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Why 13th Chords
- mml 15y agoWell, that pretty much explains why people have a hard time "getting" music theory. Gibberish+Goobeltygooksus7
- diN0bot 15y agoIronically, the situation is very similar to math. It's relatively easy to read music theory notation, so that the Gibberish and Goobeltygookus make sense, similar to learning mathematical notation. (I personally believe this is easier than learning the alphabet, but that's a different story) However, understanding what the abstractions mean is difficult. The difference between memorizing formulas and intuiting patterns. Maybe this is no harder than understanding the abstractions behinds words. Like most "hard" things, the largest reason for difficulty is one of obtaining persistent practice. If it were common to sing piano music using theory words rather than a single "lalala", for example, or if our language made use of specific tonal changes (up a second v down a major third), or if everyone learned the theory at the age where we now learn the alphabet, the gibberish goobeltygook would seem "easy".
- kabdib 15y agoThe problem I always had with math (when it came to integrals, anyway) was the whole 'dx' notation, where you apparently just had to "go with the flow" and understand what was being expressed. It ain't "d times x", it's this other thing that's syntactically similar to saying "ab" which means "a times b". Someone on HN is going to hammer me. I just muddled through the ambiguity. Then again, what I used to think was the real solution (an exensible grammar -- say, s-expressions -- which would remove the ambiguity) would result in really ugly-looking math. [Don't get me started on denotational semantics. I tried, I really tried to understand the foundation of Standard ML through some DS-based books on the subject, but in the end I just got sick of yet another system of poorly defined heiroglyphics. Maybe I'm just allergic.]
- juiceandjuice 15y agoOne thing you learn in math/physics is all the different ways you can denote a derivative. It makes a lot more sense when you get into Lagrangian mechanics, ODEs/PDEs, QM, complex variables, your first analysis class, etc... classes where you learn why they denote operators and variables in certain ways because other ways don't make much sense given the context.
- agumonkey 15y agoAbout that, one author of SICP build a new physics class based around functions for every physical operator, no more syntactic craze, just functions ( higher order though ). Check SICM on google.
- WildUtah 15y agoThis is exactly what I was going to reply when I saw the GP. SICM is a brilliant book I've only started that revolves around putting concrete understanding ahead of notation. Unlike most books of that type, this one is a seriously advanced math/physics work. At world class universities, upper division undergrads in Physics can study Lagrangian Mechanics in their third year if their calculus is good enough. One note from the excellent introduction focused how to learn math (q.v.): "In his book on mathematical pedagogy [15], Hans Freudenthal argues that the reliance on ambiguous, unstated notational conventions in such expressions as f(x) and df(x)/dx makes mathematics, and especially introductory calcu- lus, extremely confusing for beginning students; and he enjoins mathematics educators to use more formal modern notation." Plus, Lisp!
- nandemo 15y agoI disagree. Mathematicians care much more about notation than do musicians. Mathematical notation should be precise, concise and consistent. The hard parts of maths are the abstraction and the formalization of stuff we take for granted. In contrast, the essence of music theory is fairly easy (if you have a math background, you could learn it in a few hours!). But music notation a strange mix of time-tested, concise notations with cruft that remains due to backwards compatibility. So we write "𝆮" to mean pedal down, but "𝆯" to mean pedal up. We write C7, Cmaj7 and Cmin7 but the modifiers "maj" and "min" modify different parts of the chord. And so on. And sometimes the notation is there, but people simply don't use it consistently. For instance, the usage of 6th and 13th interchangeably without proper justification (e.g. the post in question).
- dextorious 15y agoActually it's a perfectly succinct and easy notation. Not many musicians have a "hard time" getting it, except for those that never cared to study it. In fact, in the history of jazz piss poor black kids that never went to school managed to master music theory just fine. And an enormous amount of people all around the world. The particular example you mention (chord naming) has something like 1/100 the difficulty of something like regular expressions. And it's several orders of magnitude easier than actually learning to play your instrument. Which also millions of people manage to do.
