Saturday, December 5, 2009

Lesson 4: A breif overview of Midieval music

Ok, so we've now covered the basics of what makes music music.  Once we're done with this series of posts, we'll move on to counterpoint, something that is incredibly boring and doesn't seem useful, but I'll explain why we learn it in the post.

Anyways, now we're moving on to history.  Some of you may be wondering what exactly is the point of learning Music History, since a lot of it has very little to do with music today, and in fact, as we'll learn in this series, the very basics of what we think of today as composing didn't exist until about the 19th century.  I mean, sure, it's great a parties(you have no idea how great at parties.  You whip out the knowledge of Palestrina mass structure and the ladies just can't get enough of you), and for some academic smart person reason it's important, but really on any practical level why?

Well... in a way a lot of it isn't important.  But there's a reason music sounds the way it does.  There's a reason that the rules of counterpoint exist in the way they do.  There's a reason we think of everything in the way we do.  There's a reason dominant chords go to Tonic chords, and there's a reason 4 measure phrases happen.  And knowing why things are the way they are today is still useful.

Also, I spend quite a bit of time in a room with boring professors being told how to read goddamn neumes, which haven't been used in notation since 1100 or so and dammit now you all have to deal with that shit because I'm writing this blog so neener neener neener.

So we start our overview of history in the times of the Ancient greeks.  We don't really know, unfortunately, really anything about Grecian music.  We know, for instance that the philosophers talked about the emotional and dramatic impact of music, and we know that they had the same general pitch relations as us, at least to a point(More correctly, we based our pitch relations on what they discovered).  In fact, I'll add a little PS for the people interested in the physics and psychology interaction we can draw from history, starting with the Greeks, because I think it's fascinating, once I'm done with the history series.  Anyways, we know, for instance that they knew of the relations in string length for different notes, such as cutting in half to get an octave, cutting to 1/3 to get a fifth, etc.  This is the basis of why we call unaltered fifths, fourths, and octaves "Perfect".  They are the simplest mathematical intervals, and so the Greeks, according to our reading of what they thought, referred to them as "perfect" since the greeks had such a hard-on for math.

And that's... well that's pretty much all we know about Grecian, and really any "Classical era" (We'll see a different classical period later, totally different classical era) music.  You see, when there was the whole rampaging barbarian problem in Europe and all those fancy civilizations with all their Aqueducts had all their cities burned and pillaged.  So we don't have any manuscripts of their music, nor did any of the oral tradition, assuming there was one, survive.  Whoops.

Anyways, then there were the dark ages.  Unless "People being impaled on pikes" counts as a musical work then we don't really have any music from there either.

But starting around 500 C.E. we start seeing manuscripts again.  According to tapestries and legend, as it were, right around the end of the 6th century, Angels or the Holy spirit or some sort of heavenly herald came down to Pope Gregory I and gave him music, or gave him divine inspiration to create music, or something like that.  Now, maybe God's just a crappy musician, or maybe Gregory I was a shitty student and after the first day of class started making paper airplanes out of his divine inspiration parchment, but in Gregorian chant, there is max two notes, one of which can move, there are no key signatures or clefs(well, there's close to a clef), and instead of writing notes, they just scribbled on a paper and told people to sing it.

It looked something like this

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This is what is known as Neumatic notation.  Instead of notes, we have Neumes.  That picture is an example of unheightened neumatic notation, which was the earlier form.  You may be able to see that each of those little scribbles has a direction and is separated from others.  For the first word, you would sing the first pitch on "Au", then a short, 2-note descending run on "bu", followed by a three note ascending run on "la", then a two note ascending run on "re".  As you can see, there's no absolute pitch, so there's no indication of what note to start on, nor exactly how much we descend or ascend in the runs.   So we can't really easily transcribe this into modern notation because while this does give us the contour of the music, there still obviously had to be an oral tradition part to it.  That is to say, it would be impossible with unheightened neumes to perform music that you haven't heard before.

Now, what we're pretty sure actually happened with Gregory, and the story outside of the tapestries and stories, is that he called for the codification and organization of music.  And for the time period, when we say "music", we really mean "Church music", though I'll talk a little bit about secular music.  So basically, before Gregory came along, this was pretty much all oral tradition, with perhaps something like unheightened neumes as a reminder, but there was no standard, and Gregory changed that.  Since it's the first codification, he got the chant style named after him, hence Gregorian chant.

So we have music that we can read assuming we know the song already, but that's not so useful, right?  I mean, we still have that, just look up any songs chords and it'll be in a notation where you need to know the piece, but you're pretty limited in what you can do with that.  You can't really hand a chord chart to an orchestra and have them play a piece, now can you?  Even if they have heard the piece it probably won't be too great of a performance.

So let's look at heightened neumes, which look something like this:

Heightened neumes

I know it looks still kind of like scribbles and random dots, but holy shit so much clearer.  So first off here, we're moving to a staff with lines.  This is awesome, because now we have distance between notes instead of just general movement.  Now, also, we have a clef.  Do you see it?  If you look at the very beginning, while it looks just sort of like other notes, you'll find a unique neume that looks almost like the letter C.  Well, that's the clef, and it is around where C is.  So C is the 4th line of the staff.  After that, we have what's known as a "podatus" neume, which means we'd sing two notes ascending, followed by a "Climacus", though an interesting one, since normally you'd see that with a single starting note, so it's more a compound neume.  It means we have three notes descending, though I believe since it's in a compound neume we'd count the last note of the previous neume.  

Anyways, so we have all of this, and I was about halfway through typing up the different types when I realized that wiki probably has an article on this, and it turns out it does.  And apparently is where those scores were from.  Good to know, GIS.  Thanks.  Anyways, here's the full version of what these mean, as far as we know

So interpreting this score, it looks like we're based on G, which puts us in Mixolydian mode(I'll explain that), and put into modern notation, the notes would be:  B G G F G C B A B A A G

for that first little snippet before the words and giant letter M come in.  We're still unsure of how rhythms work out in heightened neume notation.  There's debate as to whether certain neume types do indicate a rhythm or lengthening of note length, or doubling, but we really are unsure.  It's also possible, I guess, that the rhythm would still be something that the singer would have to know, or would be implied by something else.  But the common interpretation is that all notes are equal in length.  So if we want to have different length notes, we still really can't exactly write it, we just don't have the capability to notate rhythm yet.

