As I play fingerstyle I study hands separated by separating the bass and melody as thumb and fingers, then move to hands together.
I also analyze the piece to find the hardest as well as the most repetitive measures, work those out and pick up the rest of the piece. You also work these measures with transitions, by playing the preceding measure or half measure leading in and out of the measure you're practicing.
I typically don't get a lot of time to practice so I will pick up my guitar at random and play measures that I'm working on.
Awesome article. But tbh still very vague, I'd love to hear about some of your guys' specific practice schedule. Below is mine,
Guitar Practice: I do repertoire, technique and improvisation. For repertoire, I usually focus on the hardest passage and run it three times to the best ability and then connect the whole song together for 3 goes before I finish. For technique, I usually rotate on scales patterns/licks/ear training; review the last pattern I learned and learn a new pattern. For improvisation, I just doodle with jam track and listen and try to iterate on how I can improve (e.g., better timing on stressing notes on chord changes, building tension).
Dota Practice: I sometimes watch youtube casts on warding and laning. Also what different heroes are good to counter different heroes. But mostly I just play ranked games and try different heroes.
I play trumpet, my routine usually starts with long tones and slow articulation exercises. As I get warmed up I extend into lip slurs, faster articulation, and flexibility. After I'm completely warmed up then I go into a mix of technique work, etudes for fun, and whatever other repertoire I need to work on for performance.
Repertoire that I'm just maintaining is a mix of full runthroughs and reinforcing small segments. For new repertoire I usually work through it measure by measure, mixing air+valves reps with playing reps to save my lips.
Good advice. My wife (a pianist and piano teacher) just read the article kindly submitted here and said that that is how she practices. I've heard over the years about how she advises her students, and, sure enough, one of the key ideas is to distribute practice across multiple days each week rather than piling into one lump of time just before the lesson.
After my reading of the article, I have to say that getting a good night's sleep each night is definitely crucial for learning anything challenging. Sleep makes connections and consolidates learning.
The one thing I don't see mentioned in this article that my wife tells most of her students, after learning about it from one of her university music teachers, is how important it can be to analyze a new piece of music through multiple modalities. My wife's university teacher has a book about "music mapping,"[1] an approach to reading musical scores and adding visual notations to them, which is highly individualizable and works wonderfully for helping musicians learn where the music is in a new piece of music. Playing with musicality rather than just memorizing notes is always the key idea.
I think pulling 'all nighters' (seriously, being in the computer lab when the sun comes up in totally not cool - especially with the gradual lightening of the sky and realization that you are bone tired and still have 2 hours left of work...) is part of the culture that college students expect at some but not all schools. Similar to binge drinking, there is a lot of peer pressure to 'pull an all nighter' or 'do a funnel (of beer)'.
Peer pressure doesn't stop after high school. In fact, it might not "stop". As some of us grow older, your peers change until they reflect what you really want in life (for most, in my experience, that means having peers who are settling down and having two kids and a family). I'm sure there is definitely peer pressure at senior citizen/assisted living homes to be 'cool' (whatever the norm is).
Startup culture is similar in the bubble of San Francisco. The norm is so skewed from the median/average of what most people in a business environment do.
As David Foster Wallace said, the fish doesn't know it is in water. [1]
> makes me wonder why sleep deprivation is such a large part of the college experience
In my experience, all-nighters were due to a combination of several factors: you start having large projects to do, there is little supervision to ensure you are making steady progress, you are starting to figure out how to organize on your own, and the projects are cooler and more open-ended so the sense of perfectionism is stronger.
Agree that sleep is important, however you soon learn how well you know something when trying to do
it whilst tired. If you get something ingrained enough you can still do it when paying almost no attention.
In one study, where they tried learning both ways, people felt like blocked practice was better, even though their ultimate performance was measurably better after the random practice!
Though you might improve at a task during practice, you’re less able to carry forth that improvement to the next day.
Studies have shown that consistently getting a full night’s sleep (eight hours) plays a huge role in learning motor and auditory skills
The surprising parts are usually the places that they did not account for in their mental practice.
Forget about the nasty passages for now. Instead, spend two weeks getting in touch with the musical aspect of the piece and practice it through, just for musicality.
The linked essay in the article also gives a timeline on how long in takes for neurons to connect: it takes about a week to happen.
