Among Dr. Tymozcko's 5 principles of what makes music sound good to the typical western listener is this: "In 30 seconds of a song, you will hear 5-8 different notes." He forgot one extremely important Jimi Hendrix quote: "With the power of soul, anything is possible." My band, Via Audio played at Union hall about 4 years ago, and the band after us was Colourmusic. I was an immediate believer. They brought an amazing amount of energy to the stage. Their whole set was excellent, but the most memorable song was the most simple. That song was "Yes". That song sounds great to the typical western listener - as evidenced at every Colourmusic show by the ecstatic masses of people. From :32 to about 1:14 there are only 3 different notes. (Take that, Dr. T!) From 1:50 to 2:14 there are only 2 notes! (no background vox)
Lead vocal is only on B (1)
Background vocal on G# (6)
Guitar and Bass are on B(1) then E (4), so the implied chord progression is I, IV.
After every IV, we go back to I so we have the plagal (Amen) cadence happening constantly. The feeling of the cadence mirrors the affirmative lyrics.
Then at 2:14 there's a rainbow-like arpeggio that comes in containing the notes of a B7 add 9 chord. Whenever you see a dominant 7th chord, you can watch out for the authentic cadence. We western listeners are conditioned to expect 7th chords to resolve to the major chord a 5th down. That is the case in this song, as the chords resolve from B7 to E. Your western music conditioned brain is being given exactly what it wants over and over in this song. It's brain candy! This I7 to IV device is quite common, especially in blues influenced music but I've never heard it in such a pure form, and executed to the fullest as it is here.
"Tog" from Colourmusic's album PINK is also worth checking out!
"Tog" is quite a rare type of song, tonally speaking, because it is neither in a minor key, nor a major key. It just... exists. The Key is A. Most of the notes are A(1), B(2), D(4), and E(5). By avoiding the 3rd note of the scale, they avoid minor (if there were a C played) or major (if there were a C# played) classification. At a couple of points in the song, the bass hits the major 3rd, but then it's immediately followed by the minor 3rd. Another element to note is the eerie IV chord played on the keyboard in the background. It's happy in a displaced way.
Here's another great track by Colourmusic... also from PINK! This one might be my favorite!
Dr. Dmitri Tymoczko is a professor or music theory and composition at Princeton. He asked the question: "What makes music sound good to typical western listeners?"
With much research and thought, he came up with 5 principles.
1. Melody travels short distances most of the time
2. Chords are structurally similar in a piece
3. Harmony is intrinsically pleasurable or consonant
4. 10-30 seconds in the music contains 5 to 8 different notes as opposed to all 12 notes in a chromatic scale
5. Some notes are more prominent than others, establishing a tonal center
On a demonstration on his website, (If you click on "What makes music sound good") he uses a computer to generate notes randomly. Then he applies his principles one by one to the music. The random notes get more and more musical and less random seeming as his principles are applied! Check it out!
Another really interesting thing Dr. Tymoczko did was create computer programs that map out music in geometric shapes. He uses the shapes to demonstrate music following his principles. Watch this whole video below if you have time, or at least check out some of these highlights:
4:29 - what makes music sound good?
7:30 - why have avant-garde 20th century composers have a hard time finding audiences
8:50 - Aleatoric Eatery
10:42 someone asks where those 5 principles came from
11:35 which are innate, which are culturally variable of the 5 principles?
12:50 how does geometry get into the picture
19:27 The ear has developed to care a lot about the distance between notes, but not at all about the position of the notes on the circle. (or keyboard) "It probably has to do with our need to hear similarities in the contour patterns of male/female/adult/child speech."
21:45 Voice leading makes the circle dance
24:00 2 note chords represented on a Mobius strip
26:38 "That's Weird"- singular space.
33:00 Chopin Prelude in Em moves through a hypercube
36:00 Chopin Fm mazurka and his Tritone subbing.