- mml 15y agoI'm afraid you miss my point. I'm not sure who the article was for, people who already know its contents perhaps? Anyone else would have to have a solid background in theory to understand much of anything in it. "I find not only the 13th chord a great substitute for a 7th now, especially when it's the dominant resolving to the tonic, but I also love the 7th+3rd+13th/6th way of voicing it too."
- jtauber 15y agoIt was for people who know music theory but not jazz
- ericflo 15y agoIt's no different than an article about some Rails or Node.js technique, which appear on HN frequently. That is, lots of jargon and techinal foundation that the reader is assumed to know, but within that context some instructive text.
- dextorious 15y ago"""I'm not sure who the article was for, people who already know its contents perhaps?""" No, just anyone who already knows a bit of music theory. Not even a great deal of it. Something that can be learned in a week, tops. Tons of articles on HN have titles like: Djikstra's algorithm, advanced types in Haskell, currying and memoization in Scala, A Graphical Notation for the Lambda Calculus, and similar content. Is someone expected to understand those without knowing the underlying naming schemes, theory, basic domain knowledge etc? Or do people seeing stuff like "^[ab](foo)^[k])/i complain that: "that pretty much explains why people have a hard time "getting" computer science theory. Gibberish.Goobeltygook$"? There a logic behind regular expressions, and there's a logic behind chord/interval notation. And the second is a lot easier, too, and it's used because it's succint and it works. Urban legends about qwerty keyboards ( http://www.utdallas.edu/~liebowit/keys1.html http://www.utdallas.edu/~liebowit/keys1.html ) and railroad gauges ( http://www.snopes.com/history/american/gauge.asp http://www.snopes.com/history/american/gauge.asp ) aside, bad solutions don't last 400 years. """Anyone else would have to have a solid background in theory to understand much of anything in it.""" The naming scheme used in the article takes like 10 minutes to grasp --and requires no great background in music theory. 7th, 13th etc are like numeric indexes. As for dominant / tonic, those are are like music theory 101. Similar to knowing what "Objects" and "Interfaces" mean when discussing OO programming.
- code_duck 15y agoIt seems pretty straight forward to me. The entire article, and this type of music theory, is about intervals and combinations of notes at different intervals.
- deleted 15y ago[deleted]
- swiecki 15y agoVery much baby steps in jazz music theory, but this will probably be helpful to some people!
- jtauber 15y agoyeah, as I said in the post, it's Jazz Theory 101. But anyone coming from a classical music theory background will hopefully find it a helpful insight.
- deleted 15y ago[deleted]
- chrisguitarguy 15y ago> C9, C11 or C13 respectively instead of, say a Csus2, Csus4 That's actually not correct. sus, as in "suspended", implies that the third is absent from the chord. Cadd2 or Cadd4 would be more correct. A major chord with an added forth is kind of a weird sound, however -- too unstable, the fourth wants to resolve. add2 chords are fairly common, though!
- jtauber 15y agoyep, I'll tweak it to say Cadd2 / Cadd4
- jergosh 15y agoWTH is this doing on HN?
- walrus 15y agoIt's here because someone found it worth sharing. From the HN guidelines: Please don't submit comments complaining that a submission is inappropriate for the site. If you think something is spam or offtopic, flag it by going to its page and clicking on the "flag" link. (Not all users will see this; there is a karma threshold.) If you flag something, please don't also comment that you did. http://ycombinator.com/newsguidelines.html http://ycombinator.com/newsguidelines.html
- agumonkey 15y agoEinstein thought in musical ideas.
- jergosh 15y agoNot sure what this proves.
- MrTortoise 15y agoim not sure any comment could prove anything apart from something is posting on HN?
- dextorious 15y agoFrom the down-voting count, it looks as if it's your comment that doesn't belong in HN, rather than the musical post. (And maybe my comment too, but mine is double-meta, so I would understand any down-voting to it).
