Music Theory 8: Rise of the triads

Well hello again, after a nice break it seems it's time to get back into the swing of writing about theory. Today's discussion revolves entirely around triads and how they function. While the dyad is your functional basis for outlining basic harmony, your triad is really where your chords, keys, and tonalities are established. Triads are the foundation of harmony, and their importance cannot really be overstressed.

So what is a triad? Well, it's like a dyad, but with three notes instead of two. Triads usually come in a common form, but do not have to. So to properly define a triad, it is a combination of three notes played in manner in which they end up sounding at the same time, that can be stacked into an arrangement of major, minor, augmented, and diminished thirds. This does not necessarily mean they are played at the same time, merely that they all sound together at some point. Technically they don't even need to sound together, but in close enough proximity that your ear's tonal memory interprets it all as cut from the same cloth, but that isn't really an important detail to remember at this time.

As per normal, we'll start with C Major. This is a C Major triad. A chord chart will notate this as either CMaj or C. There are a few interesting things to note (haw) about the structure of this chord. Firstly, our root note is the tonic, C. Roots are just the same as they are in plants, the thingy at the bottom of the structure, be that note or delicious nutrition intake. Our second note is E, a major third up from the tonic. Our third note is G, a minor third up from the E, and a p5 up from C. Consequently, we can describe our chord structure as being 1-3-5. Now, while a p5 sounds like an empty restful interval, a C Major triad sounds full and restful. Your standard major triad possess a 1, which is to inform you which key the triad is in, and a 5, which gives you a good frame using the strength of the p5 interval. I feel like there are way too many commas in the previous sentence, perhaps I should start using ellipses? With this strong frame we add in a 3rd to color the chord. The 3rd, or something functioning like a 3rd, provides us with the needed color in any chord.

With this knowledge, can we then infer what the composition of a C minor chord is? Yes, yes we can. The only difference is the 3rd . We can see this chord is hanging out in a very strange composition, since he was given a time signature, but not a double bar. A single minor chord doesn't make the most interesting harmonic motion, but hey I'm open to it if you are. Notice that from 1-3 we have an m3 and from 3-5 we now have an M3. Keeping that intervallic ratio works across any key, but you probably already knew that by now. Meaning that an Amin would be A-C-E.

So returning to our CMaj chord for a bit here, remember how we talked about inversions a few lessons ago? This becomes much more interesting and important as it pertains to triads. I have no idea why this image decided to go with half notes instead of the standard whole notes. On the left you can see the root position, with the C on the bottom like God and Jesus intended. Next to that we have first inversion, where they took the C and moved it to the top. Our chord is now E-G-C, but still functions like a CMaj chord. The root note is no longer on the bottom, but it still acts like a root in this chord, because if the chord was re-arranged it would be on the bottom. Looking at intervals, we have an m3 followed by a P4. Since there is no P5 in this chord (even though there might be one were the chord in root position), it is not as strong and decisive as if it were in root position. Additionally, the P5 isn't framing the 3rd, further weakening the chord. By weakening I mean that were you to hear this chord as the resolution of a build up of inevitability, it would not sound as satisfying as if the chord were in root position. Moving along, further on the right we have second inversion. First inversion is where the root is on the top of the chord, second inversion is where the root and 3rd are now on the top of the chord. Third, fourth, etc inversion exist when your chords have more notes in them. We can get to that later though. Second inversion has a P4, followed by an M3. Arguably this is stronger than first inversion because it has the M3, but not as strong as root position due to the lack of the previously mentioned. In practical use though, no one really cares. Both are weaker than root position, which is really what matters.

Do inversions work the same in minor as they do in major? Yes.

We now have two good triads under our belt, which means we can talk about something a bit more complicated. This is a C Diminished triad, or Cdim. Notice the diminished 5th interval. This is not a stable chord, and should never be used as a rest point unless you are writing something super weird or really know what you're doing. This is because of the natural tritone, it wants to pull itself apart into different chords. The strength of this chord is lessened with inversions, but not by much. There isn't really a good reason to know about the diminished triad at this point, but I'm covering it for completion purposes. This is similar to our next chord:

The C Augmented triad! Notice that while the diminished triad had a minor third, the augmented triad has a major third, and the quality primarily comes from the 5th tone, which in this case is an augmented 5th. This chord is totally weird and you'll almost never see it. It sounds pretty cool and dissonant, and is better as a rest point than the diminished chord, but still isn't very good. It's also very hard to approach and resolve from, so it as an actual presence is exceptionally rare. I honestly haven't seen it much at all, and so anyone who can provide examples of it's use is more awesome than I.

As I'm sure you can see, this is all a simple extension of the concepts covered in the previous lessons, and you can probably guess where things are going to go from here. Some intrepid soul might ask, "How come we don't take a C, add an augmented 3rd on top of that (F), and then another augmented 3rd? (B♭)" This would end you up with a chord that you could rearranged into F-B♭-C, which is another type of chord that isn't technically a triad, no matter how much I may have wanted to write about it. Basically there's a limit to how many ways you can rearrange chords and associate notes with eachother, and that configuration, although spread way out, would sound more like one thing than a triad, and would function as such. As always, questions & comments are appreciated.

Music Theory 7: Do a deer, a female deer!

Well its the 7th post solfege extravaganza! It was brought to my attention that the lesson on intervals was missing a few key points, and that doing some ear training on the side would be very helpful in understanding how they function. This post will be audio heavy, and we're going to do some analysis on melody and how it works too. All in all it should be pretty interesting.

Solfege is the process of assigning syllables to musical notes so that you aren't singing a melody without words as 1-4-5-3-6-3-5-1 or something like that. The system is pretty well known due to that song from the sound of music, but most people don't know how to do half steps with it. Nor are they necessarily competent at actually singing in the appropriate tones. There are two systems which assign solfege syllables, called the movable do system and the fixed do system (do is pronounced the same as dough). The fixed do system is primarily (to my understanding) used in Europe, and since Europe is full of communists and terrorists, we will not be using it.

The movable do system is a pretty easy concept, it simply means that the syllable do, attributed to the tonic in the established key, is dynamic. If you are in the key of E, the E is do. Key of F, F is do and so on. The fixed do system has each note on the keyboard assigned to the same syllable every time. I think do is always C, but I'm not sure because I'M A RED BLOODED AMERICAN ALL I EAT IS STEAK. I prefer the movable do system on principal just because it is much more clearly demonstrable to the relationships between the various notes than the fixed do system is. Let us remember our chromatic scale now!



