
Music Theory for Musicians and Normal People - kick
https://tobyrush.com/theorypages/index.html
======
pubby
Here's my layman explanation:

Pick a frequency. Let's say you picked 400 hertz. If you multiply this
frequency by a simple fraction (1/2, 1/3, 2/5, etc) you get a new frequency
that _harmonizes_ with your original frequency. That means they sound nice
when played together. The simpler the fraction, the better the two frequencies
will sound (1/2 sounds nicer than 7/13, for example).

If you pick several of these fractions between 1 and 2 (such as 3/2, 4/3, 5/4,
2/1, etc) you create what's called a scale. All the frequencies in the scale
harmonize with the starting frequency, but they don't necessarily harmonize
with each other.

Musicians don't always want to play with the same starting frequency so they
invented "equal temperament". The idea behind equal temperament is to create a
scale using logarithms/exponents instead of fractions. Because it's
logarithmic, any frequency in the scale can be used as a starting point and
you'll get the same result.

~~~
cousin_it
Ready to get your mind blown?

Pure sine waves don't harmonize. If you play a sine wave at 400Hz, and
continuously vary the frequency of another sine wave from say 700 to 900Hz,
you won't hear any special consonance at 800. It will sound just as ugly as
the neighbors.

What really harmonizes is the overtone series. The human voice, and
instruments imitating it, have overtones at integer multiples of the main
frequency. For example, if I sing a note at 400Hz, it will consist of a sum of
sine waves at 400, 800, 1200 etc. When two such notes are sounding at the same
time, and their overtone series partially match up - that's when you hear
harmony. It's easy to see that it happens at small integer ratios.

The guy who came up with this idea (Sethares) also came up with an easy way to
test it. He synthesized bell-like sounds whose overtone series aren't exactly
integers. And sure enough, melodies with integer ratios of pitches sound
horrible when played on that instrument, but melodies with tweaked ratios
sound perfectly fine.

EDIT: Thank you HN! I believed this for years, but after writing this comment
and getting some replies I went and checked, and it's not completely true.
Matching overtones play a role, but simple frequency ratios sometimes work
even without overtones, and there are proposed explanations for that.
[https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2607353/#idm139...](https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2607353/#idm139704480569216title)

~~~
onnodigcomplex
If I open 2 tabs of [https://www.szynalski.com/tone-
generator/](https://www.szynalski.com/tone-generator/) and then listen to
440+880, and then change 880 to 850 it is a world of difference. I would
definitely describe that difference as dissonance and consonance.

Now the overtone series IS important and is not always 'simple ratios', a good
example in a real instrument is the strong minor third overtone of a carillon,
and as expected writing in major for that instrument is hard.

~~~
geofft
I'm not sure if this is the same thing as consonance/dissonance, but the graph
of sin(x) + sin(2x), an octave, is regular and pretty and the graph of sin(x)
+ sin(sqrt(2)x), a tritone, is much less so.

[https://www.wolframalpha.com/input/?i=sin%28x%29+%2B+sin%282...](https://www.wolframalpha.com/input/?i=sin%28x%29+%2B+sin%282x%29+from+-100+to+100)

[https://www.wolframalpha.com/input/?i=sin%28x%29+%2B+sin%28s...](https://www.wolframalpha.com/input/?i=sin%28x%29+%2B+sin%28sqrt%282%29x%29+from+-100+to+100)

~~~
etatoby
If you plot them as XY it's even more obvious which one is perfect consonance
and which one dissonance:

[https://www.wolframalpha.com/input/?i=%7B+x+%3D+sin%28t%29%3...](https://www.wolframalpha.com/input/?i=%7B+x+%3D+sin%28t%29%3B+y+%3D+sin%282t%29+%7D+t+%3D+0+to+100)