37:25 Chopin's "Feeling for advanced mathematics"
SMALIN
While searching on youtube, I found another interesting way to demonstrate harmony. This person has a midi version of Chopin's Nocturne opus 27, #2 mapped out in dots. The higher the dot is on the screen, the higher the note is in pitch. The dots scroll across the screen as the music is played. As each new note is played, it interacts with the other sounding notes in a certain way depending on what interval the new note is relative to the sounding notes. "Smalin" (the name on the youtube account) shows the relation between Perfect 4ths, Perfect 5ths, Perfect Unisons and Perfect Octaves by drawing a blue line between a note and any note a perfect interval away sounding at the same time. He then draws relation between minor 3rds, Major 3rds, minor 6ths, Major 6ths by illustrating those intervals with a green line. Major 2nds and Minor 7ths are purple, Minor 2nds and Major 7ths are yellow, Augmented 4ths and diminished 5ths are in Red. Here's all that in a short hand chart where "m" means minor and "M" means major, P means Perfect, A means Augmented and d means diminished.
Blue = P1, P4, P5
Green = m3, M3, m6, M6
Purple = M2, m7
Yellow = m2 M7
Red = A4, d5
I find his choice of color interestingly intuitive: His blue intervals are the most consonant or easy on the ears, his yellow and red are the most dissonant. Red is associated with aggression and blue is associated with peace. Notice how much more common the peaceful blue and green intervals are. Does that have something to do with life, the universe, and everything? Let's question and comment.
Note: A guy jump-ropes with a girl as the jump-rope in this video.
HOW TO UNDERSTAND MUSICAL ROMAN NUMERALS: The song starts in the key of E major, so the E major chord is "I". A capital roman numeral means a major chord. Lowercase means a minor chord... so "i" would be an E minor. Then to understand what IV means, you can just count through the musical alphabet to the 4th letter, E, F, G, A. A major is IV. If there's a key change, then there's a new "I", and all roman numerals are relative to that "I" at that point. So when we change to the key of F#: F# is "I" and B is "IV". Moving on....
After the brief drum intro comes the Beach Boys signature big "I" chord, establishing the key and the mood immediately. We're already transcendentally happy. Another voice comes in to reinforce the chord... which leads all the other voices to the "IV" chord.
Next, an important musical device: The voices stay on the IV chord when the bass goes to the V.
INTRO
Vox: I(E)...I(E)...IV(A)...IV(A)... (The vocals are in Roman numerals to show that they are in chords)
Bass: 1(E)...2(E)...4(A)...5(B)... (The bass is in arabic numerals to show that it plays single notes)
That chord: IV in the high register, 5 in the low, (A over B) creates a nice complex harmony: A chord played in the higher register which has a root note a minor 7th above the note played in the bass. In this case, it functions as a V7 chord. You can find examples of this chord in many pop songs that have a more harmonically complicated sensibility. Examples: "Don't stop 'til you get enough", "P.Y.T.", (Probably many more)- Michael Jackson, "Still Remains"- Stone Temple Pilots, "Babies"- Via Audio. The chord always creates the same cozy tension.
VERSE:
I...I...IV...V...
The verse is harmonically a little simpler, just that good old cliche of I IV and V. The melody is quite interesting and deserves its own post. Let's talk about the melody in the comments of this post. (As well as any questions or comments you have on this harmonic analysis!)
PRE-CHORUS:
ii...V...iii...VI(V) (key change to F#)...
The prechorus modulates to F# major through a common modulating device. The ii chord (F#m) to the V chord (B) repeats in a different key, resolving to the I of that new key. When you make a ii_V, you've made an unresolved musical phrase. If you repeat any musical phrase, you can get away with playing it in a different key without sounding too strange. If it's an unresolved phrase, tension can be built with repetition of that phrase in the same key or a different key. The next chords in the song, iii and VI are basically the same phrase as ii... V, a whole step up. (The melody over the iii_VI chords is also the same, just a whole step up!) The VI is a pivot chord, acting as V in the new key of F#. If you want to modulate, a V chord in the new key is a very common and effective way to reinforce a new key. Cadences establish stability in music. The V chord to the I chord is the most obvious example. It's known as the "Authentic cadence". Whenever we hear a V chord, we want to hear a I chord afterward. The prechorus contains the only V chord in the song that isn't immediately followed by a I chord. The Beach Boys are good at giving you what you want, like candy.