Let us now assume for the sake of argument that we're in the key of C Major, I see no key signature so its a pretty safe assumption. C is therefore Do. Moving along, we continue up the C Major scale first with the basic syllables. C = Do, D = Re, E = Mi, F = Fa, G = Sol, A = La, B = Ti. These are pronounced Dough, Ray, Me, Fah, Soul, Lah, Tee. Now we shall look at the chromatic syllables. Like the melodic minor scale, this differs depending on whether you are ascending or descending. Notice a theme? I'm going to include pronunciations in parentheses next to the syllables.

Ascending: Do, Di(dee), Re, Ri(ree), Mi, Fa, Fi(fee), Sol, Si(see), La, Li(lee), Ti, Do!
Descending: Do, Ti, Te(tay), La, Le(lay), Sol, Se(say), Fa, Mi, Me(may), Re, Ra(Rah), Do.

Please notice that the flat 2 when descending is Ra, the glorious god of the sun! I'm sure you were on pins and needles waiting for him to show up since he stood you up at the bar last week. To get these really cemented in your head I seriously recommend singing a few chromatic scales with the syllables until you get it so you embed the ratios in your brain.

So lets do some listening here to analyze what we're doing. To start, we will use Mary Had a Little Lamb, which is a little ditty that most people are taught when they initially learn how to play the piano.



I chose this selection because it was somehow less annoying than the other example I found. I'm still not quite sure how this works. Listening to our melody, which is sung by a totally kawaii girl ^_^, we can analyze as being 3-2-1-2-3-3-3, 2-2-2, 3-5-5 etc. Or: Mi re do re mi mi mi, re re re, mi sol sol, mi re do re mi mi mi mi re re mi re do.

Ok! That was easy, so lets get a bit more complicated. Here is a series of scores by Robert Schumann (you may need to click a link to get them to let you open the page), and here are the associated works so that you can listen along. Let us examine Melodie first.

First off, notice C in place of the time signature. That indicates Common Time, or 4/4. Secondly, notice that the bottom staff on our grand staff is also in the trebel clef. Finally, those 2 dots in the 4th measure indicate that you are to repeat those 4 measures one time before moving on. Our melody, which is always the topmost note in this case (but that is not always true), starts off with mi re do ti la do ti re do sol. It then continues with sol fa mi do ti la sol. About the only other thing of note with this work is the use of the natural sign in the 8th bar, to cancel out the sharp C in the bass line.

Soldatenmarsch just below it is also a good example to look at, and will help us examine the movable do system a bit. The melody is on top as per usual. We have a couple clef changes in the bass too, but we don't really care about that so much. Starting on B, we go mi fa sol la sol fa mi re do, mi fa sol la sol do ti la sol, then that line repeats. Skipping down to the next set of lines, right after our repeat sign that's facing to the right (meaning when you are directed to repeat a passage, you go back to that sign and begin there), sol la ti la sol la sol fa mi, now this gets interesting. Our melody is briefly transferred to the bass note, as we have a nice little chord here, then back to the top notes. Notice how, when we go up an octave, the syllable does not change. This is a limitation of the system.

For my last example, we're going to get considerably more elaborate. I've had a hell of a time finding decent examples that have sheet music too, such that you can follow along. But I found something that's more complicated than what we've done, and is a song everyone should know because it is awesome.



And the transcribed solo is here. We're going to be looking at Miles Davis' solo for this song, which starts at about 2:13 or so. Take a couple listens to it so that you're familiar with what he plays. Notice our key is Bflat, so we'll use that as our do. Also please notice that the eighth notes are not played in a strictly even fashion, this is a stylistic choice present in jazz known as swung eighth notes. More on that later.

Easy enough, we start out with do do do. A couple rests, then la do la li re. La do me fa me la. Do te te re la sol. Ti la ti la sol la ti do sol la li fa. Le do mi sol sol te la la fa.

And so on. Feel free to poke through the rest of it. Please notice that context is important for the syllables. In general when a passage is ascending you use the ascending ones, and vice versa. In the case of the me in the 3rd group, it functions as a flat 3 in that passage due to the tones surrounding it, this will make more sense in subsequent lessons. The te at the very end is approached through an ascent, but is then used as part of a descending phrase, and is thus more applicable to the 7th than a raised 6th. Fudging it is ok though, no one is going to yell at you for using the wrong syllable.

I feel like this lesson is somewhat lackluster, but it should give some general grounding about how to interact with intervals. Thanks as always.

Music Theory 6: Oh no, I lost my keys in the cycle of fifths!

Having intervals under your belt, you may feel all high and mighty, as though you can conquer the world. If you can analyze and understand the basic relationship of 2 notes, adding another would be really easy! While I could certainly do that and go into that direction, I feel it would be easier to discuss keys, key signatures, and scales before doing so, as the topics covered therein assist the learning of more complicated chord structures.

So returning, as we so often do, to C. The first key that we will be looking at it is C Major, as it is the easiest, and who doesn't like easy? Hint, the answer is terrorists. So first off, what is a key? A key is a collection of tonal structures that surround the resting note, or tonic. The tonic is also the 1. In C Major, the tonic is C. So C Major is the collection of tonal structures that surround C. Keys come in a number of shapes and sizes, but we won't get into most of them until we cover a more advanced subject. For now, just know that there are Major keys and Minor keys. C Major and C Minor are similar in that they both are centered around C, but have totally different chord structures centered around them. Major keys are those which have the 3rd interval be a M3, Minor keys are those which have the 3rd interval be a m3. The 6th interval is also important to this concept, and follow suit being either M6 or m6, respectively. Every key possesses a Key Signature, which is some notation on the staff which denotes which key you are in (this makes it easier to read the music).

C Major's key signature is easy, it's totally blank. When we get into another key I'll discuss how to notate key signatures. For now, lets go about figuring out what intervals are present in C Major. By figuring this out, we then establish the C Major Scale. Remember, a scale is a sequential ordering of tones in a specific order, to produce a result. The chromatic scale being all tones present in an octave, any other scale must be a reduction of this. Traditional scales are of 7 notes(+ 1 at the octave), I'm not sure why. So if you've taken any beginning piano, you have played the C Major scale, its simply start on C, then play all white keys up to the next C. However we're erudite theoryographers, and we can break this down to a more useful format, so that we might play Major scales in other keys (I know, heresy).

The C Major Scale, in all its glory:

Exciting, no? So to analyze it, our first interval is M2, C to D, one whole step (or whole tone). Continuing on, we get another whole step, D - E. E - F is a half step (m2), then M2, M2, M2, m2. The cheater way to tell this is to watch the lady's key presses, the black keys are half steps (semitones). This ends us up with a pattern of "whole whole half whole whole whole half", in terms of step duration. Now you can play any major scale starting on any note. Simply follow the whole step & half step pattern. What does this net us in terms of overall intervals? M2, M3, P4, P5, M6, M7, P8. Easy now to see why this is a Major scale, huh? Now it is interesting to note that there is one other scale that falls into the concept of Major, but its quite a bit more advanced, so for all intents and purposes, this is the Major scale. Moving along by 5th, we head to G Major, which is the P5 of C
Major, for our next scale.