So before I talk about how we do get to modern notation, let's look at what I posted up there about being in Mixolydian mode.  The fuck?

Well, as I mentioned, we don't have key signatures.  We only have one accidental, and that's, interestingly enough, the flat, which can only be placed on B, and does exactly what it does in modern notation.  What's fun is that the meaning actually changes slightly in later early music before coming back to what it is now.  

So with no key signatures, we only had the "white notes"(Think like on a piano).  But we could still base music on different tonics.  So for instance, imagine a scale starting and ending on D, but F and C aren't sharp as in D major, and B isn't flat as in D minor.  We could do that, theoretically, based on any white note.  Well, these scales are referred to as "Modes".  Modes exist today, though they're now just different scales.  They're the same note relations as the original modes, but they can be moved anywhere.

So anyways, what this gives us are the 8 original "Church modes", as we call them.  We have 4 "Authentic" modes and 4 "Plagal" modes.  and here's a chart of authentic modes from what note it's based on:

D: Dorian

E: Phrygian

F: Lydian(Note: This mode has Bb naturally in it)

G: Mixolydian

Ok, now here's where it gets a little confusing.  Each church mode has a "Final", which is about the equivalent of the tonic in todays music, it's the "resting note" as it were, a place to end and move around.  For the authentic modes, the Final is the note that the scale is based on.  So dorians final is D.  For Plagal modes, the final is the same as a corresponding authentic mode, but the scale starts and ends a fourth below the corresponding authentic mode.  So the plagal modes, in the same order as the authentic modes up there are:  Hypodorian, Hypophrygian, Hypolydian, and hypomixolydian(This one's my favorite.  It's fun to say).

Ok, so that's modes.  And neumes.  You know, for a history lesson, I'm really not covering much of the time line.  This is more Ancient music theory.

Anyways.  Whoo boy.  So that's how music is put together back then... so what about how it sounded?

Here's an example of basic Gregorian chant.  You'll note that while they extend the last note of each phrase, mostly the notes are all the same length.  Also, there's only one note.

I want to note that during this period there was also Secular music, specifically from the precursors to the Troubadours.  Basically, traveling minstrels.  Their music was pretty much completely of an oral tradition, because printing at the time was incredibly expensive, so only the church could afford it.  The result of their oral tradition is that we don't really know all that much about their music.  What we do know is that they would often sing with instruments, and that much of their music was in what is known as "Strophic" form, which is basically A-A-A-A-A-etc.  Again, I'd love to go into more depth with this, but unfortunately there are just so few records and I can't for the life of me find any recordings without delving into my anthologies, and I'm not sure where they are.

Now music pretty much continued along this way for about 500 years.   Single line, monorhythm, all that.  Around the beginning of the 11th century or so, we started to see something rise called "Organum".  Organum was essentially music that involved two notes.  At the same time!   That's right, it took 500 years of singing one note before anyone thought "HEY!  WHAT ABOUT TWO?!"  I imagine the early adopters were burned for their witchcraft, but eventually people realized holy shit two notes.  Now, this took a few forms.  The earliest form was "Organum Purum", which involved a single drone note over which a melody was sung/played.  An example of this is in Ordo Virtutum, by a very well known early composer who we'll get to soon.  As you can hear, we're still dealing with the idea of a single melodic line, but we do have emergent harmonies between that line and the drone.

Later, we started to see something known as "Free Organum", which involved two voices moving together, or sometimes in Oblique motion(One part stays on a note while the other moves), but not in the same fashion as the drone of Organum purum.  An example of this is in, once again, Ordo Virtutum, elsewhere in the work.

The reason I used Ordo Virtutum is because it's by one of the most famous and influential people in every field in the middle ages: Hildegard Von Bingen.  Hildegard did everything, there are a ton of fields in which she's pretty famous for.  She's so famous that we actually know the stuff she did.  At the time, most of this chant stuff was written by monks and nuns who wouldn't sign their works, so 90% of early music will be by Anonymous.

Around this time as well, Guido d'Arrezo basically decided that it was probably a good idea to be able to write music down.  One of his semi-famous ideas was the Guidonian hand.

Guidonian hand 

Basically, Guido D'Arezzo could point to parts of his hand and it would serve as a mnemonic device to aid in sightsinging.  There's a reason we don't use it today, though, while we do use the other forms of notation.  Basically, the hand required memorizing locations on the hand and couldn't be used outside of the performance, basically.  You can't really go home and practice when you need to see someone pointing at their hand.  It was essentially less a basic form of notation and more a basic form of conducting.

The big thing we see from him though was Guidonian notation.  Guidonian notation is also known as "What we do today"  Guido D'Arezzo was around the 11th century, and we've been using, though it's changed a little, his notation system since.  It's wonderful, because it allows someone who has never heard a piece to play it correctly.  Essentially, it's the final movement away from the oral tradition into a written one.  It wasn't quite the same as today, we'll see "Mensural" notation, which doesn't quite look like things to today, but it is much more clearly closer to modern notation than neumatic notation.

But back to music.  With these advancements, we started to see something called "Organum duplum", another form of two-voice singing.  We enter a period known as Ars Antiqua, and we'll get to why it's called that soon.  Essentially we see a movement towards more going on in the pedal voice, and this is where see see what almost sounds like a rudimentary system of chords, where there is a changing bass note at certain points in the melody.  This stuff sounds something like this.  It's also known as the "Notre Dame school", because that's where it was practiced often.  Leonin and Perotin are famous composers of this style, and pretty much always mentioned together because their names are similar.  This went on 'till about the early 14th century.  We also start seeing composers with hilarious names like "Adam de la halle", or "Adam of the hall".  Love it.

It's important to understand the philosophy that's going on here for a second, to make the next period make sense.  While today we hear the interaction as almost a vocal line - Bass line relationship, they didn't really see it that way.  Their interpretation was that they were two simultaneous lines of Organum.  Well, with Guidonian notation, we can start to have that second line do a lot more than just sit on one note until the other line has sung a few notes, and the lines don't have to move together or even be all that related.  In fact, if you look at manuscripts from around this time, you'll sometimes see that each part has its own bar line placement... there isn't just one bar line for everyone like there is today.