[https://www.wolframalpha.com/input/?i=%7B+x+%3D+sin%28t%29%3...](https://www.wolframalpha.com/input/?i=%7B+x+%3D+sin%28t%29%3B+y+%3D+sin%28sqrt%282%29t%29+%7D+t+%3D+0+to+1000)

~~~
tripzilch
Except that if you use a frequency ratio of sin(x)+sin(2.01 x), which is
really very close to an octave and really sounds just as consonant as an
octave to almost all people, you almost the same "dissonant" picture:

[https://www.wolframalpha.com/input/?i=%7B+x+%3D+sin%28t%29%3...](https://www.wolframalpha.com/input/?i=%7B+x+%3D+sin%28t%29%3B+y+%3D+sin%282.01+*+t%29+%7D+t+%3D+0+to+1000)

The strange thing is, none of these "simple ratio" theories account for the
fact that our brains allow a lot of "fuzziness" around these simple ratios, so
much that you can't really call them simple ratios as they encompass a whole
bunch of not-simple ratios as well.

------
ianamartin
One of the things that these explainers often miss is the context around music
theory, and what it means to be consonant or dissonant. As some comments below
complain about, this seems woefully incomplete and extremely restrictive. And
it is.

These are the rules of taste and style about what was considered correct in a
specific style and location in the 18th century. The way this is taught in
basic forms like this isn't much different from Rameau's treatise in 1822. The
names of things have changed a little, but the basic concept is that.

For people who say, "Wait! This doesn't account for all the stuff that sounds
sooooo good in Jazz, atonal music, or even later classical music! This is
bullshit!" You're kind of right, but mostly missing the point.

The fact that Finnegan's Wake was written and works and is a work of art,
doesn't change the definition of what a Sonnet is. A Sonnet isn't the only
form of poetry out there. But it's a useful thing to study if you study poetry
because it's a massively influential form on lots of stuff that developed
after it.

The music theory fundamentals from the 18th century are roughly analogous to
that. Massively influential on everything that happened later, and therefore a
good place to start. But they shouldn't be read as a complete or correct
statement of "how music works." Just a snapshot of time, taste, and technology
that serves as a convenient starting point for exploring what happened before
and after.

The other thing that's often missed here is the role of music theory in the
history of music. Theorists have operated across a spectrum of prescriptivism
and descriptivism for thousands of years. At some points in time, theorists
are laying down the rules about what music _should_ be and claiming
artistic/philosophical authority. But at other times in history, they are much
more interested in simply describing how composers achieve certain musical
effects. This fluctuates every couple of hundred years since the time of Plato
or Aristoxenus.

You see the same kinds of divides and fluctuations with linguists and
dictionary editors. Some are very focused on capturing the language as it is
currently used, where others are very insistent on laying down the rules of
correct usage. Music theory, broadly speaking, should be understood in the
same way.

~~~
memset
I do not get a sense that these posters are incomplete or restrictive, except
in the broadest sense that any work which attempts to teach a topic will
necessarily not be able to capture the entire breadth of what is possible (and
doubly so for a "cheat sheet").

The author of these posters is a theory professor, and the rules he describes
here are perfectly _fine_ cheat sheets, in my opinion, for students. They
describe idioms that students will likely run across, both in the repertoire,
or in their assignments. I don't think there is anything wrong with that, and
I'm not sure the author is claiming that this is intended to be a prescriptive
set of rules for composition. Just a useful one in a classroom setting where
you probably need to start out learning some things, prescriptively, when
starting out.

I'd say, take these PDFs for what they are - a learning tool for music
students.

Species counterpoint was exactly that - a set of rules intended to be a
pedagogical tool.

~~~
ianamartin
I don't disagree with you. But when these get cross-posted to sites like this
one and lack the context of what they are, they often lead to really
unproductive discussions about how broken music theory is or how there are
better ways of understanding things or how they are fundamentally incomplete.
You can see a lot of that happening in the comments of this article here. So I
was simply trying to provide a little more background about how to view these
kinds of tools.

~~~
memset
This is my sole frustration with most composition-related libraries: they
misspell pitch classes because “they’re the same note.” It isn’t just
mathematics!

------
huseyinkeles
I can recommend Lightnote [0] on music theory. It has tons of interactive
courses, for which made it really fun to learn the music theory for me.

Disclaimer: I’m not associated with lightnote, but just a happy customer who
paid for the premium package.

[0] [https://www.lightnote.co](https://www.lightnote.co)

------
onnodigcomplex
To add the all the resources here, Alan Belkin is a composer with many very in
depth and practical videos for fellow composers:
[https://www.youtube.com/channel/UCUQ0TcIbY_VEk_KC406pRpg](https://www.youtube.com/channel/UCUQ0TcIbY_VEk_KC406pRpg)
one of the best theory youtube channels.

And [https://musescore.com/groups/counterpoint-and-
fugue](https://musescore.com/groups/counterpoint-and-fugue) is one of those
well hidden small internet communities centered around contrapuntal writing
with many knowledgeable members, original music and in depth essays about
contrapuntal details.

------
uhhyeahdude
Heck yeah!

I have a link to this in my toolbar, as it is one of those sites I find myself
returning to again and again. I recently committed myself to becoming a better
guitar player. I didn't think I'd dive head first into theory, but I'm so glad
I did.