Wait, why did we move by P5? What's wrong with P4 or M2? Nothing at all, but P5 makes things easiest, as keys apply to a concept known as the Circle of Fifths or Cycle of Fifths. Those are synonyms, so don't get confused now. Why they follow this will become evident as we explore.

BEHOLD! G MAJOR! Wait, what's that F# doing on my staff? I thought I had topical cream for that. Anyways, that's a key signature! It tells you that when you see an F on the staff (in any position, not just that one), that it should be played as an F#, and not a regular F (or F♮, read as F natural). The natural sign, ♮, means that you should play a note that was augmented or diminished by some means (including key signature), in an un-augmented/diminished manner. G# becomes G, G♭ becomes G. Make sense? Back to key signatures, when you see a lonely F# next to your clef, that indicates that you are now in the key of G Major (this is not true, but we're running with it for now. Stay tuned for the thrilling conclusion!) (I like parentheses).

To figure out how this works, start on G and count your whole step/half step pattern. You come up with G, A, B, C, D, E....then you need a whole step to go from E. A whole step up from E is F#. That also lends us the half step needed to finish out the scale, as F# to G is a half step. Cool huh? Now, if C major had no sharps or flats, and G Major has 1 sharp, what logically follows as the key with 2 sharps?

That's right! It's D Major! Counting up a P5 again, we get to D from G. Once again, count your whole and half steps to figure out where the sharps lie. If you guessed that the sharps present were F# and C#, you would be correct. Wait, F is sharp AGAIN? Is it going to be sharp for all of these keys? Well, for all the sharp keys, yes it is. Sharp keys being ones that are defined by having sharps in their key signatures. Yes, there are flat keys too! So if F is going to be sharp for all subsequent keys, does that mean it needs to be present on every key signature? Yes it does! For simplicities sake, the F# is the first sharp on any sharp key signature.

BEHOLD! D MAJOR! We can see our F# in the same position before our C#, which is in its own position. These positions do not change in key signatures. The idea being by having them consistent its quick and easy to tell what key you are in. So this idea of moving by P5 (remember how important I told you it was?) seems to be working, so lets run with it.

Next up then is A Major, which has 3 sharps. After that is E Major, with 4 sharps, B Major with 5 sharps, and F# major with 6 sharps. F# major is extra special, for reasons we'll go into in a bit.

BEHOLD! F# MAJOR! Here you can see the full list of sharps as they apply to key signatures. According to Wikipedia there is apparently a C# and G# major, but anyone playing in those is making their lives unreasonably difficult. Also according to Wikipedia, Miley Cyrus' 2009 smash hit "Party in the U.S.A." was written in F# Major. Ahh the wonders of technology.

Onwards and upwards, lets return to C. Now, that whole moving up by P5 was pretty exciting, but I think we can get more exciting by moving DOWN a P5. That takes us to our first flat key, F Major! Now using our same formula of half-step counting, lets look at how F Major works. F-G-A, uh oh we need a half step. A half step up from A is B♭. Why isn't it A#? Because it is functioning as the 4th interval (or 4th scale degree). We already have an A, so it has to be a B, which means its B♭. A whole step up from B♭ is C, and then we're back on track with D, E, F.

BEHOLD! F MAJOR! Notice our B♭ there on the 3rd line, not giving a hoot about who sees him. Continuing on, you should be able to parse out the succession. I'll write it here for brevity. Major keys in increasing numbers of flats are B♭, E♭, A♭, D♭, G♭. The interesting thing here is that we have G♭ Major, which is nominally the same as F# Major, right? Yep! This is called enharmonic equivalence. A note that is enharmonic is one that is the same as another written representation. Sometimes people write stuff in G♭ Major, sometimes in F# Major, although people who write stuff in F# Major are clearly masochists who don't like playing in a proper key. Anecdotally, most classical musicians I know prefer the sharp keys, and most jazz musicians I know prefer the flat keys.

BEHOLD! G♭ MAJOR! As you can see, it has 6 flats and is much neater and better organized than that stupid F# Major. I link that so you can see the organization of the flat key signatures.

So now we've spent a lot of time talking about Major keys, but none talking about Minor keys. So with Minor keys you don't start with C Minor, as it's a bit more complex. We start with A Minor.

BEHOLD! A MINOR! Wait a cotton pickin' minute! That looks like C Major! This is because A Minor is comprised entirely of natural notes too, and the scale simply starts on A instead of C. This is called relative minor, which is that every major scale has a relative minor scale, which shares key signatures. Remember how I said that the key signature meant we were in G Major, but that it wasn't actually true? This is why. When you notate these, the key signature only indicates that you're in one of the two, and whichever one it is does not actually matter. It will become clear because it will either center around the tonic of the major key or the tonic of the minor key.

By starting on a different scale degree, we change the whole step and half step pattern, which makes the scale sound totally different. It is interesting to note that while there is one (technically two, ignore this for now) Major scale for a key, there are 3 Minor scales. If you were looking for a reductionist reason for why musicians are so whiny, this is probably as good a place to start as any. So our relative A Minor scale is the 'natural' minor scale. Natural minor is classified by having an m3, m6, m7.

It sounds like .

Please notice him play the scale for 2 octaves, and also horribly mispronounce Aeolian. He is correct that the natural minor scale is also called aeolian, but don't worry about that for now. Second on our minor scales is harmonic minor. It got this name because it was originally used purely to identify proper chord tones for use in harmonic structures. It has a somewhat exotic sound, because of its augmented second at the end (in A Minor F-G#). The only difference between it and natural minor is it possesses an M7 instead of an m7.

It sounds like this!

Please notice that the scale you care about comes about a minute in, and that he has completely idiotic opinions on the usage of the natural and melodic minor scales (being as that using the harmonic minor scale for a melody in the 1600s would likely get you burned at the stake). He does give some good information on the whole step/half step ratio, which I will cover down below.

Finally we come to the melodic minor scale, which is different going up than it is coming back down. On the ascent, it has the standard m3 (the main descriptor of a minor key), but it has a M6 and M7. On the descent, the 6 and 7 become m, so m6, m7, but the m3 is untouched. This scale was developed for melodic writing in the old traditional days, as ascending up to an M7 created good inevitability.

It sounds like .

Please note that I have no idea what the hell that dude is saying. Also notice that all of these minor key examples have guys saying "Deriving this from the major key is the easiest way". Now lets get to the whole and half steps.
Natural minor: whole half whole whole half whole whole
Harmonic minor: whole half whole whole half aug2 whole. Augmented second is a whole step + a half step.
Melodic minor: (ascent) whole half whole whole whole whole half (descent, think organized as coming down from the upper note) whole whole half whole whole half whole.