So music slowly was becoming more filled with advanced rhythm and individual parts, and then Phillipe de Vitry came along and said "Fuck it, we'll do it live!I'm going to move us forwards myself!"  And he started the Ars Nova period.  What's funny here is that he decided that his stuff was "New Art" and everything else was "Antique art".  I'm sure he was awesome at parties.  Anyways, this was like a super-explosion in music.  It's actually not too wacky to suggest that his stuff really did make everything else look, well, antiqua.  In fact, there are developments in music during this period of time and immediately following that we don't see again until the music of the 20th and 21st century.  It's whack as shit.  Essentially, this school ascribes to the Voltron theory of music.  The more lines you add, the more stuff going on, the better.  So you would have just a billion things going on at once.  Specifically, Ars Nova as a period is known for its Isorhythmic motets.  The motet was a song form we saw arriving around this time, and Isorhythm, which translates from Greek as "The same rhythm", is... well it's wacky assed shit, so let's see if I can explain it.

Isorhythm consists of two parts, the talea and the color.  The talea is a specific rhythm, and the color is a specific melody line.  What's important to note is that the talea and the color have different amounts of notes.  They are repeated over each other however, in each line.  So imagine that you have 4 pitches with a rhythm of Quarter-Eighth-Eighth.  When you get to the end of the talea, the Q-E-E rhythm structure, just repeat it, starting on the last pitch.  Since you're now done with the color, repeat it over the remainder of the rhythm.  Just keep doing that.  That's the basic line of an Isorhyhmic motet.  Now do that with 7 other voices.  It'll sound something like this, which is a Mass by Guillaume de Machaut, one of the two more famous Isorhyhmic composers.  The color, by the way, was taken from a Plainchant.  So we're still pretty much just dealing with chants at this point, just cut up and messed up and remixed until they're not really recognizable anymore.

Oh by the way, during this period there was also something I find absolutely hilarious and completely off the wall happening.  Sometimes, in order to get more tenor lines(The "tenor" in this period, refers to the melody, not the voice part), composers would just sort of... borrow from other works.  Which is sort of weird but ok, like a mashup.  Except that they would also start to borrow from secular works.  For their sacred works.  So it was entirely possible in this period to see a love song about a rose(which, in case you didn't know, is during pretty much all of music, code for a vagina) being sung alongside a sacred chant.  Basically, they were doing mashups of Ave Maria and Baby got back.  In churches.  This was still sacred music.  It is a tradition I think we should totally bring back.  Because it's awesome.

Also, while listening to this sort of stuff, it's important to hear that we're starting to hear the emergence of thirds.  This wasn't really a big thing that suddenly happened, but originally Fifths and fourths were considered consonant sounds, and thirds and sixths dissonant.  You can still clearly hear a ton of use of fifths and fourths during this stuff, because fifths and fourths are like, super-easy to tune, and as I mentioned, their ratios make easy mathematical sense.  Once singers starting singing thirds and sixths correctly though, they found that it had a sweet warm sound to it.  This slowly crept across Europe, and was known as the "Sweet British sound".  Guess where it originated.

I'm going to end this post for now, next update we'll look at Renaissance music.  Once we get past that and into the 17th century I'm sure we'll be able to cover more eras per post, but there is a lot of development that goes on in what I covered, and it's like, 1,000 years of music history.  Keep in mind that between Bach and today there are about 350 years.

Before I go though, here are some more examples of Ars Nova stuff, because holy shit it's so goddamn pretty to listen to.  I love this stuff so much.

As a note, Rose, Lis, Printemps, Verdue there is one of my favorite pieces of the era, because it's like, as textbook Ars nova as you can possibly get.

Oh yeah, sometimes they used instruments.

Ok, that was super-long.  As always, questions in the comments and I'll try to answer them.

Thursday, December 3, 2009

Lesson 3: Chord construction

Ok, so we know how to read music, we know about keys and scales, and we know about intervals.  So what about chords?  Most people, especially if they play guitar, are going to know about chords, probably that there are minor, major, 7, and power chords.  But that doesn't really tell us too much.  I mean, that tells you all you need to play maybe 90% of rock music, but it doesn't tell you the why to anything.

Now, since we know that certain intervals can be major and minor, and chords can be major and minor, they're obviously related, right?  They are, but not quite as obviously as you'd think.

Also, before I go on I should mention that I'll start using some shorthand to refer to intervals, so I'll quickly go over them:

The number is the interval, so a 3 would be a third.  A 5 would be a fifth.  Etc.

The letter/symbol is a little specific:

M = Major

m =  minor

aug = Augmented

dim = diminished

So, what are chords?  Chords are combinations of 3 or more different pitch classes.  With those, you have two or more stacked intervals.  Also you can measure an interval between the lower and upper note.  To make this a little clearer, let's look at one.

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So between C and E there, we have a Major third.  Between E and G there's a minor third, and we can measure a Perfect Fifth between C and G.  Also, this particular type of chord is called a "Triad".  A triad is any chord of two stacked thirds, and is probably what you'll see most often for a lot of music, unless you play jazz or grunge that has its own sets of standard chord construction.

Now you'll notice that the chord I posted has both a Major and minor third.  So which is it?  Major or minor?  Major-minor(This is also technically correct, but no one would say it)?  And what would happen if we had two Major or two minor thirds?  Would it be super-Major?  What if it had a fourth?  Or a fifth?  Holy crap!

Well, it turns out this is our intro to one of the annoying things about theory.  For a grand unified system that catalogs and explains like, everything in music ever, there isn't always a standard rule.  A lot of things with theory everything behaves in some standard fashion, and sometimes we just have nomenclature that you have to pretty much just learn.  There are still patterns and some ways to go about thinking about the whole thing that make it a little easier, but not so much a hard fast rule that everything obeys.  I'll try to give as many ways to think about this as possible, so hopefully at least one will click.

So we know of 4 different interval types, Major, minor, Augmented, and diminished.  To start off, let's look at the relations between thirds in different triads.