- mirkules 15y ago"gives the chord a very different direction it wants to go" I struggle with this every time I write songs. How exactly do you know which direction you should go, and how to transition from verse to chorus (i.e. how to pick good transition chords/notes). Currently, I do this by ear, whatever sounds good, but I know there is a better way.
- autarch 15y agoNo, there really isn't a better way. All the rules behind music theory are based on what sounds good, not the other way around. What you can do, however, is push yourself to try out new harmonic structures. You can make your chords more complex, you can delay resolution much longer, you can shift keys. There are also other musical idioms like polytonality, alternate scales, etc. that you can use to expand you horizons. But ultimately, you still should pick something that sounds right to you.
- jtheory 15y agoDefinitely agreed that theory follows practice, not the other way around. BUT it's still good to work on a better grasp of the theory -- if you try chord progressions at random until you hit something that sounds good... yes, there's a better way. The whole point of documenting lots of rules around "what sounds good" is that you can refer to the rules and save a hell of a lot of time in your experimentation.
- mirkules 15y ago"if you try chord progressions at random until you hit something that sounds good... yes, there's a better way." This is definitely what I meant, and it's what I currently do. My grasp on music theory is shaky at best, and I'm not exactly sure where to start to fill in the gaps in my knowledge (this may be true of any self-taught skill).
- jtheory 15y agoOne day I may finish up my website that will guide you in an engaging way through to a good grasp of the useful stuff, but at the moment it's just some practice drills and no guidance at all. :( Dunno if you'll even see this comment.. but my short-version recommendation is to learn different types of chords, (major, minor, 7th, etc., inversions, different spacings) and chord functions, then figure out what the progressions that "sound good" are doing in those terms. That's a big step up right there, I think.
- baddox 15y agoSo, why is it called a 13th chord? Am I missing something obvious, or is it just arbitrary convention that "13th" means "with the 6th and 7th added"?
- splat 15y agoThese chords progress in units of 2. So you start with your triad (1st, 3rd, 5th). For the 7th chord you add the 7th, naturally enough. The next chord is then a 9th chord, so you add a 9th interval, but it wraps around modulo 8, so it's really a 2nd interval (since intervals are 1-indexed). Next it's an 11th chord, but the interval is really a 4th, and so on. The idea is to think of them spread out though, as successive thirds.
- jtauber 15y agobut the idea of my post is to point out why it isn't just the module 8 wrapped version. C13 means C + 6th + 7th not just C + 13th = C + 6th
- cliffbean 15y agoThis has always bothered me. In what's typically called a 13th chord, the 11th is almost always omitted because it either clashes, or it changes the chord into something completely different. Stacking 3rds doesn't actually explain how jazz chords work. And it tends to produce corny voicings. To make an analogy with computers, it feels like the classical notation is an abstraction layer which has been extended beyond its usefulness.
- jtauber 15y agothat was sort of the realization I had that led to the post; it isn't about stacking 3rds and that's what misled me for all those years.
- gruseom 15y agoI was puzzling over the same question. Some of these words are semantically overloaded, and as far as I can tell there's no single interpretation that makes it all "work out" the way you would require if this were math. There are two meanings to "adding 7": 1. adding 7 arithmetically to obtain the same note an octave higher; 2. adding in a 7th note to whatever chord you are playing. But the way the chords are named isn't what you'd guess from those two meanings. If it were, you'd add a 6th to C major to get C6 (that part is true) and then a 7th to C6 to get C13 (that part is not true). Instead, there's yet a third way the notes are "added", namely cumulatively in the following sequence (I've cribbed most of this from the OP): C C+E+G C7 C+E+G+B♭ C9 C+E+G+B♭+D C11 C+E+G+B♭+D+F C13 C+E+G+B♭+D+F+A (The author's argument is that while the chords are theoretically defined to include all these notes equally, some notes - especially B♭ - are more important than others. So even if you drop E,G,D,F and only play C+B♭+A, that's still arguably C13. He's saying that's the essence of the chord.) I suppose some arbitrariness is inevitable, because there are only so many letters and numbers to go around, and more chords with a plausible claim to the "best" names -- which, if you know regular expressions, would be something like [A-G][1-9]+ -- than there are names available. One beautiful thing about music is that it isn't math (we have math for that). It seems to overlap with math and then mixes everything up in mind-blowing ways, at which point all you can do is feel. Well, memorize and feel. Does anyone know historically how C13 got to mean "C+E+G+B♭+D+F+A" rather than "C+E+G+B♭+A", which if you consider things only symbolically, seems more likely? Obviously, it must be because that's what people were playing - but who? Presumably jazz musicians? When was this name settled upon?
