Basic Music Theory in ~200 Lines of Python(mvanga.com) |
Basic Music Theory in ~200 Lines of Python(mvanga.com) |
Haskell School of Music http://www.euterpea.com/haskell-school-of-music/
# Assuming note values are of Jazz style.. i.e, '1', 'b3', '#5', or '♭3' with unicode-sub after
jazzAllFlats = ['1','b2','2','b3','3','4','b5','5','b6','6','b7','7']
sharpStrs = ['#','♯']
flatStrs = ['b','♭']
accidentalStrs = sharpStrs + flatStrs
def stripAccidentals(note:str) -> str:
return ''.join([c for c in note if not c in accidentalStrs])
def jazzToDist(jazz:str) -> int:
dist = 0
degree = int(stripAccidentals(jazz))
while degree > 7:
dist += 12
degree -= 7
dist += jazzAllFlats.index(str(degree))
for c in jazz:
if c in sharpStrs:
dist += 1
elif c in flatStrs:
dist -= 1
#Here you could add support for double sharps and double flats if you want.. although unlikely as font support for these glyphs is horrible overall.
else:
break
return dist
print(jazzToDist('bb3')) # returns 2
print(jazzToDist('1')) # returns 0
print(jazzToDist('♭♭♭♭♭♭44')) # returns 68
print(jazzToDist('2')) # This one is strange as it's the only one where input == output
The shape of the jazz system is the same shape as a change in the key of C. You would just separate the accidental part of the note's name like I did and look up let's say the index in all keys, giving you distance from C instead of what I showed there which is like distance from what is called 1 in Jazz.
So yes I prefer to make helper functions like this that actually kind of "get it" about what the languages/ways like Jazz or note names are actually saying.. then you can go one to another, or different keys really easily. If interested in more of my "Way Of Change" algorithms I can share.
I think your article is cool and I could comment more.. maybe if you want you could read my repo I could pm it to you. But it's long. In the meantime I have a new website using some of this type of logic. unfortunately js instead of python (where my bigger codebase resides).
Google thinks this site is a security threat and I literally posted it two days ago but it's got all scales/chords etc, and other stuff. Still in prototype phase. https://edrihan.neocities.org/wayofchange%20v14.html
https://lotushelix.bandcamp.com/
Wow, I'm very captivated by it, such high musical weirdness! Excellent stuff.
But every once in a while I'll throw it on and be truly weirded out (in a weird/good[?] way). The album is kinda like getting your brain hit by a truck in space. In the future I would like to make stuff that is slightly less dense. And also more focused.
But ya I recorded, composed, produced, played most of the instruments on that piece and am hypothetically available for musical services. Of course peeps can use the wonders of the www and just get weirded out whenever, wow! For free! I guess that's why people like me get minimum wage jobs in kitchens!
Ya that album will always be a personal memento and all round strange banger. I'm glad you enjoyed it!
Most of the stuff on my youtube honestly borderline sucks. Different phase of idea.. more improv and raw.. but there's like 2 or 3 good ones. Then I quit youtubing like 6 months ago cause I had to go frame houses to pay my rent which put my hand out of commission for a while. If you like Lotus Helix maybe check out a more solo-project one I did last year on the youtube.
It's about where I was born, outside among trees and stuff. I was actually born in the middle of a place called Riverdale.. but not like the tv show but the real one by the river. The tune is called Edrihan - The Riverdalian. https://www.youtube.com/watch?v=E-XZx1DUGhM
You might just realise how this approach goes back into keys.. like Ab, C#, F.. it's almost exactly the same, but you have to account for the accidentals being on the right side of the string as opposed the the left, as it is in Jazz.
And ya! - I actually originally wrote almost exactly what you wrote.. but I kept adding enharmonics of things.. like ['3','##2','b4','bbb5'] # and so on..
So I got to a point where it's like.. yeah this should just understand it. I'll give you another hint for the keys.. Use the scale degree to get your root note name. Get rid of the accidentals (do it after). Once you know that Major in dist == [0,2,4,5,7,9,11] you can use the list that contains all 12 notes in one spelling to find it. That's why I'm getting rid of accidentals. That way if you're looking for C# but you wrote as I did with all flat-spellings, it throws away the "#", finds the 'C', counts from there, and finally adds the sharp back if necessary. Just kinda paying attention to adding a flat to a note with a sharp.. they cancel out etc. Usually that's why it makes sense to keep the degree part separate from the accidentals part in some way. At the end you reconcile a difference between distance and degree-distance. Really easy to do double sharps or flats that way cause you know that all valid note names will work.. don't have to worry about giving it a particular format.
Not only can you use any names notes may have, but you can specify an odd rule.. like for example the difference between looking at the scale in "Western" vs. "Indian". Let's say a scale like Mela Vanaspati/Raga Bhanumati/Zaptian (number 1129 on my site). If it's Zaptian, then let's say we're Western. I'd say it's spelled like the first line following this. If it's a Raga or Mela and we're looking at it that way then even in Jazz we can correctly see it how it's originally stated as the second spelling.
1 b2 2 4 5 6 b7
1 b2 bb3 4 5 6 b7
For me in this case the Indian numbers make sense as you are just counting up integers.. albeit with the "ugly" double flat. And yes it's ugly unless you were using a system that doesn't express it as uglily. Here I'm just comparing the first three notes in a few ways. Let's say for a bb3 a system that would express that less ugly than some would be in the key of C#.. as in [1 b2 bb3] == [C# D Eb] == [Db Ebb Fbb]. Of course all these can be described as [S R1 G1]. This is how it's notated in Indian.. but equivilent to Jazz in that there is a part that talks of which nth note of the change and a part that talks about how far from where it usually is. Obviously C# is better for this change than Db. Even if you use the Western Jazz to derive it it's not good unless in C#. Of course the Western jazz statement to me is more ugly because it doesn't count up in degrees sensibly from 1 through 7. The ugliness of the jazz numbers is equal to the ugliness of putting it in the key of C, like I said before. On other changes Jazz wins because Indian won't let you use #4 or b5.
I'm glad you'll use my codes too. Eventually once you have it working you can do a scale in the key of like... let's say Abbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb.. which is actually also known as C or even B#.. ok stay sharp out there in code land. ;) Music theory is an obsession of mine and fun with codes. There are always many options. There's more than one correct answer. And there are ones that make less sense than others.
