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 Post subject: Music 101: A Primer
PostPosted: Wed Nov 17, 2010 12:18 am 
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Goblin
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I started writing this guide because of the varying artistic backgrounds of the people who use this forum. Some of us may have recieved formal education on this topic, may write music as a hobby, or may only have the benefit of being casual listeners. The purpose of this primer is to serve as a refresher for the veterans, and as a crash course for newcomers. It will focus mostly on western music theory, since that is what I know, but if anybody else has anything they want to contribute to this, feel free to add to this thread.

To begin understanding music, it's helpful to understand the physical basis for sound, as well as how we percieve it. Sound is essentially our response to the compression of the surrounding medium. These waves are essentially the movement of local increases in pressure. Such changes in pressure lead to the vibration of the ear drum, which starts a process of converting the mechanical sound wave into an electrochemical one for our brains to deal with. For an analogy of a sound wave, consider a slinky: if you compress one end of the slinky, the compression will progressively travel to the other end of the slinky.

Because sound is a wave, it has the shares two attributes with other waves: amplitude and frequency. In order to illustrate this point, let's visualize the wave by plotting its energy versus time, with time on the horizontal axis. The region between the start of the graph and the blue line (inclusive) is one "period" or "cycle" of the wave. If the wave remains constant, we can pick any arbitrary point on the wave, and draw a line to the point where that value repeats itself. (represented by the red line) That is the wave's wavelength, denoted by ?. The reciprocal of ? ends up being a quantity known as the frequency (f), which incidentally also corresponds to the number of cycles per second that this wave will have.

Attachment:
File comment: Figure 1.1: Properties of a Sound Wave
wave.png
wave.png [ 7.68 KiB | Viewed 10190 times ]


The amplitude is merely some measure of the energy of the wave. There are various measurements of amplitude which will come in handy. One can talk about the peak-to-peak amplitude, which is the measure of the maximum energy of the wave. Another useful value is the root-mean-square (RMS) amplitude, which is a statistical measure of the amplitude over a period. A greater amplitude corresponds to a louder sound, while a lesser amplitude makes the sound quieter.

What's incredibly strange about sound is that we perceive it logarithmically. If you take a given frequency f, and steadily increase it, the pitch will rise in kind. However, a very peculiar thing happens when we double the original frequency: the sound of 2f is percieved to the same as that of f, except that it is somehow lighter. The same is true of 0.5f, except that it is lower. It should also be noted that the medium has some effect on the pitch that is based on the speed of sound in that medium. Air (at 0 C, with zero humidity, and at sea level) has speed of sound of about 330m/s, while lighter gases such as helium has a faster speed of sound.

Of course, sine waves are not the only kind of sound once can possibly hear, although they serve as a basis for constructing other waves. Most waves that will end up hearing are the composition of several sine waves. It turns out that when two or more waves get in each others wave, they interfere via additive synthesis: that is, the energies add together. In this case, there are usually at least two frequencies called harmonics present in the combined wave. There is always a fundamental frequency (also called the first harmonic) that is generally considered the "main" frequency for calculating the above metrics, and is typically what you hear first when interpreting such a wave. Several additional harmonics can be combined into the wave to give it it's distinctiveness (or timbre). These higher-order harmonics are typically integer multiples of the fundamental, although it is possible that non-integer harmonics of the fundamental may also be introduced into mix.

We can also talk about the lifetime of sound. Most things that produce sound are not strictly controlled, and have parameters that can change over time. Let's consider amplitude as an example. Suppose you are playing a wind instrument like a saxophone. When you blow into the mouthpeice, it takes a finite amount of time for the horn to hit its peak volume. After hitting the peak, the volume of the sax will taper off slightly until it reached a point of stability, which is called its sustain period. As long as you blow into the mouthpeice, the sax will continue to produce sound; however, once you stop blowing, it will eventually (and probably very quickly) lose energy stop vibrating.

This model of sound is modeled by something called an ADSR envelope. An ADSR envelope consists of four phases: attack, decay, sustain, and release. The attack phase is the period of time it takes a value (such as amplitude) to reach its peak value. Shortly afterwards, the decay phase is entered, where the amplitude decreases to the beginning of the sustain phase. As long as the wave continues, it will remain in the sustain phase. Eventually, moves to the release phase, where the value tapers off to zero.

