Good post and I'll chime in if you don't mind. I teach this stuff for a living and even highly skilled musicians struggle with it in various ways (myself emphatically included).
The main thing I want to say is that there's a reason why essentially all music education consists of many years of rote learning. Obviously, that rote learning works better if it's guided in appropriate directions, but I really don't know of any alternative to what you describe when you say "an orders-of-magnitude-less-efficient mechanism for memorizing note-to-note mappings for every note and every pair of keys." I hate to say it, but ... yep. [EDIT: eh, let me qualify that a bit. See point (A) below.]
Sight-transposition (i.e. sight-reading plus on-the-fly transposition) is a ninja-level skill. Some instrumentalists (usually those who play non-concert-pitch instruments) can do it reasonably well for at least some transposition intervals, and a few people like professional vocal accompanists and church organists need to be able to do it fluently as an expected part of their job. But outside of those folks, even professional musicians rarely have that facility.
Here's something that directly supports your point at (D). As you know, pitch intervals in tonal theory are given names that break arithmetic—a second plus a fourth is a fifth, even though 2+4≠5. A certain well-known music theorist often expresses the view that this blatantly illogical convention is almost entirely responsible for the popular perception that music theory is a really, really difficult subject. I think this exaggerates things, but he's got a point. However, most musicians know those interval names really well and have never thought much about how stupid they are, and so then high-level music theory becomes opaque to skilled musicians because we start by renaming intervals correctly (i.e. a second is diatonic interval 1, and you can add them like normal numbers).
In the case of the frustrating conventions of staff notation, there are historical reasons going back a millennium why we write pitches like that. Various reforms have been proposed, but path-dependency basically makes it impossible that any of them would ever be adopted. Far more likely (and well underway for decades now) is that musicians will stop using notation altogether.
Just to briefly answer your other questions with my personal views:
(A) Personally yes, I have all the note-to-note mappings memorized. I do this completely via thinking in scale degrees. I can name any scale degree in any key, so questions like the one you mentioned just revolve around thinking "B-flat is scale-degree 4 in F major. What's scale-degree 4 in C or A-flat?"
(B) Yes, I do think this is plausible, and underappreciated in the specific case of music, since most musicians don't think much about the ways in which notation isn't an optimized system.
(C) Maybe this is too glib, but ... social interaction? "Overthinking it" isn't a path to doing well in social settings. For that matter, natural language might be another. In many respects it's best learned by rote (along with some theory—just like music) but I've certainly had classmates in language courses who get too hung up on the illogic of grammar to progress well in basic skills like speaking and listening comprehension.
In the case of the frustrating conventions of staff notation, there are historical reasons going back a millennium why we write pitches like that. Various reforms have been proposed, but path-dependency basically makes it impossible that any of them would ever be adopted
I know very little about this, but I have noticed guitar tabs, ocarina fingering guides, mouth harp tabs with simple numbers exist.
Very true. Staff notation essentially says "Here are the pitches and rhythms, now it's your job to figure out how to make them happen on your instrument." As you point out, a very real alternative to staff notation exists in tablature, which (in general) is any notation system that instead says "Here's what you need to do physically on your instrument. Follow these instructions and the notes will automatically be the right ones—you don't need to worry about what they 'are'."
Tablatures are surprisingly old, apparently going back 700 years or so in various forms. Of course, their drawbacks as general musical notation are clear enough. Namely, if you want to understand what's going on in the music or play music on a different instrument, tablature is really only a kind of lookup table for actual notes, and often a very cumbersome one.
Far more likely (and well underway for decades now) is that musicians will stop using notation altogether.
This seems like a radical claim. Can you clarify or elaborate? I certainly don't plan on stopping using notation any time soon. Indeed, this sort of statement seems to imply that composition as we most typically understand it (where a "composer" creates a "work" which nonidentical performances may be understood to be realizations "of", to possibly varying degrees of "accuracy") will stop, which seems highly unlikely to me.
(I realize you only stated it as a comparative -- that this is more likely than some other unlikely thing -- but the "underway for decades now" comment suggests you take this as a serious possibility.)
I actually like musical notation, and wish that its expressive possibilities were exploited (even) more. (However, I'm with you on interval nomenclature.)