Ok! We now know our major and minor keys, key signatures, and scales! You should be able to identify your key signatures at a whim, and quickly discern what note I'm talking about if I say "4th scale degree of A♭ Major!". You understand some of why the P5 is such an important interval too. Most importantly, you now know what a tonic is. Trust me, that one is going to come up a bit. As always, questions and comments are welcomed.

Music Theory 5: Intervals, Satanism, Dissonance oh my!

Tag team, back again. Today's very special episode of Music Theory is starring the interval! An interval is the measurement of distance between two notes, and how the notes relate to each other. This measurement refers, in basic theory, to the measurement as it pertains to and including the octave. The main thing to remember here is the number nine, but we can get to that in a bit.

Remembering where we left off with half-steps, we are going to define our distances with the name, as well as their distance in half-steps. There are five types of interval, Major, Minor, Perfect, Augmented, and Diminished. Perfect intervals are the easiest to explain, because it is the smallest subset. A perfect interval is one which when inverted, remains Perfect, is perfectly consonant, and appears early in the harmonic series. The question now becomes, what the heck does that mean? An inversion is when you change the organization of a set of tones, such that the lowest (or bass voice) tone has changed, while preserving the initial tone set. I'm not really simplifying this very well, am I? With examples it quickly becomes clear. I should add that this is an overly complicated explanation for a very simple concept.

The first perfect interval is P1, or the perfect unison. Lets use C for our example note. Our plucky musician plays a C, then plays the exact same C a bit later. He has represented P1 (P for perfect, 1 for unison) well, perfectly. The measurement here is zero half-steps, it is the same note. Since it is the same note, it cannot be possessed of any natural dissonance above and beyond what is present in the sound generated by the sound source itself. This is initially somewhat confusing, because there is a trend towards thinking that a measurement of zero is nothing, but that is not the case here. Unison functions in a very specific manner in music, and thus is not nothing.



The second perfect interval is P8, or the perfect octave. Using our C from the previous example, our musician hammers away at a C one octave higher, playing both notes simultaneously. Two notes played in tandem is called a dyad(I think that is how it is spelled). Since both notes are the same note, just an octave apart, this too cannot be possessed of any natural dissonance. Now that we have two simple intervals, lets revisit that inversion business and see what we can figure out.



In our perfect unison example, we have 2 instances of the same note. Let us now assume that both notes have been played simultaneously by 2 players, so we have a dyad. To invert this interval, we take the bass note and move it up an octave. Since both notes are the same, one of our players just begins playing a note an octave higher. Our P1 has now become a P8, meaning the intervals retained perfect status through inversion. OH MY GOD IT IS LIKE HE SELECTED THE COMPLETELY RANDOM EXAMPLES SPECIFICALLY FOR THIS PURPOSE!!!! Wheels within wheels, maaaaaaaaan. Now the really interesting thing to note about this is when you add the numbers up, you come up with 9. It is tough to keep track of all of the wheels in motion here!

That's all easy to follow, so lets elaborate. Same set up with two musicians. First musician plays a C, second plays the G above that C. This is a perfect 5th. We can identify this in a couple ways. The easiest is to count note names: C, D, E, F, G. C is the first note, G is the last, there's a total of five. We can also count half steps (go ahead and count, I'll wait!), of which there are seven total. This is transitive across any dyad, it doesn't just work for C to G. The perfect fifth is one of the most important intervals there is, and has perfect consonance.

Which leads us into an excellent opportunity to explain consonance and dissonance. If you want to talk about concepts that have really defined and shaped western music through history, these are two of the biggies. Consonance is the listening state of being at rest, and means that your sonic quality does not have any warbling or beating to it. Dissonance is, conversely, the listening state of being in motion, and means that your sonic quality does have beating. To explain, being at rest means that your ear is completely satisfied with that which it has been presented, and does not feel like it needs to continue musical motion (whether or not further musical motion is presented). To hear this we should consult a master. Go to this website and click to listen to the Minuet in F Major. Direct linking appears to be disabled.

This piece is in 3/4. Listen to the melody, and how it seems to express a musical thought over the course of 4 measures. This then repeats through the work. At the end of every set of 4, notice how your ear doesn't seem to like that held half note at the end, but much prefers the last quarter note when played. This is especially noticeable at the end, as our second to last set of 4 does not end in a satisfactory manner, instead we have to wait for the last 4, which is then held for a longer period of time and feels like a proper ending. That feeling at the end! That is rest. We have brief periods of rest at the end of every 4 measures, but they are de-emphasized in order to keep the work light and fanciful. Those held notes that seem to pull you to the final note in the set, those are in motion. They're pulling you towards the end, which establishes a good sense of inevitability. Remember that one from AC/DC? Now, this is not to say that ending in motion is bad or not acceptable, it is just a different sound that is unsatisfying to the listener. Sometimes you can't get no satisfaction. Please also note that consonance and dissonance are somewhat of a sliding scale. The perfect intervals are as consonant as it is possible to get, and all other intervals are of relatively increasing levels of dissonance.

Onwards and upwards, our next interval is the P4. Composed of 5 half steps, it functions differently than all of the perfect intervals. Before we discuss how it functions differently, lets talk about inversions again! The inversion of the P4 is, naturally, the P5 and vice versa (oh look, they add up to 9). This is good to keep in the back of your head, because the P5 will take a major center stage in the near future, while the P4 lies forgotten by the roadside, having to scrape together cash by begging on the street. Sure the P5 is going to occasionally kick some cash P4's way and they'll both pretend they're ok with how things have turned out but really P4 keeps on plugging away trying to make the chords work, while P5 is covetous of P4's laidback lifestyle. The main thing that's interesting about P4 is that it is a restful state when approached in one manner (Herbal Tea) and is in motion when approached in another (Coffee). Approached in this case means stuff played before we get to the the P4. This means that it possesses perfect consonance, as is required of a perfect interval, but can be used as dissonance when prepared properly. The reasons for this have to do with the harmonic series gobbletygook I posted about above and which I'll explain at some point.

That takes us out of perfect intervals, and onto the other 4, which are more complicated, but will be quicker to explain. Most of their complication will take place in subsequent lessons.

One point that needs clarification is that to define an interval one defines the note by the scale number and position first. Because our starting point was defined as C for this, that is the first note, or the 1. The 2 would then be a variation of D, the 3 would be a variation of E, etc etc. Since we're using the chromatic scale, when ascending (Remember it is notated differently depending on directionality) the C# would be defined as a 1 also.

The Major intervals are M2, M3, M6, M7. M2 would be C to D and possesses 2 half steps. M2 is a dissonant interval, and is one of the most dissonant intervals. M3 is C to E, is 4 half steps, and is a consonant interval. M6 is C to A, 9 half steps, and is a consonant interval. M7 is C to B, 11 half steps, and is a dissonant interval.

