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How to play the guitar by ear, for mathematicians and physicists (2000) [pdf] (foundationwebsite.org)
149 points by lelf 9 days ago | hide | past | web | favorite | 45 comments





I have been a software developer for 35 years (started learning in 1985, I've accomplished several pretty successful things in this time), and it's also taken me over three decades to become a good musician (which I've only allowed myself to call my self very, very recently - I play piano and sing, a little bit of guitar and drums too). Programming and music are very different beasts, both very tough, both very worthwhile. I just wanted to post because the documenta above has a lot of great information (on a quick browse) and I'm sure it's filled with good intentions, but it's a very poor way to learn music. If you're a mathematician or physicist or software engineer trying to learn how to play the guitar, be it by ear or in any other way, it's not going to cut it. It's great if you read it and learn the information, but only the last 6 pages or so really talk about actually playing, and they are not going to teach you.

If you want to learn to write and play music, don't delve into the math except as a side project. Learn to play a few simple songs that you like, using 3-4 simple chords (there are a ton of tutorials for that), and then spend 1,000 hours playing around on the vicinity of that musical environment. There is no shortcut, it is not about learning patterns, music is a different language, and learning music is about awakening your musical self.

Learning to accompany yourself while you sing a few songs needs no understanding of the mathematical foundations at all (and they don't really help), it's mostly about learning a few basic patterns (3-4 chord finger positions) and then being good at performing (mostly tied to self-confidence). Learning to play common songs doesn't take much more. Learning to improvise and to write your own songs requires 1,000+ hours of the type of "playing/dancing/exploring" I was mentioning above. You'll learn the theory on the 10% of those 1,000 hours that you are resting and browsing the internet.


Chaun C. Chang's The Fundamentals of Piano Practice [0] does a fantastic job of describing the relationship between practice and improvement, and how to make the most of your time.

You'll probably come across advice you've already figured out on your own, but there is a wealth of information for even experienced musicians.

> Learn to play a few simple songs that you like, using 3-4 simple chords (there are a ton of tutorials for that), and then spend 1,000 hours playing around on the vicinity of that musical environment.

I would fundamentally disagree. I picked up guitar 12 months ago, and while I couldn't play you a single cover song, I have written over a hundred fleshed out songs. My practice time and creative time were intertwined, and I let my practice sessions inspire my songwriting and vice versa.

It created a clear path of progression for me, and through learning about and writing dozens of different genres I successfully brute-forced my songwriting skills into maturity. I didn't get locked into any particular style as to not limit myself; I intentionally didn't learn 12-bar blues, for example, until about two months ago. I'm not boxed into referring to the Circle of Fifths every time I write a progression.

I still have a long way to go, for sure, but my fundamentals are solid, cohesive, and broad instead of defined by a narrow perspective of playing three-chord songs for 1000 hours. I have written a hundred songs and am preparing to gig, while my friends who have been playing guitar for 10+ years are still struggling to write their first full original song.

[0] https://fundamentals-of-piano-practice.readthedocs.io/


I would take your audacious claims with a grain of salt. Unconventional progressions don't equate to creative or good song writing. You could be the next Nick Drake or Erik Satie, and I am all for deliberate focused practice, but you have to crawl before you can walk. Limit yourself to three chords and write a song, you might learn something.

Audacious? I never said most of them were good. Most of them were awful. But I followed through till I was finished.

I never made any claims as to my abilities, just my personal accomplishments. I didn't mention unconventional progressions. You need to read my post again, because your criticism is unwarranted.

> Limit yourself to three chords and write a song, you might learn something.

Learn more than three chords and write a song, you just might learn more than the average guitarist. Fundamentals of Piano Practice emphasizes the importance of never getting comfortable, of always pushing yourself during practice. Why settle for mediocrity?


> Most of them were awful.

In that case let me rephrase: Limit yourself to three chords and try to write a really good song ;)


Now you're assuming they're all bad songs, and you're also making the ridiculous assumption that every song someone writes is supposed to be good. The whole point of practicing songwriting is to get better at it.