And P.S. to anyone just dropping in.. we're lazy so we type b instead of ♭, and # instead of ♯. The former is pronounced flat, is equal to the number -1 and is pronounced double-flat if there are two. The latter is pronounced sharp, is equal to +1 and same rule applies about not pronouncing something like "sharp sharp" in music ever. This way I can pronounce C septuple-sharp, which I made up. That particular strange way to describe a note is equivalent to G because music is weird like that. Also if something has six sharps then you could just as easily say it has six flats. So B♭♭♭♭♭♭ is the same note as B♯♯♯♯♯♯. And yes those are the very sexy-sounding sextuple type words ;)
[1] https://www.youtube.com/playlist?list=PLTR7Cy9Sv285kV3pohsMt...
Modern college textbook writers are doing a decent enough job of not focusing strictly on classical music. You could find out what your local university uses.
Launching soon http://ngrid.io.
Play the piano on your computer with Python:
https://jugad2.blogspot.com/2013/04/play-piano-on-your-compu...
The post got some interesting comments with info about Western music theory, which I knew nothing about. And suggestions on how to improve the program to make calculation of note frequencies more accurate.
The most basic aspect of Western music theory overlooked here is the relationship between tonic and dominant. If you know the "home" chord aka "the I" aka "tonic" is C major, the dominant will be G major, aka the V chord. Add just the F major chord, and you'll know 1-4-5 in a "basic" key: C major. 1-4-5 is the simplest chord progression, you can play amazing grace, you are my sunshine, even The Beatles, you'll be rocking with 1-4-5.
Next level, if you add in the minor 6 (a minor) and minor 2 (d minor), you realistically know 95% of the chords you'll ever hear in C major pieces. And on the piano, this is ALL white notes, so even someone with zero musical knowledge can "solo" over your chords by just plunking any white notes while you play these chords (kids LOVE LOVE this btw, highly recommend trying with a kiddo).
I wouldn't consider double-sharps and double-flats "basic" music theory. They really aren't needed for beginners, since they're relegated to keys like C# major where you'll occasionally sharpen a note like E# (aka F) into E## (aka F#). I didn't run into these until around 5 years into my piano training, playing Chopin's F# major nocturne Op 15 No 2, there's a bunch of double sharps in that piece.
In any case, don't worry about double-flats and double-sharps or the precise notes of various modes and scales. Just learn pieces you enjoy, preferably with a mentor or teacher who can suggest improvements based on their trained ear.
I am not really a programmer, but the thing I always wanted wasn't a "how to program guide" but "what is all this syntax" guide.
It is funny, but when you learn a written language, you spend a lot of time learning grammar and punctuation, but when you go to learn programming it all seems conceptual. there are lots of demonstrations of grammar and punctuation, but I rarely see nice, succinct lists of all the syntax you might encounter.
He is pretty good at explaining music theory without boring you to death. He even has a video on 1-4-5
On a song in C major (or A minor), you can play any white key.
Chords are sections based around a note.
The notes played during a chord give mood and color to the chord (harmonies). The main notes of a chord (that will sound the best) are found by taking every two notes (the note+2+2), e.g. for the C chord it’s C, E and G.
Also the sequence of the notes is the melody.
And also simultaneously the ordering of the chord “drive” the song and also the mood. The 1-4-5 the parent is talking about is a very common chord progression (C major, F major, G major). The numbers here are simply the 1-index of the note in the scale used as the base for the chord.
So while you have three dimensions simultaneously which can feel overwhelming the parent was saying that simply following the 1-4-5 progression and playing randomly white keys will sound ok.
Next step try to hit one the main notes of the chord when it is playing (C E or G for the 1 for example).
Having learned music theory on a guitar rather than a piano, I learned this in a different order. C Major wasn't the focus at first. We started with Am Pentatonic and learned the common 1-4-5 progression and how to build chords and progressions out of that. Then added the rest of the notes of the Am scale in before finally going into root notes and relative scales and learning C major.
It's just my conjecture, but i think Am works better on guitars for learning because it's right in the middle of the guitar starting on fret 5 on the 6th string. Makes it easy, like you say, for someone to solo along with a 1-4-5 progression just by running up and down the scale. As long as you hit the right frets, it'll sound decent, you don't have to stretch too far, you get a nice clear view of the scale's 'pattern' on the frets. Plus, it's the relative minor of Cmajor meaning, you can still play along with someone just hammering white keys on a piano.
We also learned using a lot of blues music. There's a lot of easy variations you can do on a guitar in an Am blues key that can teach you all those fundamentals.
Modes were also worked in at the same time. This was probably not the best though, cause i really didn't get them at the time and only fairly recently sat down to study them and actually figure them out.
This made me smile.
Any suggestions about theory learning beyond of what you've described?
Something that would help with composition perhaps? Music phrasing? Some book to read?
Also, OP is leaving out lots of ways to modulate these basic chords into more complex ones (adding a seventh step, inversions, power chords, etc.).
Finally, as with a lot of pseudo-Pareto type things, often the few exceptions are what make or break a piece musically.
It's like bringing brownies to a potluck. It won't blow anyone's mind, but everyone will happily eat them.
> The chromatic scale is the easiest scale possible
So far so good-- in both programming and music we're just stepping through the smallest values (half step for music, the integer "1" in programming). So "easy" definitely applies to both domains.
> We can generate a chromatic scale for any given key very easily
For programming, sure-- you just find your offset and go to town.
For music, however, this is a wrong warp. The chromatic scale is a special case of a symmetric scale which cannot be transposed. There's literally only one such scale-- each transposition brings you back to the same exact set of pitch classes.
Figuring out what it means to have a chromatic scale "for a given key" is advanced music theory. In fact, I can only think of a few places where that makes sense:
* studying the complex harmony of late-19th century Romantic music
* studying the choice of accidentals in chromatic passages of Bach, Beethoven, etc. to infer the implied harmony
Those are important things, but they are definitely advanced concepts.
Long story short for programming, the author moves logically from an array to stepping through an array. But in terms of music, they start with the simplest possible scale and then jump to a third year undergrad theory concept.
(1) Theory of how things sound like: Tones, melodies, scales, chords, based on the frequencies of individual sounds.