CHORUS:
I...I...ii...V...
The chorus is a harmonic cliche: The I...ii...V chord progression in the key of F#. The familiarity of the chord progression reinforces the lyric: "Don't worry baby".
POST-CHORUS:
bVII 2nd inv. (I 2nd inv.)(key of E) V...
The post-chorus establishes the key of the verse as E again through a 3 part authentic cadence. The first chord of the post chorus is a little shocking...sounding a bit like the non-diatonic bVII chord, but then we immediately hear two chords that people have been hearing since the Baroque era. The first chord is also acting as the I chord of the new key in an unstable 2nd inversion, which resolves partially when we hit the V chord and then fully when we get to the I and begin the verse again.
(That I 2nd inversion chord is also called a cadential six-four chord! You can wikipedia "cadential six-four chord" for more details!)
I wanted to talk about melody and texture for this song, but there was a lot to say about the harmony. That other stuff will be discussed in the comments section!
Funkytown started it all. A friend asked for a "merits of funkytown" discussion on facebook. Then another friend on the thread asked for Knights of Cydonia. Then another friend said "You should make a blog!" So I did. Anyway, here are the 2 that started it all.
FUNKYTOWN:
It's appealing because it plays with some very basic musical elements. The rhythm of the first melodic phrase is a series of four 8th notes, (1+2+) followed by two syncopated 8th notes (,+,+), and then the four 8th notes again. (1+2+) So ...rhythmically, that first little synth line (1+2+,+,+1+2+) is a palindrome, which happens to be quite satisfying in line with the human subliminal desire for pattern. Then when you keep repeating and embellishing those four 8th notes throughout the song, you really catch people's attention!
KNIGHTS OF CYDONIA:
For Muse, I'll do harmony, because it seems like the more important element in this song. Muse's appeal is a lot like Bach's. They use canonical phrases and counterpoint, like the first phrase...
Part 1 Part 2
Voice: E E D C# C# B
Bass: E F# G A A B
That phrase follows the rules of classical counterpoint exactly. You can also play parts 1 and 2 simultaneously (Canon). Muse also often uses the "Authentic cadence" which is the 5 chord going to the 1 chord. They also use the "Plagal Cadence" also known as the "Amen Cadence" (4 chord to 1 chord) quite often.
In the following verse section, they use "Pivot chords" followed by plagal and authentic cadences to change keys 3 times per phrase of chords and make it sound natural to the audience. Each phrase of chords starts in a different key, and follows the same harmonic analysis. It starts on Em, then Cm, then G#m. At the end, we are back to Em, and able to go back to the intro section, which is also in Em.
Here are the chords in the verse along with my harmonic analysis:
i III VI(IV) I III IV bVI I vi I(III) IV I III IV I(bIII) V I Em G C G B C D# G Cm G5 Ab D# G Ab D# G Cm
Cm Eb Ab Eb G Ab B Eb Abm Eb5 E B D# E B D# G#m
G#m B E B D# E G B Em B5 C G B C G B Em
The number at the top of each column of chords indicates the harmonic function in the key for every chord below it. For example... the number atop the first column... "1" refers to Em, Cm, and G#m. Those are the starting chords of each of the three phrases in the verse. The "1" means Root note of the key. "5" would mean 5th note in the key, for example, G is 5 in the key of C. (CDEFG, 12345.)
Each key change is indicated by parenthesis. When you see a number followed by a number in parenthesis, the first number is the chord's function in the old key, the number in parenthesis is the chord's function in the new key. Those are the Pivot chords.
You can see there are plenty of "Amen cadences" (4 chords going to 1 chords), which are especially useful to confirm the new key to the listener. We end each line with the most satisfying cadence, the Authentic 5 to 1. Also satisfying is the grand resolution of the three verse phrases back to Em, from where it all started.