Attachment:
File comment: Figure 1.2: A basic ADSR volume envelope.
volume-envelope.png
volume-envelope.png [ 9.42 KiB | Viewed 10105 times ]


Now that we have that out of the way, the next you might have is "What is music?". Unfortunately, this is a much more difficult question to answer, with some lack of universality involved. If you're reading this, you probably have some vague idea what music is and what it means to you. It's generally defined as the combination of pitch, rhythm, dynamics, and texture to form an artistic work. These concepts are important, and it is my intent to cover them in some detail throughout the remainder of this primer. However, if you plug a function generator into a pair of speakers, and tweak the knobs a bit, you might be surprised to find that this very much sounds like music. And you might also say that someone blindly banging away at a keyboard, despite their intent, does not constitute music, although to the player, it might. This is a warning before you get too far down the rabbit hole: some of the material that will be covered in later sections is subjective. That's OK, because music is art.

However, it is also my hope, by this point, that you do not confuse something being artistic with something that cannot be studied in objective terms. In this sense, musicianship shares a great deal with engineering, in that one takes what is objectively known about a given topic, and works it into something that (hopefully) betters society. Try not to think of the information contained foreward as some kind of formula, but rather as a set of tools, and use that information to write some kickass songs.

_________________
"Pray, Mr. Babbage, if you put into the machine wrong figures, will the right answers come out?" ... I am not able rightly to apprehend the kind of confusion of ideas that could provoke such a question. -- C. Babbage


Last edited by thylordroot on Sat Nov 20, 2010 12:38 am, edited 2 times in total.

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 Post subject: Pitch: The Basics
PostPosted: Wed Nov 17, 2010 3:59 am 
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Earlier, we discussed the ability of our ears to differentiate between different frequencies of sound, which get translated to pitch by our brains. We also learned about a very interesting property of this process: that each doubling of the frequency produces a pitch that is perceptually the same, except for the "lightness" of the pitch. It would make sense, then, that we divide pitches into a numeric domain, where we can talk about things like adding and subtracting pitches, and where pitches have an order.

In Western music theory, this is taken a step further, where pitches are divided into discrete units. After all, you rarely hear someone say, "this song is in the key of 325.7 Hz Major". The result is that Western music theory has eight important pitch divisions, known as whole steps, each denoted with a letter from A to G. (this is not the whole picture; there is more to follow) Pitches in Western music theory use modulo addition: for instance, adding an A to an A results in an A. We can also talk about the distance, or interval, between two notes. If we go from a lower A to a higher A, then these notes are 8 whole tones apart. This interval, not surprisingly, is called an octave.

An octave can occur between any span of tones that are 8 notes apart. Separating these notes can get rather tricky, so it can sometimes be useful to differentiate two pitches that are classified as the same symbol. If we were to define "A-0" as some frequency f, then we could call the next A, the "lighter" A, "A-1". This works well, because information about the frequency is preseved. Sometimes, this distinction doesn't matter, in which case, A is just referred to as "A". Of course, for any of this to make any sense at all, we have to have some idea of what "A" means. Somewhere down the line, when our understanding of sound became sufficiently usable to do so, somebody decided that a particular "A", from which the frequencies of all other tones are derived, would be given a constant value. And so it is: for most intents and purposes, this value of A is equal to 440 Hz. While this value can shift for a variety of reasons, this is typically what most musicians consider to be their baseline "A".

The formation of Western music theory is one describing a slow and gradual process. In its beginnigns, Western music was practiced in a discriminatory manner. If you wanted to be a musician with any kind of formal knowledge, you were a member of the clergy, which also meant that you were a man, and that your music was largely limited to chants and hymns. While that meant terrible things for women, and in general, those not content with religious music, it did mean one thing: the notation was as simple as necessary for Gregorian chant. When Western society evolved enough to relax the reins a bit, composers had to deal with a number of varying ranges which men could typically not produce.

The notation for most Western music is the placement of several notes onto a series of 5 lines called a staff. The music is read left to right, and each space in the staff corresponds to some whole tone. Of course, it can be difficult to remeber where notes are on the staff, so special markers called clefs are placed on the staff. These clefs may look completely foreign to you, but you may notice that they bear a striking resemblence to the letters "F", "G", and "C". In fact, this is entirely by design. With some careful attention, you may also notice that these clefs, in fact, point to the relative "starting note" of interest. For instance:

  • The dot on the serif of the F clef shows where F may be found
  • The center of the hole formed by the G-clef shows where G may be found
  • The gap between the two "C"s of the C clef show where C may be found

The F and G clefs are perhaps some of the most commonly recognized clefs. The G clef is commonly used as the Treble clef (with the G on the second line from the bottom), while the F clef is often used as the Bass clef (with the F found on the second line from the top). Most other uses of these clefs are out-moded. The C clef is more rarely used, but tends to show up in viol parts. In these cases, the C clef may either be the Alto clef (with C located on the third line) or the tenor clef (with C located on the second line from the top). The C clef is also freely expected to move up and down the staff.

