Why 13th Chords

http://jtauber.com/blog/2008/09/23/why_13th_chords/

by llambda • 15 years ago

131 92 15 years ago

jtauber.com

mml2• 15 years ago

Well, that pretty much explains why people have a hard time "getting" music theory. Gibberish+Goobeltygooksus7

diN0bot• 15 years ago

Ironically, 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• 15 years ago

The 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.]

nandemo2• 15 years ago

I 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).

dextorious8• 15 years ago

Actually 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.

mml2• 15 years ago

I'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."

fredsanford• 15 years ago

Piss poor black kids that never went to school can still have good ears. It's all about the ears.

sudoscience• 15 years ago

I disagree. I was a professional musician at one time and regular expressions are far easier than music theory, in my opinion.

code_duck• 15 years ago

It 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.

swiecki• 15 years ago

Very much baby steps in jazz music theory, but this will probably be helpful to some people!

jtauber8• 15 years ago

yeah, 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.

chrisguitarguy2• 15 years 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!

jtauber8• 15 years ago

yep, I'll tweak it to say Cadd2 / Cadd4

jergosh2• 15 years ago

WTH is this doing on HN?

walrus• 15 years ago

It'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
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http://ycombinator.com/newsguidelines.html

agumonkey2• 15 years ago

Einstein thought in musical ideas.

jergosh2• 15 years ago

Not sure what this proves.

dextorious8• 15 years ago

From 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).

mirkules3• 15 years 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• 15 years ago

No, 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.

jtheory4• 15 years ago

Definitely 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.

mjw• 15 years ago

Definitely this.

It may be counter-productive to over-analyse these things too, at least beyond a point.

I ran myself into a bit of a dead end with jazz piano trying to be ever more inventive when it comes to harmony. I probably thought about it too much. The result was that I ended up pursuing it to its conclusion as far as my abilities went and then feeling like I had nothing left to do but flog a dead horse with the same improvisational tricks. Then I got tired and rusty.

(Any tips from musician hacker types here on how to get past this kind of 'improvisor's block' ?)

I guess my advice with hindsight would be: trying to get better by being cleverer with harmony hits a dead end. Instead try to get to a point where you can feel harmony in a textural way. Theory can help with that, but a little of it goes a long way, try to get as much as you can just from playing and listening. Watch out though as it's easy to get stuck in a feedback loop doing that which converges on a local optimum that bores you. Seek input into the loop which is outside your improvisatory comfort zone. And not necessarily in the sense of technically harder -- just different.

The best stuff I've been able to play has been when I'm in a state of mind when I'm able to play texturally without thinking very much about what I'm playing, but it's quite rare these days.

the_cat_kittles2• 15 years ago

voice leading is always a good thing to think about

bryanh• 15 years ago

Let's be honest, a large majority of charts follow convention, if not transparently in the case of a straight "I Got Rhythm" changes or blues, but more opaquely with substitutions or variations of predefined changes. This is true with jazz and even more so in pop music.

A trick I always use it to transpose into a common key and watch the overlap develop. It may surprise you to find most tunes are the same I IV V or II V I progression in various keys...

Of course, blindly creating something from such patterns is a not very fulfilling, but adding your own variations and color can be. Or, deviating from convention for effect becomes viable when you deeply understand those conventions.

tmroyal• 15 years ago

"Music was born free; and to win freedom is its destiny." - Ferruccio Busoni

baddox• 15 years ago

So, 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• 15 years ago

These 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.

jtauber8• 15 years ago

but 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• 15 years ago

This 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.

gruseom4• 15 years ago

I 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?

jaylevitt• 15 years ago

Been out of Berklee a few years, but a few nuggets that might shed light:

In Jazz theory, the 7th scale degree is part of the chord. C7 isn't C (C+E+G) plus a B♭; C7 is its own flavor of C chord, C + E + G + B♭.

More generally, the ^3 and the ^7 are the two most important notes in the chord. The ^3 tells you its quality (minor, major) and the ^7 tells you its, uh, seventhness (dominant, diminished, maj7). It's common for players to leave off the 1 and the 5; they're low-information notes, and those fingers are better put to use playing the tensions, which are "chord extensions", the 9th, 11th and 13th. Critically, all three tensions are considered part of the chord, unlike Csus4, which means substitute a 4 for the 3, and don't play the 3.