- kroger 15y agoThat's one of the reasons that a 9th chord inverted, were the 9th is on the bass, was frowned upon in 19th Century music theory. They argued that the 9th in the bass is a 2nd, not a 9th. To give you an idea of how conservative people were regarding music, even in the beginning of the 20th Century, the Vienna Music Society rejected playing Schoenberg's Verklärte Nacht at first on the ground that it had inverted 9th chords [1]. See [2] for an example, it's the first chord in the second bar. [1] See "reception" in http://en.wikipedia.org/wiki/Verklärte_Nacht http://en.wikipedia.org/wiki/Verklärte_Nacht [2] http://www.youtube.com/watch?v=_Ic3ZLj5RPw#t=3m12s http://www.youtube.com/watch?v=_Ic3ZLj5RPw#t=3m12s
- scrozier 15y agoGrew up playing classical and pop music, basically 3-4 chords (maj, min, 7th, etc). Went to the best jazz school in the world (U of North Texas) and woke up to jazz...an order of magnitude more harmonically complex than classical. Will spend the rest of my life learning to play jazz. Why is this on HN? Because there is a giant overlap between hackers and musicians. For those of you interested, but confused, go to a music store and ask for a "fake book," a big collection of tunes in "head chart" format (just melody and the kind of chord symbols being discussed here. Study it like a new programming language. Bang out the chords on a piano, if you can. (Most fake books have a "glossary" of the chords in the front or back.) Donald Knuth said that when a new CS grad student arrived at Stanford, they didn't ask, "are you a musician?," they just asked, "what instrument do you play?"
- dextorious 15y ago"""an order of magnitude more harmonically complex than classical. """ Depends on the classical. There's classical stuff that's harmonically miles beyond jazz music. Contemporary classical, that is.
- scrozier 15y agoAbsolutely, dextorious. Something of a semantic issue. Maybe we should say, "serious" music or "concert music" or some such. I really don't like any of the terms. In any case, your point is well taken. It would be interesting to trace the parallel development of harmony in "serious" music and jazz. (Which, of course, someone has done.)
- chrisguitarguy 15y agoI always liked the term "art music" to refer to the entire classical music genre. "Classical" implies a certain period to me.
- scrozier 15y agoYes, not bad. Perhaps as opposed to "entertainment music"?
- guscost 15y agoThat counter-intuitive, 1-based, Ionian-biased indexing still causes a lot of problems... People usually measure things with natural numbers when the things to be measured share some of the properties of natural numbers, like equidistance.
- Jgrubb 15y ago...And this is what I love about Hacker News. As a 33 year old musician who got the programming/entrepreneurial bug only more recently, it brings me great hope to see things like this on this board. It brings me hope because a lot of times I feel like such a late comer to the party, surrounded by folks younger than me with many more years of experience in the programming realm having conversations about others' technology articles that are, sometimes, stratospherically over my head. Yet occasionally another programmer/musician type, who maybe got into the game the other way round, writes a post like this that expounds with mystery and wonder upon a topic that I know inside and out. And it gives me hope that the years that I spent in the musical woodshed learning those things inside and out were not wasted in the context of the startup world, but giving me a massive amount of (what I now know as) domain expertise. So thank you HN, and happy new year. May this be your year, as I'm feeling pretty good that it will be mine and my family's.