The Minor intervals are m2, m3, m6, m7. Looks familiar doesn't it? Please notice that the m's have become lowercase, that is to distinguish between major and minor. Minor intervals are simply Major intervals that have been diminished by a half step, and function similarly. Thus, m2 is D♭. Remember, defined by scale position first, so even though this could be called a C#, it doesn't function as one. m2 is one half step, is a dissonant interval, and is even more dissonant than M2. m3 is C to E♭, is 3 half steps, and is a consonant interval. m6 is C to A♭, is 8 half steps, and is a consonant interval. m7 is C to B♭, is 10 half steps, and is a dissonant interval (technically).

Inversions for Major and Minor intervals function a bit differently than Perfect intervals, since Perfect intervals invert to other Perfects. Major intervals invert to Minor intervals, and vice versa. Don't believe me? Lets look at M3! M3 is C to E, 4 half steps. E to C is how many half steps? That's right, it is 8 half steps, which is m6. What is major, now is minor. The other conversions should be easy to figure out.

Finally we get to discuss Augmented and Diminished intervals! I'm sure you're on the edge of your seat waiting to see how all of this will resolve. Augmented intervals are ones that have had their pitch raised. Diminished intervals are ones that have had their pitch lowered. So if we have a M3 that is then diminished, we get an m3. If we then take that m3 and diminish it further, we get what would ordinarily function as an M2, but is in fact a d3 in this case. Now we're discussing actual theory! Things that are technically correct but practically useless! Function before form! I'm only half joking here. There are very good reasons why a dim3 would be used instead of a notation that would make more sense at a first parse. Those, however, are much more advanced than we're going into this lesson, and so just take my word at face value, as you must do with creation science as well.

More applicably, were we to wish to modify a perfect interval, it always immediately goes to a diminished character. Some of you may have noticed that we are missing the G♭ from these examples. This fine young gentleman is the diminished 5th (d5), the augmented 4th, also known as the tritone, or the diabolis in musica. Weighing in at a middleweight of 6 half steps, it acts as its own inversion (4.5 + 4.5 =???). The tritone has a lush, storied history. It is considered the most dissonant interval (which I personally disagree with), and is indeed so horrifically dissonant that it was COMPLETELY BANNED FROM USE IN MUSIC BY THE CATHOLIC CHURCH FOR A COUPLE HUNDRED YEARS. Music that had a single tritone in it was considered Satanic and heretical. You call yourself a person of conviction? Are you willing to be excommunicated for your music? Needless to say, as the cultural domination of the Catholic church weakened in Europe, the tritone went from being entirely unused to being a staple of modern music and even ended up defining a genre.

Augmented intervals are the opposite of diminished ones. a4 is our good buddy the tritone that we just talked about. a5 is the same tone as m6, but functions differently depending on situation. A lot of these conditional situations are going to be in subsequent lessons, so just internalize that they exist. I don't want you scoundrels thinking that an m6 is an a5 and then going out and spraypainting that on a wall somewhere!

As always, questions, comments, and further instructional material are appreciated.

Music Theory 4: Whole steps forward, the chromatic scale hertz.

For this lesson I'm going to return to a topic I brushed on at the end of the first post, and we're going to leave timing entirely behind for now. Let it simmer on the back-burner and become something you understand. We'll get back to it at some point because it is good stuff. Lets dive in, shall we? I'm glad we agree! We're going to be referring to this image quite a bit.



Start by looking at the treble line up there. We have 12 notes there +1, with the note names underneath them. Lets look at the E there, the 5th note in the sequence. In the treble clef, the E occupies the first line. This refers to a specific E in terms of pitch, which I will explain later on in the document. For now we are going to focus on the natural notes, which is to say the ones that are not sharp or flat. In the example above, those that we are ignoring for now are the ones with the #'s (sharps). So the next note up is F, and F here doesn't occupy a line, he gets a space. Look at the next note in the sequence (ignoring F# for now), and we have G. G occupies a line, and so on. As you can probably see, the pattern is that notes alternate lines and spaces. This means that, once you know the clef, you can figure out what lines and spaces mean what. Traditionally, this is taught through mnemonics, and there are literally dozens to remember the line arrangement for the treble clef.

The lines are EGBDF. You can remember this with: Every Good Boy Does Fine, Every Good Boy Deserves Fudge, Empty Garbage Before Dad Flips, Even God Believers Drown Fast, Even God Buys Dark Funeral, etc. Pick one and memorize it and you'll know your lines in the treble clef. The spaces are even easier, and is always remembered as simply being FACE. The easiest way to remember this is, of course,

To balance this out, the letters for the bass clef lines are GBDFA. Notice these are almost identical to the treble clef, except that the treble clef starts with an E, then goes into GBDF. The bass clef doesn't have that E, but adds an A at the end. This is the way it was taught to me, but it doesn't have a catchy mnemonic, and what's the fun in that? We can take one of the ones up above and modify it a bit to be a handy mnemonic, and also reference everyone's favorite Swedish black metal band! God Buys Dark Funeral Albums should do nicely, I think. The spaces for the bass clef then, are ACEG, which sounds kind of like a terrible rapper. I also don't have a mnemonic for this one that has been hammered into my head since I was a child, because it is so similar to the treble clef. Anorexia Creates Emaciated Girls?

Anyways, the important part is to recognize what the lines and spaces mean, and how when you go one line or space apart the note name changes. The astute reader has noticed that for that first C on the staff there has an extra line through it. As we proceed downward from the E, we have the D there, which could be construed as being in a space, were there to be another line beneath the staff. For the C, we have added a small little line, and it functions exactly how a regular line would. This is called a ledger line, and is meant to allow us to notate things that don't fit into the traditional staff. Ledger lines can go up or down as far as is necessary.

This C is actually a special one. The first C just below the staff in the treble clef is called 'Middle C', and is the C right in the middle of the piano. Look now at the last note on the bass clef. It is one ledger line up from the last line on the bass staff. Counting our notes, we go from an A on the line, to a B on the space, then for our ledger line we have a C again. THIS IS THE SAME NOTE AS IN THE TREBLE, IE: MIDDLE C. Middle C sits in the middle of the grand staff (the traditional manner piano is notated) and is in the middle of the keyboard. Middle C is not a piano-exclusive term either, its the traditional name for that note on any instrument. Starting to get an idea of just how much involved with musical notation is piano-centric? More on this in a bit.