(2) How to name things.
(3) How to handle the mess of naming things in Western music theory, where things have 12 different names, depending on which note you choose as the base.
This post seems to focus on 3.
I would be delighted to see a follow up article that explores frequencies and harmonics while sticking with the code demonstrations and incorporating a simple tone generator for the practice side of things
(1) Melody
(2) Harmony
(3) Rhythm
:-)
You are missing the point.
hmmm
Deriving the piano keyboard from biological principles using clustering (Jupyter)
https://fiftysevendegreesofrad.github.io/JupyterNotes/piano....
Wow that's interesting enough to share as a standalone post, so I took the liberty! Thanks for the link!
To get things, people need to hear sounds, not just see note names and pictures.
You can define interval structure as a sequence of large L, small s, and optionally medium M steps.
For example, the Major diatonic scale - a 7 note scale from 12 EDO - in Ls notation is:
LLsLLLs with L: 2 s: 1 (12=2+2+1+2+2+2+1)
LLsLLLs with L: 3 s: 2 (19=3+3+2+3+3+3+2)
LLsLsLsLsLs with L: 3 s: 1 (19=3+3+1+3+1+3+1+3+1)
And chords based on those ratios: https://github.com/robmckinnon/pitfalls/blob/main/lib/chords...
The above links are Lua code files for a monome norns library for exploring microtonal tuning: https://llllllll.co/t/pitfalls/37795
Plenty of music around that is recorded using actual perfect intervals, so why muddy the waters?
It feels like grumping about some inaccuracies/glossing over in elementary school mathematics because of the existence of imaginary numbers.
I'd say removing the beats from your partials is way more fundamental to both music making and music theory than chromaticism. Chromaticism is the next step, beyond basic music theory.
While true, I find this interpretation harmful to the understanding of modes. It didn't provide me with any insight and instead it seemed irregular to the other theoretical constructs we have and thus deterred and misled me in the beginning.
To me, it all clicked when I took all the modes, except Lydian, and constructed them by putting down the augmentations to the major scale in a circle-of-fifths sorted way:
Mixolydian: b7, Dorian: b7 b3, Aeolian: b7 b3 b6, ...
You can see that the modes appear walking left on the circle of fifths or walking along fourths (or going "darker", as some prefer to say). Try this out when starting at e.g. C and you see the pattern immediately.
Then take Lydian: #4
That's going right on the circle of fifths or going in fifths going "brighter".
Also, tangential comment: My music and my life has changed profoundly when I found out how to use the Lydian mode. I can't explain it, but it is just exciting.
my brain kind of cannot accept this fact and I struggle with it
R ⟷ 5 (stable)
2 ⟷ 4 (unstable)
3 ⟷ ♭3 (modal)
7 ⟷ ♭6 (leading)
6 ⟷♭7 (hollow)
♭2 ⟷ ♯4 (uncanny)
[1] https://www.youtube.com/watch?v=et3CMn2oCsA
[2] https://www.youtube.com/watch?v=SF8CdxcdJgwCome on, that is not for "historical reasons", that is because those notes are only one semitone apart!
"For historical reasons the notes B/C and E/F are one semitone apart."
The names of the notes and scales are due to historical reasons, but a major third and a fourth is one semitone apart due to math, not history.
Mmmm yes, and that’s also a bit confusing because it dodges around why the scale was and is 7 notes to begin with.
It's common in Bebop to add a passing tone to otherwise heptatonic scales. Consecutive semitones are also a common feature in blues.
> And then - just to keep it confusing - we have to split both of those groups of five semitones, so... we arbitrarily split them as 2-2-1 (i.e. WbWbWW keys). Thus the white/black keyboard pattern, starting at C, of WbWbWWbWbWW. If only someone had explained all this in grade school.
We don't arbitrarily split them! It was very much made on purpose to match the diatonic scales, which are very natural due to being a chain of fifths. E.g. from F ascending 5ths: F-C-G-D-A-E-B-¡F!
It's not arbitrary that we based modern keyboards around heptatonic scales! Then we added some black notes so we can transpose, which is pretty convenient on 12-TET.
I don't know what's with the current flagging/downvoting trends on HN, comments get dead before I can reply.
That said, your view seems rather extreme. What would be the downside of illustrating at least some of the samples with audio clips?
In my opinion (and experience) it is better to do a little work "up front" and "in the back" to convert to the line-of-fifths representation since that is more friendly to formalization. In other words you can take input in traditional musical notation and give output in traditional musical notation, but "in the middle," formalization should be done in the line-of-fifths representation.
Above I have used "formalize" to mean something like "mathematicize" (if that's a word) or "be precise" or "be able to compute" or "be able to express in a programming language (like Python)". For example, I consider the line-of-fifths representation to be a good one in which to formalize music theory because in line-of-fifths representation, transposition can simply be formalized as integer addition, and integer addition needs no further explanation or formalization, i.e. it can be taken as sort of axiomatic.
Here's another way of putting it: if you wanted to be able to add Roman numeral strings, would you write code that directly operated on the Roman numeral strings, or would you first convert to a compute-friendly representation like integers, and then do your adding from there? No doubt there are tradeoffs involved, but I tend to think that it is usually worth it to move to a compute-friendly representation, both with Roman numerals and music notation.
An added benefit of line-of-fifths representation is it provides a good basis to formalize many important historical European tuning systems.
F# is in turn named after C#, as it is the functional equivalent to C# in the framework.
I vaguely understand that complications arise because we want nice harmonics, ie frequencies whose ratio is a "nice" rational number, such as 2/3 or 3/5 or so.
But our chosen notes should be invariant under doubling of frequencies ("shifting by an octave"), because that's basically the same note.
The problem then is that roots of 2 are irrational, that is, one cannot find (p/q)^2 = 2, or (p/q)^n = 2, or even (p/q)^n = 2^m. Therefore, one cannot find a "nice" interval that, applied several times, wraps around to an octave (or multiple octaves).
However, in a neat coincidence, (3/2)^12 = 129.7463378906... which is close to 2^7 = 128. So, based on that ("Pythagorean comma"), something something something, and we end up with 12 half notes that are basically of frequency f_i = f_0 * 2^(i/12), which are all horribly irrational, but apparently sound "nice" enough, largely (because they are close enough to some "nice" fractions), but only if we pick out some specific 7 of them.
