Music Theory: An Education from First Principles
lightnote.co
lightnote.co
Focused more on practitioners. Includes exercises with MIDI/USB piano keyboards in the browser: https://www.teoria.com/en/exercises/
These resources also can be useful:
1. https://www.musictheory.net/lessons (exercises included)
2. http://www.earbeater.com/online-ear-training (ear training exercises)
3. https://www.iwasdoingallright.com/tools/ear_training/online/ (ear training)
4. https://trainer.thetamusic.com/
5. http://music.stackexchange.com/
N. Wikipedia is a good reference. E.g., https://en.wikipedia.org/wiki/Glossary_of_musical_terminolog...
If someone wants to try music, start with playing an instrument and then pick the theory. If in physics theory says how the world works, music theory is mostly about labeling things that sound good vs noise. And it's hard to get the words without playing first.
6. https://www.hooktheory.com/hookpad (interactive composition tool)
7. https://www.hooktheory.com/theorytab (searchable database of chord progressions in popular songs, playable in abovementioned tool)
They also sell an interactive music theory primer, which I've not read, but everything else there is free (and amazing).
> When a song says that it is in the key of C Major, or D Minor, or A Harmonic, etc. this is simply telling you which of the 12 notes are used in this song.
Small nitpick, this is not accurate, C Major and A (natural) Minor have the same notes but different starting notes so they are different scales, and pieces written in them sound different from each other. It's one of those things that's slightly hard to explain if you don't sing/compose/play an instrument/read music but very obvious if you do.
It's easy to switch between them (although that makes sense since they are the same notes...)
I suspect that there are no first principles that explain these traditions (and many more), but they work well enough that they can be relied upon (for instance) to reinforce the emotional experience of a movie, sports broadcast, or religious ceremony.
Perhaps a psychological effect worth exploring is how we remember aspects of music, and how that memory shapes our experience of new and familiar music.
It is accurate that it tells you what notes are used. It's just not all it says.
Your move.
Also I would say "X is simply Y" means "all X does is Y", but I guess this isn't universal
We're not so different after all!
Only because they follow usual (classically derived) patterns about the chords played in each key (e.g. 1st, 4th, 5th etc, with are different in each key, and thus give different priority to each note of the scale).
One could play absolutely the same song in C major and A minor (same chords, not same relative chords) -- and it would sound 100% the same, the chords would just have different relationships with each key.
Finding it nice to listen is the cultural convention. Other cultures enjoy microtonal works, or completely different harmonies just fine.
https://en.wikipedia.org/wiki/Equal_temperament
If you optimized the tuning for harmony, the notes would be largely similar, but some of them would not line up that well. Playing one scale with you instrument tuned for the other wouldn't work that well.
https://arxiv.org/html/1202.4212v1/#sec_3_3_0
Read that whole article. Super interesting. It was posted on HN this summer.
EDIT: You might benefit from filling out the intervals section. Clearly articulate each interval, which are classified as consonant vs dissonant, etc. That would get the user/student thinking about 5ths vs 7ths, etc.
I would also lose the "from first principles" by-line. The pentatonic scale description was neat in that you talked about how frequencies that sound good together have certain clean ratios, but when you jumped to chromatic scale, there was nothing about how that was derived other than "filling in the blanks." I love the site in general, but the "from first principles" by-line implies a few things that are kinda missing. It's more accurate to call it a visual introduction to western music theory.
A while back this article popped up on HN: https://arxiv.org/html/1202.4212v2 That one dived more into the physics and math that derive different music systems. As I was reading it, I wanted some interactivity like this. So well done! There's a lot of detail in there that could give you ideas for additional visualizations. It was also criticized here on HN a bit for also failing short of it's "first principles" promise, so worth finding and reading that discussion too.
The other thought I have is make the notes keyboard-playable. A lot of the examples are around playing notes together, and shifting between them using a mouse is too slow.
Awesome site overall!
99% of the music people write and listen to in the west is western-focused, and not even that adventurous at that, so this is a little moot point.
Yeah, but by people like Schoenberg, Alban Berg, and the like, or the wilder jazz guys. Not exactly what most people enjoy with a cup of coffee.
>Modern music has moved on to use other notes and sounds and in many cases is not even pitch-centric.
I think that for e.g. electronic, dance, experimental music etc, the chromatic scale/classical harmony/etc. is still a good foundation -- the additional not pitch-centric focus is either in rhythm (which is orthogonal) or in sample/noise-based focus which usually just goes with "if it sounds good, it's ok" kind of approach.
So, not much micro-tonal or other approaches going on in practice.