Attachment:
File comment: Figure 2.1: Usage of the F, G, and C clefs, as well as their relative note placement.
clefs.png
clefs.png [ 8.79 KiB | Viewed 10169 times ]


This phenomenon of things notes around is, for the most part, one of the axioms of Western music theory. A lot of tricks related to pitch would not work well or cease to work entirely if this were not the case. This also introduces an interesting concept: the scale. The scale can be considered a collection of ascending note across an interval. Let's start with the C major scale. The C major scale is simply all of the whole notes between a C octave. (figure 2) Notice that the scale begins on a C, and ends on a C. This scale is one of the most common scales you'll find, and generally has a distinctive positive feel to it.

Since we can do this with C, one might be tempted to think the same process will apply to other notes when forming a major scale. But say we pick a scale based off of D, for instance. When you play the resulting scale, you might be shocked to learn that this scale does not sound at like the the C Major scale. Instead, it has this kind of mysterious quality about it. This is because it is, in fact, not a Major scale at all, but a scale in something we will later discover called the Dorian mode. The problem is that we're still missing some important tones to make the D Major scale possible.

The way that Western music solves this is to add five extra tones that are somewhere in between two whole tones, giving us a total of 12 tones before the start of a new octave. We can then talk about a note that is a half-step (or semitone) above a tone, or one that is a half-step below. These are respectively known as sharps (#) and flats (b). At this point, you might be asking why there are now 12 tones, instead of 14. This is because raising certain whole tones a half step will result in another whole tone. Our new tones are Ab, Bb, Db, Eb, and Gb. This can alternately be expressed as G#, A#, C#, D#, and F#. That means that lowering C and F a semitone results in B and E respectively; or, alternately stated, raising B and E a semitone results in C and F. Instead of saying "one semitone above C", you can say "C-sharp", or instead of saying "one semitone below E", you can say "E-flat". You can refer to the whole-tone version of C by saying "C-natural", or simply "C".

This level of division is, oddly enough, still insufficient for some modern forms of music, and so finer-grained divisions may be required in these cases. However, introducing semitones into our musical model has solved a number of problems, including the precarious situation of not being able to form a D Major scale. In fact, the insertion of semitones into a scale is so useful, that by default, we might want to make these adjustments automatically. The profile of tones that need to be adjusted are called that scale's key signature. Now you have an idea of what is meant when one says, "this song is in the key of D Major": it means that it has the D Major scale's key signature. (figure 2.2)

You can make a major scale from any note. This means that, ordinarily, you would have to remember 12 scales, for a total of 96 notes, all in sequence! Add on top of that, there numerous other scales to chose from. For instance, there are also minor scales, the most basic of which are the natural minors. Fortunately, you don't have to take this approach. If we assume that with most tones in the scale, we raise the next tone two semitones (a whole step), then we only have to keep track of when to raise a tone by one semitone. If we denote whole tones with "W" and half tones with "H", then we get the following formulas:

  • Major - W W H W W W H
  • Natural Minor - W H W W H W W

By the way, you might be curious as to what a Natural Minor scale actually is. Well, aside from the above definition of a Natural Minor scale, it's the musical complement of a major scale. Without any qualifier, this is what is usually meant by "Minor". Typically, this scale has a more serious or melancholy feel to it than its counterpart, the Major scale. Think about it: your game's music can't be uplifting all the time. The Natural Minor scale is another tool that you can use at your disposal to alter the game. As we progress, we will learn about other scales which can help you write music appropriate for the mood you're trying to capture.

Now, if you sit down and practice the above formulas, you may notice something else odd. Perhaps you noticed that, for instance, the scale A Minor has the exact same key signature as C Major. And perhaps you also noticed that the scale for F Major scale has the exact same key signature as D Minor. In fact, it turns out that every Major scale has a corresponding Minor scale in the same key signature. The Major scale is called the Minor's relative major, and conversely, the Minor scale is the Major's relative minor.

Attachment:
File comment: Figure 2.2: D Major, and its relative minor, B Minor. The first two scales are exactly the same, but the second expresses the key signature of D Major.
relmaj.png
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Before we wrap up, there is one more important scale you should know. This is the scale from one end of the octave to another, but with all possible notes in between. You could technically have different scales for each one of these, but they all follow the same pattern, so this is simply known as the chromatic scale. This one has a distinct sound that tends to quickly build up anticipation.