I didn't have anything really radical in mind. I think it's pretty clear that there's a long-term trend toward high-level music-making relying on notation to a decreasing extent. I have a number of friends who are professional composers, and some of them use notation to write for instruments, while others use electronics and largely don't use notation at all. (The latter group, who compose for video games, movies, etc., are the ones who actually make money at it, so I'm by no means just talking about avant-garde electronic music.) A lot of commercial composers who would have been using paper and pencil 30 years ago are using Logic or Digital Performer today.
The other factor, of course, is that notated genres of music ("classical" music and its descendants, and some others) are increasingly marginal in Western culture. This trend is often way overblown, but is clearly visible at the timescale of decades or longer.
What I certainly don't mean to suggest is that individuals who use notation in our musical lives, like you or me, will stop using it. It'll be a cohort replacement effect, and no doubt a very gradual one. Nor do I think that music notation will entirely go away at some foreseeable point in the future. But reading and using it will slowly become a more specialized skill. My impression, though I don't have a reference for this and could be completely wrong, that the ability of American adults (not pro musicians) to read music notation with some fluency has hugely declined over the last half-century.
All this is very much the framing argument of Taruskin's Oxford History of Western Music, with its much-criticized focus on what he calls the "literate [his needlessly inflammatory term for 'notated'] traditions" of music. Within that frame, he casts the present day as essentially an "end-of-history" moment.
Correct me where I'm wrong here! I'm not a specialist in these issues.
Let me add that, like you, I absolutely love music notation, borderline fetishize it, and say all this with more than a trace of a Luddite's sadness.
Nor do I think that music notation will entirely go away at some foreseeable point in the future. But reading and using it will slowly become a more specialized skill
That I find more believable; but specialization is probably the wave of the future in general. I'm much more bothered by the prospect of interesting things dying out completely than that of their being "restricted" to a (possibly vibrant and vigorous) subculture. (These days I tend to think that most of "real" life takes place in subcultures or smallish communities -- maybe even cults! -- anyway.)
My impression...that the ability of American adults (not pro musicians) to read music notation with some fluency has hugely declined over the last half-century
I don't myself have enough data to confirm or deny this (I'm not a specialist in such topics either), but one should make sure to take into account the rest of the world: I have the impression, for example, that the Western art music tradition is currently in ascendance in China.
(I also suspect in general that people's impressions of what past populations were like are biased toward reflecting the elites of past populations, about which information tends to be more readily and reliably transmitted, which they then compare to a more general cross-section of the current population visible to them.)
komponisto has an explanation for that, saying that what is being played is not chords, but temporal sequences moving between chords.
What? I don't understand what that means, which suggests that it isn't something I said.
Here are some points to consider:
Sight-reading is nice to be able to do, but it's far from essential. Reading music is the fundamental skill. There's nothing wrong with learning a work of music layer by layer, component by component. Indeed, complex contemporary music is often too difficult to sightread, even for the world's most skilled performers; they have to practice it bit by bit, just like you do for the music you play.
If you're reading music properly, you don't see
.
What you see instead is
or
,
or, since we're talking about piano music,
or
.
These are visually distinct stimuli that happen to share some features; you seem to want the shared features to have more significance than they do, which is a form of misunderstanding the notation.
Are you aware of the concept of the grand staff? The upper and lower staffs of piano music can be conceived together as a single entity, with middle C lying in between them. This wouldn't be possible if, for example, the lower staff used the sub-bass clef, which has the same note pattern as the treble. (Now, admittedly, a lot of piano music doesn't treat the grand staff this way -- often putting the bass clef in the upper staff and the treble in the lower, sometimes both at the same time -- and I'm not much of a fan of it myself, generally preferring to regard the each staff as autonomous. Still, I have to admit to finding the notation in e.g. the second movement of Webern's Piano Variations, which has both upper and lower parts frequently changing clefs, somewhat awkward and confusing -- even though it's done for a specific purpose.)
You should, in any case, be able to play
with the right hand or
with the left.