That said, I don't consider the blues guitar playing a major example of microtonic music, $10 words or not. There are some elements, but you can find much more impressive examples in African music for one (part of which could have been inspiration for early gospel/blues musicians).
There is a huge, potentially indefinite space of possibilities of combinations of melody, harmony, rhythm and timbre, even within the constraints of the chromatic scale
You know, understand that this isn't the only way of doing it, and see how the physics could be applied in other ways (and have been). Appreciate the full breadth of complexity out there.
Still really liked it. Await the chord progressions stuff.
One thing that you did that helped me get further is sticking to that rainbow row of notes, as you explained notes and chords. I think most of the lessons I've tried move quickly to piano keys, where the relationship among the notes is more cluttered, because of the black and white keys.
Also the interactive little things, simple as they are, are very helpful. I know even these simple things took quite a bit of work to throw together. I think they are critical to how engaging your lessons are.
I feel like I'm a musician at heart. If I could delve into music with a purely exploratory and child-like fascination, I think I would enjoy it immensely.
But I can't fathom beginning. Every. single. intro. into. music., is a lecture forcing theory unto you as though "theory" is the very definition of "music". The consensus from experienced musical folks is to shove theory down your throat; you should not be allowed to even touch an instrument until you've drunk the "super serious music cool-aid"! Music is supposed to be one of the most intimate ways we express ourselves, and yet Western culture dictates that there is a singular method to begin exploring it, and it's far too serious and far removed from any kind of natural process.
Had my introduction to programming, starting at the age of 7, been the shoving of books down my throat about Object Oriented programming and how to write 20 different sorting algorithms, I never would have become a software developer. It took me 5 years of accomplishing nothing - and enjoying that exploratory process - just to figure out the basics. Another 5 years to begin digging into the core things that make a developer a developer. And then another 5 years (and counting, a decade later) actually learning how to tie it all together and use the acquired knowledge as a set of skills.
Music in the Western world is taught in such a way that they're trying to cram 10 years of knowledge - that you should be picking up along the way - as pre-requisite knowledge. It is taught as a job aiming to produce immediate ROI rather than skill/talent that accumulates over time.
Sample phrases from the OP that are spreading the all-too-serious cool-aid - the same things you hear from every music professional (italic emphasis mine).
>> A lot of music theory is about limiting which notes to use in your song to a small set that sound good together.
>> not all of them sound good together... Lets listen to some garbage
>> Because not all of the 12 notes sound good together, we must select a set of notes to use in a song.
>> start exploring which chords are safe to use in each Key
Why is it deemed necessary to instruct first-timers about "limiting" the notes we might use (some notes are not "safe" you know!), and telling me what does or does not "sound good". Music should have absolutely no "must"s attached to it. Let alone labelling certain combinations of notes as "garbage" - the use of that term is horrifically off-putting to someone who is looking to explore. This method of teaching completely destroys the discovery process. You tell me that "XYZ" chord is garbage, so I avoid it from day one. What if, left to my own devices, I were to discover that chord - and wind up loving it?
tldr; Teach me to play an instrument without teaching me anything about theory. Don't even teach me how to read sheet music. Just teach me how to play a few songs I enjoy. Once I can actually play with some confidence, then - and only then - bring in the information that ties together with what I have first learned hands-on. Basically, how any 3rd-world child with instruments carved out of wood would learn. No books. No sheet music. Just an instrument and a patient MENTOR, rather than a classroom teacher who's trying to make a classical prodigy out of me in record time.
But just because this course exists doesn't mean you have to go through it first. Go and learn your instrument. Then come back in a couple years when you want to round out your understanding.
I'd need the human element - a real person, in an intimate setting - to guide me through the initial pains. A mentor, to the extent that someone would be teaching me their trade - or perhaps even their (our?) ancestors' traditions. Someone who is going to have the humble attitude of: "You will learn this, and it is OKAY for you to be complete garbage for the first year. A music teacher would give up on you after 3 months, but I will not and we will get through the tough beginning together."
Yep, like a helpless dog who keeps peeing on the carpet and just can't figure out why the humans are so agitated - until it finally clicks and the problem permanently vanishes. ;)
On the other hand, Rocksmith really is far more than guitar hero. It's instrument-learning gamified, with a somewhat quasi-human guide who's always talking you through what's going on, what you're learning, how to tune, etc. You get to tackle learning songs at your own pace, and there are quite a number of silly little games that--for me, having first picked up a guitar and messing with them off an on since I was 17--have really helped cement actual chords in my head ... without overloading me with theory and all that. I tend to make natural connections with things as I learn them, and Rocksmith has been a pretty fun way to engage with guitar & bass.