Attachment:
File comment: Figure 2.3: The Chromatic Scale, with C as the first note
chromatic.png
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This pretty much sums up our introduction to the basics of pitch. At this point, you might be asking what the purpose of learning about all of these scales were. As you shall soon find out, the manipulation of scales is half the job in writing music. Getting a grasp of scales early on will give you important tools that should be in anyone's arsenal. In the next segment of this primer, we'll cover another basic half of writing music: rhythm.

_________________
"Pray, Mr. Babbage, if you put into the machine wrong figures, will the right answers come out?" ... I am not able rightly to apprehend the kind of confusion of ideas that could provoke such a question. -- C. Babbage


Last edited by thylordroot on Sat Nov 20, 2010 12:40 am, edited 1 time in total.

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 Post subject: Rhythm: The Basics
PostPosted: Fri Nov 19, 2010 11:56 pm 
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Now that we know a bit about pitch, it is now time to consider another important aspect of music: rhythm. Rhythm is the property of music which describes the placement and length of tones within time. This is what puts the "beat" into music. Various representations of the note can denote duration. You can divide the representation of a note into two fundamental parts: a note head, whose primary purpose is to place the pitch of a note, and an optional stem rising from the

In Western notation, the fundamental unit of time is the whole note. (or semibreve) A whole note's head is a hollow oval, and has no stem. A whole note can be divided into many divisions, most of which are binary in nature. Common divisions include the half note (minim), quarter note (or crotchet), the eigth note (quaver), and the sixteenth note. Half notes consist of a hollow note head with a stem, and quarter notes consist of a filled note head with a stem. Notes of lower divisions have a flag coming out of the staff for each successive division of the note.

We can also talk about periods of time in which no note is played. These are called rests, and like notes, also have a fundamental division. A whole rest is a filled rectangle with a line across the top, a half rest is a rectangle with a line across the bottom, and a quarter rest is a squiggly thing. Rests of lower divisions are a slanted line with flags coming out of it for each successive division. Because the whole and half rests look so similar, a simple mnemonic device can help keep things straight: think of the rest as a hat. Half-a-man will leave his hat on, but a whole-man takes it off.

Attachment:
File comment: Figure 3.1: Various note divisions in 4/4. 1) Quarter, half, and whole notes; 2) quarter, half, and whole rests
divisions-in-4-4.png
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Let's take a brief overview of the staff. There are probably a few elements you remeber from last time. There is a clef which, in this case, tells us where G is located on the staff. There are also a collection of sharp signs denoting the key signature of this song. But there are also some new elements that you may not recognize: right after the key signature, there are two numbers called the time signature, and the notes are now divided by lines. At the end of the staff, there is a thick double-line that indicates the end of the music.

What is this time signature thing, exactly? Well, you may have noticed that while we have come up with the concept of a "whole note", and we can say various things about a whole note, (for instance, that is is twice the duration of a half note) we have had no reasonable way of measuring what duration should really be. The unit needed to tie this together is the "beat". Let's decompose the time signature to get some meaning out of it. The bottom number refers the division of a whole note that will be counted towards a single beat. In figure 3.1, that number is 4, which indicates that a quarter note recieves one beat. This is said to be the time signature's beat unit, and implies a few things. For instance, we know that a half note recieves two beats, and a whole note recieves four.

Knowing this, you may have noticed a pattern regarding the placement of the thin bars in figure 3.1. If you add up all of the durations between each line, you might notice that they always add up to four beats. This is because the top number is 4. The region between these two bars is a unit called a measure. A measure contains the same number of beats. So, the number at the top tells us the number of beats in a single measure. (or the beat count)

4/4 is not the only time signature. If you vary the beat count, common time signatures include 3/4 (for waltzes), and 2/4. (for marches) You can also vary the beat unit, for which common variations include 2 (half notes get one beat) and 8 (eighth notes get one beat). Common time signatures for these classes of time signatures include 2/2 and 6/8. Most of the time, however, you will probably work in 4/4 time. In fact, 4/4 time is so common, that it is also known as "common time", and has a special shorthand symbol that resembles a C. 2/2 also has some significance, and similarly has another name ("alla breve" or "cut time") and a shorthand symbol. (a "C" with a line through it.)