Also: You will be much better off practicing your orchestra music for 15 minutes a day until the concert, rather than “wood-shedding” the day before the concert. Why? Because you’ll have all those nights of sleep for your brain to process the new music.
Good article, i discovered it right after i bought my violin (could have been after i got a viola, can't remember). I think you can apply these tips to learning, say, rust programming, or convex optimization. I also think a random beat generator is sort of similar to backing tracks i record in Garage band or ableton, and you should leave pieces/charts you're learning out on the stand next to your computers, and look at them often, 5x/hour.
Another tip, always remember the first time you tried to play a clarinet, cello or violin (if you can). Those for me were special moments.
Here's some other (comprehensive) books about practicing, which go from mechanical prescriptions about washing hands and brushing teeth beforehand, to the zen, in the vein of the motorcycle and archery books, like long tones/long bows/drone notes/son filé (the last is Galamian's term, his violin technique book highly recommended).
I assume you are minimizing -- maximizing
is easily NP-hard.
So, get some supporting hyperplanes
of the convex epigraph and use
linear programming to minimize
subject to those hyperplanes as
constraints. Then add a constraint
and try again. There is also
a cute way to do central cutting planes
that can be better numerically.
So, for many non-linear problems, if are
maximizing, then the dual is a
convex minimization, and that can help.
This can be called Lagrangian relaxation.
I never thought that how to do violin practice
was so tricky -- just work to get the fingers on
the notes, in time and in tune, and then
do it a lot until get a lot of facility
(hear the note(s) just before playing them),
sometimes return and play very slowly and
deliberately, and then work on
expression -- the fun part.
But then I never made much progress.
The best I did was the D major
section of the Bach "Chaconne",
and that was fantastic fun --
I played the repeated notes
that made them sound insistent!
I regard the end of the D major
section as the climax of the piece
and find it fantastic.
That reminds me, somebody borrowed my Galamian and never returned it... I want to read that bit about vowels and consonants again.
I think all of this is about you need to figure out how to practice or learn CUDA or Mandarin or whatever for yourself. My dad's advice on learning math was simple "Stare at the book til something sinks in, do the problems, figure out if the answers in the answer key are right". For some students, that's all they need to be told
What this guy talks about at the bottom of page is similar, i.e. there are people who know the materials and teaching methods that have worked int he past, but the only person who can teach yourself is yourself: http://www.allaboutjazz.com/janek-gwizdala-cooking-up-a-litt...
> "Stare at the book til something sinks in, do the problems, figure out if the answers in the answer key are right"
In Rafe Esquith's classroom, he talks about how they take that a step further. They knock the ball out of the park on standardized testing because they specifically try to come up with wrong answers for a math question. They learn the psychology of making test answers by doing - and don't fall into the traps.
It worked for me, in violin,
As we know, things should
be as simple as possible but not simpler.
My approach to learning mathematics is
quite different from learning to play violin
but also is based mostly in independent study.
In violin, I got started when I was a math
grad student at Indiana University. Of
course there is a terrific music school there,
and at the time my dorm was next door with
a lot of music students. One day one of the
violin students, darned good, a Stern protege, put
his violin under my left chin, and I was off
and running, took a violin course in the
music school.
After some years of work from Galamian's book
and just self-teaching, I went for
some lessons. Sure, I started with the
"Preludio" of the Bach E major partita.
Of course early on there is a fast shift
from 1st position to 5th; I happened
to get the note after the shift right;
and the teacher exclaimed "You could
play in an orchestra!". Gee, that shift
is the main issue for playing in an
orchestra? I doubt that!
Maybe he thought I was sight reading that
music! Not a chance! I'd worked hours
on each note, note by note, checking
intonation over and over, etc. That
shift I'd likely done 1000 times.
I hadn't really been learning just the
piece but had been using the piece
as an exercise to learn to play violin,
starting from very little!
So, that shift to 5th position,
at two places in that music,
was the first I'd learned. Sure,
I could have used that skill with
that shift elsewhere. I learned
the whole piece; the learning was
a lot of fun.
But, I learned it, self-teaching.
I had a good ugrad math major but didn't
like what the IU math department had me
doing: Of the three courses they started
me with, two of them had just what I'd already
learned in ugrad school, and the third
started with what I'd learned in an NSF
summer program the previous summer.
