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Author Topic: Bards - Threas Theory with Therise - Take Notes  (Read 514 times)

darkstorme

Bards - Threas Theory with Therise - Take Notes
« on: June 03, 2011, 02:46:02 am »
(The first installment of this series is here; the subsequent installment is here.)

*a pair of burly dwarves haul a heavy baby grand piano into the centre of the room, by the slate the elf has set up.  She nods and gives them each a few coins, and they walk out as the last of the students seat themselves.  She plays a quick set of chords, at which point all the students turn to her*

How do we know what we are singing?
Or which of a harp's strings are ringing?
Or all of the manifold players who make up a band?

The notes that they read are the key
And if you will listen to me
You'll find these notes are easy to understand.


/ / / / / / / / / / / / / / / / /


*Therise turns from her seat at the piano, again clad in red jeans and an Ilsare t-shirt*

Hello again!  Today's discussion will be about notes and notation.  I'm going to move pretty quickly through this, so be sure to ask me any questions you have after class.

First, a bit about sounds.  A note, whether sung, strummed, or played by some other means, is sound at a particular frequency.  As an example, the note to which most orchestras tune, A (more on why it's "A" later) is four hundred and forty vibrations per second, or hertz.  It sounds like this.

Now, different cultures use different subdivisions, but every culture has a sense of what is known as the "octave".  This is the range of notes that occurs between two pitches that are "alike".  As it happens, these "like" pitches occur at frequencies at powers of two.  So if you play pitches of 440 Htz, 880 Htz, and 1760 Htz, it sounds like this.  You've probably experienced this yourself when singing along to a piece that's outside your normal vocal range.  You are still singing the "same" notes, but lower or higher than the tune to which you're singing.

So that's an octave - a range from one pitch to another at twice its frequency.  Why "octave", suggesting eight?  Well, come over here and look at the piano keyboard.



The two keys in red are both "A", the note you just heard.  If you count from A to A on the white keys, you'll find that there are eight.  That's why it's an octave.  *she grins*  But why the black keys?  That makes twelve from A to A, after all.  Well, in some cultures, there are as many as twenty-four notes in an octave; in other cultures, fewer - you can feel free to ask about that after class.  But as I mentioned in the first lesson, we're going to be working from a largely western musical tradition... and there's a reason rooted in physics for the way that the western note scheme is laid out.

*she takes a breath* If you sing a note, or play it on a piano, or violin, you're not just playing the one frequency.  You're playing what's called the "harmonic series" - the base frequency, plus a set of overtones.  *she takes her harp out of its case and sets it on the piano*  If I pluck one of these strings, it has one frequency which has a wavelength that corresponds to exactly the length of the string - that's the base frequency.  But other frequencies appear as well: the frequencies whose wavelengths are integer divisors of the base frequency's wavelength.  

So there's one wave that's half the length of the base, and therefore twice the frequency - and, as we just discussed, that's the octave above our base.  The next wave is a third of the length of the base, or three times the frequency, and that's a very important note as well.  It's a "fifth" above the root, and is often referred to as the "dominant", or, more tellingly, a "perfect fifth".  The frequency above that approximates a fourth, then a major third, then a minor third... but we'll get into intervals later.  The fifth is the important note, because it's the first "different" note in the harmonic series, and the one that sounds "best" to the ear - for that very reason.

But how do we get from this to our twelve notes in an octave?  Well, this is a neat little musical trick called the "circle of fifths".  Let's get that piano keyboard back, but we'll put some note names on the keys...



So, for the sake of precedent, let's start on A.  A perfect fifth above A is E.  A perfect fifth above E is B.  A perfect fifth above B... isn't F.  It's about halfway between F and G, pitchwise.  You'll note, conveniently, that there's a key between F and G - that's F sharp, or G flat.  Got it?  Alright, moving along.  A perfect fifth above F sharp is C sharp.  (It's the key just between C and D.)  A perfect fifth above C sharp is G sharp.  A perfect fifth above G sharp is D sharp.  A perfect fifth above D sharp is A sharp.  A perfect fifth above A sharp is... F.  (Makes sense, doesn't it?  If B's perfect fifth is F-sharp...)  A perfect fifth above F is C.  A perfect fifth above C is G.  A perfect fifth above G is D, and a perfect fifth above D is... A.  And there we have it: A->E->B->F# ("#" is the symbol used to denote "sharp")->C#->G#->D#->A#->F->C->G->D->A.  Twelve different pitches, in a circle of fifths.