Attachment:
File comment: Figure 3.2: Various time signatures: 1) Time signatures in which the crotchet is the beat unit; 2) Time signatures in which the minim is the beat unit; 3) Time signatures in which the quaver is the beat unit
timesig.png
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If you can keep time, then interpreting rhythm isn't too hard. If you can remember that the start of each measure if the first beat, then all you have to do is count out the measure length, spacing each beat equally apart. So, for instance, two measures in 4/4, one would count out "1, 2, 3, 4, 1, 2, 3, 4, ...", and for 3/4, "1, 2, 3, 1, 2, 3". You can keep track of this by tapping this out with your foot, or by mentally repeating this sequence. If you're having trouble keeping time, there are a number of ways you can train yourself. One way is to march everywhere you go; this can work because people generally keep a constant rhythm when they walk. You can also acquire a metronome (it can be software) and spend a little time each day trying to count in sequence with the metronome.

Of course, you have durations less than a beat. For instance, an eighth note in 4/4 represents half a beat. Counting this out might seem like it would be hard, but all you have to do is say "and" in the middle of the beat, like "1-and 2-and 3-and 4-and...". Sixteenth notes, which are twice as fast, introduce the syllable "e" a fourth of the way through the beat, and "uh" three fourths through. This means that counting out in triplets would sound something like "1-e-and-uh 2-e-and-uh...".

You can also have irregular divisions, which are called tied notes. A tie is something called an articulation, which is a way of modifying how notes transition or continue. If you take two notes and tie them, then the resulting duration is the sum of the notes that have been tied. For instance, you can tie a half note and a quarter note to get something that has the duration of four quarter notes. A shorthand way of doing this exists: if you put a dot to the side of the note, then that is the same as tying the note with one of half its duration.

Attachment:
File comment: Figure 3.3: 1) two measures of ties; 2) The same sequence as above, except using dot notation.
tied-notes.png
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I thought I should mention some more issues with notation. As we discovered in the last chapter, a whole tone may be raised a semitone with a sharp, or lowered a half-step with a flat. These half-step changes in pitch are known as accidentals, and have properties which we must now consider. First, when you use an accidental, it remains in effect for the entire measure, until it is replaced by another accidental. This means, for instance, that if you raise A natural a half step on the third beat, it will remain sharp until the start of the next measure. However, if you return it to its original tone by using a natural accidental, (?) it will return to an A natural. In this case, flatting it will not have the desired effect: it will be understood as A flat. Accidentals also refer to a specific pitch when they are used: they do not apply to notes of the same tone, but an octave lower or higher.

Technically, we have enough now to begin writing some form of music by experimentation. While this is a good start, we will find there are other things that will be useful if we wish to deeper music. We will begin this discussion with a more in-depth look at articulation.

_________________
"Pray, Mr. Babbage, if you put into the machine wrong figures, will the right answers come out?" ... I am not able rightly to apprehend the kind of confusion of ideas that could provoke such a question. -- C. Babbage


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 Post subject: Rhythm: Articulation
PostPosted: Sat Nov 20, 2010 4:57 am 
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You now have some idea of how to read staff music, and possibly how to record, at a basic level, music that you might come up with when messing around. However, we currently cannot record some substantial information about that music. These embelishments give us greater control over the way we move from note to note, how long we might chose to play certain notes, or how we might otherwise interpret certain notes. These things are known as articulations.

We already have been introduced to one articulation: the tie. Recall that the tie allows us to connect two notes as if they were a single note combined. What if we take the concept of a tie, and extend it to notes of different pitches? This results in something called a slur. In a slur, the notes are somewhat graceful, as the end of one note and the beginning of another are somewhat indistinct. The slur results in a special form of articulation called legato.

However, there are other modes of articulation. For instance, the stacatto articulation denotes that notes should be separated and distinct. Stacatto is usually represented as a dot opposite to the stem of the note. In a more extreme case, marcato (sometimes known as "accented"), means that notes should have a very short duration. This is represented by an angle bracket (">") in the same manner that stacatto is represented. Sometimes, legato is show with lines under the note head.