I suspect you simply don't read enough music to get in the habit of seeing the notation the way it's meant to be seen (and automatically knowing such things as how notes map under transposition). I also have a "highly trained" mind, and I don't have the difficulties you do, so the thesis of your post seems obviously false to me. In particular, I don't think you've made a convincing case that music is more difficult for amateurs who happen to be scientists than for other kinds of amateurs. If anything, I would (continue to) expect the musical literacy of scientists to be higher than that of the general population, on IQ/having-an-interesting-mind grounds alone.
On enharmonically equivalent notes (e.g. E# and F), you say:
Yes, I know they're not really equal in most historical intonations, blah blah etc.
but it's not (primarily) a question of historical intonations. Being acoustically distinct is not a necessary condition for being musically distinct. It's a question of the "same" entity being conceived differently in different contexts. Homophones in language (two/to/too) are a close analogue: they might actually be pronounced differently in some dialects or some contexts, but even if they're pronounced the same, they're still different words. (I don't think this actually falls within the scope of your "blah blah etc.")
I share your difficulties with reading music and transposing. However, I doubt that the reason is that your (or my) mind is too highly trained. Instead, I think that people who have trouble sight-reading simply have not made the transition from a conscious processing of the musical notation to a state of automaticity in which the low-level details of interpreting the musical notation are performed by the brain unconsciously. I am curious; as a child did you study with a piano teacher or are you self taught? I suspect that one of the purposes of formal piano lessons (and all the practicing that lessons entail) is to make the interpretation of the notation automatic; as you point out, the notation is complex enough that most people won't be able to interpret it consciously in real-time with enough fluidity as to produce anything very musical.
It is worth noting that some very accomplished musicians never learned to read music (albeit probably no accomplished classical musicians who would presumably need to be able to read notation). Unfortunately I can't come up with any examples, but it is common enough when reading about blues, folk, jazz or rock musicians to read about musicians that never learned to read music. So, I think that being able to produce music and being able to read the notation are two separate, albeit related, skills.
My highly musical mother and brother seem to have simply memorized the relevant patterns, as you say.
Thinking along the lines of the in-progress Math Ability sequence, I think some people (including myself) are so reliant on being able to quickly derive and compute things in our heads that we have allowed our facility of memorization and memory-recall to atrophy. The prospect of learning, for example, all the individual notes on a guitar fretboard feels so agonizing to me that I still just "derive" the notes when I need them, even though this is terribly slow, after many years of playing the instrument.
As to Question D, a large fraction of scientists I've known are also musicians, so I think all we can surmise is that there are different ways that different brains can achieve the same objectives.
Thinking along the lines of the in-progress Math Ability sequence, I think some people (including myself) are so reliant on being able to quickly derive and compute things in our heads that we have allowed our facility of memorization and memory-recall to atrophy. The prospect of learning, for example, all the individual notes on a guitar fretboard feels so agonizing to me that I still just "derive" the notes when I need them, even though this is terribly slow, after many years of playing the instrument.
I have a horrible problem with foreign language vocabulary for a reason very similar to this: there's no way to derive the word for "green" from a list of every other color word except "green"...
Phil, you've probably seen this already, but a bunch of proposals for alternative notation systems are collected here. Some of them are basically exactly what you would prefer to be reading. It would be really cool if someone wrote a Lilypond package that could output in some of these systems. (Maybe someone has, I don't know.)
So C D E F, transposed into the key of B, becomes B C# D# E [2].
Are you familiar with the circle of fifths (also known as the Camelot Wheel)? Once you know about that, transposing notes between keys becomes rather trivial. Diatonic notes map "linearly", modulo any accidentals in the key signature. (Preserving this property is an important motivation for using enharmonic notes like E# vs. F). The key of B major has five sharps, viz. F, C, G, D, A.
(You can see that this is correct, by noting that the "last" sharp sign gives the leading tone in the major key. Here, A# is the leading tone in B major. With flats, the second-to last flat sign gives you the tonic in major - so, if B and E are flattened, you can tell that the major key is Bb.)
When I tried playing musical instruments as a teenager, I usually transcribed the music to my own notation. Something like "C D E F". Then I could play much faster.
In hindsight, maybe this was a wrong approach. Something like when people learn foreign languages the wrong way (most of them do), and instead of "foreignWord -> concept" associations they train "foreignWord -> nativeWord" associations. Then they speak really slowly because they have to translate twice "foreignWord -> nativeWord -> concept". The key to speak foreign languages fluently is to associate the foreign words directly with the concepts, skipping the translation to your own language. This usually also happens to people who learn languages the wrong way, but it can happen years later, and come as a surprise. Learning the right way, you can do it from day 1.