But there was other material I wanted
to learn. So, IU and I didn't get along,
and I went, got a job, and studied on
evenings and weekends, independently.
That study worked out well and was,
really, except two graduate courses
all I needed for my Ph.D. I did the
research for that independently in my
first summer after the two courses.
So, my approach to learning has worked.
Computer science and programming? I've
taught college and grad courses in it,
but I never really took one.
What I'm saying did work for me.
Of course if you want then you can
try more complicated ways.
For the OP, she was concerned that
her playing sounded mechanical.
Well, once she has the notes on time
and in tune and practices until
they are "in her fingers" well enough
that she can concentrate on the expression,
then she should, just think about
how she wants it to sound.
For convex minimization, once a guy
had a 0-1 integer linear program
with 40,000 constraints and 600,000
variables. He'd tried simulated
annealing without much luck.
I looked at his constraints, and
16 of them were special, and I put
them in the objective function
with Lagrange multipliers.
Then the dual problem was
to maximize a concave function, and
I did the linear programming and
supporting hyperplane approach
I outlined. After about 500
primal-dual iterations in 900
seconds on a 90 MHz PC, linear programming
via the IBM OSL, I found a feasible
solution, guaranteed from the
duality, to be within 0.025%
of optimality. It was fun!
But I do recommend the central
cutting plane idea.
Kenny Werner's philosophy if you can summarize it in one sentence - is if you are a trumpet player - you must master breath control, fingering so by the time you are in performance - you are truly playing without thinking of the mechanics.
There are many analogies to really focused coding, Kenny Werner's philosophy, and Mihály Csíkszentmihályi's concept of flow [1]. You must master the syntax, the grammar, the idiosyncrasies, the rules and unwritten and written customs, and the is-isms of the language before you can "effortlessly" write code in a given platform/language. This is one of the reasons beginners to programming may stumble on the hike - they are so focused on the writing of the lines of code that they are often pushed by themselves or their otherwise well-intentioned teacher to produce code. The building blocks of code are not the lines of code - it is the concepts and the system and framework and mental model behind it (the whiteboard so to speak).
"This year, forget about the year as a whole. Forget about months and forget about weeks. Focus on days."
An excerpt from Kenny Werner's book that I just pulled out of my giant stack of books Jenga style (p.85).
> Practice
Perhaps music feels great as long as you're fifteen feet away from the instrument, but as you move closer, a different energy takes over and your connection dwindles...
How can we retain the bliss of freedom as we approach our instrument? We must let go off all desires and focus on love. To have the nectar flow through us, we must honor our inner being, and practice receiving what is being given. We must practice and strengthen this conviction daily. We may even have to go outside of music to do it. This is really important, because playing, being so addictive, pulls us easily from the true goal and draws us back into more mundane realms.
But when you have made the inner connection, playing becomes more like taking dictation from within. Work with the thought, I am the master, I am great. Then just put your hands on the instrument, trust them, and eventually it will be so.
"Do not fear mistakes. There are none."
-Miles Davis
>When she does this with students, she asks them afterwards, “Was anything fuzzy?” It’s usually the part that they were messing up that’s fuzzy.
This is genius. Reminds me of the rule that if something feels fuzzy at the instrument it's always a conceptual error about the piece rather than poor coordination or poor finger strength.
>Why is it better to practice every day for an hour, instead of seven hours on one day of the week?
For the same reason that it's better to practice for 10 minutes several times per day instead of one hour straight.
Sleep is a given. The brain is learning continuously, not just during sleep. Go back to a section of a piece after 15 minutes doing something else and notice it has become easier.
Sometimes it's even easier after just 1 minute away. I code and play music, and I've made a habit of occasionally walking around the house, petting the dog, then back to where I'm working/practicing. It doesn't take long, but it works strangely well.
Yes. There's something about walking isn't there? Returning attention back to the body and the senses amounts to relaxing after hard concentration. Perhaps petting the dog enhances that, the body being where emotions are felt. Scientists seem to suspect that walking or just standing occasionally is important for health.