Attachment:
File comment: Figure 4.1: 1st Verse of Jack Judge's "It's a Long Way to Tipperary", showing utilization of various accents
tipperary.png
tipperary.png [ 19.46 KiB | Viewed 10093 times ]


A special class of articulation is that of dynamics. Dynamics basically affect volume. Dynamics are usually given special markers, and stay in effect until otherwise negated by another dynamic. There are several words (which derive from Italian) to describe various dynamics. These are described in ascending order:

  1. pianomisso (pp) - extremely soft
  2. piano (p) - soft
  3. mezzopiano (mp) - somewhat soft
  4. mezzoforte (mf) - somewhat loud
  5. forte (f) - loud
  6. fortimisso (ff) - extremely loud

Sometimes, you don't want to leave the volume fixed. For instance, you might want to gradually increase the volume to build up for some critical point in your music. The device for this is called a crescendo. A crescendo is represented by a triangle, with the point representing the softest part of the music, and the base representing the loudest part. As you might expect, a descrescendo is the exact opposite of this: gradually getting softer. These often work well with another articulation called a fermata. A fermata basically says "Hold this note until I otherwise say so". Beethoven's Fifth Symphony has plenty of examples of dynamics in action:

Attachment:
File comment: Figure 4.2: Excerpt from Beethoven's 5th Symphony, showing usage of fermatas and dynamics.
beethovens-5th.png
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Another important class of articulations include those that modify, overall, our treatment of a series of notes. We call this ornamentation. These include trills, mordents, and glissando. Trills are chromatic sequences that rapidly alternate between the specified note and a note a semitone apart. In the notation, this is usually represented with a bold, wavy line above the staff, and sometimes preceded by "tr.". A mordent is a similar device, but alternation only occurs once. Two kinds of mordents exist in notation: an upper mordent, where the note is raised a half step, and a lower mordent, where it is lowered a half step. The two can be distinguished in that a lower mordent has a line through the center.

A similar concept is that of the grace note. A grace is a note that, over a very short period of time, slurs into the next note. It is typically represented by a smaller note (usually a quaver) with a slur attached to the main note. There are two forms of grace note: the acciaccatura and the appoggiatura. An acciaccatura is meant to occur so quickly, that it is barely perceptible, and so is considered to have zero time value. An appoggiatura, on the the other hand, is somewhat more pronounced and usually take the amount of time specified by the grace note from the main note. An acciaccatura can be differentiated from the latter in that it has a small stroke through its stem.

Finally, there is glissando. Glissando can be described as a glide from one pitch to another. Some instruments are capable of performing a perfect glide from one note to another: this continuous glide is called portamento. Instruments capable of this feat include the trombone, fretless bass, and the oud. However, for many instruments, this is exceedingly difficult or even impossible. In this case, portamento can consist of a slurred chromatic scale. Glissando is usually represented as a straight line from the starting note to the ending note.

Attachment:
File comment: Figure 4.3: Except from Rhapsody in Blue; 1) extensive use of ornamentation was made in this clarinet solo; 2) A possible interpretation of the above representation.
rhapsody.png
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An excellent example using ornamentation to evoke an emotion can be found the intro clarinet solo for George Gershwin's "Rhapsody in Blue". This solo tends to evoke images of guilty pleasures. You can see that by using the special ornamentation marks, the score is considerably compressed, and more freedom is given to the performer. Aside from the fact that United Airlines used this as their theme song since the '80s, this song is also famous because of the provactive nature of this solo.

Hopefully, you can see that with a little bit of articulation, the songs that you write can be that much better. Effective use of articulation can help bring enhance some qualities of your song that might otherwise be lost. We are now ready begin tackling some proper music theory. In the next post, we shall cover aspects of basic songwriting.

_________________
"Pray, Mr. Babbage, if you put into the machine wrong figures, will the right answers come out?" ... I am not able rightly to apprehend the kind of confusion of ideas that could provoke such a question. -- C. Babbage


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 Post subject: Basic Songwriting
PostPosted: Sun Nov 21, 2010 8:59 pm 
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Now that you are equipped with the basics, you are probably eager to get started writing songs. You can, of course, practice experimentation and hope to, every once in a while, stumble upon a song that fits what you're trying to write. However, just as with programming, this approach can only take you so far. Experimentation is not a bad thing, but it's helpful to augment it with some basic techniques that will help you understand how Western society interprets music. You've already got a foot in the door; you likely have an idea of what you think good music is, and you have some idea of the elements that make music.

I'll start by saying that at its simplest, Western music is fundamentally the manipulation of scales. Scales are designed for this purpose: they're essentially algorithms that determine notes that go together well. As we'll find out, we can extend scales in many ways to produce the desired effect. Let's take Figure 3.1 from the last example to clarify this point. We can look at the key signature, and see that it is in the key F major. Incidentally, you'll also see bits and peices of the F major scale. Don't see it? Well, it might help to know that we can also run the scale backwards! In some places, however, the author makes slight deviations from the scale: for instance, making the F in measure 4 sharp.