I'm grateful to the people who have created resources like this, because I
wouldn't have overcome previous biases w/r/t theory were it not for the
different approaches and perspectives available on the web today.

edit: a link to another theory project for anyone interested

Open Music Theory:
[http://openmusictheory.com/contents.html](http://openmusictheory.com/contents.html)

------
defanor
A single-document version (unfortunately only linked in the end there, after
enabling JS): [https://tobyrush.com/theorypages/pdf/en-us/the-whole-
enchila...](https://tobyrush.com/theorypages/pdf/en-us/the-whole-enchilada-
set.pdf)

Another article on the same topic, which I found to be helpful when tried to
sort it out: [https://noise.getoto.net/2016/09/16/music-theory-for-
nerds/](https://noise.getoto.net/2016/09/16/music-theory-for-nerds/)

Edit: fixed a link.

------
bartproost
Awesome to see this here. I used the development & Form section to create the
beat generator for Strikefree[1] with the web audio api. I've been
experimenting with pitch as well but for some reason complete randomization
leads to better compositions. Honestly when I made music, I'd also come up
with better compositions when I let go of everything I knew, and enjoyed the
happy accidents.

[1] [https://strikefreemusic.com](https://strikefreemusic.com)

------
PaulMest
This site is pretty great. I would love to re-learn some of the basics in this
format.

Here are some previous discussions since this content has hit the front page a
couple of times:

* 5 years ago - [https://news.ycombinator.com/item?id=8472157](https://news.ycombinator.com/item?id=8472157)

* 7 years ago - [https://news.ycombinator.com/item?id=4807091](https://news.ycombinator.com/item?id=4807091)

~~~
kkarakk
i was gonna say the website design is weird(why pdfs to download instead of
pngs?) but considering it's 7 years old it's held up well

~~~
PaulMest
I have no affiliation with the author and this is the first I'm seeing the
content, but I'd guess its's because PDFs can be vector-scalable and never
lose their quality as you scale up/down and PNGs cannot.

~~~
jacquesm
And they can be printed.

~~~
canofbars
You can print a png

~~~
jacquesm
Sure you can. But it isn't nearly as certain to generate the same kind of
output when changing printers; platforms or programs. PDF at least does that
part well and I totally support the authors choice and think .png would be a
terrible format for this.

They're meant to be posters, pdf is entirely appropriate.

------
adamnemecek
I'm working on an IDE for music composition. I'll launch soon.

[http://ngrid.io](http://ngrid.io)

~~~
widdershins
Hmm, so am I. Does your IDE come with a special language, DSL or something to
control the transformations you mention on your home page? Or are you using an
existing language? I'm using Scheme, but I have a kind of 'declarative DSL'
for defining patterns, transformations etc.

~~~
adamnemecek
It doesn't. DSLs are terrible for expressing music.

------
nprateem
I think music theory is just tricky. Lots of rules that are "just so".

Does anyone know a resource that explains music in terms of the "idioms" of
each genre. E.g. what makes 50s rock n roll sound the way it does, what makes
funk sound the way it does, etc?

~~~
acephal
What makes 50s Rock n Roll sound the way it does are the chord progressions
they preferred. All modern music is just trends in _how_ to layout rhythm and
melody on certain chord progressions.

~~~
yesenadam
> What makes 50s Rock n Roll sound the way it does are the chord progressions
> they preferred.

One thing I learnt from composing (with software) is how much the
instrumentation determines what style/genre the music sounds like - almost
totally. Play "50s Rock n Roll" \- the same notes, chords, rhythms - with
string quartet or orchestra and it's classical. Get The Ramones, Metallica,
Dead Kennedys, Sex Pistols to play it and it will sound like those bands. Or
it will be jazz, folk, country etc when played with the instruments of those
genres.

Also, I strongly believe in _learning from the music_. If you want an answer
to such questions, don't believe anyone's word, but _listen for yourself_. I
guess it sells books to discourage people from doing that. But there's a lot
of wrong or plain loopy stuff printed in books about music. Those who know,
don't write books, and those who write books, don't know, I suppose.

~~~
nprateem
> One thing I learnt from composing (with software) is how much the
> instrumentation determines what style/genre the music sounds like - almost
> totally.

Interesting.

> If you want an answer to such questions, don't believe anyone's word, but
> listen for yourself.