Let's for now only deal with Major and minor thirds, as, as I'll get to when talking about inversions, pretty much any triad can be boiled down to combinations of thirds.  In order, let's say we start stacking minor thirds.  A minor third on top of a minor third is a "Diminished" chord.  I know, there aren't diminished thirds in a diminished chord, but the chord is diminished.  Building from the root(The root is the bottom note of a chord when in the form of stacked thirds, it's also the note that we use to name the chord) up, if we have a minor third and then a major third, it's a minor triad.  Building from the root up if we have a Major third and then a minor third, it's a Major triad(Such as the example up there), and if we stack major chords it's an Augmented triad.  Ok, that's simple enough, though it doesn't really explain why diminished or augmented chords are called that.  However, it does lay the groundwork for looking at chords with more notes than triads, like 7ths.  

So let's look at the intervals from root to third and from root to fifth(In general, when talking about notes in a chord, we go by the scale degree if we were in the key of the root.  That sounds confusing, but essentially think that in C Major, with a d minor chord, f would be the third of the chord.  It's hard to explain but it does make sense and work out).  If we have a minor third and a diminished fifth, the chord is diminished.  If we have a minor third and a Perfect fifth, the chord is minor.  If we have a Major third and a Perfect fifth, the chord is Major, and if we have a Major third and an Augmented fifth, the chord is augmented.  This way makes a lot more sense, but part of that's because we're just ignoring half of the internal intervals, and when we add 7ths to chords this method falls apart a little bit.

Another way to think about it that sort of bridges the two, is if the fifth is unaltered, kind of pretend it doesn't exist, because it's not really giving the chord any value.  A perfect fifth is like, the quintessential "Open" sound, without any specific sonority.  So if you have a major third, it's a major triad, and a minor third makes it a minor triad.  The difference between it just being a third or a triad is the existence of the fifth, but the fifth doesn't do anything to the chord.  If the fifth is altered to make the chord smaller, it's diminished, and if the fifth is altered to make the chord bigger, it's Augmented.

And finally, we have the scale degrees above root with modifiers.  So 1 - b3 - b5 is diminished. 1 - b3 - 5 is minor.  1 - 3 - 5 is Major.  1 - 3 - #5 is Augmented.

Ok, hopefully one or all of those ways to think about this stuck, so we can move on to inversions, and then 7ths.

So what if there's a P4(Perfect 4th), in there?  There's nothing in any of those guides that accounts for a P4.  Well, let's take a look at something:

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Ok so.  What is this?  It's got a minor third and... a perfect fourth.  The interval between the... root? and.. fifth? is a minor sixth.  What?

Well what are those notes?  E, G, C?  Where have we seen those notes before?  What if we take that top note and throw it on the bottom?  Hey we know that chord!  Yeah, so that picture is a C major chord, just rearranged a little.  This is what's known as an inversion.  Inversions give a different sound due to their different bass note, and once we get to voice leading, can make bass lines move more smoothly than just always being on the root.

If the bottom note of the chord is the root, so C-E-G for our example, then it's in "Root position".  Pretty simple.  If the bottom note is the third, then we're in "First inversion", and if the bottom note is the fifth, we're in "Second inversion".  We haven't talked about roman numerals for chords yet(and it'll be a few updates yet), so for now we'll deal with probably how you've seen inversions and different bass notes, with a slash.  So C/E for instance indicates a C major triad with an E in the bass, or first inversion.  Now, some of you may notice that they're not exactly the same thing... sometimes you play the chord in root position in the right hand or on the guitar, for instance, and then like two octaves below that the bass player is sitting on their open 4th string and is that really the same as a stacked m3(minor third) and P4?  Well, as far as sound is concerned, not really, but as far as we're concerned with analysis pretty much, yeah.  Sometimes the bass note doesn't fit in the chord either, but that's a whole different bucket o' worms.

For those of you who haven't seen "C/E" or have any idea what that is, we'll cover that really soon, but first let's talk about 7ths.

So, triads we've got, they pretty much only come in 4 varieties.  What if you add another note?

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I apologize for that example, it was the only Major 7 chord I could find without having to search around too much or go through more shit than I want to for a single chord to come from Finale.  But let's look at the notes there.  G-B-D-F#.  Allright well that's four notes.  And what are the intervals?  Stacked we've got M3-m3-M3.  Above the root it's an M3, P5, M7.  Now, with an extra interval in there over triads, we have more combinations of minor and major thirds we can combine.  I'll just give you guys a list here of what the different 7th chords are, starting with the most diminished going to the most augmented:

Stacked thirds | Intervals above root | scale degrees with modifier : Designation

m3-m3-m3 | m3, dim5, dim7 | 1, b3, b5, bb7* : Fully-diminished 7

m3-m3-M3 | m3, dim5, m7 | 1, b3, b5, b7 : Half-diminished 7

m3-M3-m3 | m3, P5, m7 | 1, b3, 5, b7 : Minor 7

m3-M3-M3 | m3, P5, M7 | 1, b3, 5, 7 : minor-Major 7

M3-m3-m3 | M3, P5, m7 | 1, 3, 5, b7 : Dominant 7

M3-m3-M3 | M3, P5, M7 | 1, 3, 5, 7 : Major 7

M3-M3-m3 | M3, Aug5, M7 | 1, 3, #5, 7 : Augmented Major 7

M3-M3-dim3 | M3, Aug5, m7 | 1, 3, #5, b7 : Augmented 7 (This one's really hard to remember and stupid)

*No that wasn't a typo, that's a double-flat.  Double-flats behave pretty much like you'd expect them to... they're two semitones down.  So essentially they're a whole step down.  For double-flats, you just have two flat signs in a row, and for double sharps you have sort of an x.  In fact, an x will work in text.

To hear these, check out wiki, it has them all.  Also it has Triads.  

Ok, I've got go meet a vocalist to go over part of a studio recital, so we're going to end the lesson now, but I want to as a last thing go over the ways of writing the modifiers for chords, in case you see these symbols and don't know what the hell they mean:

Major Triad: M, Maj, Nothing(For instance, C would just be C Major)

minor triad: m, -, min

Augmented triad: Aug, +

Diminished triad: dim, o

Major 7: M7, Maj7, Δ(In my life, I have never seen that one used.)

minor 7: m7, min7, -7

Fully Diminished 7: o7

Half Diminished 7: ø7, m7b5, -7b5

Minor-Major 7: mM7, mMaj7, mΔ7, -Δ7(Again, those last two... I've only seen them in books, never on a score)

Augmented Major 7: Maj+7, Maj7#5, M7#5, Δ+7

Augmented 7: +7

Those triangle ones.... maybe as I think back I've seen them on one Jazz chart, but it's very rare.  Mostly if you remember that + is augmented, o is diminished, m is minor, M is major, you're pretty good.  

