Intervals: The DNA of Music

Hello !

Thanks for reading this !
Before we start off one very VERY important note:
Music Theory is just a tool used to understand and appreciate music and to help you play better. They're not absolute rules or guidelines (there are no rules in art). Never use music theory as an excuse to not experiment and never restrict yourself to it. The art of expressing what you feel through music always comes first. The theory is just to help you express those artistic aspects better if you wish to do so. 

and now..   INTERVALS !

Music is an awesome combination of melody, harmony, rhythm, feel and all that stuff. Music Theory is simply a way or method to understand how this all works and why music is the way it is. To understand it thoroughly we must strip it down completely and start from the beginning.

Scales, chords, arpeggios, modes are all made from notes. A note is nothing but a sound in a particular frequency. This is the fundamental building block. But its just a lone note. What matters is the relationship between various notes which makes it musical. This relationship between two notes is called the INTERVAL.

Intervals are always relative i.e. its always taken with reference to something. In our case its the Unison or ROOT NOTE as its more commonly known.

So as we all know we have twelve notes in music (starting from C):

C   Db   D   Eb   E   F   Gb   G   Ab   A   Bb   B

and its en-harmonic (real fancy names ppl come up with o_O) equivalent is:

C   C#   D   D#   E   F   F#   G   G#   A   A#   B

I'm assuming you guys know what flats and sharps are and what tones and semitones are so i'm not gonna insult your intelligence and waste space explaining that (unless, of course, you're a drummer.. then you're on the wrong page.. but do come back.. extra cheese and pepperoni next time :D).

The interval is nothing but how these 12 notes relate to the reference root note.
So we should have 12 intervals to establish that. Those 12 intervals are:

1     - Unison, or the root (the reference note)
b2   - Minor second
2     - Major second
b3   - Minor third
3     - Major third
4     - Perfect fourth
b5   - Diminished fifth or Augmented Fouth or Tritone (3 whole tones apart)
5     - Perfect Fifth
b6   - Minor sixth
6     - Major sixth
b7   - Minor Seventh
7     - Major Seventh
8     - Octave (same as the root but one pitch higher)

Remember the order of the intervals.

After the octave we have the b9 (which is the b2 played an octave higher), 9, b10, 10, 11, b12, 12 and so on.. We hardly use the 10ths or the 12ths intervals. Just know the 9th, 11th & 13th (2nd, 4th and 6th one octave up, respectively)

Now lets take C as the root or reference n figure out the intervals

1      -  C
b2    -  Db
2      -  D
b3    -  Eb
3      -  E
4      -  F
b5    -  Gb
5      -  G
b6    -  Ab
6      -  A
b7    -  Bb
7      -  B
8      -  C

so we have the various intervals with C being the reference note.
a flat third or minor third with reference to C is a Eb.
a perfect fifth with reference to C is a G and so on. you get the picture.
This can be applied for any reference note. Here's an example using Eb as reference.

1      -  Eb

b2    -  E

2      -  F

b3    -  Gb

3      -  G

4      -  Ab

b5    -  A

5      -  Bb

b6    -  B

6      -  C

b7    -  Db

7      -  D

8      -  Eb

Piece of cake. Like I said just remember the interval and the note order and you're done !

CHARACTERISTICS OF INTERVALS:

Ok.. Now, lets take it one step further and. Each of these intervals have a certain quality and the usage of these note impact the musical piece as a whole.

We can rate the intervals from dissonant (very unstable and not pleasing to the the ear), imperfect consonance (not that stable but you don't have anything against it either... think of it as a friend of friend of a friend with a weird habit who's made to sit next to you during a big dinner party) and perfect consonant (very stable and pleasing to the ear).

Try playing each interval with the root and actually LISTEN to the tonal characteristics. If you have human ears you'll end up assigning these attributes to each interval.

