Is Cb The Same Note As B? (A Response To Adam Neely)

Actually Adam's mostly correct.

So, recently, Adam Neely decided to use his platform to weigh in on the debate about whether or not Cb and B are the same note, and surprising no one, he got it wrong. Wait, no, that's not true. He got it pretty much entirely right. But! I feel like there are important aspects of the debate that got left out of his video, and while I don't disagree with any of his arguments I found his conclusion unsatisfying, so now I'm making a really long video about why he's only mostly correct. Enjoy? Or I'm sorry? Whichever feels more appropriate to you.

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[tone]

Some additional thoughts/corrections:

1) One could argue that if there are _any_ contexts where the difference matters, that means they are different, making Adam correct. And… sure, I guess, but I think it's also important to be very clear that a) sometimes the difference is irrelevant, and b) sometimes the difference is actively misleading. All of those can happen, and the "Cb isn't B" argument, including in Adam's video, regularly fails to acknowledge it. They generally wind up implying (or, in some cases, explicitly stating) that you're a worse, less qualified musician if you don't "get" why this distinction needs to be stressed, despite the fact that in many cases it doesn't.

2) In case you're wondering, the complexity of the pivot chord example has nothing to do with the enharmonic nature of the notes. (Or at least, of the roots.) If we move the question up a half-step and try to pivot from F to B, they'd both agree to call the resulting chord C7. This is why I think it's a valid example: If it absolutely required them to have different names, then sure, they'd be different, but as I mentioned in the video, the only reason it does in this case is because no one wants to write in the key of A# major. The whole thing _can_ be spelled consistently. It just shouldn't be.

3) The All By Myself example is interesting to me because, looking it up, in Dion's original version on Falling Into You, it's a whole step higher. There's no Cb anywhere. The pivot note is F, and they move from A major to Db major. The Cb only happens in later live versions where her voice isn't up to that high note, which don't seem like the most obvious reference point, implying that Adam actively sought out a recording that would let him include a digression about Cb? I dunno. Maybe he just wanted to use a clip that he could include a visual for, but the song has a music video, so... yeah.

4) Yes, I know, lambda represents wavelength, not frequency. But frequency is just an f, and wavelengths of light are directly correlated with their frequencies, so cut me some slack please.

5) I'm from Massachusetts, I can say whatever I want about the Patriots.

6) To be fair to Adam, I would probably default to measuring this interval in major 3rds as well: Most of Western harmony is based in 3rds, and it's a relatively simple calculation relative to most of the other options. If we're tuning in the key of Eb, it's probably correct. Although, of course, Eb isn't the only key in which this distinction comes up. These notes are also both potentially relevant in the keys of Bb, Ab, and Db, along with their relative minors, which opens up even more possible definitions. Just for fun, here's a couple more: You could go up a whole-step from Eb to F, then up two 5:6 minor 3rds, giving you a Cb of 504hz. (The B we derive this way is equivalent to the one we got with Adam's method, but the Cb is new.) Or we could break out of 5-limit tuning and go from that F up or down a 5:7 tritone, giving us Cb as 490hz and B as 500hz. The 7:11 and 8:13 ratios are also reasonable direct candidates for the #5/b6 interval, although it's not generally specified which ones they would correspond to so it's not clear whether the resulting frequencies would be B or Cb. But it would still give you even more valid, nameable frequencies within that range.

7) That said, the fact that we default to 3rds is probably a knock against the universality of just intonation, since that system pretty clearly implies that 5ths should be the higher priority, and yet we abandoned pure 5th-based tuning (called pythagorean tuning) pretty early on because we didn't think it sounded good. I don't know how fair an argument that is, though, because in something like quarter-comma meantone the 5th is much closer to the correct ratio than the 3rd would be in straight pythagorean tuning, so you can view that as a compromise between the inherently incompatible 2:3 and 4:5 intervals, rather than an admission that the underlying philosophy is broken. Still, though, the decision to prioritize these specific intervals is a choice, not a mathematical fact, and it's misleading and potentially dangerous to imply otherwise.

8) I cut this out of the Gamelan section because it was getting long and I didn't feel like this part was necessary for the point I was making, but one particularly striking feature of Balinese Gamelan is the concept of ombak, which is basically an intentional detuning between pairs of instruments that play together, creating this really cool acoustic beating effect that most Western musicians would call being out of tune but is actually an essential component of the style. Importantly, these notes differ by a consistent number of _hertz_, no matter the register. It has nothing to do with ratios. Just intonation can't even begin to explain why you would want to do that, and yet clearly people do, and they consider it beautiful. (It is.)