This is probably no mistake. This particular excerpt is something called a "phrase". A phrase is basically a musical idea. As with programming, you build your song out of smaller, high-level components. What is Jack Judge doing here, exactly? Well, you'll notice that the song is written in a major key. If you remeber from section 2, major keys are usually considered positive or light-hearted. Yet, the accidentals negate that to some degree, and that causes a bit of anticipation. If one looks at the lyrics for that phrase, this is a reasonable idea:

It's a Long Way to Tipperary wrote:
Up to mighty London
Came an Irishman one day.
As the streets are paved with gold
Sure, everyone was gay,
Singing songs of Piccadilly,
Strand and Leicester Square,
Till Paddy got excited,
Then he shouted to them there:


There's this concept that songs should build some degree of tension that will later be resolved. With just this phrase, you might have wondered, "Shouted what to them?" This is already a bit annoying, but perhaps you could live with it. Perhaps I also cheated, because I had the lyrics. Of course, if you don't believe me, there's another example that perfectly illustrates my point from that very same section.

Imagine if Beethoven had stopped writing his 5th symphony 20 measures in. (Figure 3.2) However, given that this is what people generally remember from Beethoven's 5th, let's assume that it was considered a staggering success, anyway. Would this, as the entire song, make you comfortable? Of course not! In fact, it would be very unusual for you not to be disturbed by this. In these three phrases, Beethoven has built up enough tension to put you on edge. You need a release of some kind to resolve the tension.

This is very important to know, because it can explain a lot about how your listeners function. Think about when songs get stuck in your head, when songs get annoying, and when songs leave you disturbed. You can and should leverage this to your advantage when you're writing a song, but be careful: the last thing you want is somebody refusing to play your game because the music creeped them out too much. What causes tension? Tension is basically caused by note sequences that are percieved by us to be unstable. So how do we solve this problem?

Let's go back to scales: if you remeber correctly, our scales had 8 notes. This, as you probably know, is no coincidence either: there are eight whole notes in an octave, and so this makes sense. Particularly, the first two scales we looked at were in a special category called diatonic scales. The simplest definition of a diatonic scale is one that can be played on all of white keys of the piano, or can be transposed to do so. Major scales fit this category: the C Major scale has no sharps or flats in it, so it can be played on all white keys. The natural minor scales count as well, since there is a relative minor for every major scale, and in C Major's case, that scale is A Minor.

With diatonic scales (and many other scales), we can categorize each note in a scale as a scale degree. Scale degrees basically give the distance from the root of the scale (the tonic) to the note in question. Here is a list of scale degrees, and their names:

  • tonic (I) - +0
  • supertonic (II) - +1
  • mediant (III) - +2
  • subdominant (IV) - +3
  • dominant (V) - +4
  • submediant (VI) - +5
  • subtonic (VII) - +6
  • leading tone (VIII) - +7

Tension can derive from a number of things. One way we can use scale degrees to manipulate tension is through the utilization of consonance and dissonance. A dissonant note tends to increase tension, while a consonant one tends to release it. There are two kinds of consonance: perfect consonance and imperfect consonance. Our perfect consances are the tonic, dominant, and leading tone. Imperfect consonances consists of the mediant and submediant. Perfect consonance have a higher degree of consonance than imperfect consonances. By a process of elimination, we can then say that the subdominant and subtonic degrees are dissonant. Generally, one wants to end a song on a perfect consonance to help expedite the release of tension; however, the imperfect consonances have some

Let's write a short song in D major. Using our major scale formula, we know that the D major scale is D, E, F#, G, A, B, C#, D. The final result is in Figure 5.1. To build some tension, we can start on a dissonant note; here we'll us the subdominant. (G) This creates a fairly strong dissonance which we can further amplify by ending the measure with a subtonic. We can somewhat relax the tension the tension in the next measure by starting on a consanant note, such as the mediant used. The next measure consists of very few consonant notes, leading to increased tension. Finally, we release in the last measure this tension by utilizing only consonant notes.

Attachment:
File comment: Figure 5.1: 1) Scale degrees for the D Major scale. 2) A song in the key of D Major written to exploit the Tension-Release paradigm.
scale-degrees.png
scale-degrees.png [ 15.02 KiB | Viewed 10053 times ]


You may have noticed something strange going on in the last measure. The last few notes seem to work together very well. This pattern is called an arrepegio, and is related to a concept called the chord. Up until this point, we have only discussed music in which a single note is played at a time. This kind of music is called monophonic music. We can more easily manipulate tension if we can take advantage of multiple instruments playing at a time. This is results in polyphony. A chord is simply a collection of notes that play at the same time.