Also, finally, alt bass notes... I said I'd explain that.  When dealing with absolute chord notation like I have been so far, that is to say, not measuring with roman numerals, just the notes of the chords, if we have something like dm/F the F is the bass note, and we read that as "D minor over F", or "D minor, F bass" or "D minor, 1st inversion".

So if we see "D", we play a D major chord.  If we see "F+7" we play an F Augmented 7 chord.  If we see "Aoaddb6", we play an A diminished chord and add in a flat 6(F, in the example).  For anything not covered by the symbols, you'll often see something like "b5" in the chord designator, which really just means whatever else you're doing, flat the 5.

Tuesday, December 1, 2009

Lesson 2: Pitch relations

Allright, so now that we have the basic vocabulary down, it's time to start dealing with the nuts and bolts of what makes music music.

If you ask a theory professor, someone who will probably have glasses, a sweater vest, and lots of tweed, what a scale is, they'll probably give an answer like "A scale is a collection of unique pitch classes". Awesome. Of course, this tells us absolutely nothing. That could describe, like, everything in music.

What we're mostly concerned about, what you'll deal with most often, are "Diatonic scales" Wiki says a Diatonic scale "is a seven note musical scale comprising five whole steps and two half steps, in which the half steps are maximally separated" Awesome. Well that's correct, but what the fuck? What does that even mean? Maximally separated? Allright, so what it means is that there are 2 or 3 whole steps between each half step, depending on which diatonic scale you're using as well as when you ascend through octaves. Basically, a major scale is (W=Whole step, H=Half Step) W-W-H-W-W-W-H, and a natural minor scale is W-H-W-W-H-W-W.
This is a little easier when seeing and hearing it, so here's a C major scale
C Major
To make it a natural minor scale, we would flat the third, sixth, and seventh scale degrees, or E, A, and B for C minor.

Here's a C major scale being played, both ascending and descending.  You'll notice it sounds "Happy" 

And here's a c natural minor scale ascending and descending.  It's "Sad"

There are two other scales commonly used in common practice tonal theory, both of which are variations on the minor scale.

The first is the harmonic minor scale, which raises the 7th scale degree(from minor.  So it is in fact the normal, unaltered scale degree in major), both ascending and descending.  It sounds something like this:

The reason this is known as a harmonic minor comes a little later, when we start talking about the basic chords in a key.

And then finally we have the "Melodic minor", which is confusing because it changes depending on whether you're going up or down.  If you're ascending, you raise the Sixth and Seventh, so that the only note that is different from the major scale is the lowered third.  However, descending, the melodic minor is exactly the same as the natural minor.  It sounds like this.

Now, when we talk about "Scale degrees", we count in ascending order, and while in chord theory later on we'll be talking about 9ths and 11ths and 13ths, for the most part, after the 7th scale degree, we loop back to the 1st scale degree, but in a different octave.  So the third scale degree Now, n C Major is E.  The fifth is G, the seventh is B. 

And speaking of octaves, I've used that term a lot, what exactly is that? In order to lay the groundwork for some later theory stuff, each specific frequency, as well as any frequency which is derived by x^2/f or f/(x^2), where x is any whole number, is a "pitch class".  That is to say, a pitch class is any frequency as well as its double, its quadruple, eight times it, its half, its quarter, it over eight, and so on(Any math people, feel free to correct me if that formula doesn't say that). in other words, all "C"s are of the same pitch class. But they are not all the same note, because there are really high and really low Cs. What an octave is is the interval between two neighboring notes of the same pitch class. It looks something like this

Both of those notes are C, and the interval between them is an Octave(So names because they are the 8th scale degree apart from each other). Since an octave has the same pitch class for both notes, it's also an easy to discuss boundary for ranges of notes. So when I say that something is "In a different octave" or "crossing octaves", I'm normally referring to it being between a different octave of the 1st scale degree.

  So, for example, the scales I posted are all within the same octave, in that none of the notes extends above the 3rd space C or below Middle C the ledger line below the staff, with C being the reference because we're in the key of C

Which gives me a nice segue into keys.  When we're talking about key signatures and what key something is in, we're essentially talking about what notes are modified to fit into a specific diatonic scale.  So if we're in the key of A Major, as we looked at last update, we see that F, C, and G are sharp.  That's because in order to build a major scale based on A(meaning that A is the first scale degree, also known as the "Tonic"), we need to have those notes be sharp.  If we had no key signature, we would be in a minor, as the a natural minor scale needs no modified notes.  We name the keys based of the the Tonic, or the first scale degree.  So the key with modifications to build a major scale with the tonic of D is D Major.  The key with modifications to build a minor scale with the tonic of B is b minor.

For reference, here's the key signature for D major:

D Major 

And here's b minor:

b minor 

HEY WAIT!  I messed up and posted the same key signature for both!  D Major and b minor are examples of "Relative" keys.  Relative keys are keys that share the same key signature, but a different tonic.  The relative minor of any major key is based on the 6th scale degree, and the relative major of any minor key is based on the 3rd scale degree.  So C and a are relatives, D and b, E and c#, etc.  The other common relationship you'll see is what is referred to as "Parallel" keys.  A parallel key is one with the same tonic, but a different key signature.  So the parallel minor of C Major is c minor.

There's a trick here to telling what key you're in, too.  If the key has sharps, you go one step above the last(right-most) sharp in the key signature, and that's your major tonic.  So the last sharp in D Major/b minor's key signature up there is the C#.  One step above? D.  The sixth scale degree?  B, so the relative minor is b minor.  Specifically you go one half step above the last sharp, but you only go there when in really awkwardly written keys like B# or E#.

If the key has flats, then the second to last flat is the Major tonic.  So if you have two flats, Bb and Eb in the key signature, then you're in Bb Major/g minor.  If you have Bb, Eb, Ab, Db, Gb, you're in Db major/bb minor.

