Finding key signatures

[yewtree]

As a beginner in music theory, I have a question.  

Is it possible to use the Circle of Fifths to work out  HALF STEPS, WHOLE STEPS
 and SCALE FORMULAS , like for instance, Major scales formula is W, W, H, W, W, W, H  to find whether a scale has a sharp or a flat?


I hope that doesn't sound dumb.  

[iansinclair]

Not quite sure where the circle of fifths comes in -- but keys are named by the tonic note, and then the intervals above that determine whether it is major or minor (or what mode!).  Your example is fine, and the major scale does have exactly that structure.  So -- pick a note, any note, and use that formula to go up from there and you will have the sharps or flats for that scale just nicely laid out.

Now there are some exotic scales, out towards the ends of the circle, where things get a little strange and you start to get sharps where you don't quite expect them... C# major, for example; the third is E#, which is the same key as F... but I wouldn't worry about that at this point!

[dcstudio]

Key signatures line up according to the circle of 5ths--you are on the right track...

start with C--a P5 above C is G--the key of G has one sharp (F#)
--a P5 above G is D which has 2  sharps (F#, C#)
--P5 up is A which has--you guessed it--3 sharps--(F#, C#, and G#)
--up another P5 and we have E with 4 sharps--(F#, C#. G#, and D#)
--and then up a P5 again and we have B with 5 sharps (F#, C#, G#, D#, and A#)

notice some properties and patterns here... each time we add a sharp we include the previous sharps plus the new one which will always be a half-step below the root... i.e. A# is a half step below B--the key.  If the key signature contains sharps--the root will always be a half-step above the sharp furthest from the clef sign.  

notice that each new sharp is a P5 above the last... F#--C#--G#--D#--A#--E#--B#

you can remember the order of sharps with the saying--Fat Cats Go Down Alleys EveryBody--it's the standard way.. are you with me so far?

ok flat keys...

lets start with C and we will DESCEND by P5s  (or if it's easier---ASCEND in P4s)

C--down a P5 and we have F--with 1 flat (Bb)
F--down a P5 and we have Bb--with 2 flats--(Bb and Eb)
Bb--down a P5 and we have Eb--with 3 flats--(Bb, Eb, and Ab)

NOTICE THAT THE KEY SIGNATURE IS ALSO THE SECOND TO LAST FLAT--Notice each new flat is a P5 below the last.

I am going to let you figure out the rest of the flat keys...

the order of flats is BEAD GCF--

hint... memorize your intervals until they are second nature...

I was in a hurry... let me know if I lost you...lol

[adodd81802]

Key signatures line up according to the circle of 5ths--you are on the right track...

start with C--a P5 above C is G--the key of G has one sharp (F#)
--a P5 above G is D which has 2  sharps (F#, C#)
--P5 up is A which has--you guessed it--3 sharps--(F#, C#, and G#)
--up another P5 and we have E with 4 sharps--(F#, C#. G#, and D#)
--and then up a P5 again and we have B with 5 sharps (F#, C#, G#, D#, and A#)

notice some properties and patterns here... each time we add a sharp we include the previous sharps plus the new one which will always be a half-step below the root... i.e. A# is a half step below B--the key.  If the key signature contains sharps--the root will always be a half-step above the sharp furthest from the clef sign.  

notice that each new sharp is a P5 above the last... F#--C#--G#--D#--A#--E#--B#

you can remember the order of sharps with the saying--Fat Cats Go Down Alleys EveryBody--it's the standard way.. are you with me so far?

ok flat keys...

lets start with C and we will DESCEND by P5s  (or if it's easier---ASCEND in P4s)

C--down a P5 and we have F--with 1 flat (Bb)
F--down a P5 and we have Bb--with 2 flats--(Bb and Eb)
Bb--down a P5 and we have Eb--with 3 flats--(Bb, Eb, and Ab)

NOTICE THAT THE KEY SIGNATURE IS ALSO THE SECOND TO LAST FLAT--Notice each new flat is a P5 below the last.

I am going to let you figure out the rest of the flat keys...

the order of flats is BEAD GCF--

hint... memorize your intervals until they are second nature...

I was in a hurry... let me know if I lost you...lol

In all the theory I have learnt, nobody has explained as well as this, just how easy it is to learn Major piano scales. Bravo.

[yewtree]

Yes, I agree adodd, it is fascinating , I shall set to study it all.   Thanks also iansinclair for helping out too , all valuable information. 

[dcstudio]

thanks guys!  it is fascinating isn't it?   blew my mind when I learned this stuff..  want some more mind blowing info?  Pythagoras the father of modern geometry was walking past a blacksmith in 1500 BC (or so) and listening to the pitches as the "smithy" struck each of the anvils in front of him.   Pythagoras noticed that when the blacksmith struck an anvil then another anvil that was exactly twice the size of anvil #1 the pitch dropped exactly an octave.  He was the first to apply the ratios that gave us our modern tuning scheme--which is not quite the same as his (Pythagorean tuning).. but based on the same equations.  

Before this discovery tuning schemes were erratic and completely inconsistent.  Can you imagine what it must have sounded like?  argghh.


that always just freaked me out..  he was just walking down the street...when he had this stroke of genius and basically gave every single musician there has ever been in the last 3500 years something to play.

[timothy42b]

thanks guys!  it is fascinating isn't it?   blew my mind when I learned this stuff..  want some more mind blowing info?  Pythagoras the father of modern geometry was walking past a blacksmith in 1500 BC (or so) and listening to the pitches as the "smithy" struck each of the anvils in front of him.   Pythagoras noticed that when the blacksmith struck an anvil then another anvil that was exactly twice the size of anvil #1 the pitch dropped exactly an octave.
that always just freaked me out..