- scrozier 15y agoJgrubb, as a 53-year-old musician/programmer/entrepreneur (formally trained [in parallel, mostly] in the first two), may I posit that you're not a late-comer to anything yet!
- davesims 15y agoA big ditto from me at 42 (programmer/musician)
- gtani 15y agoNot a musician, but 14 years of lessons in piano, woodwinds and percussion as a kid, and recently acquired keyboards, guitars and clarinet. Recently I started coding in a language i was sort of afraid of, haskell, and playing an instrument I was afraid of, fretless bass, at the same time. I had a "Dammit, go somewhere, do something" moment. Which reminds me that i was going to google for how string, brass and woodwind players aren't locked into equal temperament, they can intonate as they like.
- drumdance 15y ago
- tibastral2 15y agoExcellent Will do more of that stuff as soon as I'm able to work less (soon) Jazz is life Happy to see that kind of sruff on hn :
- robocop 15y agoSorry to be pedantic, but a 9th chord actually has a 9th and a _flat_ 7th. For example C9 has the notes C-E-G-Bb-D. 9th chords are part of the dominant group, not the major group. A chord with a 9th and a 7th is a _major_ 9th. For example, the chord C-E-G-B-D is Cmaj9 (sometimes written C triangle 9).
- jtauber 15y agoWell, I'm assuming by convention that the 7th is flattened, as the notation "C7" does.
- robocop 15y agoI think the convention for chord notation is different to the convention for scale degrees. The 7th note in C major is B, but a C7 has a Bb.
- _mayo 15y agoMajor 7 chords are explicitly written as such. So in the case of a C chord with a major 7, it would be noted as Cmaj7.
- robocop 15y agoTBH I think you should delete this post. I think I would have been confused had I read it when I was learning harmony theory. Please see http://www.idlewords.com/2005/04/dabblers_and_blowhards.htm http://www.idlewords.com/2005/04/dabblers_and_blowhards.htm.
- oxxx 15y agoFor the record, F7 wants to resolve to Bb, not C.
- jtauber 15y agoyep, corrected.
- owensmartin 15y agoI'd like to tack on another key feature to these 13th chords (no pun intended)-- and that is of spreading out the voicing across the instrument's (usually piano's) range. There's a sort of rule of thumb in jazz that the only interval that sounds genuinely BAD is the flat 9. Try it on your piano right now (say, C and C# an octave up). Notice that a similar interval, the major 7 (C and B) sounds pretty, even though the notes are kinda clashing because they're so close. But on the other hand the flat 9 sounds GREAT if you voice it right. To see this, hit a low C, then E, B-flat, and D-flat. Similarly this chord works with all the other color tones: 9s, 11s, 13s. I think ultimately what makes jazz piano truly musical is when the musician has spent a lot of time trying out different voicings, spreading them out or crunching them in, and listened to each one to see which sounds the best.
- josscrowcroft 15y agoFantastic article, short and sweet. Reminds me why I did music at university!
- tripzilch 15y agoA few people in this thread mentioned that the notation used in this article is in fact quite simple and could be learned in 10 minutes or so. Personally I find the article quite incomprehensible, and I thought I knew a littlebit about music theory :) Just a tiny bit, however, and I don't even play an instrument--I always found it very hard to even just make a passable tune on a tracker/software synthesizer. Even though I love music and spent a lot of times creating mixes and mash-ups in software such as Ableton Live and Traktor (which were pretty good according to those who heard them both on and off the dance floor), as well as coding software synthesizers, instruments and sound effects (which were also pretty good according to my rankings in 4k demo-competitions over 10 years ago). I wonder, can anybody perhaps provide a couple of links to some good introductory articles that would tell me about how to interpret the things discussed in this article? (I'm willing to spend more than just 10 minutes on them, btw ;-) )