Stop being a jerk for a second, stop being aloof, and try to consider that I might actually know what I'm talking about, that I actually might be a decent musician. Your attitude is just toxic and mean.


I did not want to push your buttons. Good luck with your songwriting.

Such language is an attempt to deflect responsibility from you to me, but I assure you, the problem here is how you approached this conversation.

Fun book.

"When mass produced, the cost of self-tuning options will be small compared to the price of a quality piano. You might think that this would put piano tuners out of work but that will not be the case because the number of pianos will increase (because of this book), ..."

That's confidence in the method, right there.


I'd have to agree that a 1000 hours of practice on a few chords is not the best way to learn musicality.

My parents spent a fortune on private guitar tutoring to modest effect and I'd say in my case the single biggest thing was freestyle practice while listening to the progression and trying to react to the teacher. So practice indeed, but one where listening and technique are both part of the exercise at the same time. Some theory (for the mathematically inclined) did help for me to understand progressions. Things like landing on the right note are instrumental for the audience and based in theory.


Could you link some of your songs?

Sure, I'll post another comment to this one hopefully this evening with a couple tracks. It's been a busy day.

> Learning to improvise and to write your own songs requires 1,000+ hours of the type of "playing/dancing/exploring" I was mentioning above. You'll learn the theory on the 10% of those 1,000 hours that you are resting and browsing the internet.

This has been my experience as well. When I first started I thought I would rush into the theory and that would allow me to improvise, but what was lacking was the playing of songs and getting a feel for the music. Learning the theory was easy -- getting a basketful of songs under my belt and then getting good at playing them took much longer, and required much more effort -- and now improvising comes more naturally, including being able to use use my ears to hear things like keys, intervals and so on.

Practice, practice, practice! Learn a lot of different songs well, and fully understand the Circle of 5ths.


I agree. Beatles songs are great for this. But I would say don't stop after learning a few simple songs, always keep learning more. one new song each week maybe. Keep in mind that most of the musicians whose music you are learning probably learned this way as well. of course, if you want to learn classical or play like Coltrane, you'll need to learn the theory.

> it is not about learning patterns, music is a different language

So much this.


On the fourth page he talks a bit about inability to sing a certain note.

My first ever exposure to learning an instrument was a particularly cruel violin teacher - before he would let me pick up the violin he pressed a note on the piano and have everyone sing it. Everyone could do it, except to my shock, me.

We went through this routine for weeks, (while my friends were actually being taught how to play their instruments) every time I sang I knew I was singing the wrong note - the problem wasn't that I couldn't hear the note, it was that I couldn't replicate it with my voice - I also couldn't fathom what the relationship between singing and violin playing was (and still couldn't until I wrote this up where I see now that it is obvious, but hilariously misguided) - but I persisited, fighting back tears of frustration until I eventually got right.

I still can't play violin - but I do have a lifetime hatred of singing.


Pro guitar teacher her. TLDR: Pitch skills are incredibly hard to reliably improve.

Inability to vocally reproduce pitch is a reliable filter for limited musical talent, _but_ it should always be used together with other filters because on its own, it produces some very important false positives. Your teacher was being lazy filtering students based on just that filter. He was probably trying to discourage you from continuing to study with him. That's cruel, the opposite of what a good teacher should be, whatever your abilities.

You being able to catch the right frequency, but not being able to reproduce it by voice is very rare, but not unheard of! Anecdotal evidence: I had a friend at music conservatory with perfect pitch hearing, and zero pitch control of his vocal cords. Our professors came to this conclusion in very early screening.

Another interesting to know is that there are incredibly many pro musicians who have less than optimal pitch recognition. I'll tell you even more: most are bad at recognising chords, let alone imagining them. I can tell, because I'm in the top decile of pro musicians on this. And before you think I'm bragging, I'll admit I'm situated much lower when it comes to fine motor skills...


Yes - it took me a long time to realise he was cruel and lazy, years later I picked up the saxophone and was always lauded for my intonation.

I can hear the notes (and I also seem to be way more sensitive to key clashes than anyone else I know)

I just can't sing very well.


