Awaken: Yes's M.C. Escher staircase of harmony.

   All you need to know to appreciate this post: 1.  A major triad is a three note major chord.  It's the most commonly used harmony in western music.  I like to number the notes in a major scale 1-7... using that system, you can think of notes 1, 3, and 5 (Do, Mi, Sol with moveable Do) played at once as a major triad.  2.  An ascending perfect 4th interval can be thought of as the distance between notes 1 and 4, (Do and Fa) or notes 2 and 5 (Re and Sol).

      Yes fans are a dedicated people.  (They are my people, so I will refer to them as "We".)  Many of us didn't love this song at first listen but here we are after 1000 listens, and we can't imagine the world without it.  I want to talk about why we're so into it.

    This song in its 15 minutes of glory can be hard to make sense of, but it can be thought of simply like many other pop songs, and broken down into 4 different sections.  The main difference is, Yes does it bigger.

 Intro/outro,
A: mostly a drone guitar riff in E minor.  at 1:33
B: all the major triads in ascending pattern of 4ths at 5:13
C: Ambient bridge of many organ scales at 6:35

The B' after C at 10:35 is our favorite part...  It's the mostly the same harmonically as B, but in a different rhythm.  Less predictable at first listen, more satisfying as you start to feel it.

I want to especially look at the harmony of the B and B' sections.  That's what makes Yes fans weep.  (Really, weep).

  There has been a lot of fascinating research on music and the brain.  My favorite study of the moment concludes that we receive dopamine from being able to predict music.  For most people:  Music that's too predictable is boring.  Music that's completely unpredictable is unsatisfying.  The predictability of Awaken is a perfect storm for Yes fans.  The constant feeling at first listen to the B section is: "What a confusing harmonic structure, but a small part of me knew that particular chord that was coming".   WHY?

  Reason #1:  It's a perfect pattern.  The first chord goes up a 4th to the next chord, then up a 4th to the next chord, then up a 4th to the next chord.   Here's the chord progression:
E      A    D    G    C    F     Bb     Eb     Ab   Db   Gb      B
|      |      |      |      |     |     |         |        |       |       |        |       |      

  Reason #2:  Going up the interval of a 4th from one major triad to another also happens to be the "AUTHENTIC CADENCE"!   If you freeze any two of the adjacent chords in this chord progression, and play them in order, what you get is the most familiar cadence in the tradition of western music.  For example, if you play the major triads E, then A, you feel like you have gone from unstable to stable, and you are now in the key of A.  That authentic cadence happens over and over again- 12 times in the chord progression.  The feeling of the music getting more and more powerful comes from constantly moving to what feels like a more resolved place in the harmony after being in a place you thought was the final resolution.  That is the musical illusion of this song.  From there they use other musical devices to increase the drama as that chord progression is repeated.  By repeating the chord progression, they are resolving the B back to the E again, which is another authentic cadence.  The constant temporary resolve doesn't end at the B chord, it just keeps looping.

  It was an inspiring moment when I spoke to Jon Anderson about this song.  He said:  "I heard Steve Howe playing the A section riff down the hall and I really liked it, so I wanted him to develop it.  I asked him to do it in a few different keys, and that section came together easily.  Then I said Ok.  Now I want you to play as many chords as you can." Steve Howe, being an excellent musician and guitar player threw down all of the major triads one by one in an ascending pattern of perfect 4ths and the epic B section was conceived.  "We wanted to bring that section back and Chris said 'Wait!  Do it in Halftime!'"  Exciting music often comes from simple ideas.

Enjoy!

Colourmusic's "Yes" - The song that only needs 2 notes to be amazing, plus bonus "Tog"!

 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!

The Big Question Part 2: Dr. Tymoczko, "Smalin" and Chopin

DR. TYMOCZKO:

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!

http://music.princeton.edu/~dmitri/

 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.

Beach boys Part 1 "Don't worry Baby"

"Don't Worry Baby"

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, Knights of Cydonia

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.

Theory lesson: Intervals, Sharps, and Flats. Chopsticks! Dog Police!

(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. 

The Big Question Part 1: Meshuggah, Pandit Jasraj, and the Minor 2nd

       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.