282 points by _zhqs on April 17, 2015 | hide | past | favorite | 108 comments

 If anyone has interest in harmonic theory and why I/IV/V progressions are so pervasive, I highly recommend "The Harmonic Experience" by W.A. Mathieu.He really gets into the harmonic series, and how intervals are really low prime ratios.I read this book after being a professional musician for 15 years and it was an ear opening experience. there are lots of great singing exercises for really hearing the overtone series.it's pretty much the "art of computer programming" for music.
 If you are more into the songwriting / application side of music theory, definitely check out "Hooktheory I" http://www.hooktheory.com/music-theory-for-songwriting, which is the music theory / songwriting book written by the creators of the API used in the OP.
 That book looks really interesting - thanks for the recommendation.What still twists my melon about harmony is the Pythagorean Comma.Harmony equating to integer ratios seems so right... But the fact that a perfect 5th on a piano isn't really a perfect 5th troubles me at some existential level.
 The comma is not a big deal : it's a problem caused by tone equalizing (aka temperament). Think of instruments as ladders : they have all the same steps, but start at different heights. When combining several types of instruments, the resulting steps are not aligned.Equal temperament solve that problem by normalizing the steps' absolute height. It's a trade-off between the instrument's perfect harmony, and the orchestra's overall one.
 I don't mean to be rude, but I'm not sure you understand the comma. It has nothing to do with combining types of instruments. It's a problem that exists even with a single instrument.The problem is that, even on a single instrument (say a piano), if you start on some note (say C0), going up seven octaves should land you on exactly the same note as going up twelve perfect fifths (C7). The problem is that the precise tuning of that C7 is different depending on if you followed the perfect octaves or perfect fifths.If you followed perfect octaves, which have a ratio of 2/1 (or just 2), C7 should have a tuning of precisely (2^7)·C0 = 128·C0. If you followed perfect fifths, which have a ratio of 3/2, C7 should have a tuning of precisely ((3/2)^12)·C0 = ~129.74·C0. The difference between these two is the Pythagorean comma.Equal temperament solves this problem by keeping the octaves perfect (2:1), but compromising on everything else. It defines a half-step as the 12th power of 2, so a fifth ends up being a little narrower than a perfect 3:2 perfect fifth.
 I'd recommend "How Equal Temperament Ruined Harmony" if you are interested in the nuances and trade offs of the imperfections of tuning.
 I understand that pianos have to pick a frequency for each key.I wonder if there is any effort in electronic instruments to produce "better" frequencies on the fly? I'll explain:On a piano hitting C+G plays something close to a perfect fifth.An electronic instrument could move the G slightly to produce a perfect fifth when that key combination is played.
 It's not just a matter of 'better' frequencies. It's trivial to have a softsynth or something similar set up to use just intonation (and many modern composers have experimented with this), but that has practical problems of it's own. Problems which were the very reason that equal temperement took over in the first place. This page has some wonderful examples http://www.nesssoftware.com/home/asn/homepage/teaching/exp-l...
 jpitz on April 18, 2015 You cant do that, without a large effort in music education or ensembles of all electronic instruments implementing this feature. Everyone else will be out of tune.Edit: you could do it, but you'd better implement it on a feedback system that can re-tune in a hundred milliseconds or so.
 I'm just talking about an individual keyboard, though if all instruments are digital, which is pretty common these days, you could have a whole orchestra dynamically adjusting pitch to make "perfect" harmonies.What I wonder is mostly if that would sound any better.
 graycat on April 17, 2015 Nice. I'd go with the 2^7 and not the (3/2)^(12).> It defines a half-step as the 12th power of 2Uh, instead, "12th root of 2".
 foobarrio on April 17, 2015 I've always seen equal temperament similarly to digitizing or any other form quantization. It's "close enough". Any type of dissonance heard in what are supposed to be perfect intervals is like grain in film.
 m-photonic on April 18, 2015 The Pythagorean comma is nothing to worry about -- it's tiny and more or less negligible. It's the syntonic comma that's the killer.The fifths in equal temperament are completely fine, but the thirds are really quite a ways off from the harmonic 5/4 major third. I would recommend experimenting with the traditional meantone tuning system if you're interested in this -- it offers almost as much flexibility as equal temperament (with 6 adjacent keys on the circle of fifths being free of wolf intervals), and it lets you play with "real thirds".