Also, there is a strict order to how you add sharps and flats that makes that work out correctly.  With sharps the order is: F C G D A E B.  With flats it's B E A D G C F.  There's a trick to this that won't make sense until the next part, which is that Sharps you add by going up by perfect fifths, and flats you add by going up by perfect fourths.  Which is also how the keys loop around.  The keys in order of increasing number of sharps are C(no sharps) G(one) D A E B F# C# G# D# E# B#.  With flats it's C F Bb Eb Ab Db Gb Cb Fb.  Again, that's a little more advanced, so I'll return to it later.

In fact, let's look at intervals now, so that makes a little more sense.

Intervals are the distance between notes.  They're also the term used for the notes when played together or sequentially.  So a "Third" is a combination of notes a third apart.

Lableing them is pretty easy, we name them based on how far apart they are.  If the notes are one step apart, they are a "Second".  If the notes are three scale degrees apart, they're a third.  Here are... well all the natural major intervals.  For the audio, they're all in C major, and they'll play the notes C - interval above C - notes together.

Major second

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Click here to download Major second.mp3

Major Third

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Click here to download Major third.mp3

Perfect Fourth

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Click here to download Perfect fourth.mp3

Perfect Fifth

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Click here to download Perfect fifth.mp3

Major Sixth

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Click here to download Major Sixth.mp3

Major Seventh

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Click here to download Major 7th.mp3

Ok, so quick thing, why are some intervals "Major", and some "Perfect"?  And for that matter, you may noticed I didn't mention "Minor", "Augmented", or "Diminished" yet.  Well, there's a historical explanation for the specific term "Perfect", but ultimately, There are 3-4 ways of defining any specific interval.  The interval remains the same in terms of diatonic scalar distance, but the pitch class distance isn't necessarily the same.  So a minor third is between, for instance C and Eb, while a Major third is between C and E.  They're both between a C and an E of some sort, but the chromatic modifier is different.  For fourths and fifths, there is no such thing as a "Major" or "Minor" interval.  If you look at Major v. minor scales this will start to make some sense, in that the fourth and fifth scale degree aren't modified.  Now I know what you're saying "But Khavall!  The second scale degree also isn't modified!"  That's true, but again, that's specifically the historical and mathematical reason.

For intervals with Major and Minor sonorities, the Major is the one that would occur in a scale based on the lower note in major.  It's a little confusing with that saying, but for instance, a C Major Third is C and E, and a c minor third is C and Eb.  An A major third is A and C#, an a minor third is A and C.  For diminished intervals, you shrink the interval one step chromatically from the minor, so a diminished third would be, for instance, D and Fb(Yeah, I know), where D and F is a minor third.  For augmented intervals, you expand the interval one step chromatically from Major, so C and E#(Yeah, I know), while C and E are the Major interval.  For perfect intervals, Diminished is one chromatic step smaller than Perfect, and Augmented is one Chromatic step larger than perfect.

Ok, so... some of you may have noticed something here.  Like, if you play a diminished triad on your instrument of choice it sounds exactly the same as a major second.  For a visual version of this idea, take a look at these two intervals:

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They look different.  They sound the same.  If you go one half step up from G, or one half step down from A, you arrive on the same key/fret.  So are they different?  Are they the same?  Why do we have both?

Well here's an important concept in theory: Behavior, and context.  You'll notice that I've been trying to separate the concepts of "Pitch class" and "note".  G# and Ab are the same pitch class, but they are different notes.  The difference between them are one of two things.  One is purely notation, the other is function.

     An Augmented fifth is probably going to be followed by the interval expanding, where a minor sixth is probably going to be followed by the interval collapsing.  Even without the interval, a G# will probably be followed by ascension, where an Ab will probably be followed by descent, if they aren't simply functions of the key signature.  They sound the same, but the specific note used is an indication of behavior.

Now, I mentioned key signature there... that's the other function of different notes for a specific pitch class.  In keys with flats in the key signature, a flat or even a double-flat is simply easier to read than a sharp, because if a performers mind is thinking in flats, suddenly reversing that to add a sharp in can be very confusing.  Sometimes a double-flat or double-sharp are even easier to read than Natural signs.  Essentially, if certain notes are in a chord are modified in one way, modifying other notes in a similar way means that the thought process is only "Down by X or Y" instead of "X is down by Y but Z is up by A and B is up by C from being down by D".  

Either reason can be why a certain pitch class is portrayed with a certain note, and like many things in theory, there isn't really a hard and fast rule to a lot of it.  Note that, for instance, I mentioned that Augmented fifths normally expand.  I'm sure with even cursory searching someone could find an Augmented fifth that collapsed, but the general use of an Augmented fifth is that it will expand.

And now that we know intervals, let's briefly return to key relations.  Once again, the order of keys with sharps is: C G D A E B F# C# G# D# A# E#, and flats is C F Bb Eb Ab Db Gb Cb Fb.  So what's the relation between them?  Sharp keys are what are known as the "Circle of fifths", while Flat keys are the "Circle of fourths".  That's because to get from one sharp key to the next, you ascend by a perfect fifth.  To get from one flat key to the next, you ascend by a perfect fourth.  

So today we've covered Scales, Keys, and Intervals.  Next update we'll cover chord construction, and then we pretty much will have covered the basics of construction of music, and can move on to what to do with all of it.

As always, if you have any questions, please don't hesitate to leave a comment and I'll try to get back to you.

Lesson 1: The most basic of basics

      I'm going to start this off with a quick note(ba-dum tschhhh):  I have not taught music at the absolute beginner level like this post is, and I cannot remember a time before I knew it.  Therefore, I may miss mentioning some things that are now natural for me to do or think about, and this will probably be my weakest explanatory post.  Hopefully I'll cover everything, however if you have any questions about anything I cover, please feel free to leave a comment with it and I'll do my best to answer any and all questions.  For that matter, the question thing will go for all the blog. 

     If I don't get this post out of the way now, I'm never going to remember to talk about a lot of these things, and there's a good chance there will be a lot of very confused people later on when I try to build on these concepts.  Many of you will already know all of this, but it's probably a good idea to make sure everyone's on the same page.

     So music.  Chords and shit.  And notes maybe.  Awesome.  What are those?  Why is there a squiggly line at the beginning of the lines?  And why are there fractions?  No one said anything about math.