To complete the argument about learning: you play the tough section, correcting a few errors. Then you go away for a bit, and during that period the brain updates its hardware to include those corrections. The mistake is to hammer/saw away repeatedly and interfere with what you have already achieved, wasting time and effort. I think the OP kinda acknowledged this by recommending switching at whim between different tasks within a practice session.
I found this article very interesting, but I'm not a musician. I know they mention sports briefly, but I'd love to see a more detailed account of this advice applied to other topics.
I don't find this to very useful, and I think the approach of this study is probably not so great. My background on this is that I'm a professional violinist. I started playing when I was 4 and was performing professionally when I was 8. I'm 35 now, and I still play as a soloist, in chamber music, and with an orchestra. I happen to make most of my money by writing code, but the violin is still a big part of my life. I teach kids, and they win big important violin competitions.
My specific issue with this article is that it seems to think of practicing as one monolithic event--as though you are really just doing one big thing when you practice: getting better at what you are practicing. I think the concept of randomizing tasks is sort of getting at a good point, but it's really not all the way there. And also, you have to understand that you are, in fact, getting something extremely valuable out of the block practicing: the ability to focus on a singular task for a long period of time. That's a skill itself. You will never do well in a 3-5 hour rehearsal with a string quartet or an orchestra if this is not something you are accustomed to doing on a regular basis.
Here are some more details.
The big thing to do when I was a kid was to send your children to a practice camp like Meadowmount, where all the Juilliard School teachers spent their summers teaching kids like me. That was all block practice. 5-8 hours a day, and a lesson every day or so. That kind of block practicing went exactly as described in the article. An hour of scales, and hour of etudes, an hour on a piece of music, etc.
In my opinion, that's a mixed bag. You need to be able to pull a scale out and just lay it down. Any scale. Any time. It's a kind of a musical Fizz-Buzz problem. You just need to be able to do it even if it's not really interesting. Although, it's not like Fizz Buzz because scales are actually really hard. Etudes are a sort of micro-problem to solve. You isolate a particular bow or finger technique, and you spend some time every day working out that physical skill--the logistics of getting x fingers from point a to point b in the requisite amount of time.
Putting in a block of time on your musical piece is also important in itself because you have to commit that music to memory. Not just the notes and the finger motions involved, but all the little things like the bowings and phrasings and dynamics and stuff. The parts that take notes and turn them into "music."
The reason I think the study is flawed is that I think it's studying a strawman of an idea. No great players actually practice in the way that this article describes. There's this idea of a mindless slaving away that we do for hour after endless hour. That's not real. I mean, it's probably real for some people. But great players don't do that to begin with. And good teachers don't recommend this approach.
There are some popular methods of learning difficult things. There's a thing that people do to tackle a difficult bit of notes where you just practice slowly with a metronome and you gradually increase the tempo. Start with a tempo slow enough for you to get the notes out, no matter how slow. Then you just gradually make it faster and faster. This should work, right? No. It should not work. And it doesn't work.
--a brief interlude before I explain why that doesn't work--
What you're doing when you play a musical instrument is that you're solving physical problems--usually without the necessary tools. You are working a variety of physical challnges. The logistics of moving fingers from one place to another, you're solving acoustical problems by managing the friction between your bow and your string(s). Or if you're a wind player, you're dealing with the physical properties of your breath interacting with a vibrating reed or you're vibrating your lips when you play a horn of some kind. There are two parts of every musical problem. 1. There's the conceptual problem: "How should I be trying to execute this solution?" 2. The physical part: "How do I train my fingers, arms, hands, lips, whatever to perform this solution?"
Tempo matters when you are planning out these solutions. A slow tempo uses different physical motions, and it takes a different mindset. Slow tempos (yes, tempi, I know, but I don't feel like the word is so foreign that I need to pluralize it in Italian, so tempos) allow for larger motions and gestures. Slow tempos do not need to have efficient motions the way fast ones do.
--back to my point--
Practicing slowly will never get you to perform things quickly. You are practicing the wrong thing. If you want to learn to play things quickly, you have to practice them quickly. But in small chunk. Take 2 or 3 or 5 notes. Play them even faster than you ever intend to perform them, and do it with a metronome, so your rhythm is good. Chain them together, and gradually slow down and enlarge your motions.