 im3w1l on April 17, 2015 Just intonation is just a theory. In practice slightly detuned intervals sound good. Imo they can even sound better than when they are perfectly in tune.Sometimes musicians deliberately use detuning to create a sound, for instance in the "chorus effect".EDIT: Another interesting fact is that pianos aren't actually tuned to equal temperament. The intervals are tuned slightly bigger than it would dictate, to accommodate pianos' slightly inharmonic overtone series.
 analog31 on April 17, 2015 In my view all it means is that an approximation of perfection is good enough. And the notion of temperament only really applies to keyboard instruments. Strings are tuned to perfect intervals, and even 'good' intonation of fingered notes is a matter of interpretation. Wind instruments are a hodgepodge of compromises.
 > Wind instruments are a hodgepodge of compromises.It depends on the wind instrument and the setting.For woodwinds, yes, this is typically true; it's very difficult to adjust the tuning of a particular note on-the-fly.For brass, however, this becomes less and less true; more sophisticated brass instruments will have easily-accessible "tuning slides" (in addition to the main one) meant to adjust the tuning of a particular note, making them well-suited for situations where absolute tuning is necessary (it's really useful for brass-only ensembles) and where temperament is dominant (like orchestral and symphonic settings).This is taken to the extreme with the trombone, which is basically just a giant tuning slide with a mouthpiece and bell, allowing for effectively-unhindered tuning flexibility akin to that of a chamber instrument or a human voice.
 It was all too easy for me to adjust the tuning of any particular note on my oboe, unfortunately usually in the wrong direction. The violin players in front of me, who had much better pitch recognition than me, would shoot me dirty looks and I'd get my pencil out to mark up the sheet music with arrows pointing up or down.
 Ah yes, forgot about oboe (and bassoon and English horn and double-reeds in general), which tend to be much more sensitive about embouchure when it comes to pitch if I remember right.
 analog31 on April 17, 2015 All good points. I played flute at one time, and there were notes that had to be shoved around a bit, unless hidden in a fast passage, such as C sharp. And I'm told that french horn players use the hand in the bell as a tuning slide.
 > And I'm told that french horn players use the hand in the bell as a tuning slide.You can do this, since how far your hand is in the bell can determine pitch up to even a whole semitone or more (I forgot which way, though, but I think it goes flat as you shove your hand in further; it's been a few years since I've played French horn on any semblance of a routine basis, and I don't have one on hand (those things are damn expensive...)). However, this will also affect tone; the further you shove your hand in, the more muffled it'll sound.French horn players usually opt for double-horns (F/B-flat) in order to avoid needing to use their bell-hands for tuning; since both "sides" (the F side and the B-flat side) of each rotor can be tuned independently of one another, it means that a skilled French horn player who's learned how to transpose F-keyed notes to B-flat-keyed fingerings (which is actually pretty easy if you already know how to play a bass-clef'd valved brass instrument like a baritone or euphonium or tuba, since F-key and bass-clef C-key have the same note positions on the staff, so you just need to be aware of various differences in accidentals and you can transpose very easily) can pick either an F-side fingering or a B-flat-side fingering for a given note depending on which one is closer to the desired pitch.
 meggar on April 17, 2015 I think there is a similar situation with guitar tuning where the G string can either be tuned to a 4th above the D string, or a Maj3 below B string, which are not exactly equal, so guitar chords are usually a tiny bit out of tune.
 No, the Maj3 interval between the 2nd and 3rd strings on the guitar is unrelated to this issue. It's just the fret spacing on the guitar that causes it to have equal temperament and therefore makes chords slightly "out of tune".
 Incidentally, a just (non-tempered) guitar fingerboard might look something like this:http://jsnow.bootlegether.net/cbg/fingerboard_at_a.svgI swapped fingerboards on an old Harmony Archtone with one based on the above design. Admittedly, 20 notes per octave may have been a bit much; it's kind of awkward to play. The next one I do will be simpler. Sounds nice, though.
 Just remove the frets, problem solved.
 Fretless is difficult to play accurately, especially for chords. Also, you get a louder sound from frets because your fingers aren't muting the strings quite so much.