This is a staff.  5 lines.  4 spaces.(I realize with this color it looks like only 3 lines... do a right click-> view image and you'll see it's 5)  It's been that way for somewhere around the last half-century, and 90% of notation will be on a staff.  But the staff is only the most base part.  It's like a sheet of graph paper for graphs.  Without any sort of axis it doesn't really mean anything, since while we'd know the relationship between notes on the staff, we wouldn't know any specifics.  So we need clefs!



Oh look, those images already have the notes for each staff written in.  How convenient.  So yeah, those little squiggles are the clefs.  Basically, they give you the baseline for where at least one pitch is, and that allows us to figure out where every pitch is.  The top one is called the "Treble" clef, and the bottom is the "Bass" clef.  On the treble clef, that little circle around the diagonal line(The second line from the bottom) is a G.  On the bass clef, the two dots to the right of the main clef part are on either side of F(The 4th line from the top).  Each one of those notes written after the staff are in one-step increments.  So the space above the G line in the treble clef is an A, the line above that is B, next space C.... you get the idea.  Another way people think about it is this:

Treble Clef

Spaces: F A C E

Lines: E G B D F

Bass Clef

Spaces: A C E G

Lines: G B D F A

There are a lot of acronyms to learn these.  Those are for pussies.  LEARN IT, LOSER!

Ok, we've got to touch on one thing here too.  I'll be using note names when talking about notes in absolute fashion, as opposed to solfege.  I'll cover solfege to notes at the end, because if this is a complete beginning then it'll just be confusing.  Also, if you're interested in solfege I'll cover a little of that in a later post.  Some things solfege is really useful for.  I'll cover it more during the ear training stuff, because that's where it's best for.

Anyways, that doesn't give us many notes does it?  I mean, that's like 9 notes per staff, right?  So, welp, guess we need to write all music in slightly over an octave(The fuck is an octave?  We'll get to that).  So we need a way to go beyond the staff

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     So these notes go outside of the staff.  Once you are more than one step outside of the staff, you need to draw a smaller staff line(Or a few smaller staff lines) to give us some sort of reference points for just how far outside the staff we are.  Having all of these all the time would be really confusing.  The same basic rules apply for these, just pretend they're permanent lines.  So the first space above the treble clef staff is G, the first line is A, the space above the temporary line is B, etc.  These are called "Ledger lines".  Now we can also give another reference point for staffs to tell us which octave we're in.  Middle C, which on a piano is pretty much the C in the middle of the piano, is the first ledger line below the treble clef, and above the bass clef.

     There are other clefs, specifically all forms of "Movable C" clefs(Alto, Tenor are the most common).  We'll get to those a little later, but they're pretty rare unless you play Viola, Cello, or Bassoon.

     Ok, so that gives us note relations in terms of where they are, how about how long they are?

Note values

The wide open one without any sort of stick(referred to as "Stems") are Whole notes(Upper left).  In 4/4 time(I'll get to that), they get 4 "beats", and take up a whole measure.  The open circles with stems are Half notes(Lower left).  They're half as long as whole notes.  The closed ones are Quarter notes(Upper right).  Who can tell me how long they are in relation to whole notes?  The one with a little flag on its end is an eighth note(Lower right).  The one with 2 flags is a sixteenth note(Middle far right).  With any of these, if they have a dot after them, they add half their value to the end.  So a dotted half note is 3 beats in 4/4.  A dotted quarter is one and a half beats in 4/4.

     Ok, we've covered what notes are what in the staff, and how long they are.  I've been referring to "4/4" time, what the hell is that shit?

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4/4  Were you to speak it it would be "Four-four".  But they look like fractions there kind of right?  That's exactly what they are!  So that means... "One", right?  Well not really.  The top number is the number of beats per measure, and the bottom note is what note gets the beat.  So in 4/4 there are 4 beats per measure, and the 1/4 note gets the beat.  So a whole note takes 4 beats and takes the full measure.  A dotted half gets three and takes 3 quarters of the measure.  A half note takes up half the measure and gets 2 beats.  Etc, etc, etc.  In 3/4, a whole note wouldn't fit in the measure.  A dotted half takes up the whole measure, taking 3 beats.  Which is how many are in the measure.

Now, if you're confused about what a "measure" is, a measure is an organizational tool.  So in 4/4, every chunk of 4 beats is a "measure"  On the staff, a vertical line is drawn between measures.  Basically, they allow you to tell where you are in small chunks of time, and make music readable.  Also, in a lot of tonal stuff, gives a strong beat, for instance, 1 and 3 in 4/4 are strong.  1 is strong in 3.  Stuff like that.

For simple examples of this, a simple 4/4 piece would be something like, since I'm watching Scrubs while writing this, the Scrubs theme song.  You can count along with this "ONE two three four ONE two three four" pretty easily.

And a nice 3/4 piece would be, well, any Waltz.  To use an example I'm sure many of us are familiar with, Waltz for the moon, from Final Fantasy VIII.  Here you can clearly hear the "ONE two three ONE two three" sound.

Some time signatures are a little different though.  6/8 is a common one, that has six beats per measure, but instead of the quarter note getting the beat, the eighth note does.  So a dotted half note, which is 3 quarter notes, or 6 eighth notes still would take up the whole measure.  6/8 is also a fun time signature because it's a "Compound meter", as opposed to a "Simple meter" like 4/4.  6/8 is normally felt in 2 beats, each one three eighth notes.  Technically, when 6/8 is thought of in 2, the "beats" are referred to as "Meta-beats".  No one ever says this unless they need to be super incredibly clear.

The easiest way to understand this is listening to "America", from West Side story.  You can clearly hear how the strong beats shift from "ONE two three FOUR five six" to "ONE two THREE four FIVE six"  So we would count the 6/8 part as "ONE two three FOUR five six" with the feeling in 2, and the 3/4 part as "ONE and TWO and THREE and".  