Not sure I buy this story, for a couple of reasons.

The pitch of a solid object isn't as obvious a function of size as is a pipe (tube) or string.  Flutes were known in P's time, as were monochords, harps, etc. 

Secondly, blacksmiths in 1500 BC?  The bronze age was roughly 2900 BC to 1300 BC, the iron age started somewhere around 1200 to 1000BC but there weren't foundries of any scale before 930 BC.  I don't think the dates match up.

Finally, have you ever hit an anvil with a hammer?  They don't ring very much.  The cast iron they're usually made of absorbs a lot of vibrations.  Last time we played Anvil Chorus, we tried a commercial anvil and gave up.  I had a chunk of railroad rail at home that worked perfectly.

But anyway.  Inharmonicity would get in the way of determining pitch relationships. 

We now return you to your previously scheduled argument.

[dcstudio]

OK OK   ... it is a legend... and that story has been argued... you are probably absolutely right...lol.  

it's just soooo awesome of a story though... I want soooo badly to believe it. LOL.  Thanks though because after my thorough and factual explanation of key signatures it's probably not the greatest for me to post that.   It is a musical fantasy.  

In my day... everyone believed it... just like Santa Claus... and that Saleiri/Mozart fable.


ok guys... so Pythagoras may not have even discovered Pythagorean tuning...

the Grinch who stole my musical fantasy is probably correct.  

[brianvds]

It is not entirely clear whether Pythagoras actually even existed, and if he did, it was definitely not 1500 B.C. 

Nevertheless, it is true that the Ancient Greeks laid the foundation of our system of tuning.

Here's another anvil story that may or may not be true. Everyone knows that the first notes of Beethoven's fifth symphony represent "fate knocking on the door," right? But there is also a far less dramatic story, which holds that he got the idea for that famous motif while looking at a blacksmith hammering.

It is a story that actually rings more true than the dramatic, Hollywoodish one, because Beethoven is famous partially for his ability to turn the most banal material into something great.

[dcstudio]

It is not entirely clear whether Pythagoras actually even existed, and if he did, it was definitely not 1500 B.C. 

Nevertheless, it is true that the Ancient Greeks laid the foundation of our system of tuning.

Here's another anvil story that may or may not be true. Everyone knows that the first notes of Beethoven's fifth symphony represent "fate knocking on the door," right? But there is also a far less dramatic story, which holds that he got the idea for that famous motif while looking at a blacksmith hammering.

It is a story that actually rings more true than the dramatic, Hollywoodish one, because Beethoven is famous partially for his ability to turn the most banal material into something great.

funny... I saw a documentary once where music scholars played recordings of local birds species Beethoven would have heard and one of them sang that exact 4-note famous motif.    Given Ludwigs hearing problems though... the anvil story seems much more plausible... but that bird call was kinda freaky.

[brianvds]

funny... I saw a documentary once where music scholars played recordings of local birds species Beethoven would have heard and one of them sang that exact 4-note famous motif.    Given Ludwigs hearing problems though... the anvil story seems much more plausible... but that bird call was kinda freaky.

Well, he wasn't born deaf; perhaps the fifth symphony is a nostalgic trip to his childhood. :-)

He surely would have remembered such things. It is widely believed that he was somewhat talented in music. 

[dcstudio]

Well, he wasn't born deaf; perhaps the fifth symphony is a nostalgic trip to his childhood. :-)

He surely would have remembered such things. It is widely believed that he was somewhat talented in music. 

really?  lol... hmmm somewhat talented in music, Wow... you know they said that in the documentary, too.

I am still mourning the loss of Pythagoras and the musical childhood fables I was told... actually, some of that stuff I was taught in music history class at university...  that was quite a while ago, though..  no internet back then. 

still... I feel somehow... robbed... lol.

[yewtree]

really?  lol... hmmm somewhat talented in music, Wow... you know they said that in the documentary, too.

I am still mourning the loss of Pythagoras and the musical childhood fables I was told... actually, some of that stuff I was taught in music history class at university...  that was quite a while ago, though..  no internet back then. 

still... I feel somehow... robbed... lol.

I enjoyed the fables though, I makes everything more exciting and interesting.

[dcstudio]

I enjoyed the fables though, I makes everything more exciting and interesting.

and that is no doubt why we were told those stories and why they have been passed on... how else are you going to get freshmen interested in music literature?

[brianvds]

really?  lol... hmmm somewhat talented in music, Wow... you know they said that in the documentary, too.

I am still mourning the loss of Pythagoras and the musical childhood fables I was told... actually, some of that stuff I was taught in music history class at university...  that was quite a while ago, though..  no internet back then. 

still... I feel somehow... robbed... lol.

Humans are natural story tellers, and embellishers of tales. A huge amount of history eventually turns into mythology, and I am by no means talking ancient history either.

Everybody knows Mozart practically died of hunger, right? And almost no one appreciated his music, right? And he was unceremoniously dumped in a mass grave because his family couldn't afford a funeral, right?

Think again. :-)

The stories are of course entertaining, and often serve to make history more interesting. But I think they also do harm, to some extent, because they perpetuate the notion that some people are so extraordinary that their achievements border on the uncanny and mystical, and we cannot aspire to even get remotely close.

Real life, even for geniuses, is often rather more prosaic, which means their lives are not actually quite as amazing as we think, and our own lives are not quite as mundane as we think. :-)