 Of course, but it does solve all such intonation problems.
 bsder on April 17, 2015 22 frets can make some of the extended harmonies much, much closer to ideal.
 I'm reading that now! Sadly, after the first section where he derives the diatonic scale, I'm getting a bit lost. He stresses how important it is to play along with a musical instrument while reading, but I've been insistent on just reading in bed (which is how I do all my reading). But that first section is great.
 For non-musicians, here's some terminology behind this:There are 7 natural notes in (western) music: A, B, C, D, E, F, G (the white keys on a piano keyboard)... plus 5 accidental notes that half-way between: A#, C#, D#, F#, G# also known as Bb, Db, Eb, Gb, Ab ... the black keys on a piano keyboard.# means sharp (go up in pitch one-half step)b means flat (go down in pitch one-half step)7 naturals + 5 accidentals = 12 notes in the chromatic scale. These are the primary colors in music.Chords are like secondary colors. Chords are combinations notes that harmonize well when played together. Typically chords are 3 or more notes spaced at one note or one-and-half notes apart. So the C Major chord is C + E + G played together.Minor chords, noted with the lowercase "m" are made by dropping the "third" note down a half-step, so "C minor" or "Cm" is C + Eb + G, can also be expressed as C + D# + GSo put it all together, F#m means "F sharp minor" so the root note of the chord is "F sharp" and the next note from the F major chord, A#, is dropped down a half step from its major position to A natural, so the notes are F# + A + C#Fortunately when playing an actual instrument you only memorize your finger positions to make the entire common chord shapes rather than thinking about the individual note under each finger.The hook melody of song, the chord sequence that is repeated throughout the verse or chorus, is expressed as chord progression in Roman numeral 1 to 7:I II III IV V VI VIIWhy did we switch from letters to numerals now? Because lettered notes A, B, C, D, E, F, G are fixed positions (ie. hard-coded) and the numerals are relative positions (ie. abstracted) So the Roman numeral expression is a more general form of the melody structure. This lets you takes a progression likeC–G–Am–F (repeated over and over until you get a Grammy)and expressed it asI–V–vi–IV.. which you can just shift up or down to another key and everybody loves your new hit song, you win another Grammy, and few people realize it's same damn song as before with new tempo and new lyrics!http://en.wikipedia.org/wiki/I%E2%80%93V%E2%80%93vi%E2%80%93......
 But the question is, what's natural about the Naturals, and whats accidental about the Accidentals? Because taken together they are just 12 equally spaced notes.
 Accidentals are notes outside of a scale, and a scale is an arbitrary concept chosen by some ancient people who decided certain notes sound good together.
 tajen on April 17, 2015 Harmonics. They resonate well together because they have some common frequency. 13 equally spaced notes wouldn't match on multiples of 2, 3, 4 and 6.Example: The major scale (C, D, E, F etc) are the notes 0/12, 2/12, 4, 5, 7, 9 and 11. You'd expect the 6th note to sound nice, wouldn't you? Wrong: The scale is logarithmic.A nice C chord is made of 0th, 4th, 7th/12, which are 523Hz, 659Hz, 783Hz. Notice how the second frequency is 125% higher and the last 150% higher. So they have harmonics in common and it makes them sound well together.
 Yes (from the little I know) a major aspect in our hearing is that nature doesn't produce pure sinusoids. Mechanical vibration materials is bound to have a series of resonances multiples of some basic frequency. So if you have a single person, or single object, emitting sound, you expect to see this nice harmonic lineup. When the fundamental frequencies don't have a pair (a,b) s.t. a * f1=b * f2, their harmonic multiples don't match and you can tell something is odd.For f2=125% f1, for example, every 4th harmonic from f2 lines up perfectly; for f2=150% f1, every 2nd harmonic lines up; for f2= 200% f1, every harmonic actually lines up. I guess it's like looking at combs with different spacings and finding ones that superpose neatly.
