E. this error will spill over to your next notes. Also, when you divide 1:1 by 3:2, that will give you 2:3 for G not 4:3. Another flaw to this is you used 294 Hz as a frequency for D which is not the exact frequency of D but just rounded to the nearest whole number so when you multiply this with 3:2 you get 441 Hz (it’s off by 1 Hz to the true A = 440 Hz because you used an approximated value in the first place). If you want to find the exact frequency of D, type in 440*2^(-7/12) in your calculator. The frequency is an irrational number. For all the cases here, your frequencies will definitely be off by cents like the one you mentioned @2:24 because you are using the ratio of 3:2 as the ratio for perfect fifth. The ratio of 3:2 is another approximated ratio and is the main reason you are getting these discrepancies in frequencies. The exact ratio for a perfect fifth is really 2^(7/12). Use that and you will no longer get any howling.

[@CollinGill7]

i was very interested in if i could tell the difference between cent intervals, so i found some audio recordings online and i couldnt tell the difference between a 1, 6, or 10 cent interval. maybe i dont have top notch hearing (which is likely considering how many concerts and music festivals i have attended without ear protection) but being able to flawlessly transition between any major or minor key without any retuning necessary seems much more important for the advancement of music than having a true g sharp or a flat would be. maybe music today would be entirely different if we still had wolf fifths though...

[@danielcha9945]

Now I want to make some songs in different tunings

[@trevdoesweirdthings]

Music, something our brain made up, somehow being complicated is a prime example that our brain creates its own problems

[@bingbonghafu]

Will there ever be a perfect tuning method

[@ZiadKreidy]

That's not possible. Every system will have advantages and disadvantages.

[@geezerbill]

If you want to compose music using only two or three notes, or all octaves of the same note, then sure.

[@juandelavega192]

Aaron Hunt's tonal plexus is an attempt to make a "perfect" tuning method, since it's based on the lowest discernible interval. He divides the octave into 205 equal intervals (205-EDO) making each step a little bit under 6 cents. This means each desired note can be 3 cents sharp or 3 cents flat, tops. Even so, octaves are perfect and fifths are even better than 12-EDO(12 equal division of the octave, our current system).

[@rist98]

No

[@demosmemebrewery9916]

no

[@kukumuniu5658]

cdef g# a b - harmonic minor cdef g a-flat b - harmonic major

[@DanielHernandez-cz9zp]

The book "Scythe" brought me to this video

[@Zanthanee]

What a great video. thanks :)

[@danwylie-sears1134]

Since you ask -- I want to bring back key color. But I don't want there to be one universally used tuning system. I want the tuning system to be specified along with the instrumentation and tempo, when a piece of music is composed. 12TET could remain the default, the plain vanilla of tuning. But it's now feasible to design electronic instruments so that the use of a specified tuning system would be effortless for the musicians, and it's feasible to produce sound that people could use for ear training if they want to learn to be in tune in different tuning systems when singing or playing traditional variable-pitch instruments such as the violin family. An ordinary listener wouldn't need to know why one passage of music sounds different from another passage where nominally the same sequence of notes is played on the same instruments but in a different tuning, in order to be able to recognize tropes that use those differences.

[@tortillajoe9942]

3:18 you should be dividing by the ratio not multiplying. You’ve established that Pythagorean tuning results in frequencies that are too sharp so by multiplying it, you’re making it a little more sharp. Also just basic math sense 81/64 * 80/81 is 5/4, not 81/64 * 81/80

[@1Cr0w]

On instruments where you do not use keys, e.g. violins, i was taught you can actually make the difference, to fit the piece you currently play.

[@ClogDancingFiddler]

If a group of musicians played a piece of music on instruments that did not have a fixed note pitch (violin, cello, trombone etc) what tuning system would they end up playing with. This must create problems playing with piano accompaniment, playing in an orchestra or playing in a string ensemble! Or am I just overthinking and making things too complicated?

[@twominutemusictheory]

Often string quartets will tune in just major thirds. However, they will adjust some of the other intervals so that they stay in the original tonic. If they didn't, they would start drifting flat from the original key. And you're exactly correct with it creating problems in ensembles. Tuning is something that these ensembles must work on to play with each other.

[@karawethan]

It's the same issue that modern a capella choirs deal with. They rely on their ears. It's not equal temperament, but it's not just intonation either. It's something in-between. If you understand the historical context, temperaments were really made for keyboards (and to a lesser extent fretted string instruments). The keyboard set the tuning and functioned as a reference for all other parts. During the baroque period for instance, a vocalist or violinist would have to be prepared to play the same piece with slightly different intonation depending on their keyboardist's preference.

[@Quant-Beat]

Absolutely brilliant! Gold! What can you say about the bluff with 432 Hz? I truly say that I hear that a piano tuned to that, sounds slightly subtly false. The dispersion there at 432 Hz might be as perfect as 440 Hz, I don’t know I just raise the question to a man with that huge knowledge as you have in this topic.

[@2bonk22]

Equal temperament is fine for atonal music like Schurnburg but is really lacking for the tonal music of the 18 and 19th centuries. Well-tempered is better. C is very in tune and the further the key moves from C the more out it gets though none are so out as to be unplayable. Each key has its own sound and mood.