And that's as professorial as I've ever gotten on facebook.
(If you already know everything about intervals, sharps and flats, skip that and just get to the Dog Police!)
HALF STEP: The smallest interval in the 12 tone scale. One black or white note on the piano up or down to the next. One fret on the guitar up or down to the next.
WHOLE STEP: Two half steps.
INTERVALS:
An interval is the space between any two notes. Intervals can be expressed as numbers. The bigger the space between two different notes, the bigger the number. Notes go forward through the alphabet as they go up in pitch ABCDEFGABCD..etc. Knowing that: A to B is a closer interval than A to D. A to B is a 2nd and A to D is a 4th. Any letter to the next letter in the alphabet is the interval of a 2nd. (A to B is a 2nd, B to C is a 2nd, D to E is a 2nd) If it gets confusing, just count on your fingers starting with the first note as number one, then go through the alphabet. For example, if you were asked "What is the interval from C to G?" You would say C is 1, D is 2, E is 3, F is 4, G is 5... so "A 5th!". And you'd be right!
MINOR 2nds:
There are farther 2nds and closer 2nds. The closer ones are called minor 2nds, the farther ones are called major 2nds. The minor 2nd is also known as the half step, semitone, or augmented unison. The half step is the smallest possible space between two notes in a twelve tone (chromatic) scale. (12 tone scale- All the notes including white and black keys in one octave on the piano.) B and C are adjacent keys on the piano (No black key in between them), therefore: B to C is a minor 2nd interval.
MAJOR 2nds:
The Major 2nd is also called the whole step. It's the distance of two half steps on the piano. A to B is a major 2nd interval.
MAJOR and MINOR intervals vs. PERFECT intervals:
2nds, 3rds, 6ths and 7ths are always either major or minor depending on the amount of half steps from one note in the interval to the other. Minor means less half steps, major means more half steps. (See FIG. 1) Unisons, 4ths 5ths and Octaves are neither major nor minor. They are called perfect intervals. They can be modified like so: A to D is a perfect fourth, A to D# is an augmented fourth. A to E is a perfect fifth, A to Eb is a diminished 5th. Here's a list for you:
FIG. 1
INTERVAL DISTANCE IN HALF STEPS
Unison---------------------------------0
min 2nd/Augmented unison----------1
Maj 2nd--------------------------------2
min 3rd -------------------------------3
Major 3rd------------------------------4
Perfect 4th----------------------------5
Augmented 4th/diminished 5th------6
Perfect 5th-----------------------------7
Augmented 5th/minor 6th------------8
Major 6th------------------------------9
Minor 7th------------------------------10
Major 7th/diminished octave---------11
Octave---------------------------------12
As you can see, the number in the interval does not refer directly to the number of half steps. It refers to the letters in the alphabet. A to D is a perfect 4th, A to D# is an Augmented 4th. The number 4 used is purely to say "D is the 4th letter if we count through the alphabet with A as 1."
Now that you know all that, here's chopsticks! What a good demonstration of intervals! You can hear and see the intervals grow larger in the first 10 seconds!
It starts out with a major 2nd, then a minor 3rd, then a major 6th, then an octave!
SHARPS AND FLATS:
Every note is assigned a letter or a letter and a symbol. Notes go forward through the alphabet as they step up in pitch using the letters A through G. ABCDEFG are the natural notes, the white keys on the piano. Most of those natural notes have notes in between them, and therefore are whole steps apart from each other. The ones that don't: B-C and E-F are half steps apart. The notes in between the other natural notes are the black keys on the piano. They are expressed by putting a "#"(sharp) or "b"(flat) sign next to a letter. A "#" next to a note brings the note up a half step, a "b" next to a note brings it down a half step. For example: F# (F sharp) is the halfway point between F and G. Any "Sharp note" has an alternate name. F# is also known as Gb (G flat). So to mention every key in one octave on the keyboard, black and white keys from left to right... you would say:
A A# B C C# D D# E F F# G G#, then back to A.