And then the question becomes, which 7 of the 12 do we pick, approximately uniformly distributed. (Why not 6? Every second? I don't know.)
And then, you can transpose them somehow (ie multiply frequencies by 2^(j/12) for some j, but then you change the names for some reason, and everything gets complicated and tonic and Mixolidian double-sharp.
Also, instead of frequencies of the form f_i = f_0 * 2^(i/12) (which, clearly, have the advantage that any multiplication by a power of 2^(1/12) is just a shifting of the index i), you could also use non-equal tuning, with the powers of the 12th root of 2 replaced by some "nice" fraction, which means that any shifting then subtly changes the character of everything, I assume.
This is complicated, admittedly, but for me the nomenclature obscures, rather than elucidates, the issue.
ETA: I sympathise with what irrational wrote: "Is this what it is like when I talk to people who don’t know anything about programming about my work? Pure gibberish?"
What question are you trying to answer with what you just wrote?
For example, you may spend a while learning the major scale, and what can be done with it. Then you learn the minor scale, and it seems like a totally separate scale that sounds completely different. And after that you learn that there are five other scales (modes) to learn about! (Dorian, Phrygian, Lydian, Mixolydian, and Lochrian!). It can seem extremely overwhelming until you learn that they're all the same scale with different relative starting positions. Where major is [1,2,3,4,5,6,7], minor is [6,7,1,2,3,4,5], and the other modes are all the other permutations of starting positions.
My other gripe is that learning theory on piano puts a lot of bias on the notes themselves rather than the intervals. For example, the B major scale has 5 sharp notes (black keys) to remember whereas C major scale has none. These are pretty different shapes to remember. Learning these on guitar means taking the same exact shape and shifting it up a fret (so if you know one major scale, you know them all!). Not to say that guitar is the perfect instrument for learning this - folks will often learn scales as close to the 0th fret as possible, causing you to start on different strings and have slightly different patterns.
That being said, I wish there was a purely linear instrument (a piano with the black keys flattened?) for learning theory. The real magic comes from identifying the shapes and patterns, and how they're similar to each other. Like how major and mixolydian are identical except for one note, so it's very easy to modulate between them, or make a listener think they're in one mode when they're in another. Same with minor and phrygian. Being able to drop the baggage of "the second note of the B major scale is C# which is this black key here" and just focus on a floating set of intervals seems like it would make this all easier and less intimidating.
That all said, I still feel reasonably early in my theory journey. So maybe this is just my bias coming from guitar.
https://github.com/overtone/overtone/blob/master/src/overton...
I've tried to grok music theory several times. I've never understood the scale/notes, notations. The 2nd array (with sharps and flats) and couple paragraphs made it "click" instantly. Because it was in a language and presentation I understand.
Scales are not strictly necessary, but are part of an apparatus of making music work in the way that I enjoy it. They are a technology.
You're more than welcome to. If you try to discover what intervals between these random frequencies tend to be pleasing, or displeasing, you'll rediscover some of the intervals and scales covered above
One of the personality tests of an improviser is how you think about the music - do you think vertically (in the chord), horizontally (in the mode), for example.
Using scales gives people a familiar territory in which to compose music and a western audience will already be culturally attuned to those sensibilities.
Edit: I’m on the Sonic Pi core team. I mean that I’m looking to add these features to sonic pi soon
I don’t think this has “execution”/synthesis features, but it could at least provide the basis for this environment.
Interesting... Do you have any links for learning more about this - maybe some analyses?
My take on chromatic scales (in the context of this post) is that the very existence of a(n equally tempered 12 tone) chromatic scale is the axiom the OP is using but not stated - hence a comment further up/down about P5s not necessarily being equivalent to d6 in other tunings.
My take on chromatic scales (outside the context of this post) is that there is only one, like there are only two whole-tone scales, etc, and that it wouldn't necessarily make sense to say "the E chromatic scale" - instead you'd say "playing a chromatic scale over an E major harmony" (for example).
However, if there are cases where it's useful to be more specific I'd be really keen to go deeper.
Ooh, good catch-- I completely left out tuning systems!
But again-- the point of "basic" music theory is to simplify the practice of discussing music. In that context, the fundamental purpose of the chromatic scale is to introduce the complete set of note names, as well as the range of the piano pitches. This gives the student a full set from which to derive all other concepts like scales, keys, triads, and all the other fundaments of the common practice period.
So again, if you start with a chromatic scale and then start talking about the differences in half-step intervals along it-- boom. Huge conceptual warp.
Honestly, I don't know much about the intersection between symmetric scales and alternate tuning systems. Personally, it seems like it would be an incredibly esoteric niche, although I can imagine some funny musical jokes with the idea. :)
I would not agree here. I think you can transpose a chromatic scale, but you end up with the same "set" of pitches. (So you _can_ transpose, but if you only consider the _set of pitches_ you end up with a invariant.
But scales are not just a set of pitches, but also have a root note.
You can establish the key of C and play a chromatic scale from c' up to c'' and there would be the feeling to accept C as the root of the scale.
So the chromatic scale is kind of a _total_ (all 12 pitch names) and _trivial_ example, as you pointed out, very symmetric and usually not so interesting for analysis if you want to detect and describe structure.
In general it depends on the music. If the music is based on diatonics, then a major scale or it's modes will be a fitting primitive for analysis, considering chromatic notes something like side notes.
On the other hand 12-tone music uses a chromatic scale as a basis, negating the structure and hierarchy of diatonic scales.
So I don't see a problem with transposing a chromatic scale, it's useful and necessary for mathematical sound systems (helpful for computation) to define operations, even if there is no direct gain (functionally speaking - identity / mempty etc.) :
1 + 0 = 1
Thanks for bringing up the connection with symmetric scales -- these are really interesting!
A fifth might even sound off key if you're very used to equal temperament (it's about 2 cents below an equal temperament). You know it by there being no or less "wobbling" between the tones.
For listening tips, look for vocalist groups where there's "One Voice Per Part" (OVPP). Voces8, Vox Luminis, etc. When there's only one voice, you don't get the inherent wobbling happening when two instruments/voices play in unison.