The next thing to notice is that there is no sharp or flat between 'B & C' and 'E & F'. That sentence was terrible but I hope you get the idea that I'm trying to communicate. Me am dum. This is because of the concepts of whole steps and half steps. The half step is the smallest increment of pitch measure in western music. When a pitch changes, the smallest it can go and be notated (or even expressed) is a half step. The human ear can hear at a greater resolution than this, and many eastern musics involve quarter tones and more, but they are completely disregarded for western music and notation (this is not a true statement, but I'm simplifying for the sake of brevity and historical accuracy). But why?

The western (european) method is currently based on the equal tempered tuning system. Back in the olden days when there wasn't any system for tuning, pianos didn't exist, and things were actually in tune. Instrumentalists (including vocalists) used the ability to subtly change the intonation of their instruments to keep things in tune, but there was only a general idea of tuning after a piece started. For example, vocalist 1 sings a note, and vocalist 2 sings a different one that is meant to harmonize. Vocalist 2 comes in a bit lower in pitch than he'd intended, and the combined sound doesn't sound quite right. Vocalist 1 bends his pitch a little bit lower while Vocalist 2 does the opposite. When they hit the proper pitch ratio, they stop bending to ensure the sound is correct. Both of them do this automatically and very rapidly. This continues throughout the piece, and as long as both performers keep their pitch ratios accurate, the work will sound just fine. Obviously, the more people and pitches you throw into this mix, the more difficult the tuning becomes.

Secondly, the mathematics for harmonic ratios don't work out perfectly for every starting frequency. Perhaps you've heard of A440? This is a tuning system, meant to have all instruments tuned to it conform to the idea that middle A (which is the A in FACE) is exactly 440Hz. But Jack Chick, you say, Hz is a measurement generally reserved for electromagnetic radiation! Well as it turns out, Hz (being a measurement of cycles per second) also applies to vibration, and is the way you can qualitatively measure pitch.

The piano (and all of the related instruments, harpsichord et al) is different than other instruments, in that its pitches are fixed by the tuner ahead of performance. The mechanism of the instrument is to have strings pulled to various tension levels and then smashed with hammers, mechanically attached to the keys. And here you thought Cannibal Corpse didn't even know what a piano was. Thus, there is no way for the performer to adjust the pitches on the fly, requiring a system to be put in place to approximate all pitches for all keys.

Take a string and hold it at a specific tension. Pluck the string, you get a pitch. Halve the distance between the two points of the string, and hold it at an identical tension. Pluck it. Your pitch is now exactly double in frequency, because the string is vibrating twice as fast. Elementary physics, right? Consequently, we have increased by one octave. Take the second frequency and subtract the first. We now have a defined frequency range in which all of the additional pitches must fall. To do this, they simply divided the range by 12 to get the value of a half step (once again, smallest increment), then tuned each note to that value. The methodology isn't actually accurate, but provides the correct information and I really don't want to go on a sidetrack here about the harmonic series.

This is all a lot of detail to explain what the half step is and how it works. Western music doesn't use quarter tones or smaller resolutions because it has a necessity to conform to this instrument family that was considered incredibly important, so we use the half step as our finest resolution. Going back to our chart at the top of the document:



Start with C. The next half step up is C#. A whole step, which I mentioned a before I rambled on about tuning, is two half steps. So one half step up from C# is D, which is one whole step up from C. The chromatic scale, which is what we are looking at here, is defined by being the sequence of all half steps present in an octave. This then, inadvertently, answers our question about E and F. E is one half step below F. Same with B and C. I do not know historically why these two note pairs are outliers, but they are. Thus, E# is F, and F♭ is E, and C & B function the same.

To listen to the chromatic scale and understand how these half steps sound, listen to this. It's a little quicker than I'd want, but you can hear the half step motion involved. I'm not sure why the video starts with him off camera and he has to show himself sitting down, but I imagine that is part of the fetish.



So now you know quite a bit about the names of the notes, and how they relate to each-other. You're going to want to internalize a lot of the notation pieces, and when you see a couple notes on the staff you should be able to identify what they are (don't worry if it isn't very quick). As always, questions and comments are welcomed.

Music Theory 3: Don't get stressed out, this lesson was inevitable.

In our last lesson, we covered time signatures, which went over quite a bit better than I thought it was going to, so we're going to forge ahead and discuss the other part of time signatures that I left out. Sadly, this part is hard to explain and is a difficult concept to pick up, even for the experienced musician. Do not worry if you don't get what the hell I'm talking about on the first pass through, that's pretty normal. Also, I am choosing to present this lesson very early in the process, because I left some stuff unexplained in my description about time signatures (which absolutely no-one questioned, shame on all of you!), the concept is an important one to get under your belt, and as you understand it will increase your appreciation of music and musical forms. For this lesson I will be leaving off discussion of the 6/4, 7/8, 5/4 and 12/8 time signatures, because they are much less common (this will make sense after you read the below).

What I did not discuss was why different time signatures exist, and why there is a ratio method towards notation. Why wouldn't you just make quarter notes be the beat deliminator and have all other notes express their durations as adjustments to that, and have measures last for 4 quarter notes worth of time? This is a very good question, and doing things in the way I just described can and will work for musical notation. It is not good practice however, because the time signatures have an additional meaning towards the expression of the music. This is because of stress.

Stress is a slight emphasis placed in regular intervals, based on the time signature provided. To wit: 4/4 time has 2 stresses per measure. 3/4 time has 1 stress per measure, 2/4 has 1 stress per measure, 6/8 has 2 stresses per measure, 6/4 has 1 stress per measure. Now I know what you're thinking. You're thinking, "Neurotic, that sweatshirt is way too big for you. You look like you're swimming in it!" and you'd be right! But they were out of my size, and I needed a new zip up hoodie, so I went one size too large. Besides, it is comfortable as ALL GETOUT so nuts to you. Secondly, you're thinking, "Everything else so far has matched up pretty exactly with mathematics when it has gotten numerical. Why the break from this?" and the answer to that is that the time signatures grew out of the necessity to document sonic patterns, not the other way around. It makes more sense when you listen to stuff with a critical ear. So where do these stresses fall?

Lets start with 4/4, once again because it is the most common. When you count quarter notes in 4/4, a single measure is one-two-three-four. Stop me if I'm going too fast now. The biggest stress in any measure is on 'the downbeat', which is the first beat of the measure. Its called the downbeat because it refers to the gestures involved in conducting, and to go into more detail I would have to give a brief conducting lesson. Just know that when a conductor moves his arms straight downward from a high position, that indicates that beat 1 of a measure is happening. The first beat of every measure is critical, as it is your way of showing when the measure has started, and in establishing concepts such as "rhythm" and "groove". The second stress in 4/4 takes place on the 3rd beat of every measure, and is a lesser stress. So to count 4/4 properly, you would do it as so. ONE-two-three-four. So what does this sound like? Well lets look at the chorus of TNT. AC/DC is a fantastic band to use if you want to evaluate 4/4 beats since all of their songs are 4/4 medium tempo rockers.