Alternatively, you could call all those sharps by a their "flat" names:
A Bb B C Db D Eb E F Gb G Ab back to A.
DOG POLICE:
Here's a song that uses intervals well.
Note the confusion caused by the presence of the devil's interval, (the flat 5th) starting on a happy note in the key. (The major 3rd). The first loud synth plays this interval twice in a row at :02. It's like, the devil's here, but I'm happy? What? This same musical device can also be found in some important vocal hooks of some important 90's hits: Pearl Jam's "Even Flow", Soundgarden's "Spoonman" and Stone Temple Pilots' "Plush". The 90's was such a confusing time.
Why do tone, harmony, rhythm and melody make us feel things?
Let's discuss some elements, and put some knowledge together. Here are a few elemental examples for you:
Check out this Meshuggah song, "Future Breed Machine" (Don't be scared, it's just music!):
The guitar comes in at 26 seconds playing a high pitched minor second. That interval played that high in that rhythm sounds like a classic digital alarm clock. Tone, rhythm, and pitch are factors in the way this music makes us feel, but if there's one element of this excerpt that best induces discomfort, it's the harmony of the minor second. Think about a low minor second played in a slow rhythm on a marimba. Even that causes a bit of discomfort.
The two opening notes of the Jaws theme are also a minor second apart. The most important difference between Jaws and Meshuggah is that the notes in the Jaws theme are sequential as opposed to simultaneous, melody as opposed to harmony. Although the effect seems diminished, it seems to have the same discomforting principle working for it. Melody and harmony are differentiated only by time, and time can be pretty goopy when it comes to humans, music, and consciousness.
Why does the minor 2nd make us feel the way it does? The answer is not: "Because of western musical traditions". My theory for the answer is "Because our rapidly vibrating eardrums are uncomfortable and a dissonant interval like a minor 2nd carries more information, and is therefore more difficult for the brain to process than a consonant interval." The minor 2nd is one of the more complicated 2 note harmonies that we experience. Every note when played generates overtones. It would be a more simple harmony to play a fifth or an octave, because those intervals are already being heard as overtones when you hear one note. Those thoughts brings up another question: How far in music does "Simple = comfortable" go? That will be further discussed on this blog eventually. For now, let's keep our heads in the minor 2nd game.
In Indian classical music, most of the time, there is harmony between the note in the melody and the root note (The root note is usually quite constant). Traditional Indian music plays with the feeling of tension and resolve the same way traditional western music does. It often uses the minor second to cause discomfort, and resolves it to the unison or octave for relief. I love this traditional Indian singer, Pandit Jasraj!
Check him out!
I would love to hear your comments, theories and/or knowledge on this subject.
This post gets a little nerdy... I'll make sure to do a music theory basics lesson. If you ever want anything I write to be clarified, please let me know. For this post, you should understand what a ii-V-I turnaround is and what a secondary dominant is(V/III). (Wikipedia!) Note that a ii_V is the same thing as a ii-V-I, just not resolved.
Sbisaac requested an exploration of Golden Lady, I Wish and Tuesday Heartbreak. They're all amazing songs, but I chose Golden Lady because I wanted to pick apart the fancy sounding harmony and train my ears a little. It's a good song for so many reasons! Let's have a conversation about why the harmony feels good, why the rhythm is feels good, why the lyrics feel good, and why the melody feels good.... And then why the elements feel so good together!
I'd like to first explore the feeling of the harmony of this song. It really tells a story on its own. It's lubricated, mysterious, smooth and colorful. There are plenty of comfortable sounding musical devices in the song (ii_Vs, plagal cadences, and line cliches), but they are attached to quite a few non-diatonic chords (bvii, #iv7, bIIMaj7). In fact, for every ii_V in the song... each ii starts out as a non-diatonic chord before being recognizable as the ii of a ii_V.
Here it is: A Harmonic analysis of Golden Lady!