So that's why there are twelve different pitches in the space of an octave.  Hooray!  But I did promise you some notation as well, so while the students there *gestures at the Hempstead classroom* get their quills and parchment out, how about you start up MuseScore.  I'll wait.  *whistles idly to herself*

While you're doing that, a brief word on nomenclature.  In english-language western music (and a few other regions), the notes are given letters - A through G, with the black notes as "modified" letters (A sharp, B flat, etc.).  There's no particular reason for this other than the fact that having a coherent system makes it much easier for everyone to be on the same page when reading music.  Some other languages (slavic and romance languages in particular) use what's known as "fixed solfège", where the notes are represented by the syllables "do", "re", "mi", "fa", "so", "la", and "ti".  Moveable solfège (as popularized by certain Austrian nuns) is a popular teaching technique for singing, but the syllables do not represent particular pitches, simply pitches relative to one another.  Fixed solfège has correspondences - "do" is C, "re" is D, and so on, to "ti" as B.

You have MuseScore open now?  Excellent!  Go to File->New...  Don't bother filling in any of the documentation right now; this is just a 'scrap' session.  Select "Create Score from Template", click Next, and select "Piano.mscx".  What you should see ought to look something like this...



Yours will have a time signature (that's the 4 on top of another 4) - ignore that for now.  This is the Grand Staff.  What we'll look at first are the clefs.  The one on the upper staff is called the "Treble Clef", or G clef, so named because it curls around the line on which G is written.



This clef is the highest unmodified clef - it usually denotes higher-pitched instruments or voices (sopranos *she preens* and altos).



The Bass Clef or "F Clef" (so named because its dots bracket the line on which F is written) is the lower counterpart.  Taken together, the Treble and Bass clefs and their respective staves form the Grand Staff, which is employed when writing condensed orchestral music, small vocal arrangements, and piano pieces.

On the treble clef, the lines (taken from bottom to top) are E, G, B, D, and F.  As a child, I was taught these as "Every Good Boy Deserves Fudge".  (Which seems unfair.  What about girls?)  The spaces spell "FACE", which is pretty straightforward.  The space below the E line is D, and the space above the F line is G (which makes sense, doesn't it?).  The A in that FACE, by the way, is the A which is conventionally four hundred and forty hertz, as discussed earlier.

On the bass clef, the lines (again, from bottom to top) are G, B, D, F, and A.  The mnemonic for that one was "Good Boys Deserve Fudge Always" (*pouts*).  The spaces are A, C, E, and G ("All Children Eat Gumdrops").  The space above?  B.  The space below?  F.  Simple!

One more detail, however - you may have noticed that there's a note missing between the top of the lower staff and the bottom of the lower staff.  This note, known as "middle C" for its position on the piano keyboard and the staff, sits on what is called a "ledger line" - a line, just the length of the note, written just below the upper staff, or above the lower.  Ledger lines are also employed when the treble part needs to descend into the bass, or exceed its own upper bounds - and likewise with the bass.

Here, however - *she gestures and a staff springs into the air before her* - I've made a little cheat sheet.



"But why do the notes look different, some empty, some full?", I hear you ask.  "What are the squiggly things, and the bars connecting them?"  Those have to do with time signatures and duration - and will wait for another day.  The spell's almost worn off again for another week.  You can, of course, speak to me in #theory_threas on IRC - and I'll post a few little exercises to this thread later this week.

For now, 'ta!  *she mutters something and vanishes as the classroom comes back to life*

/ / / / / / / / / / / / / / / / /


*Therise looks in satisfaction as her students scritch away with quill and parchment.  She plays a few opening chords on the piano and sings, to the tune of what would, if it were not horribly anachronistic, be 'Sandra Dee' from Grease...*

Now, you see, it's A to G
Deceptive in simplicity.
Now it won't be long
'til you're writing in song...
All thanks to A through G!
 
The following users thanked this post: Hellblazer, RollinsCat

darkstorme

Re: Bards - Threas Theory with Therise - Take Notes
« Reply #1 on: June 09, 2011, 04:07:42 am »
*humming to herself, Therise hands out a quiz and goes to dust the seats in #theory_threas*

The Infinite Note Quiz.  Take it for as long as you want - and see how good you can keep your average after a hundred questions!
 

RollinsCat

Re: Bards - Threas Theory with Therise - Take Notes
« Reply #2 on: June 17, 2011, 09:31:09 pm »
A tall guy whose physique suggests incipient middle-age spread hands in his test; eight-six and change.  He sighs.

"I feel like an idiot but those notes above and below the bars seem to flummox me - the rest are cake."