So after listening to Bon Scott be awesome, lets analyze what happens on the path to the chorus. Along the way you can hear the kick drum (bass drum, I'm assuming everyone knows what this is? If you don't let me know and we can do some quick & dirty remedial ear training) counting out a 4 pattern. You can count along with it, shielded in your armor that there are 4 beats every measure. After the intro, the guitar starts its passage on the first real downbeat, then afterwards plays its chord a little bit before the downbeat, but holds the chord through. Try to hear in your head what it would sound like were he to not hold the chord over the downbeat, and instead play it quickly and step off it before the downbeat happened. This should sound kinda like blue balls. The reason is, after establishing that the line really starts on the downbeat, your ear wants to hear it start every time on that same beat, since it is such a strong musical beat. When your ear hears that chord land on that downbeat (Because it is carried through, playing the chord just before is called an anticipation, and you'll learn about how and why those work later) it presents your brain with a feeling of 'rest' (as in peace). Denying your ear that makes it feel like it is missing something. This is due partly to the nature of the chords being played, but is primarily because of the timing of how the beats fall. When the bass comes in, what's the first beat it plays on? That's right, its the downbeat again. Starting to get an image of why its so critical? This entire song (read: band) is hanging its hat on that beat. What is missing here is the 3rd beat of the measure, it isn't getting a lot of play. JACK CHICK YOU HAVE LIED TO US!!!!!!!!! That's what the chorus is for. This shit is the work of a master. Don't believe me? Listen. You get that "Cause I'm" then on beat three, we get our first 'payoff'. He sings the first actual lyric of the chorus, the letter T. The bass, drums, and guitar all kick in at the same time. This is a heavy freakin' beat. Then comes the N on beat four, but that's more of a passing sort of sound. We have downwards momentum in the song established by the first 2 chords, and the notes sung by the vocal, which generates 'inevitability'. All of this is pushing your ear towards that one beat, and you can't avoid it. When that one beat hits, we hit the original chord we heard in the song, the beat starts back up again as it was, and we now know exactly what has been established. This then repeats. The three establishes as a minor stress, generating momentum to beat 1, which is the major point.

Another example is a more recent work by Kreator. This one requires a bit more mental gymnastics.


First up let me be very clear, I do not think that, at the beginning, the drummer is counting quarter notes on the hi-hat, I believe he is counting 8th notes. Count every two hi-hat strikes as one beat, and go from there. That leaves the beat much slower than they are playing (one could certainly make a case that the beat is not there, or that they are playing in a different time signature, but I believe this is false. I think they are very clearly playing in 4/4 with this beat, based on the stresses of the music). I'm not going to analyze this one out for you, I've just listened to it a number of times, and am fairly confident that you will be able to pick up the qualities of the 3rd beat lending inevitability, and the downbeat being easily critical. I want you to listen to it yourself, and interpret what you can. Do not get discouraged if you cannot figure it out, as I stated earlier, this is a very hard concept to get. I am only presenting it this early because I believe (this belief is, notably, not shared by others) it is totally critical to one's understanding of music.

Moving on, lets do 3/4. The stress in 3/4 is on the downbeat. That's it. I've heard it stated that 3/4 is the second most popular time signature, but I'm not confident in the veracity of that statement. You count 3/4 as ONE-two-three. This always sounds 'sweeping' to me, but that's also because of its strong association to the Waltz and Minuet, and how they move around the dance floor. Now when we look at 3/4, a few pieces come readily to mind.



You may have heard one or both of these. Listen very carefully to how the music dances and twists around the downbeat, always emphasizing it. In the Strauss, notice how the lively sections (starts at about 1min in) have quarter notes playing below the melody to keep the rhythm going. Sometimes referred to as Oom-pah-pah, this is a classic waltz technique that kept people dancing long into the night. The final example that I would use for 3/4 time is the song 'My favorite things', but unfortunately I cannot find a decent example of it where it sounds truly like a 3/4. This leads handily into our next time signature though.

2/4! 2/4 is just like 4/4, but instead of having a lesser stress on the 3rd beat, it simply has another strong stress. This lends to more upbeat songs (think marches), with lots of energy and panache. Such as humppa!



Traditional polka styles are in 2/4. Notice it's peppy and carefully metered. The bass is changing tones every bar, and is providing equal stress. There is diminished inevitability between what would be the 3rd beat and the downbeat, were this 4/4 time. Now, 2/4 outside of classical music is somewhat of a footnote, as the difference between a heavy and a light stress isn't that big, and you can simply count 2/4 as 4/4 and come out just fine. I include it for completeness.

After discussing 2/4, we have to move to 6/8. I'm sorry everyone, I really am. 6/8 is a bitch, but its pretty common. 6/8 is notable in that it is a pattern that comes in multiples of 3, but is not counted as a single stress on the downbeat. You count (and conduct) 6/8 as a 2 pattern, split into equal segments counted as three.

Ok what? Seriously, what? Let us ask our friends from Scotland, Alestorm to help us out.



This is a classic 6/8 ballad. You can count this one as 4/4 too, but it will be of an extremely slow beat and difficult for a musician to follow. Secondly, there is a strong sense of 3's lying around here. Listen to that high hat, counting 1-2-3, 1-2-3. Why isn't this 3/4? Because listen to the drums. Kick on 1, snare on 1, what is this, in 1/1? The easiest way to express it is in two triptychs. How do you count it then? ONE-two-three-four-five-six. Stresses on 1 and 4, and a combination of the ideas of the two style count (2/4, 4/4) and the three style count (3/4). Another, classier example of 6/8.



Finally, before I sign off here (this has been a crazy productive three days for me, and I'm really liking doing this.), I'm going to leave you with a challenge. This song has a single time signature throughout the entirety of it. What is it?

Music Theory 2: Take notes, and measure the time you rest.

In our last outing, we discussed the very basics of how to look at a musical score. It is time for us to get a bit more elaborate, but still stick to basics that will bore the pants off anyone with a rudimentary knowledge of how to read music. I'll try to keep moving quickly and not leave the material too dry. If you haven't figured out what I'm talking about when I reference a staff, you will be very confused this lesson and should go back and read part one.

As we all remember from lesson one, there were these things called whole notes and eighth notes and also this adjustable ratio dynamic between the two. To put this idea in perspective and have it start making practical sense, a few things need to be established. Most importantly is the time signature, but that's amusingly difficult to explain without explaining a lessor piece, the measure. Trust me on this one, I just tried.

The measure is a pretty easy concept, it divides your music into bits. Measures are also called bars by those hip young upstart jazz musicians, but I don't think their flailing is going to establish more than a brief foothold in the field of music. Now, if you'll excuse me, I need to adjust my powdered wig and write a scathing telegram stop. A measure looks like so . It's that line running perpendicular to the staff. Another example is which shows us two measures, and some other crap we're not covering in this lesson. What the measure does, in terms of function, is to divide your music up so that the beat delineation is easy to follow and notate. It ties directly into our concept of time signatures, so lets just get that out of the way too.