Anyway, the fact that it's all in a game form certainly can be an understandable turn-off. But it doesn't always feel like a game. It strikes a pretty good balance. Could be just a fun thing to do in between sessions with a human. :)
Go grab a guitar, twiddle about with the machine heads so the strings are randomly tuned, and start hitting the strings with a book.
Absolutely no-one is stopping you from doing that (well, perhaps folk within earshot). Hell, there are guitarists, bass players, drummers and singers (whole bands!) who know pretty much nothing of music theory and still play stuff.
If you want to play, go ahead!
Almost every rock/blues/metal guitarist worth naming started out by grabbing a guitar and fucking around on it until it started to make sense.
(I am not much of a musician nor a serious student of music theory. If I were, I guess I would have eventually learned diatonic chords some other way. But it just goes to show you how good this course is, that a person with a passing interest in music theory was able to quickly learn even that.)
"This is known as an Octave and is not considered a new note. An Octave is the same note with a higher pitch."
Why is this so? I guess I'm totally tone deaf since I get no understanding of the sameness of notes separated by one octave by listening to them. In the same vain the good sound/bad sound example that opens the harmony section sound both good to me.
And yeah, the "bad" example is not really very bad. It's a little bit tense, but there are much worse ratios they could have chosen.
They aren't the same note: if someone plays A3 (fundamental is 220Hz) and then A4 (440Hz) you can easily tell them apart! In contrast, if they play 220Hz and then 221Hz an untrained listener will most likely hear them as the same note.
In some contexts a note and its octave can be thought of as equivalent: if you are playing a chord you can often replace A3 with A4 (and vice-versa) without changing the chord's feel and function. However, that isn't always true. For example, playing G#3 and A3 at the same time will sound more dissonant than playing G#3 and A4 (a minor 2nd is more dissonant than a minor 9th).
But TBH I know next to nothing about music so I could be off.
Most instruments produce harmonic multiples of the base frequency. (Percussion instruments don't.) So if you play a note at 110 Hz, there are also pitches at 220 Hz, 330 Hz, 440 Hz, etc. contained inside it. If you play a note an octave up, at 220 Hz, it contains pitches at 220 Hz, 440 Hz, 660 Hz... which is similar enough that it sounds like "the same note".
(This doesn't explain why 330, 660, 990, ... sounds like a different note, though. Maybe it doesn't to an untrained ear.)
Two notes played in an octave would be quite distinct since you have a clear first fundamental for both notes, and the loudness/decay of the harmonics is slightly different between both notes
That is, when you pluck a guitar string that's tuned to 400hz, it also vibrates at 800hz, 1600hz, and so on. (Do an image search on "guitar string harmonics" if it's not obvious how that would work.) But we hear such overlapping tones as a single "note", whereas a 400hz tone overlapping with a 600hz tone sounds like a chord.
Once you've established that the major scale is useful and in no way mysterious, then you can point out that if you divide the octave up in 12 logarithmically equal parts, you end up with equal tempered notes that almost line up with the ratio-based major scale. (I once threw together a diagram to illustate this that you can find here if you scroll down a bit: http://jsnow.bootlegether.net/cbg/justintonation.html) From then on, you can treat equal temperament as an approximation that implies the ratios you described at the beginning.
(Side note: One idea I try to impress on anyone who demonstrates the slightest inkling to write about music theory is that I really wish there existed something like Christopher Alexander's "A Pattern Language", but for music. Music is full of lots of little "tricks" that you can find scattered about in books, but I haven't ever seen anyone try to systematically collect as many of those as they can in one place, with a clear dependency graph.)
I agree. I'd like the course to comment on the fact that the ratios used in the pentatone scale and the 0th, 2nd, 4th, 7th and 9th powers of the 12th root of 2 don't match exactly.
Some suggestions:
I might include a bit on the diatonic scale between the sections of the pentatonic scale and the chromatic scale. Anyone familiar with Western music should recognize quickly, as a great deal of well-known music has been composed using it. It should also serve as a nice half-way point between the pentatonic and chromatic scales -- introducing more notes from which to compose melodies but all of them still mostly sound nice with each other.
I suspect the reason you covered the diminished chord in addition to the major and minor ones is because that's the chord that works on the 7th interval of a scale, as you cover in the later section. But you might want to cover the augmented and suspended chords as well (perhaps in a later section). I'm probably not the only one who, when attemting to finger a chord on a piano or guitar, missed the 3rd or the 5th, and discovered another triad that sounds interesting.
One thing that I don't see in it, but that I find fascinating, is that in western music each half step represents a ratio of the twelfth-root of two, in terms of frequency. That way 12 half steps (an octave) will double the frequency.