 ta83838 on April 18, 2015 The notes of the scale evolved gradually. Originally only the 7 notes of the diatonic (major) scale were used, sometimes fewer than seven. But if you take one of the notes in a diatonic scale other than the first and try to start a new scale starting with this note, you will find that you need new notes, the existing 7 don't allow you to create a new scale that "sounds the same" (has the same ratios between the frequencies of each note). The new notes that need to be added to allow these new scales became what are today the accidentals.This link has some information about this:
 snorkel on April 17, 2015 I don't see a good online reference, maybe I read this a guitar book somewhere, but essentially the tones for A, B, C, D, E, F, G notes were picked out by the ancient Greeks (who referred to them as Alpha, Beta, Gamma ... so on) In fact Pythagoras came up with a mathematical tuning system http://en.wikipedia.org/wiki/Pythagoras#Musical_theories_and...The 7 natural notes are based on a 7-tone equal temperament (equal tonal spacing), which gives you enough equal spacing between notes to make nice harmonies (nice complimentary resonance) so this sort of a 7-tone minimal palette, and 5 "accidentals" fill the spaces in between those 7 tones to make a fuller 12-tone equal temperament palette.
 The 7 natural notes are based on a 7-tone equal temperament (equal tonal spacing), which gives you enough equal spacing between notes to make nice harmonies But they are not equally spaced. The tonal gap between A and B is twice as big as the gap between B and C, for example (look at the frequencies on a logarithmic scale).
 The parent is being slightly confusing by bringing temperament into the discussion. They mean that the 12 notes are evenly spaced on an evenly tempered instrument, which means of course that you don't get the 'perfect' fourth or fifth you would get on a naturally tempered instrument (the frequencies are very slightly off).Nearly all music we hear now is evenly tempered, but that is a pretty recent innovation.
 yodsanklai on April 17, 2015 Good question. I don't know the exact answer, but yes I think there's nothing special that distinguish naturals and accidentals from a "listening" point of view. However, this distinction is handy for written music. For example, when you play a piece of music in a given key, let say G major, the notes are G A B C D E F#, there's only one accidental, so you can put this information in the key signature at the beginning of the score, and you can use only 7 natural notes on your staff. And this works for all "diatonic" keys (where notes belong to a major scale). You can always write your music with 7 naturals.
 But you're just describing a notation, and the notation works OK because of the convention that in any given key you only use 7 of the available 12 tones. But why 7, and why those 7?
 Sounds that sound good together have frequencies that are whole number ratios of each other. (This means they have harmonics that align. If they don't align, you get a beat frequency which sounds objectionable.)A 3:4:5 ratio is a major triad. A good scale should have as many major triads as possible with the least number of notes.So, let's call the root of our scale 1/1. You might want to build a major triad there, so you have 1/1, 5/4, and 3/2. If you build a triad off of 3/2, you'll end up adding a couple more notes: 15/8 and 9/4. If you add 4/3 as a note and build a triad there, you'll end up adding 5/3 and 2/1. 2/1 is the octave, so we can pretend it's equivalent to 1/1, and 9/4 is an octave above 9/8, so we can substitute 9/8.So, our scale is 1/1, 9/8, 5/4, 4/3, 3/2, 5/3, and 15/8, and we have the major scale. It is possible to construct 3 major chords and 2 minor chords (10:12:15 ratio) from those seven notes. If you add 10/9 (slightly flat of 9/8), you can add one more minor chord.By a mathematical coincidence, we can approximate these values pretty closely with various powers of the twelfth root of 2:x = 2^(1/12) 1, x^2, x^4, x^5, x^7, x^9, x^11The latter scale is equal tempered, whereas the former is "just" (untempered). The ET scale has very accurate fourths and fifths, but thirds and sixths are far enough off that they don't sound quite as nice in chords. We tend to put up with that in modern music, though.
 For some reason this is the first explanation of Roman numerals used in chord progression that made sense to me. Thank you!
 > Even though there is a great variety of chords and chord progressions, progressions involving 1,4,5, and 6 are favoured, probably because they ‘sound good’ to our brain.I drive my girlfriend nuts because of this. I don't typically listen to the pop/country songs that are popular with our local radio but when she has it on in the car, every once in a while a song will come on and I'll think "I know this" and start singing an older (wrong) song that fits the progression pretty well.
 Do you really listen to the chords that closely? For a lot of music, the chords are either largely hinted at (bass notes, the lead guitar or rhythm guitar lick, and how the melody move) and if there is an instrument banging out the exact chord progression, it's usually buried under the stuff or at least the vocal.If I'm writing a song, I'm spending almost all of my time doing things tangential to the chord progressions, but rarely any time on the chord progressions themselves. So usually I'll start with a guitar lick or vocal melody, put a chord progression behind it, and then figure out the rest of the arrangement.If there's a song that's memorable to me, it's almost always because of the main melody or guitar, not the underlying chords.I'm only talking about pop-based music here, so rock, pop, country, etc.