[@VodkaTheAntiAlcoholic]

Jesse, excellent video. Just an error I caught. at 5:08 where (correct me if I'm wrong) I think you said 5:4 = 25:16, but 5:4 ≠ 25:16 because you squared them, meaning you multiplied the 2 sides by different numbers.

[@TimpBizkit]

It was (5:4) x (5:4) = 25:16 which isn't exactly equal to 8:5

[@YLIU]

As a flute player, it's good to know what does we sacrifice for using Equal Temperament. So far, what I know is, for example, if the notes are for leading melody, then it's not big deal. But if the notes are part of harmonics for supporting the melody of other instrument, then just intonation should be included into consideration. In conclusion, as a flute player, it's good to know this concept. Because it motivates me to read more music notes, understanding the harmonics/structure before blowing the air into my flute.

[@peternospam342]

People who tune piano's play two tones and listen for beating. The closer the interval is to small integer ratios 2/1, 3/2, 4/3, 5/4 etc the slower is the bearing (if exact match there is no beating). When you tune equal temperament there is beating (except for octave). On standard piano tuning a C major chord beats. There is a special old style of tuning where C major chord doesn't beat at all and sounds pure and resonates for a long time (maybe that's Bach's well tempered). Then each of the chords has a different texture but the C really feels like home.

[@D1amondweaver]

Is this why sometimes when writing music a certain note will feel off, even though it's the right note?!?!?

[@joshuagavaghan224]

Yeah.

[@Heather_Morgan]

That's what I was thinking too.

[@derik2nicolai584]

A real important video. If Bach didn’t fix the scale to Well-Temperament we will no have the great music for Mozart, Beethoven, Brahms...etc.

[@karawethan]

Bach did not "fix" anything. Well-temperament(s) were in vogue during Bach's era, and represented a transition between meantone temperaments and equal temperament.

[@ValkyRiver]

3:18 That's the syntonic comma

[@henrydanielgatlin9774]

But can you play "Free bird"?

[@fgk2588]

Pythagorean comma isn't 81:80. 81:80 is syntonic comma. Also, to get 5:4, you don't multiply 81:64 by 81:80. Instead, you multiply it by 80:81.

[@Zaphod313]

I was about to write this! You need to take away one syntonic comma from the Pythagorean major third to turn it into the flatter 5-limit JI major third. You do this by multiplying 81/64 by the reciprocal ratio of the syntonic comma (80/81), giving you 5/4. What was instead done in the video was adding another comma to the Pythagorean major third, making it even sharper.

[@piotrpopczyk8154]

Tell me please, I am very confused, I am doing tutorial on non diatonic changes in Music and scales best fitting them, but I encounter a problems, when want to put secondary dominant and other non diatonic chords both on the same example - I actually do not know, for example: I start tune with C major chord, go to A7, next for example Eflat7 chord or Dsharp7 chord should I give a name for that chord (somebody told me not to mix sharps and flats on the same piece of music), then I am confused, please help me. Because A7 chord consist of csharp note using for example chord Aflat7 instead of Gsharp7 would not be proper? Many thanks for the answers in advance🤗👍

[@hilarytoussaint7295]

How is that on the violin. Do they have separate notes for g# and ab?

[@B3NICKY22]

Thank you Josh Peck

[@bledlbledlbledl]

well i guess that explains the slight discrepancy always encountered when tuning a guitar by ear

[@gandalfgrey91]

Keep the quote by Harry Partch in mind as you listen to Schoenberg

[@cyndie26]

So how come we don't use Werckmeister or something like that?

[@twominutemusictheory]

I'll admit, I'm not very familiar with that temperament. But. I have looked it up, and I have to say, I am intrigued. Thanks for bringing it to my attention.

[@petel738]

Well, should we cut the G# or Ab into two pieces?🤔

[@albuch520]

I've a question. I'm a pianist and I wonder if I am in E major but I must write a C minor chord can I just write It B sharp D sharp and and G natural, on the piano it sounds the same, but is it musically OK? if not how can I write it

[@DIYbanjo]

Actually, F double sharp (or enharmonically, G half-flat).

[@peterm3964]

Thank you . You are a genius . Do you know chop stix?

[@cju4300]

Just started studying music theory, so I didn't understand. But I will get there 👍

[@chubbieminami3274]

6:27 I am a violinist and yesterday when I was playing C and then G on a perfectly tuned piano, I felt like the G seemed slightly low. I told the tuner that G seemed low. He got his device out and told me that it was in tune. My question was did I feel that it was slightly low because of the just intonation? When we tune the violin, we play perfect fifths all the time. When a perfect fifths on the violin is out of tune, we can really tell. I had do this research because it felt low on the piano. Can trained people tell the difference of 2 cents?