Analogically, if we tried learning music this way, we should skip the "C", "D", "E" sounds and try to create an immediate association between the shape on the screen and the position of the fingers. I have never tested this hypothesis, so I have no idea whether this is what skilled musicians do.
So I see two possible approaches here. They can also be combined: just because you may have learned to use some notation in a wrong way, it does not prove it is an optimal notation. The approaches are: 1) invent a better notation, and 2) invent exercises to associate the notation with movement on a level of reflex.
If I tried to invent a perfect piano notation today, it would probably be written top to bottom (instead of left to right). Because the piano keys are horizontal. A longer sound could correspond to a visually longer symbol; but the symbols would also slightly differ in shape (to make it easier to see how long exactly a long sound is). For example, there could be vertical lines corresponding to the black keys, small filled circles for short sounds, and something like filled letter "8" for twice as long sounds. That alone could be enough for a beginner.
My piano teacher usually hummed the first few bars of a piece to identify it when the title was not sufficient. When I try to emulate this with a new piece it's much slower to go "note -> D -> D-sound". If it's a piece I've heard before, at some point my head fills in the rest without reading further, and then I only have to verify the score matches the sound in my head. This seems to agree with your hypothesis.
Top-down notation reminds me of vertical scrolling rhythm games like DDR and also Synthesia (though I have no experience with Synthesia specifically). My difficulties in learning to read piano sheet music were/are:
- different clefs and clef changes
- notes with many ledger lines
- off-by-one-line errors (e.g. reading G as B)
- following fingering recommendations
The last one might be entirely on me, I have a tendency to improvise fingerings and mess things up. But I think the other three are quite common problems to have. One of the things that trips me up with ledger lines is that the same note up an octave has different line/space parity.
My experience with rhythm games (and reading some sheet music rotated 90 degrees just now) suggests to me that fencepost errors are just as likely with top-down reading, and are greatly exacerbated by increasing the number of columns. I'm not sure it's worth losing consistency with other music notation or western left-to-right reading systems. Maybe an anchor-note-position (say, a small mark on every bar line indicating C) would help with this, and possibly with clef changes too.
One other thing I used to not pay much attention to in piano were rests, and I would often hold notes until I had to play the next note regardless of whether there was a rest between. Playing rhythm games with hold notes has gone a long way in stopping me from doing this, as I have to pay attention to when to release the note also - extending the note-symbol to span its length could accomplish the same thing.
The "too highly trained" part is mostly a question of motivation. If you already understand the patterns complete pushing all the concrete instantiations of the pattern into the unconscious (i.e. rote memorizing to complete fluency) looks just too much pain to be worth the effort when you already know it.
I'm just plying a few piano pieces for christmas and such and do not have much need for sight reading much less transposition. My solution therefore is to just memorize the actual notes skipping the sight to finger step altogether. My pattern memory is good enough to read the scale a few times and memorize the complete piece. Simplifies playing it in any case.
A - I can transpose at sight, but not very quickly. Like grouchymusicologist, I do it using the concept of scale degrees.
B - I suppose it is plausible. But I can't think of any real-life examples. Learning good posture isn't going to hurt any athletic skill you try to develop. Having studied linguistics is only going to help you when you start to learn .
C - I've never heard of such. Natural systems tend to be pretty intuitive.
D - Artists are the people who understand that what's on the page isn't music. It's just instructions on how to play the music. Theorists are the people who develop the notation, and they have a lot in common with scientists. (Many musicians are both.) Yes, some aspects of music notation and theory are counterintuitive. So are some aspects of mathematics. Plenty of people can do both with a high degree of skill.
Other than that, I don't really know what to tell you - except to use your highly trained mind to come up with ways to practice doing the things that you have problems doing, until you can do them well enough to please yourself.
A - I also use scale degrees for this. I'm not fast enough to sight-read and transpose at the same, but I sometimes switch to intervals when transposing a single melody line. Most of my experience transposing and playing comes from trying to play songs on Bb trumpet written for concert pitch. I had some note-to-note mappings memorized from frequent use, but not anymore.