It doesn't work for chords for me, but for playing the melody by ear without any talent whatsoever there's a very simple trick that my uncle (who's a proffesional musician and plays many instruments) taught me in less than 1 hour:

1. start with any note (don't need to be in the same key as the original song - if you don't have absolute hearing just don't worry about that)

2. remember the song you're trying to play in your head and consider if the next note sounds higher in your head than the first one or lower

3. guess how much higher/lower and try to play it quietly - usually 2 or 3 tones is a good guess, if it's not 2 try 3 if it's not 3 try 1, etc. - it sounds bad after the first note if you hit the wrong one so you will know when you hit the right one, and there's not that many reasonable options, usually you will get it in 2 or 3 tries

4. when it sounds good you know it's the right note so you hit it hard to have a reference fresh in your memory and go to the next note in your head and repeat the steps

This is all you need to learn to play any melody from hearing it by trying it for 15 minutes or so. Eventually you get very good at guessing the intervals and can play any melody by ear in real time

I still can't play chords by ear (I can kinda cheat by playing chords based on every second note in the melody or so - it isn't dissonant but sound meh).


This is when I learned I really am tone deaf. I have an extremely difficult time deciding if something is higher or lower in my head. I can tell something isn’t right when I play them but I can’t discern how much it’s off nor if it’s higher or lower if it’s really close.

Try moving the throat as if you were humming "happy birthday" but not pushing the air with your lungs.

Your throat will constrict for higher notes more. Or maybe just try humming, dunno.

In the end you don't really need the step 2 - you can try +2,-2, +3, -3, +1, -1, ... it will only slow you down by by a factor of 2 and you will train yourself to recognize the differences eventually anyway.


I generally only would have trouble if there are multiple notes played simultaneously (I can't figure out which one to focus on), or if they are different instruments (the different timber distracts from the pitch).

This reminds me of this test about whether you can tell if one pitch is higher or lower than another: http://jakemandell.com/adaptivepitch/

Unfortunately it requires Flash. Maybe I should try to duplicate it with webaudio.


Well I found this one:

https://www.nidcd.nih.gov/tunestest/hearing-test-results-0

> You correctly identified 25 tunes (out of 26) on the Distorted Tunes Test. Congratulations!

That was easier tho because it was identifying very popular tunes that were off.


I'd argue that spending a few weeks learning/absorbing scale degrees and some basic theory will enable you to learn any melody in much shorter time.

Well it worked for me. Would you learn to play a melody be ear if you just learn the music theory? You still have to practice, right?

> Would you learn to play a melody be ear if you just learn the music theory?

Learning the theory gives a framework for your brain to work in. It's helpful because it gives you incredible hints as to what the next note in the melody is.

> You still have to practice, right?

Scales/theory should be a part of practice.


It’s all about getting an intuitive connection between your ears and the instrument. The same kind of intuition most people naturally have for their voice to some degree. Music theory can give you some tools to start thinking in terms of scales and harmony, but I think the intuition for it can only come from playing.

This sounds frustrating. But it made me appreciate my own musicality, which maybe I take for granted too often.

Know that it’s a lot like learning to read, or learning to touch type. You struggle for a long time, but it gets better, and once you get past a certain threshold your body just does it for you.


> This sounds frustrating.

Not really. It's like a game - you get instant feedback and after a while you learn a new song.


This is something I struggled with for longer than I should have. For me, the turning point was just diving in and practicing playing along with real songs every day until the patterns became clearer. No matter who uncomfortable and hopeless it felt at first.

I recommend going to HookTheory and working your way through every song you're familiar with in the "beginner" section. These songs tend to stick to the big four chords (I IV V vi) and once you nail them, you're half-way there for most pop and rock. https://www.hooktheory.com/theorytab/difficulties/beginner

You'll make more progress doing that for an hour a day over a month than you will in five years of theory.


Another thing that will help you get good fast is that after learning I-IV-V-VI, learn how to play those chords everywhere they can be played on the neck.

> patterns

verse-chorus-verse-chorus-bridge-chorus.