Verse:
(Starts in Eb Maj)
I Maj9 ii9 iii7 #iv7(ii7/III) V7/III
Eb Maj9 Fm9 Gm7 Am7 D9 (Repeat)
The verse is twist on a familiar ascending chord progression. We've all heard plenty of chord progressions like "Lean on me" that go up the major scale in order, I ii iii IV. This chord progression has a little surprise! When we are getting to what we expect to be a comfortable sounding IV chord, we instead get this feeling like we're on a rising wave, this wonderesque moment of a #iv7 chord, which is acting also as the ii7/III going to the V7/III. After all that, the ear expects G Major(III), which would change the perceived key to G Major. (foreshadowing the key of the chorus!) but you don't get G! Instead, the chord progression simply wraps right back to the beginning, and we are quickly brought down to earth with the first chord hitting us again, while fresh in our memory. (It has been quite an eventful 5 chords, and we do have to be reminded that we're in the key of Eb. He gives us a short term memory loss moment.)
The Prechorus also sets you up the key of G Major which feels sort of fulfilling in an unfulfilling way when you arrive at the chorus. It starts out with an Eb, which sounds like the key to the listener for a second, but then the listener is quickly informed that Bb is actually the key by the comfortable plagal (IV-I, amen) cadence. This is a good example of Stevie's magic... things are not quite what they seem! Then that bvii7 chord comes in, sounding evil, but then quickly resolving itsself, becoming a ii by virtue of going to the V and happily resolving to the I in the key of Gb. Then Stevie does a classic jazz harmony trick.... he goes straight from the I to the i, which becomes another ii in the unfinished sounding ii_V(Gbm, B7) heading toward E. Instead of delivering the E, it hops to another ii_V (with the ii disguised as a iv) in the key of G to set up the chorus! It's so satisfying to finally hit that chorus in G after the verse teased us, and after going through so many unsettling non-diatonic chords and key changes in both the verse and pre-chorus. That transition to the chorus also comes with a twist... after an Am7 and a D9, the ear expects a G Major chord, but what you hear next, the chorus, is in G minor.
Now that he's given us that big semi-satisfying Gm chord, he's not going to waste it. We hit a nice minor line cliche, which stings a little, and feels nostalgic. Then we hit that beautiful moment when the bIImaj7 chord gives us that mysterious lift...Perhaps a hint that the world he'd like to go to (in the lyrics) is better than nostalgia. After a repetition of that feeling, we are gently placed down on the earth again with the GMaj7 chord... the chord we have been waiting the WHOLE SONG to hear. The transition back to the verse goes through an alarming bvii which becomes ii in a ii_V in the key of Eb, bringing us smoothly, back to the verse, and we accept this world in her eyes as unattainable at least for now.
At about 3:33, there's an easy modulation... just before the chorus, the D7(V7) becomes a Eb7(V7) and the whole chorus is bumped up a half step to Ab. Then there's another up a half step modulation: When we go up to the bIIMaj7 (AMaj7) he simply does the old Jazz trick again and changes the AMaj7(bIIMaj7) to an Am(i) just before starting the chorus again in Am. This repeats and modulates up again at least once more, creating a slow climbing feeling.
Don't you think that the feeling of the harmony in the chorus works well with the lyrics? "Golden Lady, Golden Lady, I'd like to go there"... Lyrics, melody, chords, all yearning for the heaven in the Golden Lady's eyes.
I am hereby opening this Blog to share my thoughts on the endless topics of Music Theory and Philosophy and to hear your thoughts as well. This all started when a friend asked me to discuss the merits of the "Greatest song of all time, 'Funkytown'", which lead to another friend asking for an analysis of a Muse song called "Knights of Cydonia" (Also the greatest song of all time). Please feel free to participate in any discussions and start some new ones. I want this page to be an explosion of information and opinions. I'd like to explore the concepts of quality, collective consciousness and music as they relate to each other. Please post your thoughts! To start things off, let's discuss your favorite songs! Give me a song title and I'll do my best to give you a musical analysis that sheds some light on why that song feels the way it does.