1      -  Root - Consonance (obviously)

b2    -  Dissonance

2      -  Dissonance

b3    -  Imperfect Consonance

3      -  Imperfect Consonance

4      -  Perfect Consonance

b5    -  Dissonance

5      -  Perfect Consonance

b6    -  Imperfect Consonance

6      -  Imperfect Consonance

b7    -  Dissonance

7      -  Dissonance

8      -  Octave - Perfect Consonance

So, the next time you hear a melody or a simple song, you should be able to figure out which interval influences it and gives it flavor.
          A perfect example is "Black Sabbath" by Black Sabbath. The strong disturbing nature of the diminished fifth (b5) interval imparts a very dark quality which compliments the lyrics, the mood and Ozzy's haunting vocals.

Initially, it's not necessary to be pitch perfect but you need to have a good idea about relative pitches.
There's a simple way to get used to the sound of various intervals. By using songs !!

1      -  Root

b2    -  Remember the typical 2 chord spanish guitar bull fighting stuff :P

2      -  Happy Birthday  ! the underlined part is a major 2nd interval

b3    -  I always think of the first bar of "Californication" by RHCP. The first guitar lick ends on a b3

3      -  the second "na" in Hey Jude. 

4      -  That howling into of the Good, the Bad & the Ugly theme.. its just root n fourth howled rapidly

b5    -  Black Sabbath by Black Sabbath

5      -  The second note of the Star Wars Theme

b6    -  "Take a bow" by Muse.

6      -  The typical rock n roll riffing where you play the power chord and throw in the 6th alternatively.

b7    -  Helter Skelter.. the first has a chord prominent flat seventh interval (key of the song in reference) 

7      -  Superman Theme

8      -  My Sharonnah ! :D

FINDING YOUR INTERVALS:
What you read above is the general music theory. Best part of it is, it can be applied to any damn instrument. So how do you apply it to you bass and locate these intervals?

First, You need to know the notes on the fret board. I think you'll find this crap online on any guitar tutorial site but be a bit smarter and learn them (its not rocket science ) on your own. Works better that way. Second, before we get into diagrams, figures n shit like that, let me brief you on the importance of patterns. I can't stress enough on the importance of learning various patterns especially for the guitars and bass as its a very symmetric instrument. On stage, I don't think any of us will be a able to think note by note while playing. Its mentally impossible. Patterns help us to remember where the nice friendly notes. Plus the symmetry of the fret board helps us to utilize one single pattern in many ways. so remember to learn and work on your patterns. ITS ALL ABOUT PATTERNS PEOPLE !!!


The pattern below shows you where the intervals are located within 2 or 3 frets. So make sure you memorize this pattern. This will be really really useful when you're learning chords.

(apologies for the lousy fret board representation, this was done in a hurry)

Not that difficult it is ? ;)
The root is on the E string in this diagram but its really versatile and can be applied anywhere on the fret board using any reference note on any string. So make use of the symmetry of the instrument.

Ok... Here's some fun stuff called,

 INVERSION OF INTERVALS:

An interval is inverted if we change it's sequence. So a C to D is inverted to D to C.

D is a Major 2nd of C. Inversely C is Minor seventh of D.

2 + 7 = 9

The intervals add up to 9.

This applies for all intervals. The inversion and the original intervals all add up to 9 !

So here's how inversion works.

1. minor intervals become major n wise verse (minor 3rd ---> major 6th, major 2nd ---> minor 7th)

2. The diminished becomes augmented (diminished 5th ---> augmented 4th... which is pretty much the same thing)

3. The perfect intervals remain perfect (perfect 4 ---> perfect 5)

Alrighty then !
Now you have a decent basic idea of Intervals and where to find these intervals on the fret board !

But i'm not done yet..


While reading this blog did any of you actually bother to question the
ORIGIN OF INTERVALS ?!!

So another lesson: Remember that the history of a musical concept is as important as the concept itself. They were born outta necessity and not randomly. Understanding the history will help us understand the application of the concept. So, plz take that extra effort to read a little about the origin of musical ideas. It'll help you understand it better.

So, how did the whole idea of  intervals come about ?
As legend goes, the great Greek mathematician and philosopher Pythagoras (yeah that same s.o.b who did the right angled triangle theorem stuff) was walking by a blacksmiths shop when he noticed that certain sounds of the hammers on the anvils sounded more consonant (more stable or more pleasing to the ear) than others. Upon investigation, he discovered that the nicer sounds came from hammers whose weights were in simple proportions like 2:1, 3:2 and 4:3.