 > Do you really listen to the chords that closely?> I'm only talking about pop-based music here, so rock, pop, country, etc.I rarely willingly listen to pop-based music. I don't consciously focus on the chords that closely, but then again I haven't really thought that maybe how I hear songs is different than another person (like the "do you see a duck or rabbit" visual illusion, but with sounds).For the really curious, the first album I really remember getting into as a kid was Paul Van Dyk's Seven Ways album, which is a pretty minimal trance album (compared to today's "edm") with very few vocals. At the same time, I was getting into guitar with my cousins and playing instrumentals such as Metallica's Orion or Call of Cthulhu. Also around that time my stepfather entered my life. He played violin for a symphony and exposed me to the world of classical music.So while I've realized my musical tastes are strange (trance, heavy metal, classical are still my go-to genres), I haven't really payed attention to how I listen to music.
 twerquie on April 18, 2015 OP mentioned the pop/country genre, which is typically very heavy-handed with the chord progressions.
 I'm fond of this video that illustrates this: https://www.youtube.com/watch?v=oOlDewpCfZQ
 That video is, of course, linked in the article... ;)
 This is a different one actually than the one in the article!
 That is incredibly beautiful. :')
 1-4-5 songs are great for jams for that reason. You can play along to a lot of songs even if you don't know them.
 I created a similar visualization of part of HookTheory's data:http://briancort.com/songviz/At the time they didn't have an API, so I emailed them and they sent me a sample to work with. Would be interesting to see how it handles such a large amount of data.If you're interested in this sort of harmonic analysis, you might also like a little visualization I created of the harmonies within a chord:http://briancort.com/chordviz/Great minds... ;)
 I'm the author of this article, and I signed up to ycombinator just to tell you I can't get over your visualization. It's just friggin top. Any chance you feel like explaining how you did it? mexindian@gmail.com
 To see how popular the 1-5-6-4 progression is you need only watch Axis of Awesome ... https://www.youtube.com/watch?v=5pidokakU4I
 Though Pachelbel's Canon is twice as long; it has a iii between the vi and the IV, and a I IV V tacked on the end.
 Right. You'll notice this in the Pachelbel rant; he very specifically only sings "da, da-da-da, da-da da-da-da-da-da-da--" (the first half of the violin theme) before abruptly cutting off because with this progression you essentially only get the "first half" of the Canon.
 markbnj on April 17, 2015 Awesome! Hadn't seen that one before. I think Axis of Awesome almost ripped him off.
 I was surprised though to see that in the data the 1-5-6-4 progression is not the most common. Maybe I'm reading it wrong?Looks like 1-4-* is more popular.
 I think what the amusing videos linked above show is that 1-5-6-4 is very common in certain styles of music, especially modern pop. But when you consider music in its entirety then I'm not surprised to see it recede. So much folk and blues, for example, are built around completely different progressions.
 Good point. I guess my musical experience is limited to the rock/pop side.
 Sounds like something that could be used to generate endless but still decent elevator music with some Markov chains.
 It's funny, whenever I look up algorithmic music, it never seems to be the usual pop cadences. The Phd who make this their field seem to prefer atonal or dissonant generated music.
 The field of generative music is very under-researched, but there are some great things out there, including tonal and "harmonious" ones.Try David Cope: https://www.youtube.com/watch?v=CgG1HipAayUAnd xoxos' "BreathCube" and "New Blend": http://www.xoxos.net/software/software.html
 mjn on April 17, 2015 I think of classical music as a more "canonical" target than atonal or dissonant music, though it depends on what community of researchers you're looking at. One of the more famous researchers is David Cope, who spent much of his time on algorithmically modeling composition in the style of J.S. Bach. There's also an intermittent stream of papers on jazz improvization, e.g.: http://scholar.google.com/scholar?q=jazz+improvisation+icmcThere is a good deal of avant-garde experimentation as well, in part because computer music has in many places/eras been larger in the field of music, rather than the field of computer science. Contemporary composers like Iannis Xenakis, Karlheinz Stockhausen, Pierre Boulez, etc., picked up and developed new technologies as they became available. But they were avant-garde composers interested in using these technologies as part of their compositional toolkit, not CS researchers interested in automating generation of music per se.One driving question for a certain group of composers is along the lines of: how can this new technology/technique help us make new, different music? Which leads to different experiments than the question: how can this new technology/technique help us automate the production of existing music? Sometimes that still ends up popularly oriented, e.g. in the '60s and '70s there was quite a bit of crossover between avant-garde synth experimentation and popular music, with Brian Eno as one hub in particular, and Moog synths finding their way onto all sorts of top-charting albums. Other times it's ended up less popularly oriented, like most of the granular-synthesis music.