Certain notes within this are close, but not exactly, on a "simple ratio". It's just coincidental that it works out pretty good. (although you could make it work out just as good with something other than a 12 step scale....a 19-step scale has been used: https://en.wikipedia.org/wiki/19_equal_temperament )
Anyway, I think that would fit in well with what you've done so far, but obviously, explained in the nice simple graphics that you seem very good at.
I also must say I love the way you use color, I have a music project of my own (that I'm hoping to debut very soon) that also uses color in a very similar way. Did you know that Isaac Newton fixated on 7 colors (ROYGBIV) because he thought there was a connection between the diatonic scale and colors? That's why indigo seems to have been promoted from some obscure color to one of the "basic" colors of the rainbow. (I prefer BOYGBPP, red-orange-yellow-green-blue-purple-pink)
It isn't coincidental. Equal temperament was a fork of just intonation.
The 12-tone equal temperament scale is historically a development of just intonation (a "fork" in software terms).
So it's not a coincidence that 12-tone equal temperament intervals are close to ratios of small whole numbers.
I think the biggest thing that's missing at the moment is a section on rhythm/time. I'm sure you have plans for that. Looking forward to seeing finished course.
On the Sensation of Tone by Helmholtz is also worth checking out if you want to understand where a lot of the modern understanding of just intonation comes from.
True first-principles music theory must (A) focus primarily on psychology over physics (B) not tell people that complex ratios sound bad but simply help people notice that they are different from simple ratios (C) actually go through the full logic of how the tempered system is derived from chains of harmonic ratios adjusted to temper out commas. The easiest approach to the latter is to simply teach diatonic scales as harmonic ratios and not introduce temperament at all until much later.
Far far far from perfect but having the direction that this attempt is missing: http://www.tallkite.com/AlternativeTunings.html
Anyway, I'd write the ultimate thing if I ever found the time. There's at least some good elements to this attempt so far. It really needs to be licensed CC-BY-SA though so that people can adapt and contribute and improve to get it to where it's really good.
I do agree that making it more intuitive would make it more useful for, e.g., kids in middle school.
The "must" in your claims seems a bit too absolute / dogmatic to me.
The "must" in my comment is precisely about what is required to achieve the "from first principles" premise. To learn a subject, "from first principles" is not necessarily the right way to go, but there are things that are or are not from first principles.
Sure you would...
Here's the thing, it's not that your criticism isn't valid, because I actually agree with it, but what's the point of finishing your remarks with "So anyway, this is why you're wrong and I'm right. Also, I would actually write the ultimate thing myself except I don't have the time."? Yeah, and I would write the ultimate language and compiler, if only I had the time, and I would invent fusion and cure cancer, if only I found the time. I mean, what's the point of remarks like those?
Physiology: Some of this may be speculative, but it seems likely that "harmonious" intervals, that have a superposition of harmonics, have a physiological effect.
Technology: The 12 tone scale could be described as a technology for tuning an instrument with harmonious intervals. Temperament is a technology for solving the problems of tuning primarily keyboard instruments.
Naturally, math is involved in understanding these things, as with many areas of science and technology.
I would talk about a handful of widely used instruments, such as keyboards, strings, winds, guitars, and drums.
Then you can begin to talk about scales, chords, melody, form, and so forth.
You explanation makes perfect sense and it is so clear and so well that once you read it you can remember it forever.
Thanks!
One nit: At the top of each section there is a section title, at the bottom of each section, there is a "Next section" title, a description, and a next section button, and on the side there is a list of sections. Some of the titles are inconsistent from list to top of current and from bottom of current to top of next. It's a little confusing right now, and there are only a few sections; when there are more, it will be far more confusing. I don't have a suggestion as to how fix it, just pointing out the confusing inconsistency.
RAINdrops on | ROSes and | WHISkers on | KITtens [beat] | BRIGHT copper | KETtles and | WARM woolen | MITtens [beat]
Fast syncopated 4/4 (trochees) is Johnny B. Goode:
(deep) | DOWN in LOUsi|ANa CLOSE to|NEW or [BEAT beat] |LEANS [beat BEAT] way | BACK up IN the | WOODS aMONG the | EVer [BEAT beat] | GREENS [beat BEAT] there | STOOD...
Okay, maybe not the best example. Other common times are just variations on those two.
My piano teacher's refusal to explain these to me is one of the reasons I lost interest in the instrument
I previously thought music was composed without any rules.
Certainly not in modern pop music. By far the most common chord is power chord.
But they're also not major chords, they're fifths - E5, A5, etc, although I personally often add the octave to make it 3 notes.
Can anyone suggest good resources in this vein that apply these basic principles to guitar?