Not all genres are possible to have just (jazz chord colors would sound rubbish).
A clause that says "assuming twelve-tone equal temperament" would be sufficient here, but you can really go down the rabbit hole if you start digging into scales (see microtonal), and your page is meant to be more basic.
Our harmonies are built on stacked thirds, and the stacked thirds line up perfectly on a staff. Line, line, line; or space, space, space. Three dots stacked neatly on top of each other. Easy peasy. Easy to read all the common intervals at a glance, once you get past an octave it starts getting a bit harder.
If you had chromatic notation, you'd allocate a bunch of extra space and names for things that you spend most of your time not using. An octave would have eleven spaces in the middle, which is practically unreadable.
I think in the long-run chromatic notation is just hostile. Go ahead and use chromatic solfege, that's super useful, but chromatic notation is usually not.
Most often I hear the criticsm from people who are not musicians or do not know how to read music. It's often smart people with an analytical mind, but people who don't have much experience with music. Just speaking from my own experience, it's much harder to read a chord from a piano roll than to read a chord from traditional notation.
Because of that, it took me way too long to figure out that there was any sense in the note names.
A B C D E F G. Seven notes in the scale, seven letters. Seven positions on the staff.
Thats fine as long as you're in C Major. As soon as you depart from C Major it all starts going wonky. Why is C Major baked into the notation as if you'd never want to use anything else?
It's an idea, and possibly somewhat arbitrary, but it's a proposal at least and it will connect to other things well due to uniformity. Then there's my python code which takes a scale.. and writes nonsense with shakespeare verse using words beginning with the letters that spell them. Then words can be used to learn melodies.
But what I was really thinking about more is like depending on the vowel after that letter you will form different chord qualities.. The first most important being the unison, or 'a'.. so to play a major scale with single notes you would say Ba Fa Ja Ka Ma Pa Sa.
But to say the seventh chords that the major scale implies you'd say: BatEk FabEt JabEt KaTEk MatEt PabEt Sabat, which would be a a way of saying: DMa7 Emi7 F♯mi7 GMa7 A7 Bmi7 C♯⌀ - but way less syllables
⌀ is pronounced "half diminished" or "half diminished seventh" which is a mi7(♭5) which would be pronounced "minor seven flat five" for those who don't know.
The insanity of modern music theory is the superimposition of the number 7 (A B C D E F G) onto the number 12 (the number of notes).. everything in the system is skewed by this fundamental wonky shape. But I'll remind everyone that 12/2=6 and 12/3=4 and from these facts more logical systems can be envisioned, as opposed what's 12 notes with 7 names. 12/7=? A number that seems not to have relevance to the comprehension of music patterns.. BESIDE the fact we are forced to think like that with things that conform to 12/7 like sheet music, note names, or piano key locations...
But nature and even a guitar fretboard has less concept of the obsession with the number 7 by design.
I like your shortened chord quality convention, though MaNePu takes a different tack. Instead, it favors what I call "descriptive chord naming". Instead of being prescriptive about the quality, a chord is simply described by appending the notes contained within it. This is great because it also removes ambiguity in the cases where a chord might include certain notes or exclude certain notes implicitly. So Dmaj7 would be PuTaXaNe ("Xa" is pronounced like a "j"/"sh" sound sort of like in Pinyin). It also typically reduces the number of syllables spoken, like your system.
The superimposition of 7 on 12 as you put it, is indeed a problem, but there's also an issue with intervallic favoritism (of half and whole tones). After all, there are 7 note scales with minor third intervals, and so on—imagine a world where one of those scales was the basis for diatonicism. Representing that on a keyboard, and the subsequent accidentals would be a nightmare.
Notation is the big unsolved problem, I think, but I'm aware of some work being done in the area if you're interested. As far as the public facing projects I'm aware of, Dodeka is likely the most promising.
Unfortunately the momentum that Western music notation has, with a few centuries of tradition behind it, means one has to work within that system.
There was an interesting discussion I came across on Stack Exchange while writing the article: https://music.stackexchange.com/questions/67730/why-have-sha...
and my comment here https://news.ycombinator.com/item?id=26861415
How so? If patterns didn't exist, it would just be random choices.
Any non-random music making (and thus theory) requires patterns.
Of course, for every rule there are exceptions, e.g. we have things like (F Bb C) -> (F# B C#)
There have been many attempts at a chromatic music notation, but nothing has caught on so far [1].
Things are a little better with solfege -- there is "chromatic fixed do" solfege, where every note has its own name, rather than only having a name for the "white notes," which leaves you to mentally calculate the sharps and flats.
It's a minority thing--maybe 5-10% in Europe? Even regular fixed "do" is rare in English-speaking countries, so I would assume the chromatic fixed "do" is almost unheard of in the US, Britain, etc.
At any rate, there're are at least seeds of hope for a chromatic fixed-do solfege to catch on more. I use it for my own learning.
Now we flatten the C (after all this is the next note in the cycle of fifths) and we have.... B lydian. And the whole thing starts again.
In this way you can understand how all the modes and keys relate. You can do a similar thing with the other 3 similar modes of limited transposition in this order (melodic minor, harmonic minor and harmonic major).
Have fun.
Adam Neely recently did a great analysis of 'Hey Joe' that goes pretty deep into this stuff https://youtu.be/DVvmALPu5TU
I used to be confused on why modes required modifying certain notes from a major scale until I tried deriving them in the way shown in the article.
Of course, once you understand that, the way you go about memorizing and practicing is probably easier the way you described; that is, deriving modes in any given key by modifying notes of the major scale using the circle of fifths.
But why though? If you're improvising on a dominant (e.g. a G7 in the key of C Major) with a G Mixolydian scale, you're actually not playing a Mixolydian sound, but Ionian, since your tonal center is C Ionian. It is true, it is indeed a G Mixolydian scale and it is using the tonal contents of our key C Ionian. But our frame is Ionian, so what is the purpose of adding Mixolydian other than ease of construction of the scale?
I think that historically, people were already familiar with "standard" notation and terminology before they learned theory, so it wasn't a major hurdle. Not only do theory students (i.e., at the college level) know how to read, but they are also required to learn keyboard. I've heard people say: Don't try to learn theory without a keyboard in front of you.