I don't know the details of this study: who were the participants, where they came from, or what their experience is. But to me, this seems like a situation where the block practicers are basically dumb practicers. Because no good musicians practice that way. I think you would have positive results doing absolutely anything to break up this kind of a thoughtless, put-in-some-time-and-hope-I-get-better kind of a routine. Random exercises are probably better than that.
I can see how these results make sense. Randomization is probably a good thing for a certain type of musician. But I would argue that it's definitely not better than a thoughtful, focused, problem-solving approach applied for long periods of time.
Anyway, just thought I would throw some things out there. Cheers.
> Tempo matters when you are planning out these solutions. A slow tempo uses different physical motions, and it takes a different mindset.
I can totally relate to this. I play harmonica, and what I've been working on for fun lately is the vocal parts from some Fleetwood Mac songs: Dreams, You Make Loving Fun, Gold Dust Woman, etc.
My goal is that when I play these songs, it almost sounds like Christine or Stevie singing. (Yeah, you may say, dream on! Humor me...)
Now these are not complicated vocal parts, but given my lack of musical talent, I definitely had to slow them down to learn the notes.
You might think that the vocal part for Gold Dust Woman is pretty simple, and you'd be right. But it took me quite a while playing it slowly just to learn the notes.
And that was the easy part!
I could play the notes, but they sure didn't sound like anything you'd want to listen to. I still had to practice and practice the breathing and intonation and whatever you call it that makes the instrument sing instead of just playing a bunch of notes.
I'm getting there, but man is it a lot of work. And this isn't something that can be slowed down. Can you imagine You Make Loving Fun at a slow tempo? What would that even sound like?
So it's full speed ahead with these songs, and thank you Christine, because You Make Music Fun.
> Practicing slowly will never get you to perform things quickly.
Learning something at a very slow tempo and then slowly increasing to written tempo is a strategy taught by many teachers and in my personal experience it's worked well. Aspects of your playing are going to be different at different tempos, but that doesn't mean it isn't a valid learning technique.
You're correct. It is taught by a huge number of people. But it's not optimal for certain types of technical challenges. And there are some that it will never be sufficient for.
But the biggest issue is that it is fantastically inefficient. You can learn the same passage with greater reliability in about 1/20th of the time using the reverse technique. The slow++ method isn't guaranteed to get you where you need to be. And if it does, it will take far longer.
I started doing database work in my mid-late 20s. 27. I had a certain girlfriend who didn't care for my itinerant lifestyle and the ups and downs of being a performer. She wanted me to get a "real" job. I've always been fond of technology, but never a hacker. I messed with a lot of hardware when I was a kid; worked for the hardware repair shop at university when I was in school. Did a lot of troubleshooting, but never any code. I read a couple of books about databases, built some toy applications, and completely lucked into a job with a market research company. They were desperate for someone who could query their db on the fly and work with MR people to do ad hoc reporting. So I did that. Later, I got more into the research aspect of the data I was working with, and moved to the analytics team. It was a good match.
Went back to school for statistics, stayed in the market research industry for a while but I got tired of grinding through stuff in databases all the time. I learned some Python for a couple of things, and now I'm at a payments processing company (not one of the big ones that sometimes get talked about here). Still fairly heavy on the DB end of things, but doing a lot of Python and C#. Python for AI on our transaction data--and anything else I can get away with using it for, C# for building reports of various different kinds. SQL Server for all the DBA needs.
I'm not looking to move jobs (this one is really too good to quit at this point in my career), but I am looking for part time python web dev work so I can get some experience there. That's where I want to be in 5 years, but I don't want to have to start over as a junior developer to get there. I've got plenty of free time, and I'd love to do 20-30 hours a week for a shop that could offer some mentoring to someone like me. And some cash. But the mentoring is more important.
One of the most unexpected things to me is how good I am at hitting deadlines. But it makes sense. As a musician, deadlines don't move. You're playing a concerto with an orchestra on such and such a day . . . that concert is going to happen whether you are ready or not. Your choices are to get up there and play like a badass or get up there and fail in front of a thousands of people. You learn that when you're 8, and it sticks with you. When I moved over to coding, I never thought twice about it. A deadline is a deadline. It doesn't move. That's a thing that's been consistently talked about in my career. I nail my deadlines. Not because of any magic about me as a programmer, just a mental inability to view those as flexible. I can see, however, that this would be a weakness for me if I were to get into management: I'm awfully impatient with people who don't hit deadlines.