Speaking of which, we should deal with how to count things, since I just talked about that like it was a given.  Basically, you count the beats as numbers.  So on beat one, you say "One".  Beat two is two.  Three is three, four is four.  Awesome.   Note the "and" for America up there though.  When counting notes shorter than the beats, we need a way to keep the beats separate from the faster notes.  So we tend to use "and" to do eighth notes, so "One and two and", as well as "y"(pronounced "eee") and "a"(pronounced "uh") for sixteenths/triple notes.  So another way to count the 6/8, just keeping the meta beats in mind, would be "ONE and a TWO and a"  And if we had sixteenths in 2/4(Two quarter notes per measure) we would count "One-y-and-a Two-y-and-a" Also, sometimes you'll hear someone say "The and of two" or something similar to talk about a notes rhythmic position.  What that would mean is that the note happens when you would say "and" after "two"  So it would be "one and two AND"

I know that's all a little confusing on paper 'till it clicks, but it does all make sense in the end.  One good tool for playing around with this is something like where you can see it has preset for 1/4, 2/4, 3/4, and 4/4 with a different sound on beat one, so that you can hear the differences.

Now one final subject for today is chromatic modifiers.  What we've been looking at so far has been only the white notes on a piano, the notes that are in what is known as "Natural" position.  We would also call this the "Diatonic" form, in C major.  What that means is that the relations between the notes are unaltered by what are known as "Accidentals".  What accidentals are is they are chromatic modifiers, or modifiers of only a half step(The same distance between E and F.  Roughly a frequency ratio of 16:15.  Also, a single fret on guitar), also known as a semitone.

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These are the three types of accidentals.  The first is a "Sharp", which raises the pitch by one half step, the second a "Flat", which lowers the pitch by one half step, and the third a "Natural", which restores a pitch to its natural position(Some of you may note that there are also double sharps and double flats.  We'll get into those... quite some time in the future).  Essentially, if you see a C#(when written in notation, the accidental is written before the note, but when speaking or writing chord symbols, the accidental is after the note.  So we would say "C Sharp" instead of "Sharp C"(There are times when "Sharp C" is appropriate, but that's a whole grammar thing we don't need to get into)), then you take what a C and make it one half step higher.  On a piano, for instance, you would go to the black note right above the C.  On a guitar, you would go one fret higher.  Also, accidentals last to the end of the measure.  Once you see a "Bar line"(The line denotating the end of the measure), the accidental no longer is in effect.

In different keys though, writing every modified note would be a giant pain.  So we have what are known as "Key signatures", which we can put at the beginning of a piece or a section to basically say, for instance, in the key of G, that every F will be an F#

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Here's an example.  This is A Major, and we can figure out what notes are sharp, because the accidentals are over where the note would be.  So that first sharp sign is right on the top line of the treble clef staff, so it's an F.  Then we also have a C and a G sharp.  So until we see another key signature or the piece is over, every time we see a C, it's a C#.

Now there's a big chart I have here, that has every key signature and what key it is.

Circle of Fifths.

holy crap.  That's a lot of fucking stuff.  Again, do a "view image" to see the whole thing.  If you want to practice reading key signatures though, that's a good thing to look at.  Try to figure out which notes in which key are changed.

Next lesson when dealing with pitch relations I'll talk more about exactly what makes a Key a key, and how to figure out what key you're in from the key signature.  But for now, just know that if you see accidentals at the beginning of a piece right before the first measure, it's the key signature, and it means alllll the notes are changed in the way the signature says.

Anyways, that's the very bare bones of reading music.  I'll be going pretty fast with this sort of stuff from now on, so if you were sketchy on any of this stuff, hopefully this helped clear it up.  Next article I'll write will be on simple note relations.

And as a P.S. I'll touch on solfege to notes.  If you were using "Fixed do" solfege, that is to say, the first ledger line below the treble clef is Do regardless of what key you're in, then this is pretty easy, basically you're just learning new names.  Do is C, Re is D, Mi is E, Fa is F, Sol is G, La is A, Si(or Ti) is B.  If you've learned movable Do solfege, or solfege where whatever key you're in, the tonic note, or the first scale degree, is Do, then basically you can just follow along and keep solfege as a completely different thing, because solfege is then just a measure of relations, while this is a measure of absolutes.

so again, any questions, please feel free to leave a comment and I'll try to clear it up, and I'll see you all again next post.

Intro to Intro to Music Everything: What are you doing here?

   This is a blog about music.  Specifically, this is a blog about the History and building blocks of music.  There are many textbooks around that explain history and theory and everything I'll be covering in much greater and more detailed fashion.  Many subjects I'll write a single blog post, or maybe two, and one could easily spend an entire lifetime studying the same thing.  So why start the blog?  If there are so many resources out there, and there's so much to study, why a dinky little blog in the nowhere corner of the internet?

    Put simply, this is meant to be an overview that hopefully is less painful to read than the Norton Anthology of Western Music, 7th edition.  And less time consuming than spending a year at a music conservatory to learn why exactly an Aug6 chord functions as a Predominant and what forms of Aug6 chords there are and why and how they got their names and how were they used.

     And that's why I'm here, but why are you here?  Maybe you're asking yourself that now.

     Knowledge of the building blocks and history of music is important to every musician, be you rock, classical, jazz, whatever.  Because that knowledge gives you two things.  It gives you a broad toolset, and it gives you context.  Why does Wheezer's "Say it ain't so" go to a G# Major chord in c# minor?  And why does it have the b natural thrown in there with the B#?  And what the hell even is B#, and why didn't I just write C?  Why does Charles Ives' "The Unanswered Question" have two distinct groups playing completely different things?  What the fuck is Dorian and why do I use it over m7 chords?

     And the answer to each one of those questions is important to everyone, not just one person.  Music is a set of signs.  Some are idexes, ideas given meaning by past context, such as a perfect fourth played in a specific way evoking the idea of a wedding, because it's how "Here comes the bride" starts.  Some are iconic, an attempt to model a thought exactly in sound, such as Messiaen's use of tritones to mimic bird sounds.  Unlike language, which also contains Symbols, or signs arbitrarily agreed upon as standard, such as the word "Tree", which while it has nothing to do with a tree in form or function, and is not simply a personal association, is imbued meaning, music has very few if any symbolic signs.  Learning all these signs, learning how they often are used, learning, how they interact with each other and why, it allows a composer and a performer to have far greater control over their medium.

     This is not going to be a set of rules or laws to go by to create or perform music.  This is not going to be an exhaustive list of things to learn to be able to do music.  I'm not trying to stifle anyones creativity, or stop any one method.  What this blog will do is provide an expanded toolset to performers, composers, singer-songwriters, whoever stumbles upon it.

    Because knowing is half the battle.

     Go Joe.