Music instrumentation and notation are technologies and as such they are replete with historical baggage. I have an unorthodox view, which is that if someone is not already usefully reading standard music notation by adulthood, then they have no reason to learn it. Explanation of theory for non readers would be better served by using an invented notation that sidesteps the historical naming problems.
One such notation is the Nashville number system. It's not nearly universal, but for the purposes of just enjoying a wide swath of popular and folk music, it actually works. It's fun to see how many different songs boil down to a few basic patterns.
A computerized tutorial could show both notations. There is a lot of instructional material for guitar, that shows conventional notation in parallel with a notation based on a diagram of the fingerboard.
Programming would be just as bad if we were stuck with a 400 year old language. Fortunately we develop new languages, but that's because old programs just get thrown away, and it's easy to teach a computer to read a new language. We also teach programmers not only how to read, but how to create better notation themselves.
Of course, there is a right answer, and depending on the language, all of the above can be VERY different things. But they're also similar enough to be completely unintuitive... their distinctions take practice to master.
Likewise, in music there is a right time to call a note a flat, a right time to call it a sharp, and a right time to talk about intervals instead. They can all technically refer to the same thing, yet there is a proper word to be used in any given context.
It's all very confusing, until you start using those terms in their proper contexts on a regular basis. Just like in programming.
Some other examples:
"=" vs. "==" vs. "===" vs. ":" vs. "=>" vs. "~>"
"function_name first_parameter" vs. "function_name(first_parameter)" vs. "hash_name[key]" vs. "object.property_or_method"
"MethodName" vs. "methodName" vs. "method_name"
"function" vs. "method"
...none of these are intuitive. But we use them, we get used to them, and then they seem obvious and we wonder how we could have ever written these things differently.
I think the same goes for musical notations. I struggle with them heavily, but I'm far too casual of a guitar player to take the time and learn the language properly. It's tempting to say the problem is the complicated and confusing language of music, but I know the problem is my own unwillingness to put in the time.
Also, and most importantly, if you're playing an instrument like violin, C# and Db are not actually the same note. Since they happen in different contexts, and have different positions in whatever key they're in, they have different psychological roles and are actually played differently by the player.
If I'm not mistaken, a C# would be played slightly sharper, and a Db slightly flatter to fit the particular key.
The question isn't can you do it - because you can, with varying degrees of difficulty.
The question is what specific user problem you're trying to solve.
https://www.bbc.co.uk/programmes/b00srz5b/episodes/downloads
What I meant by "sounds that otherwise don’t exist" are sounds that are too complex to be created by physical music instruments its easier to simulate them by computer.
Also, what devnonymous says, which I agree with too (but that's another story...)
Something that would help with composition perhaps? Music phrasing? Some book to read? Something for self learning? I wish that melodies I am trying to compose would be better in reflecting what I like in music, and I whish to figure out what is missing.
I can improvise with different chords but it is getting boring and once I try to do something more comlex it doesn't reflect what I like.
I think I am missing something basic and simple but since I had no other option but to learn myself mostly it is probable that I simply wasn't exposed to something essential in theory, something that all good composers know very whell, something that allows experimenting but in a productive way.
May be there is a book that is like a bible for all composers and I simply never heard about it?
I'd consider that a performance technique before a theory aspect, like vibrato speed and control or enharmonic fingerings.
Consider this: If you were in a duet as a beginner and the sheet music had your partner playing a C and you playing an A double-flat, how would you be instructed to play it?
You'd be told it was enharmonic to a G, and play it as a G.
Until you start reaching deep into historical re-enactment or advanced theory, it's very safe to assume equal temperament and leave the ear-adjustment to performance.
If you listen to CPE Bach knowing that each note can be bent (as on a guitar, because it is a clavichord), then the written music makes more sense because each note can be tuned to be harmonic with the fundamental. The sheet is just a sketch. The presumed required bend in each note totally changes the expectations of the key it is written in.
Or, if you are listening to a gamelan, then the beating of notes becomes an essential rhythm of the instrument, informing the tempo of the ensemble as a whole.
Music theory is a combination of acoustics and music history, but the acoustic part is more fundamental/basic. Like knowing "Clueless" is based on "The Taming of the Shrew" is informative, but the fundamentals of quality movie making or movie consuming do not require you to know anything about Shakespeare.
That may well be their main function, especially in bebop (it's not so certain in blues), but they're still considered as part of the scale.
> For examples in a bebop scale you don’t tend to arpeggiate using both the consecutive tones.
That's true for any non-chord tones. The intervals are still very common (in bebop you commonly simply walk the whole scale up and/or down in straight 8ths or 16ths, playing adding the passing tone for the chord tones to end up on the downbeats).
If you tell me you're going to make my life easier by teaching me "Roman numeral Analysis", I'm gonna run away. That sounds scary and vaguely reminds me of Latin class.
"Nashville number system" sounds easy to master. It's country, and country has a well-known self-imposed reputation as simple. (In truth, country can be just as complicated as anything else. But I'm talking about first impressions.)
I used to be a part of a congregation whose band spoke in 5ths and 7ths and I had no idea what they were going on about. And then I learned that part of joining the band was learning the Nashville system. It's just the simplest way to get everyone on the same page, and when you say "Nashville" musicians immediately relate to what you're saying.
A reason for the usefulness was how recorded music was made. The recording musicians had to be able to choose a key that accommodated the singer's range, on the spot. So a transpose-able format was ideal.
I think the industry in New York had a different scheme, which was to write for a "standard" male tenor voice, and rely on the musicians to handle exceptions.
I actually find hooktheory's system, where it's diatonic and accidentals are based on the active chord, not the current key, to be the easiest to understand relationships, but also hardest to translate into concrete notes to play.
I'll just link the relevant wikipedia article:
https://en.m.wikipedia.org/wiki/19_equal_temperament
The linked article actually explains the math pretty well.
Syntax is a skill floor, but it's not anywhere close to a skill ceiling.
If you want rapid-fire example of the various forms a given language commonly uses, I recommend X in Y minute guides. Those show off the various bits of syntax for a given programming language, though without rigorously defining them as such.