 I've actually considered using this approach to build dynamic video game music.
 Have you seen the 'infinite jukebox'?http://labs.echonest.com/Uploader/index.htmlIt stretches or compresses existing music by jumping back and forth to parts of the piece that sound similar, which could be handy for dynamically adapting the timing/duration of existing pieces to the players situation.
 itsjareds on April 17, 2015 That is an awesome idea. I can imagine it would be cool in your standard one-on-one fighting games where the music could get more intense when then battle becomes more intense.
 "So for example, the transition 4->1->5->6 is one of the most popular ones" The graph does not show this or I'm misunderstanding something. The most popular looks like 1,4,1,5Also, what does the double, triple numbers mean? 664, 66 in the fist column. I know some music theory, but the article's explanation is rather confusing.
 He just said "one of the most popular", and 1 -> 5 -> 6 -> 4 is indeed the ridiculously common progression of "four chord rock".But if only the changes in chords are being notated, I bet 1, 4, 1, 5 comes from the 12-bar blues, which is even more widespread than four-chord rock. The 12 bars that dominated the 20th century could be notated as:1, 1, 1, 1, 4, 4, 1, 1, 5, 4, 1, 5And if you only notate the transitions:1 -> 4 -> 1 -> 5 -> 4 -> 1 -> 5
 Thanks, this makes sense, however the visuals did not really show the common 4 chord song pattern.Anyways, I mostly produce electronic music and this blues progression just gave me a good idea :)
 It just says "one of the most popular", not "the most popular".The double and triple numbers are Figured Bass notation (see: http://en.wikipedia.org/wiki/Figured_bass ).So, if you have the 6th and it's the second inversion, it would be 664. For example, in G that would be the second inversion of Em.
 the first number is the chord number (which should have been notated as a roman numeral, and should have differentiated between major and minor with capital and lowercase). The rest of the arabic numberals indicate the inversion using figured bass http://en.wikipedia.org/wiki/Figured_bass
 He mentions this under "Caveats":'There are several limitations to this assessment since the Hooktheory API wasn’t really intended for this type of analysis. For example, it doesn’t mention whether “6” is “vi” (minor) or “VI” (major), which is kind of a big deal.'
 > 1,4,1,5That is indeed very popular, off the top of my head, "Free Falling" by Tom Petty.However, I am puzzled because 1,5,6,4 seems much more popular in my experience, and it doesn't seem that high in that data.
 Top selling != widely used.A table of chord progressions that took into account sales figures would look very different.
 I am confused. Is "Start" always a 1? Then how can the first chord change also be a 1?
 Nope. 1 is the root (or tonic) of the key, not necessarily the first chord.
 Then what is the first chord? The beginning is labelled "Start" What does this mean? Either less than 25% of songs start on the 1 (no way this is possible) or the second chord is mislabeled as a chord change when it stays the same or those with a 1 in the second column started on a chord other than the root and instead of listing that chord, the data is thrown away. Something is messed up here.
 > Very lazily, I just normalized all probabilities across each transition so that each transition “mega bar” is kind-of the same height. I’m sure there’s a better way to do it, the community is invited to improve!The size of the bars is normalized, not necessarily indicative of probabilities. That's why I isn't any bigger than the rest.
 drostie on April 17, 2015 Why is there "no way this is possible"?The 1 is the key, which is to say, the lowest note played in the progression. If it's less than 25% then that means that 4-chord progressions frequently do not choose their minimum as the first note.