Dealing with toxic environments. I read about brogrammers and silicon valley startups with all kinds of ego problems and sexism all the time. We all do. I've even worked for a startup or two that styled itself that way. I've never met anyone with the kind of ego that professional musicians have. Not all, mind you. It's been my experience that the best people in any field are quite kind and wonderful and humble. And the worst are the ones who are actually just mediocre. But there are tons of mediocre performers who have terrible sexist, racist, and generally toxic attitudes. I managed an orchestra while I was studying statistics after I dropped out of my music degree because it seemed like a good idea. I've never seen such a wretched hive of scum and villainy. As far as I'm concerned, even the most obnoxious of the party-boy, popped-collar, douchebag bros I've ever worked with are basically nothing compared to you run-of-the-mill regional orchestra player jerk.
Being willing to learn from anyone. There are many musicians (particularly string players) who subscribe to a certain philosophy of playing. All other methods of playing are ipso facto wrong. My best teacher is a violinist, Bruce Berg, who studied with Galamian, Gingold, and Dorothy DeLay. He did an undergrad, grad, and doctorate at the Julliard School. Where he claims to have learned very little (I doubt this is true). After finishing his doctorate, he went and studied with a Cellist--heresy!--named George Neikreug. What could a violinist with these credentials possibly have to learn from a Cellist? To this day, Bruce claims that he never actually learned to play the violin well until he studied with George. I've taken that same approach, (and I picked up a lot of George's techniques from Bruce), both in music and in technology, and I think it has served me well. Go to the dark side for advice some times. Go learn a language that you don't like. Go talk to people you don't think have anything to offer you. Go with an open mind and a warm heart. And a couple hundred bucks. Because people often charge money for their knowledge. But I've learned as much about programming from reading Marco Arment talk about how he does all his web apps in PHP because his needs are simple as I have learned from reading Eevee about how much PHP is a hammer with the claw part on both ends.
I could continue on about this just as much as the earlier topic. But I should probably shut it down. So I'll close with this:
Don't be afraid to contact big important people and ask them for help. I remember when I was just learning python, I was writing an extension for SPSS to do some statistical junk that we couldn't do with the interface as it existed. So I just went and wrote one that shouldn't have worked but did and emailed him the code and asked why it worked. I got completely schooled by a total master. It didn't really work. Slightly embarrassing, but since I didn't bring an ego to that situation, I learned a ton. John Peck is a really great guy.
Here are a few things off the top of my head about practicing. And I do think there's quite a lot of crossover as well.
Practice thoughts:
Have a plan when you sit down (or stand up) to practice. Know what you want to accomplish. This gets more and more important the older you get and the less time you have. When I was a kid, I practiced for 5 or more hours a day. Even more in college. As an adult with a job and a girlfriend, I will never have that luxury again. But what I do have is 15 minutes here and 20 minutes there. It is FAR from optimal, but that's what you have to work with. I do still get up early before work so I can practice scales for an hour every morning. That might be all I can do for one day. But even with scales, have a goal.
It helps to do this if you have thought about the piece you want to work on and what you think you need to do. It's hard to generalize because you are so often in different places. But give yourself a goal, break it up into manageable tasks, and check them off the list. I'm learning the Shostakovitch violin concerto right now to play with an orchestra in a few months. Each day of the week my schedule is different. Some days, I'm going to yoga after work; some days, I'm driving an hour to my gf's place, sometimes, I just go home. This week, I'll have a few 15-20 minutes time slots, and I'll have 1 2-hour slot. I prefer to work the "hardest" parts in the smallest time slots. I'll take those 2-3 short times and work a single measure that's tricky. I'll take the longer time slot and work on performing a larger chunk.
I was a violin performance/music theory/philosophy major in school (and dropped out after 6 years, of course). So it's natural for me to analyze the music I'm playing to get the best understanding of it I can. You don't have to be a music theorist to have some grasp of the form and structure of a bit of music you want to learn. Read about the music online. Understand it the best you can. This will help you remember it. I break up my practice goals when I'm doing the initial analysis of the music.