Absolutely.
There's no point picking up the guitar if you don't listen to any guitar music.
When I was teaching bass lessons, I'd often have friends, usually also in their mid-20s ask me, "Could I still start learning to play an instrument?"
My answer was, "Yes, but you probably won't be any good. Not because you're too old to learn, but because if you had the right inclination to be good, you'd have already found your way to an instrument." (This is totally different from learning additional instruments later in life.)
Learning to play an instrument creatively (as is your stated goal) is a long process of learning to build up intuition both about the structure of music and the way your instrument works, both mechanically and harmonically. Most of that happens in your head, not in your hands. There are methods that may be more or less efficient, but they all require years of effort.
That said, playing an instrument is fun. Learning to play a few songs on the guitar or piano is a totally attainable goal for a few months of effort. Really, something equivalent to that (including, e.g. middle school band class) is where most people get started. That remains fun even if you don't get to the point that you're using the instrument as a creative outlet.
I started piano when I was 23/24 with the goal of wanting to play Jazz / improvise and quickly realized that the biggest challenge is lacking the technical skills to translate the "mental orchestra" onto the keys.
Especially before bed my mind wanders and produces these amazing Blues/Jazz riffs or Moonlight Sonata-esque ideas, but my talent is far behind my taste when it comes to either trying to play or even transcribing all that I "hear"... at least without significant manual effort.
So yeah, maybe that just confirms what you're saying, but what I realized around year 1 was that "improvisation" is really just a musician's bag of technical skills/tricks combined together in their own unique ways... And ultimately the more technical capability you have, the more "improv" things will appear.
That doesn't mean that composing becomes automatic -- often once you cross that chasm, there's still frustration between having an abstract musical idea, and translating it into actual notes. Also, by that time, the way you listen to music has changed pretty drastically, and you also realize that a lot of your own ideas are mundane in comparison to the things you can half-way understand in music that you listen to. That's where most of the work actually happens -- in becoming better at thinking about musical ideas.
If you're able to sing the ideas that you've got, I'd recommend recording yourself singing them, and then spending the time learning to play those ideas. That at least lets you work on the gap that you mentioned between thought and mechanics in a concrete way.
For most instrumentalists though, myself included, you pretty quickly get to where you can play things more easily than you can sing them. If you ask a trumpeter to sight-sing a piece of music, you'll usually see them miming the hand movements because they can imagine how it will sound when they play something, and work backwards from there to singing.
I just started his Blues Bible course[1]. Maybe that could help speed you up. It's tons of riffs to help get you improvising. But yeah, he says riffs are basically just a bag of tricks you can dip into.
[1] https://pianowithjonny.com/products/bible-of-blues-riffs-vol...
Double down on ear-training, it'll take you a long way toward being able to being able to automatically translate the imaginary sounds into real play.
Having said that... As with learning all things... It's definitely more enjoyable when you progress quickly.
Someone met a world-class concert musician after a show and said "That was incredible. I'd give my whole life to play like you," and she replied "Well, I did."
A good private tutor if your other option.
1) Think about the music you enjoy listening to the most and what instruments are most prominent in it. That's the instrument you should choose. Like getting good at anything else, practicing music is hard and can be chore at times. You won't always have the inspiration to play. The best way to consistently practice and improve is to be learning song that you really want to be able to play.
2) Playing with others is absolutely essential. You will improve more jamming with others for an hour than you will in ten hours of practice on your own. You do need some amount of skill to do this, but not an awful lot. Once you have a little bit of confidence built up, look for others at a similar skill level to meet once a week or so and play together. You don't need to form a band or anything, but you just might find that you want to.
3) Music theory is nice to know, but not essential at first. It is very useful when writing music of your own and improvising with others, but there's a bunch to nail down first before not knowing it will hurt you at all. Learn basic notes and chords, then focus on picking songs you want to know and learn to play them well. While learning songs, think about what music theory you have learned and how it works within the song.
4) The truth is that becoming "good" will take a decade of dedicated work. But if it is something you truly enjoy then after a year or so you will be able to get to the point where it is both fun and very rewarding. So really do focus on your enjoyment of it. You don't have a parent requiring you to practice for an hour a day anymore, and you won't find immediate benefit from it at the start. Anything you can do to make it an enjoyable routine is very very important. I won't recommend specific books or methods because you fall into the same problem as telling someone how to learn programming. There are so many different options, but what's important is to find what you like the best.
The ways of producing good sound and good tone are still dark arts with wildly conflicting opinions on them. To me it seems the good players already had a sense of what to do right and then built on that with tons of practice. You might end up going down a dead end with your practice and no one can really set you right because they 'just got it'.