That's good advice but presupposes a level of musical literacy I don't have. I
can play music but unless everything is in a familar key I'll get lost. Plus,
I've tried this with some things (e.g. The Killers) but I'm sure they're
playing in a different mode which explains their chord progressions. It seems
that each song/artist requires individual research instead of for genres in
general.

~~~
yesenadam
I guess it's not good advice then! :-) Not sure what you mean familiar key,
different mode etc, but anyway..

>what makes 50s rock n roll sound the way it does, what makes funk sound the
way it does

I meant, on a fairly basic level, no music literacy required: Listen to lots
of 50s rock and roll songs. Listen to what the drums are doing. Listen to what
the bass is doing. Listen to what the guitar(s) are doing, the singer, horns
etc for every part. Focus on one instrument at a time, for the whole track. Do
that for a range of songs, the more the better. (Also ask more overarching
questions - is it fast/slow? predominantly major/minor? swing feel/straight 8
feel? And the song form - intro, verse, chorus etc - what does the form do.
And how does what the instruments do change in these different sections..etc)
Then do the same with, say, James Brown songs from the late 60s. Then I think
you would have a very good idea what makes the two sound like they do, and so
different from each other.

Just reading a line or two in a book about the difference - even a page or
chapter - won't tell you much in comparison.

------
quadrangle
If you replace "theory" with "European-based jargon and notation patterns"
then this is all pretty decent though imperfect.

What most people call "music theory" is not what would qualify as theory in
any other field. At best (and it's rarely at its best), it explains music like
chemical diagrams explain chemistry.

Any actual theory of music has to be based in human psychology and then the
assertions tested against how well they explain music we can observe across
the world and through history. And that exists, but it's in stuff people call
"music cognition" and even there, folks are often too deferential to the
untested hypotheses that claim to be "music theory".

~~~
analog31
Indeed. And in fact, most music students are told this fairly explicitly.

Not talking about you specifically, but more of a generalization: I've noticed
that a lot of technical people get hung up on the arbitrariness of musical
conventions, whereas musicians tend to just grab an instrument and start
playing.

I wonder if music theory is more like engineering than science. The people I
know who studied theory did not become academic theory scholars, but learned
theory in order to use it. Lost in discussions about theory are what you
actually use it for. Music students, when they learn theory, are
simultaneously being taught things like composition, arrangement, technique,
and possibly improvisation.

~~~
quadrangle
Were you assuming that I took this position because I'm a "technical
[person]"?

Incidentally, I'm a musician and music teacher who started out focusing on
creative exploration, improvisation, composition, and world music. I found it
frustrating that I went through years of "music theory" only to much later
realize that all the deeper insights and questions I had were already
understood and studied by people in music cognition and related fields and yet
most music education never brings up any of it and most music teachers are
totally unaware.

One good intro: Music and Memory by Bob Snyder. That was written not for
technical people but for multimedia artists at the art school where he
teaches. They needed to understand music to use it better in their art. So, he
wrote a book to _actually_ explain music in a usable way. It's far and away
more insightful _and_ practically applicable than the traditional "music
theory"

~~~
analog31
Nope, it really was intended to be a broader generalization.

That book seems interesting. Oddly enough I'm a jazz musician, but I never
learned theory. I mean, I understand scales and chord symbols, but never
learned anything beyond that in a formal way. Comparing myself to players who
have studied theory, my limitations are that I can't compose or arrange, and I
struggle to improvise over complex chord changes.

~~~
quadrangle
Yeah, learning the grammar of what has become consensus-jazz (if you will)
allows you to better play that game with other people. In that sense, I do
just very much dislike that such grammar is presented under the guise of
"theory" (that's both in the word and in having a _pretense_ of explaining
music rather than just being the general rules that lead to standard jazz).

Compare to cooking: if you don't know how to use a measuring cup or the
difference between baking and broiling, you will have a harder time following
recipes or adapting them to your own tastes. And knowing deeper ideas like the
effect of baking soda or eggs or the smoke points of different oils… it can
get advanced and deep, but I _still_ insist that learning about how cooking
and digestion and taste actually work would be deeply insightful to cooking
even if you can get by without that understanding. Same applies to music. Jazz
musicians who just memorize all the scales and voice-leading ideas and forms
etc. would gain a ton by learning about what music cognition offers.

------
toolslive
The amount of work that must have gone into that!

I'm not sure about the target audience. For example, I looked at the Pitch
poster (notation-pitch.pdf), and it seems to target people starting out on the
piano. Nothing wrong with that, but people starting on instruments that don't
have pre-programmed pitches (violin, cello, trombone, ...) Probably want to
know there's a difference between fi c-sharp and d-flat.

Also, there's a cultural divide in how you read notes (movable-do versus
fixed-do) and I'm not sure what you want to do with that.

Music theory is a mess.