10) As Adam mentions in his video, there were some attempts at making keyboards that had extra keys for additional just-intonation pitches. (or at least meantone pitches, which isn't quite the same thing, but still.) However, to the best of my knowledge these were never the norm, and they certainly didn't last.


12) I should clarify that "equal temperament is merely a harmonic compromise, not a rich musical tradition in its own right" is a significant overstatement of any position Adam took in his video, and I don't think it's a claim he would defend. It is, however, the logical consequence of choosing to prioritize just intonation definitions within an equal-tempered landscape, which is a thing he's doing, (although, again, perhaps unintentionally) so while I don't think it's what he believes, I do still think it's a valid thing to push back on in responding to his argument.

13) Also, I suppose Adam never actually _said_ that B and Cb are always different. He just laid out a bunch of examples where they are and no examples where they aren't, thus heavily implying it. So maybe I'm being too harsh, or overstating his view, when I say he's insisting that one specific vocabulary is always correct, but also, that's very clearly the intended takeaway of his video, so I don't feel too bad.

14) In case you don't believe me that Abbb can have a real function, here's an example. A piece starts in Cb major. (Which, remember, is different from B major.) at some point, it modulates down a whole step to Bbb major, pivoting through the shared Fb chord. Then, it modulates down another whole step to Abb major, and finally one more time to Gbb major. Now Abbb is the b2, a real and valid function. Admittedly, we have to reach for a pretty bizarre key for this to work, but all of the reasoning holds under the set of rules outlined in Adam's argument.

15) Honestly, there is a reason to prefer F# over Gb in many cases: In major key signatures, F# is the first sharp, whereas Gb is the fifth flat, so F# is also more familiar than Gb. Just not to the extent that B is more familiar than Cb.

16) This might seem like a silly thing to argue about. And it is, but I think the conclusion at the end is important: Notation isn't a set of facts. There aren't right and wrong answers, there are simply useful and unhelpful conventions. That's important to remember when you engage with it, even if you happen to find the current standards fairly intuitive for the sorts of music you make.

[Callie_Cosmo]

I love that this is just descriptivism vs prescriptivism but in music theory instead of linguistics

[nothf]

I'm not a music theorist, I'm a chemist, but it's really interesting to me how the same types of arguments crop up in two extremely different seeming fields. For us it's stuff like "what is a chemical bond?" and "does calling this 'formal charge' or 'oxidation state' make sense" or "is this drawing of how a reaction works the best way to represent that reaction?" And...the answers matter in the same way Cb vs B matters - is the model communicating what you want it to communicate and if it's useful for that, cool. If not, well, you have a problem because at the end of the day it's a model.

[benjaminsagan]

Fun fact about F#/Gb: In the musical RENT, there's a piece of music in Act I that gets reprised at the end of the show. The vocals differ, but the piano part is identical. But. For reasons I cannot fathom, in Act I, it's written in Gb; while in Act II, it's written in F#. So you get to really test yourself in reading 6 accidentals.

[LNRDR]

I'm glad you brought up barbershop quartet. The voice is inherently the easiest instrument to tune, which makes equal temperament less important. What I find interesting is how barbershop songs and tags are notated in sheet music. They still use common tropes from previous eras, most notably ones related to the function of dominant chords, but they also include chords that are less "functional". These can usually be notated approximately with equal temperament, but there's a reason why these chords sound extra spicy in equal temperament. The purpose of these chords is not to be full chords, but rather to focus on the melodies and the relation between different notes. A big trope in the genre is oblique motion, where some notes stay still while others move around, creating harmony that's hard to decipher but nevertheless sounds competent. When transcribed, chromatic notes are often spelled technically incorrect, not because they're trying to make a different function out of it, but because they don't really care about the distinction on paper as long as it sounds right.

[BrendanoHarns]

I love the description of Pythagoras as "everyone's favorite triangle boy" and I hope it lives rent free in me head forever because I'm certainly inviting it to

[jaanaberg]

I love the fact that 2 of my favourite music theorists on YouTube disagree on these kinds of things. Adam first makes an argument and then 12Tone comes along and is like "Well yes but actually". Two people in the same field who both respect each other is my favourite kind of discourse 😂❤

[violondesocrate]

I am a violinist, and we regularly work with at least three tuning systems: just, Pythagorean, and ET. Just intonation is terrible at producing a diatonic scale, but it is an important tool for tuning intervals (especially double stops). Within that context, enharmonic equivalents can definitely have different pitches. When using Pythagorean tuning during diatonic scales, we will also differ from ET, again producing discrepancies between enharmonic equivalents. "Expressive" tuning sometimes involves playing a leading tone higher than standard pitch. Having said all this, the goal is simply to make the notes sound correct in any given context; it is not about C♭ being FIXED at a pitch that is higher or lower than B. We will move the notes around regardless of their spelling; B will be lower when played with D, and higher when played with E. The function of the note is connected to how we tune it, so the functional distinction between enharmonic equivalents can translate into a measurable pitch difference.