Except Aerosmith. Chorus. All chorus. https://www.youtube.com/watch?v=MV9-n-2x8ww&start=105


> The particular selection of notes used for a song is called the “key.” It is also called a “scale.” For a piece written in the key of C, the notes that are used are A B C D E F G. For a piece written in the key of F, the notes are F G A Bflat C D E. I will say more about keys later on, and why most music is based on a scale of just eight notes

I'm not sure if I'm missing something, but why does he repeatedly refer scales having eight notes when (common Western) scales have seven notes, like the examples he gives?


He seems to include the first note from the next octave, because that's how it is on flute, and because one easy way to make a song ending sound final is to repeat the first note octave higher.

It's about playing by ear. Play only the first seven notes of a scale, and you'll likely find that your ear really wants that 8th tone to resolve it.

Isn't that simply because of the final half-step in major scale, and as such dependant on the scale/mode played? For example in mixolydian has full step in the end so it should not have such tension towards the octave

I accidentally discovered playing by ear. So I play acoustic/electric guitar and electric bass.

It helps if you like to sing and actually have a decent singing voice.

I am a Christian. One of our daily activities is to just pray and sing Christian music (we call this activity worship) every morning after wake up and every night before bed.

One of my friend at church taught me Nashville number system. However he told only one key, G to me since that was the easiest.

I began to just look for worship music that I can play and sing comfortably in G. I found around 3-5 songs and did that daily. After a month, I realized that I did not need to look at the chord book anymore because I memorized it. Then my friend taught me other keys such as C. Then I tried to transcribe the songs that I already know to C and played it and tried to sing it as best as I can. Since those songs weren’t comfortable to be sung in C I tried to find 3 other songs, then proceed for another month to just play these.

Then my friend taught me D, and then he mentioned that if I know how to play D then playing E is just moving it up. Then he told me that I already knew A because it is just G moved up.

So I began to play around with various type of songs, slow and fast, and suddenly everything click, because it seems that majority of Christian music are 90% the same. I developed an ear for knowing which chord to play at what key.

It is really not that hard. It is like driving. Hard at first but once you got it you got it. I applied this technique to bass as well. It is mostly just patterns.

I have successfully taught one student this technique. She actually did it faster than me. I acquired CAGED keys by ear in about 6 months, around 1 key per month. she managed to play just in key of E in 2 weeks. Granted, she practiced longer than me daily.


I think light gauge strings tune just fine, and non-12-tone music might be interesting (I want to hear it, though, not read about it)

I'm an average guitar player, and I don't teach. If you want to play a song, of course pull up the tab/gpro/songbook. But find video of the original artist playing it, look on youtube for the "guitar track" version (no vocals, drums), and try to see where they play/"voice" their chords and how they dish out upstrokes / downstrokes, these things are very subtle when heard.

If you can find a video of the original guitarist teaching you their own song on their own guitar, almost nothing can beat that.

Do Not look at your hands! (play in the dark if you have to) Play the song on the computer, and just try to follow.


I sort of feel like playing or singing by ear is one of those things that you can either just do, or you can’t. I remember being 8 years old and standing next to my parents in church, and noticing the choir singing in harmony, I would invent my own harmony line to go with it. It never seemed difficult at all but I don’t think I could explain what I was doing. Most skills can be taught but in my experience when it comes to music, you’ve either got it, or you don’t. If you’ve got it, you know you’ve got it. It’s just easy the same way that walking or talking is easy, but easier, because I could hum on key before I could talk.

I don't agree with this - I think that practicing your listening skills will make a huge difference in this area. I've been teaching guitar and music technology for about 20 years (and playing for 35), and it all comes from practice if you haven't got perfect pitch (I don't).

Doing ear-training drills (listening for intervals, starting out with a simple one, such as the difference between an octave and a fifth) and slowly building on this so that you can quickly (and eventually, instantly) tell the difference between any of the diatonic intervals makes a huge difference. I've had kids who started out literally not able to know if a note was 'up' or 'down' from a previous one eventually be able to accurately discern any of the 12 semitone steps in an octave up or down, just by weekly practice using GNU solfege.

Yes, some just 'get it' and don't know what they're doing - particularly with the voice - but most need fine-tuning and practice both in their heads and on their instruments, but after doing it for long enough it's possible to get really, really good at it.