But our pal didn't keep quiet. He and his homies conducted further musical experiments with the Monochord, which is wooden block with one string and a movable wedge. One end of the string was fixed while the other was hung with a weight to maintain some tension (like a guitar).
What he discovered was when he moved the wedge he got various sounds for various ratios.
For a 2:1 (or 2/1) ratio he got an octave interval (the wedge was placed in such a way that the longer side is exactly 2 times the length of the shorter side). Then he found the perfect 4th & perfect 5th intervals for 4:3 and a 3:2 ratio, respectively. These were the most consonant sounds. The other intervals were found using the same method using different ratios

1      -  1:1

b2    -  16:15

2      -  9:8

b3    -  6:5

3      -  5:4

4      -  4:3

b5    -  7:5

5      -  3:2

b6    -  8:5

6      -  5:3

b7    -  9:5

7      -  15:8

8      -  2:1

Interestingly enough if you multiply the ratios of inverse n the original it you always get 2
ex: 7 (major 7th)  and its harmonic inverse b2 (minor 2nd)
(15/18) * (16/15) = 2
or b6(minor sixth and its harmonic inverse 3 (major3)
(8/5)*(5/4)=2
cool eh?

The Pythagorean clan became convinced that basic musical harmony could be expressed through simple ratios of whole numbers.Their general belief was that, lower the numbers in the ratio, the better the notes sounded together. Thus, the natural building blocks of mathematics (small whole numbers) we realigned with the natural interval relationships used to create harmonious music !

This was ages ago. Today we follow something called the Equal Temperament system of determining intervals to tune our instruments in which every pair of adjacent notes has an identical frequency ratio.
Our reference is the A note at 440 Hz called A440.


So....

I hope you found this a little useful at least.
And do practice and work on intervals. Its one of the overlooked and ignored topics in standard music courses. Make sure you understand the basics before you start working on the masterpiece.


Peace and bread sticks,
Leslie.

Chord Progressions in "Africa", Stealing Musical Ideas and someother BS:

I kinda did a short study of a "Africa" by TOTO a few months back with some of my students. Totally forgot about it until Slain performed a kickass acoustic rendition of it this Sunday. This song has genius written all over it. So thought i'd share what my students n I learnt and shed some light on this song and probably show u how analyzing a song can be helpful.


Now, to understand this you need to know a bit about music theory and chord progressions. For those of you who are not familiar with chord progressions i'll try to explain a bit of it.


Chord progression, as the name implies, is a sequence of chords which are in a particular key. You wud've heard musical jargon like "Beethoven's 3rd in C minor" or "Let it be" by the Beatles in C major. What they are referring to, is the key of the song/piece. Each key has a set of chords which are derived from the major scale.


Ex: The chord progresson of the first four bars of "Let it be" is C major-Gmajor-A minor-F major. Now all these chords belong to the C major progression or are in the KEY of C major. 


Hopefully this gives you a basic idea about chord progressions. I'll post a more detailed blog on it if you guys are really interested.


Ok now to Africa ! This song was written by the keyboardist David Paich & the drummer, the late Jeff Porcaro.
http://www.youtube.com/watch?v=GU_1t8kK6wA


The song was written in 3 Keys : E major, B major & A major


lets look at the chords in these 3 keys.. you'll need to keep referring to the table below. 

                  I          II           III           IV           V          VI          VII

E major key: Emaj  F#min   G#min Amaj Bmaj C#min D#dim (diminished)
B major key: Bmaj C#min D#min Emaj F#maj G#min     A#dim
A major key: Amaj Bmin  C#min Dmaj Emaj F#min G#dim
 
The chords in Africa are made up only these chords (almost all - dimished is never used though)


Lets look at it section by section:


Intro : |Amaj | G#min | C#min |
        
        Which is in the key of E maj. This is also the catchy main "motif" of the song.


Verse : | Bmaj | D#min | G#min | F#maj |
          | Emaj | F#maj | G#min | Amaj|G#min| C#min|----> n we're back to main motif.
 