~~~
andrepd
>Music theory is a mess.

Why do you say so?

~~~
TheOtherDave
Because music theory doesn't know how numbers work. The interval of A(440Hz)
to A(440Hz) is "1" in music theory even though it's 0 in literally every other
context ever in the history of everything. I mean, if they're going to use a
bunch of mathematical terminology, the least they can do is count right.

~~~
andrepd
Seriously? Music theory is a mess because intervals are counted from 1 and not
from 0?

 _> literally every other context ever in the history of everything_

Have you met a single non-programmer that counts in everyday life starting on
0? Do _you_ even start counting with your fingers from 0?

------
memset
This is an excellent set of sheets which will cover nearly all of the concepts
you would in an undergraduate curriculum (well, besides all of the homework in
4-part writing and roman numeral analysis...)

If you are studying theory, or composing, then you may find my excellent set
of notebooks to be useful! They have perforated pages, college ruled lines on
one side, and staves on the other, for note-taking.
[https://www.themusiciansnotebook.com](https://www.themusiciansnotebook.com)

------
watertom
[https://www.reddit.com/r/restofthefuckingowl/](https://www.reddit.com/r/restofthefuckingowl/)

------
abetusk
Here's my "programmer's version" of music theory:

* We've evolved to hear a wide range of frequencies from elephants stampeding (~60Hz) to flies buzzing (~200Hz) to birds singing (~KHz). To accommodate this, our ears work logarithmically so an exponential increase in frequency is "perceived" as linear progression.

* Melody, tempo and cadence of a tune are linked to how we speak, with the melody following the syllable pattern and tempo of our human language speech [1]. This is also potentially why you get 1/f frequencies when analyzing music, because human language, speech and word frequencies follow power laws themselves [2].

* Discretizing steps between the frequency doubling helps express and communicate music.

* For whatever reason, when combining frequencies we tend to "like" simple ratios of one frequency to another, preferring a small a integer numerator and denominator (maybe this is a consequence of the logarithmic pitch detection?). Discretizing a frequency doubling into 12 steps offers a happy compromise of having many combinations of frequencies that have a small reduced fraction approximations [3].

* From the simple reduced fraction idea you can "derive" why notes close together sound 'dissonant' (large numerator and/or denominator in approximated fraction) and how to construct musical chords as they're 2-3 frequency combinations that have a good pairwise small reduced fraction approximation.

* Musical scales or modes are the result of further restricting the 12 step octave to a reduced set that have nice pairwise reduced fraction approximation (e.g. "sound nice"). The modes ionian, dorian, phrygian, lydian, mixolydian aeolian and locrian are the 'step sequence' of [1,2,2,1,2,2,2] (take 'c' as root, then move one over, then 2, etc.) rotationally permuted (8 steps, 8 modes). For example, ionian has step sequence [2,2,1,2,2,2,1] (e.g. [c,d,e,f,g,a,b]) whereas dorian has step sequence [2,1,2,2,2,1,2] (e.g. c,d,d#,f,g,a,a#]).

This is my understanding so far. I haven't made any music that I would
remotely call "good" so all this should be taken with skepticism.

This is also heavily biased towards western music and I think there are many
exceptions from around the world of different cultures producing different
music that might not be classified from the above.

[1] "An empirical comparison of rhythm in language and music" by Aniruddh D.
Pate, Joseph R. Daniele
([https://www.researchgate.net/publication/10976378_An_empiric...](https://www.researchgate.net/publication/10976378_An_empirical_comparison_of_rhythm_in_language_and_music))

[2] "Musical rhythm spectra from Bach to Joplin obey a 1/f power law" by
Daniel J. Levitin, Parag Chordia, and Vinod Menon
([https://www.pnas.org/content/109/10/3716](https://www.pnas.org/content/109/10/3716))

[3] "Measures of Consonances in a Goodness-of-fit Model for Equal-tempered
Scales" by Aline Honingh
([https://www.researchgate.net/publication/267806865_Measures_...](https://www.researchgate.net/publication/267806865_Measures_of_Consonances_in_a_Goodness-
of-fit_Model_for_Equal-tempered_Scales))

------
foo101
Is it just me or the site isn't loading anymore? HN's hug in action?

------
georgecn
My thumbrules:

Middle A or A4: 440 Hz.

Every higher octave doubles the frequencies.

------
magwa101
Cutesie cartoons don't make it easier.

------
jstewartmobile
Excellent! Give this dude some money.