It sounds like you’re doing really great things for your students, I’m glad that pitch can be taught. It just feels so weird to me, I can’t imagine not being able to hear pitch! It would be like not being able to see the difference between yellow and green.

I sang off key for years, then found an exercise that worked (humming scales while away from the instrument), and a couple months later I found myself being very on key, harmonizing on the fly, noticing tiny off-key moments in popular songs, and getting compliments about "talent".

So I think a lot of these skills are just taught wrong. You can teach an untalented person to "get it" - Betty Edwards' books famously do that for drawing skill - but for many skills the right method of teaching hasn't been found yet. It's easier to pick & choose students who already "got it" and then take credit for their success (like most music education, and higher education in general) than to research teaching methods that will work on more people.


For those who want to know the whys of Music Theory, without math: https://books.google.com.br/books/about/Theory_of_Harmony.ht...

This book has all explanations you need. The best monography in subject


I really enjoy the fact that the seemingly simple equation 2^n = 3^p has so much implication for how me make music.

Maybe I missed something but he never actually addresses how to play by ear. I opened the PDF and started reading, and eventually found myself jumping past the mathematical harmonic mumbo-jumbo and into the good stuff, and unfortunately I was disappointed. He ended up covering the basics of Music Theory found in a lot of books with no real application to ear training.

1) Learning Material

I can sympathize with the author's plight about not having access to good learning materials or schools. For those who want to pick up guitar and want a bit of extra "why things are the way they are" explanations, I have found books such as "Fretboard Logic" and "The Advancing Guitarist" to be useful. There are plenty more, like Ted Greene's "Chord Chemistry" and whatnot that have insight on ear training. Also, you have software today like Ear Master, Rocksmith and others that can help and are fun as well. YouTube is full of backing tracks that you can use to practice and hear how various notes, phrasings, melodies sound on top of the backing chords.

2) Notes

Personally I have not found using "natural" note names to be that useful; using relative note names like root, second, third is to me much more functional, because the third of any key sounds like a third. The whole "returning to _root_" thing he mentions should be hint enough.

3) Ear Training

His story of his dad being a multi-instrumentalist struck a chord with me (sorry). I have friends and teachers who are like this and I've come to believe that it's less about knowing any of what he is talking about (although it is important) and more about their storytelling ability and translating it over into music. I doubt his dad was a shredder, but his dad's ability to pick up and play an instrument wowed him all the same.

To put another way - most people are lucky if they can passably play one instrument. The question is, how is it that there are people that can pick up an instrument and leave an impression on others? I doubt they have a massive IQ or some arcane knowledge of music theory.

Storytelling and Composition are the same thing. All the high brow shit about Principles of Composition and Counterpoint and whatnot does not matter. Being able to evoke imagery in someone's mind or make them feel a certain way with music is something that the first half of the author's paper cannot begin to rationalize.

I believe it's important to really _hear_ the music you are listening to. It doesn't matter if there are no vocals explicitly telling you how to feel (ie. pop music); it is on you to allow yourself to engage with what you're hearing and to eventually formulate an opinion on how something sounds and how it makes you feel. I've heard music teachers expressing this sentiment, and it's no surprise that it goes over most people's heads. It's not a subject for the dabblers. Composers for film, Classical composers etc excel at this. Learning from them is a masterclass in both ear training and storytelling. They've written plenty of books on this subject.

Take a song you know, and start hearing it on a deeper level. Start transcribing it first by singing/humming/whistling along to it and then with your instrument. Take a chunk of it, and alter it in some way. Slow it down, add vibrato if there isn't already, elongate certain passages.

I can't stress enough listening to music that actually tries to tell a story, because that's when you will hear the most _functional_ use of chord changes, progressions, melodies and vocals, which will ultimately aid in your ear training abilities and answer "why" better than the first half of the paper. Yes, you still have to sit down and woodshed (scales, progressions, metronome practice, etc) and whatnot, but that's assumed to be the case.

PS. Lastly, you can find most of his mathematical explanations on Music Theory Stack Exchange. None of it will help you play by ear any better.




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