Another interesting aspect of violin playing is that the spelling of notes influences the fingerings we choose. For example, a D♭ on the A string would likely be played with 1st or 3rd finger, and a C♯ would most likely be played with a 2nd finger. Any advanced player will be adept at enharmonically converting as needed to find better fingerings, and will be comfortable with less-common positions, but the spelling of a note still affects our natural tendencies when deciding how to play it.

Of course, violinists' fingers rarely strike the same spot twice even when we want them to, so there is always an element of chance despite our best intentions! 😆

[fortunefavorsthebold]

I just went down a gamelon rabbit hole and wow! Having never so much as heard the style before, the first three minutes or so, I must admit, ignorant as it may sound, were tough for me. It showed me how locked into looking for familiar pitches I am. But after that obsession wore off and the music took me into what it was doing, not to what my chronically western brain was looking for -- what a joy!! I had a blast with it. The unfamiliar tones became as soothing as major and minor triads, and my ear even started listening for the tonal resolutions within the gamelon framework and getting the same mini dopamine rush when I recognized them as with something in a familiar tuning. Though I'm from the western US I now live in a part of the world where I hear Muslim calls to prayer from around town several times a day, and I realized the initially unfamilar registers have become soothing and musically logical to my ear over the years in much the same way without my explicit awareness that that was happening. I'm surely preaching to the choir here, but familiarizing your ear with different scales is an experience you'll not want to miss, especially if you've trained them to look for certain tonalities. Anyway, sorry for the very self-evident and conceptually basic rant. Thank you for the great video, 12tone!

[thunder____]

The part about note names being tools is imo the most important part of this entire video. Music theories are just tools to describe and communicate music. Use whatever tool seems right for the job at hand and for the people involved. Everybody has their own way of theorizing music anyways, so there's always bound to be some amount of confusion and difficulty from time to time, and it might require adjusting what tools you pull out of your toolbox if you can wrap your head around how other people theorize music.

[mmacmartin]

As a Barbershop singer I tend to find myself in contexts where the kind of distinction between B and Cb is useful, and so I would tend to distinguish them. I have a lot of thoughts on the matter, but that's probably the most pertinent. We also tend to see a note as a collection of pitches, rather than noting a single pitch, and for a good reason: I've been thinking of Barbershop singing less as "just" intonation recently and more of a "physical" intonation system recently, where the correct intonation is the one that feels most right to sing - there's a lot of talk about the concept of "lock and ring", where lock can be considered as the alignment of the pitches into a chord that's working together, and ring is the enhancement of upper harmonics. In this kind of thinking, the specific note doesn't matter so much as chord degree of the note, and function of the chord within your current and destination keys - and indeed a key change isn't so much "from Eb to G" as "up a major third" and enough of them slowly drifts away from equal temperament.

But then again, when I'm playing my guitar, I can do some pitch shifting thanks to bends, but being a fretted instrument, the notes are otherwise where they are, so there's not really much distinction to be made. And does it matter? eh, not really. (and in counter-point to my note about Barbershop singing being what physically feels right contrasts with the simplicity of building a guitar with frets the way we do - "just" fretted guitars have frets on the strings all over the place, but an equal tempered guitar has the nice grid of frets we're all used to, lending a bit of a physical justification for equal temperament to begin with!)

[MartijnFrazer]

Love the point about the notes not being real! People tend to get lost in our own inventions and get confused about what is reality and what is just convention or practical. Arguing which made up thing is correct is missing the point: it's about what goal we're trying to achieve and which tools help us to get there. Always glad to hear when people recognise that!

[harmono]

The one-note samba showed me that context was everything. Here is the same note, but as the chord changes happen, that same note sounds different. The same goes for scale degrees. If the song is in C, the B is the leading tone, and the maj7. But in G it's the 3rd. Notes are not fixed pitches as our mind perceives it. This shows how important understanding music theory is, either by having a good ear, formal training, or "ear training".

[NegohtapakaNegsy]

Thumbnail kinda looks like it says "fight me bozo adam neely" lmao

[belindareid]

Everyone's favourite triangle boy got me giggling. :) A thought provoking and nuanced argument as always! Thank you. I go back into the teaching studio on Monday and I can't wait until one of my students brings up enharmonics again, because I will come to the question armed with my new "it depends" response. (And direct them to your video for more information haha.)