The verse is in B major , a completely different key. But Paich just din't pick up the key at random. See how he uses C#min, which a common chord in the E major and B major key (the VI of E major & II of B minor) to bring about a smooth change in keys. 


This also can be heard in the last bar of every verse line where there is jump to the main motif of the song as the word ends. Here he connects the two keys using G#min (another common chord in the E & B major key). 
  
This concept is known as PIVOTING around a common chord or PIVOT CHORD MODULATION and is used extensively by song writers and composers. Helps in creating a flowing key change.


Chorus: | F#min | Dmaj | A maj | E maj |

The chorus is in the key of A major. To get to the this key the C#min chord (the last line of the verse ends with the main motif) is used, which is a common chord in Emajor & A major to again bring about a smooth key change.
 
Last line of the chorus leading back into main motif :
| F#min | Dmaj | Amaj |        C#min | Emaj | F#min | G#min          | Amaj   | G#min | C#min|
|-------------------------------|--------------------------------------------------------------|--------------------------------
|   last chorus line      |key change to E using Amaj chord as pivot| n back to main motif|




Lets look the keys themselves. E major, B major & A major... no, these key weren't picked up randomly !


B major and A major are the IV & V chords of the E major scale !!


Paich probably decided to take the IV & V of the Emajor key after writing that catchy intro, n make them the keys for the verse and chorus. just brilliant !!


We now have a basic idea of how Africa was composed. Some of these chords are extended to give a bit of flavour and feel. When combined with the extremely groovy rhythmic drum pattern of Jeff Porcaro, the end result is simply brilliant. In essence, this song has everything that a good song should have; its technically awesome, musically brilliant n most importantly, its so freakin catchy  !!




Ok.. So how does this help you?? 
Here's how you can use the same procedure to write a song of your own.
1) Write a catchy motif.
2) Use the IV & V chords as the key changes for verse and chorus.
3) Use pivot/common chord to have smooth transitions between key changes.
So use the same procedure in a different key. Extend chords add sevenths, ninths, thirteens, suspend them, invert them etc. Then work on the rhythm itself. Do it bossa nova style, jazz, country, fusion, pop, rock, metal and what-not. There are no limits. 


As Picasso stated "a good artist copies, a great one steals". The Beatles happily and proudly admitted to stealing ideas. You can find a lot of Beatles ideas in Radiohead songs.
Heard "Holiday" by Green Day ? u'll find Africa in there somewhere ;)
Hell, just take that thunderous Beethoven's Fifth intro (DA DA DA DUM !!) n arrange it for a hip-hop/pop rythym and u'll see how close it sounds to today's crappy music. 


So steal the idea (not the song itself) n when you steal make sure you change something in it so it doesn't sound like a complete rip-off ( think of stolen cars - a fresh coat of paint and a change of license plates and the cops won't know :D).. Just don't end up getting sued like Colplay :P

(Ok.. i don't know which came first but this is a good example of stolen modified ideas :D)

The point of this BS:
Musicians want to be great song writers. They all want to write "original" material, extremely complicated riffs, lightning speed solos, have chords with names as long as a police inspectors. Sure, this is a free country and there are no rules against it. But sometimes we forget the most fundamental aspects of music. That is the simple difference between great artists and us. They don't need the flashy stuff. They can blow our minds away with 3 simple chords !!
So, if you want to know how they do it, you need to learn from their songs. 

                  TO BE A MASTER YOU NEED TO LEARN THE MASTER'S ART !


That is the whole point of learning covers, which we so casually take for granted. Memorizing chords n belting them on stage is not learning (remember the idiots in school who mugged up the whole damn text without actually understanding shit n puked it out on paper the next day?). To understand a song completely you need to rip it apart and study it inside out. Thats how you learn !! 


So plz go download/buy some old albums.. pick up Pet Sounds, Sgt. Peppers, OK Computer (in fact get every Beatles n Radiohead album), Toto IV, A Rush of Blood to the Head and anything else you can find and start learning !!


Trust me, you'll find something amazing in every song !! ;)




Peace.
Leslie.


Buy me some beer now.