Part of the reason that programming syntax is usually taught by example, rather than by formalism is that the formalisms for programming syntax, well, look like this: (cribbing from wikipedia).
program = 'PROGRAM', white_space, identifier, white_space,
'BEGIN', white_space,
{ assignment, ";", white_space },
'END.' ;
identifier = alphabetic_character, { alphabetic_character | digit } ;
number = [ "-" ], digit, { digit } ;
string = '"' , { all_characters - '"' }, '"' ;
assignment = identifier , ":=" , ( number | identifier | string ) ;
alphabetic_character = "A" | "B" | "C" | "D" | "E" | "F" | "G"
| "H" | "I" | "J" | "K" | "L" | "M" | "N"
| "O" | "P" | "Q" | "R" | "S" | "T" | "U"
| "V" | "W" | "X" | "Y" | "Z" ;
digit = "0" | "1" | "2" | "3" | "4" | "5" | "6" | "7" | "8" | "9" ;
white_space = ? white_space characters ? ;
all_characters = ? all visible characters ? ;
vs, if I give you
PROGRAM ASSIGNMENTS
BEGIN
MYSTRING := "A STRING";
MYNUMBER := 123;
END
Ultimately, most programming languages should have defined grammars in their docs somewhere, but most devs use them by intuition, rather than formally.
The other thing, as well, is that it's one you get past grammar as a primary concern that you gain true fluency. And there are a lot of things that are higher level than grammar that can aid/hurt a program much more than the grammar constructs (like various patterns, know algorithms, schemes of organization for different types of projects, and so on). A mostly human-usable grammar is table-stakes these days.
If you have a specific language you want examples or a grammar on, let me know, and I'll see if I can find it.
(edited for formatting)
Here's the thing though -- a "what is this syntax" guide does not imply that you need a formalism of the syntax. What the person is asking for, in my opinion, is a linkage between the symbols and the concepts.
For example, when reading mathematics, often the problem was not my conceptual understanding of the material, but merely that I was not sure how to parse the symbols and map them to what it was doing. I could read a formula, but the mapping of each component piece as a shorthand was not there. At the time I did not internalize that "square root" is literally just getting the side of a square (A somewhat silly, obvious-in-retrospect idea! But it gives you a perfect example of the kind of mapping I'm talking about) -- because of this I wasn't able to get an idea of what it was doing!
In such a case, your formalism would not have worked, because it's simply a grammar. I did not need the grammar -- examples can show that, wikipedia can show that, what I needed was enough information about the link between the symbolic, and the conceptual, that I could find reference material. What I found instead was either as you put down, literal grammars, or vast tomes of knowledge that required more vast tomes of knowledge to read and figure out what each one in turn was saying. So I would get lost down this rabbit hole.
What the solution to this is, again IMHO, is a listing of syntax, yes, but with a conceptual mapping on the right.
So not saying things that we already know -- like "this is a number", but having a construction of an IF statement, and then a conceptual mapping on the right in the form of written description of how it works, or a visual description like a flow chart.
The point of writing was to convey knowledge, it is possible to convey intuition, and yet in scientific fields we seem adverse to doing so! It's treated almost like an unspoken thing, it is covered in passing, but almost never explicitly. It's why much of "intermediate programming" is difficult to break into, in my opinion -- and the same for mathematics (3blue1brown is breaking this up, however)
# Add stuff to the end of a list with append li.append(1) # li is now [1]
And this is exactly the kind of stuff that keeps me from getting deeper into programming. I look at that, and wonder, "what the hell is that . doing?" Now, I know enough python to know that it is calling some function on an object called 'li', and that li is a list. or something that can take a .append() command. I also know that append() is some kind of function. But, these guides never give me enough detail on what the . means. Worse, it seems difficult to find answers to this kind of stuff in aggregate. If I google everything I can find stack exchange pages on each piece of syntax and can get to the point, but for fluency and retention I really need that conceptual piece.
I don't write software, but I use python/pandas for basic work with restructuring data. The hurdle to understanding how to slice data frames was incredible for me. I couldn't understand from the examples why the behavior works the way it does. I often feel like I can get working code without any real connection or understanding of why the code works.
You're answer is great, I wish there was a solution for this disconnect since I can't imagine I'm the only one who feels this way.
I think the best way might be to make something like Albertini's charts for file encodings, but for programming.
An example is here: https://raw.githubusercontent.com/corkami/pics/master/binary...
Of course even within that graph there could be more expansion that it would be nice to see
What is your basis for saying this?
A large number of physical objects, solids as well as hollow can be approximated as systems of springs, surfaces and tensile elements, which all have some frequency response. It isn't rare at all for a physical system to have a very sharp resonant peak in its frequency response, to the point that you'll often find mechanisms to dampen that response so the structure will survive certain inputs.
It's not just strings, either. Drum heads have varying degrees of quantized modes.
So the code thinks that human ears don't detect integer multiples specifically, they just detect sounds whose overtones line up with each other.
Actually, it works for every major scale and natural minor scale!
What are the notes in E major? E F# G# A B C# D# E.
It's still the same letters, E F G A B C D. Now, you may think that this is CHEATING because I've added sharps. But when you write it out on staff paper, the sharps get shoved off to the side on the far left in the key signature, and you basically forget that they are there. You really still just care about seven notes, so you still have seven letters, and seven spaces on the staff, they're just a different seven notes from the C major scale.
You have to know which key the song is in... but you have to do that anyway.
When I say that you basically forget that they are there... I mean it. This does not even require an especially advanced level of musical skill. People with even a passing interest in music theory should be able to breeze past it.
The idea that you can number semitones 1-12 has some mathematical elegance to it, but it's a terrible system in practice. It turns out that mathematical elegance doesn't count for much, and domain knowledge is important here.
The sharps and flats diatonic system is way easier to read because you just mentally parse "key of D" instead of "start on D but also sharp the F and C". It takes time but your brain just starts to grok shapes.
"Piano roll" notation, like in DAWs/midi editors, is actually in certain ways a lot hard to read than staff notation, due to the lower density and lack of reference frame. It _is_ easier to see chord shapes transposed up and down as the same. But I'd argue that's an anti-feature, because of said lack of reference points. The symmetry /sameness makes it a lot easier to start on the wrong note.
C major, yes, but also A minor - where it actually starts from A :)
Regarding spelling chords as the iteration over their notes like MaReVe for a major chord, my system can do this as well, by using an -a ending for each letter. In this case a major chord would be BaJaMa. Or even just B' J' M', as in "B'eatles J'amming M'usic" et al. I think this would be used melodically rather than chordally in my system.