[RJFerret]

I gotta' say, the wave diagram for "doesn't have to be consistent" at 21:40 is brilliant. The visuals usually reiterate your copy, but in that instance, the visual enhances the meaning to be more than words. Awesome communication!

[Duo_Seraphim]

Nice video! As a professional musician who performs mainly 16th - 18th century music, I pretty much live in tempraments outside of equal. While equal temperament allows for more harmonic possibilities, having a pure third, (when performing in 1/4' meantone, for example) major or minor, is one of the more important aspects for performing this music. The fifths are not pure and don't carry as much importance. As a result, key signatures never ventured outside of more than 2 #'s or 2 b's because of this. While this may be unimportant and boring to you, it matters quite a bit to us. I don't sing or play C# the same as Db as they have different functions in this music. This is also why split-key keyboards were invented, though, as you implied, they are less common, sure. I wouldn't go as far as to say that equal ruined music, but it does ruin the wonderful sonority of cadences that belong to the music in which I chose to specialize.

[liamtahaney]

This is really one of my favorite videos of yours. It goes so hard. It's like a nice stretch for the musical brain

[retstak]

I just wanted to say that I'm a layperson who's never really played an instrument, let alone delved into the deep dark caverns of musical theory, but I always enjoy your videos, not just because of the fun art, but because I always learn something interesting and get a new appreciation of the music I listen to. And thus, I'd like to say thank you.

[tesseract]

I have thought a lot about this before, and I am a strong proponent of Cb (or E#, Fx etc.). Even if you ignore just intonation, which i for the most part do. Cb does, in my opinion, actually improve readability in the majority of cases where they are justified. As long as(!!) you have actually learned properly how to play and concieve of them. This can of course be quite tricky especially for keyboard instruments, but it's certainly nothing less then what i would expect from a professional classical musician. Like in Gb major, which i would say is far from an esoteric key and is actually very common. Some might say to use sharps instead forgetting that F# major has an E#. Even in something like G# minor where you get Fx all the time adds to the ease of reading (again, provided you are comfortable with double sharps). The reason for this is that when you get beyond a certain level of reading music, you no longer really read pitches but rather intervals. So if I read a G# minor scale, I don't read: G#, A#, B, C# etc.; but I start on G# and then: a step up, a step up, a step up, etc. While adding the neccesary accidentals in my mind at the same time. Reading every single note would be extraordinarily inefficient, and a sudden dimished third in scale would certainly trip me up. This is even more pronounced when it comes to chords. So if you were to get a chord that was C#, F, G# you would likely get tripped up an maybe play F#, or at least have a second of hesitation that would disrupt the flow of reading. Like reading a mispelled word in a text. People don't recognise letters in a text, but whole words; and it's exactly the same with music.

There is of course a lot of people who hate these enharmonics with a passion, and I think this often comes from learning to play as a child. Of course explaining to a child the nuances of spelling and function is not exactly an easy task, so most of the time the teacher might just say that it's a B natural, or whatever. I think this really damages their understanding of music in the future, and of course composers who write for beginner to intermediate ensembles avoid Cb's like the plague, thus they never even learn to play them, and then they get thrust in to the scary world of Cb's and double sharps when they enter the "real" world. So they might just convert to a B natural, or a Fx to G in their heads every single time. This damages their reading ability, because it always takes an extra second to read the notes, and they maybe never properly learn to read them because they don't try. And thus you have created a strong dislike for Cb's and E#'s. And now they might pass this on to their students one day, saying that it is "just a B natural, but composers you know...". Never realising that if they just took the time to learn (or their teachers took the time to teach) them properly that it would strongly improve their understanding of the music and their ability to read it.

It's interesting why this never happens with e.g. F# and Gb. I get it of course, but it is basically in every way the exact same thing. One note with two names. It's just that it's a white note instead. It's even more interesting that say a trumpet player would have the same amount of trouble with it as there is none of the visual element. They just learn a fingering for each note, so why not just learn that Cb is the 2nd finger? A teacher should of course explain that a Cb and B sound the same, as they do with F# and Gb; but they should never say that a Cb IS a B.

There are of course many, many examples where you have to compromise, like the Giant steps example or A# major🤮. And of course you get essentially paradoxes sometimes, like a whole-tone scale which really doesn't have a nice solutions. This is only my opinion of course, and I am not an experienced teacher. I am however an experienced musician, and I think Cb's are good. They are maybe sligthly trickier than most other notes my in my personal experience they are 10 times better then an augmented second or diminished third.

Sorry for the long rant. I'm sure I forgot some points, but here are some of my thoughts anyway.