
How to play the guitar by ear, for mathematicians and physicists (2000) [pdf] - lelf
http://www.foundationwebsite.org/Guitar.pdf
======
jng
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.

~~~
soulofmischief
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/](https://fundamentals-of-piano-
practice.readthedocs.io/)

~~~
dsego
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.

~~~
soulofmischief
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?

~~~
dsego
> Most of them were awful.

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

~~~
soulofmischief
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.

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

~~~
soulofmischief
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.

------
lvturner
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.

~~~
markvdb
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...

~~~
lvturner
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.

------
ajuc
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).

~~~
leetrout
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.

~~~
Thorrez
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/](http://jakemandell.com/adaptivepitch/)

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

~~~
leetrout
Well I found this one:

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

------
jackkinsella
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](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.

~~~
wyclif
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.

------
zokier
> 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?

~~~
jachee
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.

~~~
zokier
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

------
christiansakai
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.

------
arh68
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.

------
fallingfrog
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.

~~~
djaychela
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.

~~~
fallingfrog
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.

------
amparanoid
For those who want to know the whys of Music Theory, without math:
[https://books.google.com.br/books/about/Theory_of_Harmony.ht...](https://books.google.com.br/books/about/Theory_of_Harmony.html?id=5Y5MyjbU87oC&redir_esc=y)

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

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

------
troughway
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.