B - Definitely plausible to me. Something along the lines of "when all you have is a hammer" and certain modes of thinking being more useful than others for certain skills. I don't have any particular examples, but I think in math there are quite a few abstractions / extensions of lower level concepts that are a lot more 'natural' if you think about them in a certain way.
C - Can't think of any.
D - Agree with Anomylous on this one.
great article, PhilGoetz! There is a similar, but much simpler situation that occurs when I try to play chords on a guitar to sing a song over a simple groove on a classical guitar in order to impress my girlfriend. It's easy for me to learn the first few chords but difficult to learn complicated songs with many layers to them.
I've played various musical instruments for nearly 40 years now, but some simple things remain beyond my grasp. Most frustrating is sight reading while playing piano. Though I've tried for years, I can't read bass and treble clef at the same time. To sight-read piano music, when you see this:
you need your right hand to read it as C D E F, but your left hand to read it as E F G A. To this day, I can't do it, and I can only learn piano music by learning the treble and bass clef parts separately to the point where I don't rely on the score for more than reminders, then playing them together.
Transposing is also approximately impossible for me. The musical scale is drawn as a linear scale, but it isn't linear. There are missing steps between B and C and between E and F; B# = C and E# = F [1]. So C D E F, transposed into the key of B, becomes B C# D# E [2]. Transposing music that uses notes outside the scale is significantly worse. The only way I can transpose (badly) is to not look at the music and not think about the names of the notes.
I've blamed myself for lacking some ability that would enable me to do these things. But my conversations with (a few) people who can do these things have been peculiar. They don't have any suggestions for my problem, because they never saw them as problems in the first place. When I talked about the inconsistency of trying to use separate notations for the left and right hand, they stared at me uncomprehendingly. The idea that notations should be consistent seemed never to have occurred to them.
So I've decided to blame them instead. The problem is that my mind is too highly trained.
No, seriously. I realize this is probably an unhelpful, self-defeating attitude. But is it correct?
It seems to me that if you're in the habit of working with things on linear scales, that's going to be a hindrance when you try to transpose music. Your brain latches onto the notes marked on the score and automatically constructs an internal representation that is wrong. Likewise, if you're in the habit of looking for consistent interpretations of data and compressing what you observe, your mind will keep trying to reduce the two clef notations down to one.
The system of sharps and flats is efficient in some ways; you just have to remember the order they always occur in, plus one number per scale (the number of sharps and flats), to construct that scale. You organize the music into concepts like "scale" and "chord", and map those into new keys. It's great if you're playing scales and simple chords, and if your music sticks to a few basic keys plus their minors. But it sucks when you move beyond that.
The notations developed for music work best if you don't aggressively systematize data, so that you can instead learn an orders-of-magnitude-less-efficient mechanism for memorizing note-to-note mappings for every note and every pair of keys [3], and so that your brain doesn't try to let your left know what your right hand is doing.
(A) If you can transpose music on the fly, have you got the note-to-note mappings memorized? Can you say without thinking what B flat is when transposed from the key of F to the key of C? Of A flat?
(B) Do you think this is plausible--that a very general ability or learned skill can make it more difficult to learn some things, either in this particular example, or in general?
(C) If so, are there any natural systems (not notations devised by humans) which are harder to work with for people with more mental talent or training? Idiot savants come to mind.
(D) Is part of the perceived gulf between art and science due to artists developing notations, theories, and conventions that make art more difficult for scientists?
[1] Yes, I know they're not really equal in most historical intonations, blah blah etc.
[2] Yes, I know you musicians think that's easy. That's because you're saying "scale" and "key of B" and constructing a new scale in that key, which is a pretty efficient representation for scales and simple chords, but gets messy for music going beyond that.
[3] Or mapping the pattern being played into some scale or chord or other construct, translating that into the new key, and recreating it in that key. That seems unlikely, or to require forming concepts for most of the 220+495 possible 3 and 4-note "chords", since even with simple church music musicians often can't say what chord is being played. (komponisto has an explanation for that, saying that what is being played is not chords, but temporal sequences moving between chords. But most musicians don't think of harmony that way.)