Let's say that the first measure of the melody to Ode To Joy is (in MaNePu, Jazz, Word notes):
Ja Ja Ka Ma Ma Ka Ja Fa Ba Ba Fa Ja Ja Fa Fa
3 3 4 5 5 4 3 2 1 1 2 3 3 2 2
Re Re Su Ve Ve Su Re Pu Ma Ma Pu Re Re Pu Pu
It's great to see that. I immediately notice we're both using consonants only for the first character. I can describe to you the trigram lines being referred to in MaNePu as a bottom line if ending in a, middle if e, and top if u. But the glyphs didn't work here so find the trigrams. I notice you didn't demote the letter 'u' out of your system. I personally am much more partial to the letter 'o'. ;)
We can write this passage with the bass accompaniment as well. Bassline just plays 1/Ja/Ma and 5/Ma/Ve. Weird to look at here because Ma=root for you and Ma=fifth for me! Obviously our layperson reader might not also know that Ma is a standard way to notate a major chord in music, as well.. which kind of also has nothing to do with the first two Ma's we were discussing. And we're not going to bring your mom into it either ;) Anyway here it is. Maybe mistakes (?) cause I'm handwriting here, and I just learned your system:
Bat BAt BAk BApEp Map MApAt MApAb MapEp Bap Bap BIp BAt Bat BIp Map
3/1 3 4 5 5/5 4 3 2/5 1 1 2 3 3/1 2 2/5
ReMa Re Su VeMa Ve Su Re PuVe Ma Ma Pu Re ReMa Pu PuVe
As a critique of your system if I was fluent and you read that out to me, I'd be unsure of when the root actually changes.. because when I read ReMa out I think of playing F# then D. As opposed to F#/D (at the same time).
I use an idea more analogous to the jazz chord symbol system where one specifies the root and the harmony as a compound symbol.. Like 1ma7 or b5mi7. There are actually two separate systems at work in chord symbols like this, and my system is the same as that concept. So you can go either way with "word". That is, using notes (horizontal) vs. using harmonies (vertical). I want to point out that when my system uses less letters it's because the last letters are "A" or "p" meaning no notes in this quarter. That's why some are only one syllable instead of my mentioning two. In another way if a chord is over the root we could omit the B at the beginning because it would be assumed. In this second example I included all the B's and M's (1 and 5. D and A in "normal" notes). This way the melody is seperate on top and the root motion is still specified.
My site is rudimentary but all one needs to name every chord by this method is in a small chart. I threw it in a little html file because posting a table in HN is not going to work well. https://edrihan.neocities.org/ngramcharts.html
I should actually have an explanation on the site which I will add at some point.. but basically you pick a letter for each trigram (quarter scale/chord). So there are four. If they are the first/third it's the vowel, and second/fourth is a consonant. That makes up your quality. Then you combine that with a root-letter of mine. Because those are consonants.. and my word starts with a vowel.. your five-letter word is pronounceable.
You mentioned the pinyin which I intuited on as soon as I saw the "x". You'll see pinyin on my link. Fundamentally related to way of word by its connection to the I-Ching, but not in the sense that I am using it as a sound in my system, like you are.
I like reduction of syllables for these systems. I tried to maximise this property insomuch as all 49152 expressible root-harmonies can be expressed in two syllables. I also like the descriptive property. It just so happens I designed it to be pronounceable and so seem prescriptive as well. I guess the prescriptive version here (which is also derivably descriptive) would be to use the trigram/tetragran/hexagram names. So for our major chord example.. it would be respectively,
Lightning Water Water Earth = = atEp (for some reason HN seems to censor trigram glyphs, on my system at least)
Law Increase Response = 𝌭𝌒𝌮
Sprouting Leader = ䷂䷆ = (atEp)
The trigrams and hexagrams map to this system.. but not the tetragrams. In this trigrammatic way our systems are analogous.
The 7/12 problem is one of the biggest problems with music, I feel as an artist. People have explored a small fraction of tonal possibility.
I will check out Dodeka.. Feel free to check out my material, mostly as we approach the future. I've been hoarding my work for a few years now but am unleashing things. So I guess you heard it here first cause atm I basically do not exist on the internet. But ya I wrote thousands of lines of code to get to this point.
For notation systems I like the circle geometry.. the way of word.. or simply instrument diagrams (mostly only possible with strings and keyboard instruments though, where one can visualise multiple notes simultaneously). I also like the idea of colours.
I think one thing that needs to happen in the education is for people to start learning movable-root systems like yours, mine, the jazz system, or the set system, rather than learning in static keys. People then learn 12 times as much data per neuron (-ish). I thought of a keyboard with 6+6 keys instead of the standard 5+7. Then you'd learn shapes on the instrument 6 times faster by reduction.
Ok there's stuff to meditate on.
Actually my chord naming system is "descriptive" as well but admittedly uses a slightly more compressed encoding.
I know near zero music history, but I was under the impression that that's the evolution from diatonic scales and eventually into our western music system.
Of course a lot of other stuff in music and music theory is due to history and tradition. For example the names of the intervals (octave, fourth, fifth etc.) presumes a 7-note scale. Using 7 as reference is tradition, e.g. the pentatonic scale has 5 notes.
That's our point.
What I meant was that the interval between a major third and fourth in a 12-tone chromatic scale has to be a semitone due to math, not due to some historical accident or decision.
It might be an accident of history that we use a 12-step scale in the first place though, since you can have arbitrary many intervals in an octave - but you can't just divide the octave in arbitrarily places and get music out of it. The intervals still have to be ratios.
(Well I'm sure some avant-garde composer have tried making music with intervals that are not ratios just to be clever, but I hope you get my point!)
A typical object will have multiple modes of resonance as well.
"usually", under what probability model? A random 3d or 2d shape will have zero harmonic partials with probability 1. What is hard to achieve is having even a few harmonic partials. A rectangular wooden piece is painstakingly carved to have a couple of harmonic partials, in order to become a xylophone or marimba bar.
While there are some exceptions, this is skewed in the modern industrial world. If we're making evolutionary scale arguments about sound perception it's a much tougher sell.
