~a music nerd's corner of the internet~

Archive for the ‘Intervals’ Category

on Pythagoras and the circle of awesome

I’m assuming everyone who took high-school math class is familiar with Pythagoras and his legendary theorem, a^2 + b^2 = c^2.  What fun…

But I wonder if people outside the scope of music theory know about his beautiful circle of fifths, my favorite circle.  This one circle describes every relationship between the 12 tones in our scale.  This. One. Picture.  It is beyond amazing.

Anyone ever have a music theory class, where your teacher would say, “this is the rule, and don’t ask why, because nobody really knows why”? Well, I beg to differ.  This representation of music tells you why, to almost any question about music theory that I can think of.

By looking at the outer  circles, labelled with letters, it is clear how this illustrious circle got its name.  There are 12 tones, with each one represented as a piece of the pie, and the relationship determining which order they go in, is simply “Add 5”.  So you see, from F to C is five letters or more precisely, a fifth interval (7 semitones).  From C to G, from G to D, on and on, the relationship is the same all the way around the circle.  Inversely, it can be called the circle of fourths, because going counterclockwise, the relationship between each pie piece is a fourth interval, or four letters.   Any inverted intervals always add up to 9 by the way, another unrelated piece of awesomeness in music theory (ie: a third inverted is always a sixth=9, therefore woohoo math!).

SO it here it goes.  The Key of C (and A minor)  has no sharps or flats.  The next is G, which has one sharp.  Then D with 2 sharps, and so on and so forth.  Using this, you can see the relationship between keys.  Because of this, composers can make quick observations about related keys, modulations, building harmony and chords, and essentially anything that you need to have a piece of music except your own creativity.

What I think is really neat, is that it also solidifies why everything in tonal music is built on 4ths and 5ths.  A progression in any tonal song needs to go from I to IV to V and back to I for the listener to feel satisfied, or sometimes a different combination of those 3 chords.  Other stuff is only added in for variety, basically. Why? Because math..look at that circle!

Why are the 4th and 5th scale of any called the sub-dominant and dominant (a.k.a. the most important other than the tonic)? Because Pythagoras knows everything!

Why are 4th and 5th intervals called “perfect” when no other interval other than unison gets that high distinction? Because they are perfect.

The relationship of all tones is essentially defined by this circle (which is perfect, like all circles) that is built on 4ths and 5ths.  These 2 numbers seem to be magic when it comes to music, but not magic, just math.

God I just love it when everything makes sense!


on Intervals and Songs to Recognize Them!

So here is a great list of songs to help recognize intervals.  Please add if you can think of anything!

minor second down

a descending major scale,

Joy to the World

Fur Elise

O Little Town of Bethlehem

minor second up

Chromatic scale
Jaws theme

Pink Panther theme

A Hard Day’s Night

White christmas

major second down

Mary had a Little Lamb


Deck the Halls


The First Noel

8 Days a Week

Three blind mice

Whistle while you work

major second up

Major scale ascending

Do Re Mi..

Happy Birthday

Silent night

Bye Bye Blackbird


My Funny Valentine

Strangers in the night

Frere Jacques

minor third down

Hey Jude

Frosty the Snowman

This Old man

Jesus loves me

When Irish eyes are smiling

minor third up

Smoke on the water

Joe Louis/Judgement Day

O Canada


Happiness is a warm gun

the Impossible dream

Brahms Lullaby

major third down


Good night ladies (merrily we roll along)

Shoo Fly

Swing low sweet chariot

Beethoven’s fifth

major third up

Obladi, Oblada


Oh When the Saints Go marching In


perfect fourth down

Born Free

Shave and a haircut

I’ve been working on the railroad

Oh come all ye faithful

Eine kleine Nachtmuzik

Super mario

perfect fourth up

Amazing Grace

Wedding March

Love me tender

Aura Lee

O christmas tree

Someday my prince will come

Auld Lang Syne

Hark the herald angels sing

Harry Potter theme

augmented fourth/diminished fifth/tritone down


Black Sabbath

Blue Seven

augmented fourth/diminished fifth/tritone up


the Simpsons

perfect fifth down



What do you do with a drunken sailor

The way you look tonight

perfect fifth up

Star Wars Theme

Scarborough Fair

Twinkle Twinkle

Also Sprach Zarathustra



Guards theme from Wizard of Oz

My favorite things

X Files theme

Lavender’s Blue

minor sixth down

Love story theme

Nobody knows the trouble I’ve seen

minor sixth up

Love story theme (3rd and 4th notes)

In my life

Close every door

When Israel was in Egypt’s land

the Entertainer

 major sixth down

the Music of the night

Man in the Mirror

major sixth up

My Bonnie lies over the ocean

Hush little baby

It came upon a midnight clear


minor seventh down

Watermelon man

an American in Paris theme

minor seventh up

There’s a place for us

Nothing compares 2 U

major seventh down

I love you

Have yourself a Merry Little Christmas

major seventh up

Take On Me

Somewhere over the Rainbow (1st and 3rd pitches)

Bali-Hai (1st and 3rd pitches)

octave down

There’s no business like show business

Willow weep for me

Somewhere over the rainbow (from Bow to Blue)

octave up

Somewhere over the Rainbow

Singing In the Rain


Bali Hai

Chestnuts roasting … ( A Christmas Song)

Let it Snow

Tada! and there you have it.  Any other suggestions?

on the Tritone

I love the tritone.  it’s my favorite interval. 

In western music, which uses 12 chromatic pitches, a tritone is made up of 3 whole tones or 6 semitones.   It’s also called an augmented 4th when the letter names are 4 apart ( ie: from C to F) or a diminished 5th when the letter names are 5 apart.  When played melodically  (one after another) it sounds like  “Maria” from West Side Story, and when played harmonically, it supposedly sounds like the devil or something.

Because the 4th and 5th are considered “perfect”, I guess it was really awful to imagine there was a note in between them.  For that reason,  and because it sounds comparatively awkward, the tritone is often avoided in western music.  Granted,  dominant 7th and 9th chords use a tritone in their construction, but it’s not as obvious.  However, 7th and 9th chords are super dissonant, and that makes them awesome in my book.

As you can imagine, this all started because the church hates satan and things that are reminiscent of him.  So even though it doesn’t really sound like the devil or whatever, once composers started using the tritone, they used it to suggest evil or hell, or other such terrible stuff.

I have always found that associations with words like “evil” or even “happy” or “sad” when applied to intervals is really weird.  There’s nothing inherently happy about consonance, like a perfect 5th, nor sad about a minor 3rd or something.  I think it’s all about the context.  So to me, a tritone really doesn’t sound evil.  It is all about the tension though, and everybody loves a good resolution, right?  But because it’s rarely used, it makes it super cool, something rare but not TOO weird, it definitely gets tossed around as the “devil in music” still.   Although I super-duper love the Beatles, my favorite use of the tritone is YYZ by the ever awesome Rush.  Does anyone really think Rush or the Beatles are evil? Pfft.