The time signature looks like this and tells us two very important things. You see how after our trebel clef we have a number 4 sitting on top of a second number 4? This indicates to the performer two things. The top number 4 indicates that there are 4 'beats' in any given measure that follow the time signature. A beat is the smallest measure of how the time is kept. Remember, music is a performance art, all this crap we're doing with paper and stuff is NOT MUSIC, it's just a visual representation of it. Music exists for a brief, magically beautiful period of time, and we are so lucky to be swept up in it while it is with us. What does this hippie crap have to do with time signatures? There needed to be a way to determine when instruments and parts would play, so those are measured in beats. The top number could also be a 3, a 2, a 15, whatever. A 3 indicates 3 beats per measure, 2 would be 2 per measure, and a 15 indicates you are Dream Theatre. The bottom number is which note gets the beat. That means, in the case of the 4, that the quarter note gets the beat (as in, is the note duration that delineates the exact measurement of 1 beat, remember all of the notes are reflective of relative ratios to eachother). In our grand staff example up above you can see two quarter notes written, they are the black circles with the tails moving away, perpendicular to the staff lines. A quarter note is played for a duration of 1 quarter the length of a whole note (the open circle from the last post). Notice they are shorter than the measure lines, otherwise this crap would be impossible to read. This means, since the quarter note gets the beat, a measure can contain exactly 4 quarter notes. This time signature is called 4/4 time (pronounced four four time), and is the most common time signature used by a lot. Easily over 90% of the music that exists in the world today is in 4/4 time (yay statistics that I can't back up! the actual number is probably higher. seriously.)

Now with all of this new information, I know you're just itching to blurt out all over the class and your sweatpants "But this would mean that a measure can contain exactly 1 whole note!!!!!!". And you would be completely correct. Not only that, but time signatures are usually designed to ensure that the whole note's duration spans the whole measure, but this is not always the case. At this point, we should probably cover what all of the different varieties of notes are.



The last two images I found didn't include the handy little text, and I'm not making images for you people. The last two being the 16th note and the 32nd note. Based on this pattern, can you guess what the 64th and 128h note look like? (Yes they exist, no you will likely never see them) Building on what we already know, we now know how to fill our measures with all sorts of interesting notes of varying durations. Part of the rule of a measure is that you can never exceed the total beat count per measure (otherwise the metric is totally useless) (second point, right now you should think about this as a single 'voice', or musical line. Please do not think about someone playing chords or anything more complicated, as you'll just get confused. All voices need to have their timing accounted for and have their parts add up to the total number of beats allowed in a measure). Sticking with 4/4 time, we can have 1 whole note per measure, 2 half notes, 4 quarter notes, 8 eighth notes, 16 sixteenth notes, and so on. The whole note will last for 4 beats, the half notes for 2, quarters for 1, and such. Math is hard, right?

A visual example for us to look at

So in the above link, disregard everything on the bottom line as that's some stupid guitar notation (called tablature) people came up with because they decided that would be easier than learning to read the already existing and comprehensive musical vocabulary that existed. If you know someone who wants to learn guitar, get them to understand the basics of real music notation, because tab does not transfer to other instruments. Guitar players who only learn tab do themselves a disservice if they ever want to do anything on a serious level besides "be in rock band".

So in that link, we see our staff, our trebel clef, our time signature of 4/4, and then we have a random quarter note all hanging out smoking marijuana cigarettes and lowering property values. He's called a pickup, and we can ignore him for now. Next we have a double bar, which you can see up above in our time signature example, and also in a few places around the link. A double bar indicates a stopping point, and is read with the thin line first. This first double bar we see indicates a stopping point for someone returning to the beginning. The thin bar being on the right means that we don't have to stop as we read the passage from right to left. When we encounter a double bar with the thin bar on the left, that indicates a stopping point (in this particular case, there are additional instructions, which we're going to ignore for later). So in our first true measure here, we have 4 eighth notes which are linked together (drawing all those tails gets tedious so you can just link 'em as pictured. To link 16th notes you just have 2 bars linking the notes instead of 1, etc down the line), which equates to two beats. Then we have a quarter note, so we're up to 3 beats, finishing off with 2 more eighth notes. Total beats for the measure: 4. Notice how the notes go sequentially. Time is notated horizontally. Notice the space between the quarter note and the subsequent eighth notes, as though if they wanted to put 2 eighth notes in there instead, they could and have the distances between the notes be the same? This is not necessary, but makes the thing a whole lot easier to read. If you have multiple lines, you should put notes that fall on the same beat on the same vertical plane (or as close to as possible, in certain circumstances) as possible.

Finally, before we finish this one off, we need to discuss rests, dots and ties. Rests are an indicator to the musician not to play. These are notated in the exact same manner as notes, and last for the identical durations to their more notey counterparts. Here's a chart showing what they look like and how they line up. I also found this on the same website, which I think speaks for itself.



Also there are dots. Dots extend the duration of a note for 50% of the existing duration. In 4/4, our quarter note is one beat. A dotted quarter note is 1.5 beats, and it looks like this. Make sense? In 4/4, a dotted whole note is completely ridiculous and makes no sense, as you cannot fit 6 beats in one measure. If you want to extend a note's duration over measure lines, you need to tie the note to an additional note.

EXAMPLE:

In the top example, we see 3/4 time (POP QUIZ WHAT DOES THAT MEAN), and then a dotted half note. A dotted half note would be 2 beats + 1 beat to equal 3 beats, filling out our measure. This note is then tied (that arc underneath the notes extending across the measure) to the other dotted half, meaning this is meant to be played as one note and then held for the duration of 6 beats. Below that we have the tied whole notes performing the same task in our 4/4 measure. The count bit there assumes you know how to count, and since (name of poster you don't like) is the only person on the site that isn't above a maturity level of 3 years old, I don't need to cover it. Now, in various cases within measures, you are not supposed to put dotted notes on 'off' beats (off beats are the beats between beats, in our guitar example from above the second eighth note is on an off beat, because it happens between where quarter notes would fall). You are especially not supposed to put dotted notes on off beats that cross the.....you know what? This one is full of enough information, I'm not going to confuse you guys any further.

Ok so this one has a lot more information in it, and while I've tried to be as clear as possible, some of this could be pretty confusing because there's lots of "ignore this bit for now" stuff. If you have any questions, post them and I'll answer when I can, probably will be able to tomorrow. If you do not understand stuff that is covered here you will have a lot of difficulty in upcoming posts, so no matter how stupid you think the question is, ask it.