[@Zaphod313]

In my experience, 2 cents is far too small of a difference to tell, at least with anything that has a more complex timbre than pure sine waves. Perhaps you were picking up on something else. If the strings were old, the harmonics within them could have been out of tune with themselves and the fundamental. This can produce a much more jarring dissonance within the string itself, as compared to two strings being a couple cents off from a perfect interval. Bear in mind also that many strings on the piano are double or triple. The point at which the hammer makes contact and the positions of supports vary between the strings, so they do not oscillate in the same way. The resulting effect is as if they were one or two cents out of tune with each other. It's a gentle beating that contributes to the perceived richness and fullness of the sound.

[@cpcnw]

I just wanted to know, when it comes to writing down the notes, do I actually write G sharp or A flat? I'm assuming there is a convention?

[@waltjames407]

It depends on the key. If you're in A or E or B (keys that contain sharps), it's G sharp. If you're in E flat, A flat, D flat or G flat (keys that contain flats), it's A flat. If you're ascending chromatically, it's G sharp; if you're descending chromatically, it's A flat. It can also vary depending on the surrounding notes. It is much easier to read when consecutive notes aren't written on the same line or space, so sometimes the choice will depend on that. Avoid using the same letter twice in a row to describe consecutive pitches that aren't the same. Having said that, if you're playing rock and roll or blues or country or pop or any other "less formal" forms of music, no one is going to complain if you get it backwards.

[@5Goldrings]

@@waltjames407 exactly what I was looking for, thanks! I play by ear and reading Chopin's music he has g# at top and Ab on the bottom so I was a little confused but see it now ✅

[@chipcurry]

Some interesting clues, but I would've liked a few more real world comparisons as opposed to mathematical ratios. For instance, the frets are not correct on a guitar neck, but. how do I prove that? How do I get the harmonics on the string to play a different note than the Fret can achieve?

[@philipstapert3517]

After hearing pure major thirds I'm not okay with equal temperament. I'm a fan of 1/4 comma extended meantone (where you have split black keys, so you can have both G# and Ab.) Of course early baroque music sounds amazing in meantone, but I'd love to hear some barber shop played on an extended meantone organ. The augmented sixth in 1/4 comma meantone, such as Bb-G# is actually very close to a harmonic seventh, the interval needed to make a nice ringing barbershop chord. Extended meantone makes for some interesting microtonal passages too, like in this recording: kzbin.info/www/bejne/fWabZI2AZrWmms0

[@psychosocial50able]

81/80 is the syntonic comma not the pythagorean comma

[@na-zp7ye]

Nice

[@user-yv8bw3zf6n]

Cool video! But the math starting around 01:15 is all over the place. You state that we multiply (divide) by 3:2 six times starting from D and that is precisely what you're doing in the right most Frequency column. The central Ratio column, however, is renormalised in the sense that all the fractions are made to lie within the basic octave of D. That is the factors of (3:2)^n (and (2:3)^n respectively) are multiplied or divided by an appropriate power of 2 to make them larger than one and smaller than two! For example we try going downwards dividing by (3:2), i.e. multiplying by (2:3), we end up with a frequency outside the basic octave (as 2:3 = 0.666... clearly is smaller than 1) and multiply it by two again to make it (4:3) which is neatly in between 1 and 2. Note that the very next step downwards is already different: we try dividing by (9:4), i.e. multiplying by (4:9), realise again it's outside our basic octave and try a factor of 2. The resulting (8:9) is still outside the basic octave so we try another factor of two, i.e. 2*2=4, and get (16:9) which does the trick. Also, to my knowledge, "Just Intonation" encompasses all systems that attempt to tune their intervals in rational numbers, that is as ratios A/B of two whole numbers A and B. As such, the Pythagorean tuning is just as much a "Just Intonation" tuning as the 5-limit tuning (the one allowing fractions containing 5 and is built up using perfect thirds of (5:4) intervals) which is misleadingly called "Just Intonation" here.

[@bzeliotis]

Don't string players have an advantage here? Because they don't have fretted instruments, they can play true intervals. The same goes for singers of course. Although EQ has solved the harmonic problem, it has compromised the true ratios of intervals as found in nature, which were discovered by Pythagoras. When I listen to music in Pythagorean tuning or even Just Temperament, it feels like the sound matches how I hear it in my mind. There was a lot of wisdom in ancient times, which unfortunately has been ignored today. Thanks for the video.

[@Copyrightbreaker22]

I was hoping he would let us her it but this is interesting too eventhough I don't understand most of it

[@octahedron115]

It's impossible to get back to your starting note when stacking perfect fifths and f sharp to d flat is a diminshed sixth. And plus you can stack perfect fourths too wolf fifths are just diminshed sixths trying to take the place of a perfect fifth

[@siegfriedderdeutsche1390]

What do you mean by that octaves in ET are _almost_ in tune? Why just almost?

[@twominutemusictheory]

To answer that, I recommend Minute Physics' video called "Why It Is Impossible To Tune A Piano"

[@siegfriedderdeutsche1390]

@@twominutemusictheory, I know that one, but the author does not say that the octaves are just "almost" in tune. He in fact says that the octaves _are_ in tune/the only perfect interval (just as the graphic which you use at 6:20 shows). Anyway, not that important... But I guess now that you were referring to the practice of stretching the octaves when tuning the piano, and not to ET as such when you mentioned octaves to (just) _almost_ be in tune.