 If you were a musician you'd know that in popular music the vast majority start on the 1 chord. Classical music probably does this less frequently, but it's nowhere around 1/5 of the time.
 tshaddox on April 17, 2015 "Start" is nothing. I'm not sure why they even put it there. The first chord of the songs are represented by the second column.
 Someone asked this on reddit[1]. The answer the author gave was: "the "start" is whatever the api gave for each song, which in turn is the first chord that was entered by the user that uploaded that song, which is of course, not standardized. So it's for sure not the start of songs, or the bridge or whatever... it's this and that."
 The way I interpreted it, the first chord starts at the second column. The "start" state is necessary so you can see the distribution of songs among the first chords.
 This would mean that less than 25% of songs start on the root chord. That can't be true. I would expect a distribution of about 90% 1 chord with a smattering of others taking up the rest.
 This is great work. What I really want now is a version where you can listen to the chords in the chart individually and in progression!
 Ask and you shall receive. Hooktheory's Trends tool lets you see and hear all the chord progressions of the individual songs used here. As mentioned in the article, this analysis actually used our free API for accessing our chord progression database (I'm one of the creators of the site).
 Do you have to be signed in to see this feature? I can't find it. Neat site!
 When you select a progression, click on one of the songs.
 Very nice presentation, although I'd prefer the graph settle to a steady state a few iterations earlier.Ob Lou Reed quote: "One chord is fine, two chords are pushing it. Three chords and you're into jazz." ( http://www.rollingstone.com/music/news/lou-reed-velvet-under... )
 Now I wonder if anyone has gathered data on vocal ranges. I'd love to be able to query for a list of songs in my range.
 Just learnt about http://www.hooktheory.com/ thanks to this article, and I must say that I really love the concept of the website. I've always had music production as a hobby but w/o proper music theory background I struggled to analyse popular songs. This makes the process really easy and fun!I feel this site could be huge with a couple of tweaks: real-time and proper midi interfacing. I hope the site will evolve towards more complex collaborative songwriting...
 Don't know the technical aspects of music enough to understand what is going on here. Would like examples from real songs to illustrate.
 Most songs are based on chord progressions (a sequence of several chords) that is repeated through the whole song. More precisely, there maybe different chord progressions within a given song. For instance, one per section (intro, verse, bridge, chorus, outro and so on...).In theory, there are tons of possible chord progressions but not all of them sound good. In practice some are extremely common (like I - IV - V in rock or ii - V - I in jazz) and can be shared across very different genres. Google "common chord progressions" for many examples.Now for the numbering system. Chord progressions can be described as a sequence of numbers that define the chords in a relative way (in CS terms, think of a relative path in a file system VS an absolute path). In music, what is important to the listener ear is the relation between the notes, not so much the absolute pitch of those notes.Example : A - D - E and E - A - B are the same progressions (I - IV - V) in the key of A for the first one, and in the key of E for the second one.Things get more complicated because you can have different quality of chords (minor, major, dominant...) but you get the idea.
 > ... how will humanity ever learn to be creative if everyone keeps doing the same thing over and overthis charted for the yearly top 100 selling songs over the last ~80 years would clearly show the dumbing down of popular music. The Standard Songbook contains music that everyday people sang and danced to, but has a creative variety of chord progressions.
 I'm a bit surprised that one of my favorite "poppy" progressions -- bVI bVII I -- isn't more common. Or, is it that the database isn't very exhaustive yet?
 For anyone rather confused, I wrote the majority of this wiki article on introductory music theory. http://battleofthebits.org/lyceum/View/I+Am+New+To+Music+The...
 This is really fascinating. I'd be curious to know how different genres compare, especially pop music.
 This is a cool post. There's also a bunch of really interesting related analysis on the excellent hookyheory blog http://www.hooktheory.com/blog/
 Somewhat relevant, The Million Song Dataset: http://labrosa.ee.columbia.edu/millionsong/
 Can someone please explain what the 646, b7, 36, and other numbers mean? They discussed it briefly, but I didnt really follow. Sorry if its a noob question. Looks great though!
 Seems like you could take rap genius and this resource and combine them into a Bayesian pop song generator. (Melodic and rhythmic progressions are the next step).
 Something doesn't look right.How can such a small sliver go into flat6(b6) and yet a much thicker sliver flows out into flat7(b7)?
 If this was done on the blues the chart might not be as diverse....