One good reason to do some analysis before you practice is to understand what parts are similar and what parts are different. Abstract the challenges as much as possible. If you are working on a piece in f#-minor, practice a lot of scales in f#-minor so that you have that key in your ear and your fingers and don't have to worry so much about intonation in general. If it follows a standard form, you'll spend some time in A-major and there will be at least some C#-Major(!). Practice those scales as well before you sit down to do the hard work. Composers tend to reuse material. Take the time to figure out what the composer is doing over time with the musical components, and you will save a ton of time in your practice.
In the classical world, the number one biggest priority is playing in tune. It doesn't matter what else you do or can do or what you can feel about the music or anything else: if you don't play in tune--and I mean really well in tune--no one cares. We are hyper-attuned to this because of recording technology that lets anyone sound like they can play perfectly in tune. In reality, no one does. No one even really agrees on what "in tune" means these days. But if you don't do it, you've got nothing. So! Train your ears. Spend some time, at least once a month doing exercises that are designed to maximize your ability to detect small changes in pitch. I apologize in advance to wind and brass players, I don't know what the analog is for this exercise. Obviously, this isn't relevant to fretted instruments.
The "ear cleaner" is an exercise you can do that will make you crazy obsessive about intonation. It's very simple. Start on a pitch. A fingered pitch; not an open string. You have to have total control for this. But it doesn't really matter which one because this isn't a finger exercise. It's an ear exercise. Now what you are going to do is gradually--and in even divisions--move from the pitch you are on to a pitch one half step above it. Over the course of 8 even bow strokes. So for each bow stroke, you are going to increment your pitch by 1/8 of 1/2 of a whole tone. It's very difficult. The point isn't so much that you be able to execute it perfectly so much as it is to get you to listen that closely. And when you practice this for 5-10 minutes, you'll hate yourself a little because everything will sound out of tune.
If there is a part of the linked article I agree with, it is practicing in smaller portions. I really don't think that randomizing is a good idea. But planning small segments is a great idea. The important thing to remember is that you are developing muscle memory. If you are practicing mindlessly, you are probably practicing something wrong. Which means you will be reinforcing something wrong. I suggest this: do not practice for any longer than you can maintain total focus on the thing you are trying to improve. There are too many things to think about already. If you are as planned and focused and you should be, you are still only working on one aspect of your technique, and others are not being executed properly. Choose one thing. Do it well. Stop as soon as you lose focus.
I could keep going on for a very long time, but I'll close the practice notes on this: remember to practice performing. Performing is a completely different mental exercise than practicing. When we practice, we have to be very acutely attuned to all of our little (or big) errors, and we need to note them for future reference because our ears and minds are the only error-checking mechanisms that we have (aside from audio recorders, which are a VERY good idea when practicing performing). But performing is different. You cannot and should not be thinking or hearing in the same way when you perform. When you perform you have to be focused on the music that you want to make (that you planned out, right?! Back when you analyzed the piece before you started practicing), and you can't let the inevitable mistake distract you from your performance or shake your confidence. You can't think in small chunks of technical execution one note or measure at a time. You have to think bigger than that. And you have to be listening to the other people you are playing with and responding to what they are doing. You don't have time for you when you perform. Performing is all about other people. You have to practice getting into that mindset and practice forgetting about what you are doing when you play. It's an entirely different skill. So practice that one too.
Funny observation you made about practicing slowly. Indeed, once you increase the speed, you effectively need to start from scratch and it feels like you relearn what you are doing.
I'm a mediocre hobbyist piano player, but it resonated with me.
Hoever, one day I exercise and even after some serious effort I can't seem to play the bars without error consistently. But I can the next day after the first try.
I remember in my teenage years hanging out with some friends. The son was always encouraged to perform. Even when he did not want to. Even at age 12, he was phenomenal. He now plays professionally for an orchestra in the string section. I wish I remembered more about how he practiced - I think he did it because he really loved playing.
The author made it available for free at http://pianopractice.org/
As I play fingerstyle I study hands separated by separating the bass and melody as thumb and fingers, then move to hands together.
I also analyze the piece to find the hardest as well as the most repetitive measures, work those out and pick up the rest of the piece. You also work these measures with transitions, by playing the preceding measure or half measure leading in and out of the measure you're practicing.
I typically don't get a lot of time to practice so I will pick up my guitar at random and play measures that I'm working on.