C9, C11 and C13 can exist, but you won't often find C13 in particular like that. There's a whole set of memorizable rules to tell you which chord scales go with which chords performing which functions; if that C is a I chord in the measure, you're not likely to see a C11. You may see a C7(11), or C7(add11), which is IIRC the C chord plus an 11th note - but not the 9th. Then there's C7(#11), which you'll often find when C is the IV chord, 'cause the IV chord gets a Lydian scale.. but now I forget how that explains anything.

C+E+G+B♭+D+F+A can also be looked at as D-/C7, and often is. That whole "Upper Triad" polychord stuff is a whole semester to itself.

nandemo2• 15 years ago

> 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?

Changing the question to C11 to simplify: a possible answer (take it with a grain of salt) is that C11 got to mean "C+E+G+B♭+D+F" because in classical harmony you can't just stick a 11th there without the 7th and 9th. The 11th interval (C to upper F) is dissonant; not as much as the 4th, but still dissonant. However, it is consonant with the 7th and 9th. That is, B♭ to F is a 5th, and D to F is a 3rd, or simply: B♭-D-F is a triad.

The question now is, why do books say C11 means "C+E+G+B♭+D+F" but in practice it's often voiced as "C+E+G+B♭+F"? I think the simple answer is that in some traditions (like jazz) people are OK with that dissonance; and in some harmonical contexts (when the function of the chord is such and such; say jaylevvit's comment), we can omit such and such notes because the chord still "works". If you doubt, play several voicings. The "proof" is in the sound.

(but honestly I'm not fully convinced by that answer. In particular I dislike the notational mess).

kroger• 15 years ago

That'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

[2] http://www.youtube.com/watch?v=_Ic3ZLj5RPw#t=3m12s

scrozier5• 15 years ago

Grew 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?"

dextorious8• 15 years 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.

scrozier5• 15 years ago

Absolutely, 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.)

the_cat_kittles2• 15 years ago

mmm, I wouldn't be so sure. Both can be about as "out" as possible, or about as "complex" as possible. I would say that, in general, contemporary jazz musicians have thought about harmony about as much as contemporary classical composers. I mean, they focus on different aspects of harmony, but I wouldn't claim that one school is miles beyond another. Its almost a silly comparison, anyway.

marchdown• 15 years ago

I'd love to listen to something like this, but don't know even where to start looking. Could you provide some pointers?

davesims3• 15 years ago

I went to UNT as well (not for music) and I'm still in Denton and work remote from here, not because it's a great tech hub but because of the music scene and culture I want to raise my kids in.

A good number of the best coders I work with right now are fantastic musicians, including Chad Fowler who is a phenomenal sax player, and another senior dev on my team who is a superb UNT-trained jass pianist. We talk about this all the time -- so many good coders are also musicians.

Great story about Knuth, I was never aware of that quote!

sea6ear• 15 years ago

Interesting. I'm in Denton also. Went to UNT thinking of studying music but ended up in Math/Physics, two of the guys I work with currently were in the UNT music school before getting into programming/tech.

Also married to a UNT music graduate who I'm hoping to lure into programming :-)

guscost• 15 years ago

That 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• 15 years 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.

scrozier5• 15 years ago

Jgrubb, 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!

davesims3• 15 years ago

A big ditto from me at 42 (programmer/musician)

davedx• 15 years ago

33 year old programmer just getting into music again here! I too love these posts as I'm just starting to find my way around music theory :)

mirkules3• 15 years ago

Ditto. 31 yo programmer as well, just bought my first Gibson Les Paul after 15 years of playing. I feel great because it's forcing me to learn new things so I don't have the feeling I am letting the LP go to waste.

I would love to see more music-related posts. Math and music are so closely related, I really think it switches on a creative part of the brain that is used in math/programming too.

tibastral2• 15 years ago

Excellent 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 :

robocop3• 15 years ago

Sorry 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).

jtauber8• 15 years ago

Well, I'm assuming by convention that the 7th is flattened, as the notation "C7" does.

robocop3• 15 years ago

I 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.

oxxx• 15 years ago

For the record, F7 wants to resolve to Bb, not C.

jtauber8• 15 years ago

yep, corrected.

owensmartin• 15 years ago

I'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• 15 years ago

Fantastic article, short and sweet. Reminds me why I did music at university!

tripzilch3• 15 years ago

A 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 ;-) )

Why 13th Chords

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