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.
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.
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.
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 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.
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.
What I wonder is mostly if that would sound any better.
> It defines a half-step as the 12th power of 2
Uh, instead, "12th root of 2".
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".
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.
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.
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.
I 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.
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# + G
So 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 VII
Why 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 like
C–G–Am–F (repeated over and over until you get a Grammy)
and expressed it as
.. 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!
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.
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.
This link has some information about this:
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.
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).
Nearly all music we hear now is evenly tempered, but that is a pretty recent innovation.
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^11
The 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.
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.
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.
> 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.
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:
Great minds... ;)
Looks like 1-4-* is more popular.
Try David Cope:
And xoxos' "BreathCube" and "New Blend":
There 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.
It 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.
Also, 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.
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, 5
And if you only notate the transitions:
1 -> 4 -> 1 -> 5 -> 4 -> 1 -> 5
Anyways, I mostly produce electronic music and this blues progression just gave me a good idea :)
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.
'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.'
That 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.
A table of chord progressions that took into account sales figures would look very different.
The size of the bars is normalized, not necessarily indicative of probabilities. That's why I isn't any bigger than the rest.
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.
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... )
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...
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.
this 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.
How can such a small sliver go into flat6(b6) and yet a much thicker sliver flows out into flat7(b7)?