While chord formation deserves its own section, a brief introduction to chords is still appropriate for this discussion. We can start by talking about chords by the number of notes they contain. A dyad, for instance, contains two notes, a triad contains three, and tetrad contains four. Some instruments are capable of creating chords, and some are not. For instance, you've probably heard of guitar chords, or piano chords. However, for other instruments, like the saxophone, the trumpet, or the flute, a single instrument is not capable of creating a chord. This distinction, it turns out, doesn't matter too much, because you can still cascade staves for multiple instruments to create chords.

The seperation between the notes in a chord, their interval, is key to understanding chords. You can think of an interval as a distance between two notes, where the unit is the semitone. A distance of zero semitones is called unison, while 12 semitones above the octave is called an octave. A note at unison is sometimes called the root of the chord, because it determines the tone for that chord. The names of the intervals between is named according to their position in the scale. For instance, an interval two semitones above the root is called the major second, while one that is one interval above the root is called the minor second. There are two special intervals, the perfect fourth (+5) and the perfect fifth (+7). The interval at +6 can either be called an augmented fourth or a diminished fifth. This interval is important, because it is a dissonant interval.

Looking back at our scales, we can notice a mapping between their degrees and particular intervals. A diatonic scale degree corresponds to a variation of an interval with the same name in relation to its tonic. For instance, the third scale degree of a major scale corresponds to a major third from its tonic, while the corresponding minor's mediant is a minor third. You may have noticed, that in either scale, the intervals associated with the dominant and subdominant degrees are the same: hence, the terms perfect fourth and fifth.

Let's take the major triad as an example. A major triad consists of its root, a major third, and a perfect fifth. Now that we know that scale degrees map to intervals, forming a major chord is easy: just add the mediant and the dominant from the root's major scale! If we do this, this means the C Major triad must consist of C, E, and G. Likewise, a D major triad must consist of D, F#, and A. Minor chords are similar, except that you replace the major third a minor third.

You can do two things to chords to introduce a bit of variation into your music: invert the chord or convert it into an arrepegio. When you invert a chord, the root goes at the top. The tones stay the same, but are an entire octave lower. So if we invert the C major triad (in ascending order), E, G, and C. Likewise, we can also separate each of the tones in the chord to form an arrepegio. You are already somewhat familiar with the arrepegio: we used one in Figure 3.1 near the end of measure 4. This arripegio is derived from a D major tetrad, which has an octave added in. It should be noted that chord inversions and arrepegios are functionally equivalent to normal chords, so you can use these for a little variation in your music. (which, in turn, creates tension)

Let's try a little guided experimentation. We're going to use the following information to create a bassline for the above song. First, let's consider what we have to work with. What kind of instrument is a bass guitar, and how is it usually played? Well, a bass guitar has four strings, so we know it must be capable of polyphony; however, it is usually played in a monophonic context. This means that we will likely want to form dyad chords here. As the bassline will help us keep time, I have also chosen to use quavers here. Here's a perfectly suitable bassline for this song:

Attachment:
File comment: Figure 5.2: A possible bassline for the song in figure 5.1
chording-intro.png
chording-intro.png [ 16.17 KiB | Viewed 10053 times ]


You may have noticed something strange about the second measure: instead of releasing tension, it seems to create more. This specifically happens whenever we mix the F# in the lead and the B in the bassline. This results in a B power chord. A power chord is a dyad with that has the root and its fifth. You might have noticed that the third distinguishes a major and a minor chord from one another. Because the power chord is missing the third, you can't classify it as either a major or minor chord.

Another way we can manipulate the tension of our song is through the use of articulation. Let's refer back to intro of Beethoven's 5th for a moment. Have you ever wondered why it is so tense? While the choice of notes have something to do with it, there are some very subtle things contributing to the tension. For instance, the liberal usage of marcato combined with the manipulation of dynamics makes causes the notes to be peircing. Additionally, the fermatas are placed in such a way as to encourage anticipation. This is especially true in the last phrase: the crescendo, marcato, and fermata all combine to raise tension significantly.

Finally, tension can be created through variation. Variation consists of repeating parts of the song with minor changes. These minor changes make the song less predictable and will serve to increase tension. For instance, in our song, we vary the chords we used in each measure.

To recap, one of your goals as a musician is to introduce tension that you will later have to resolve. Tension can be a good thing: it's what causes your music to be interesting. Too much unresolved tension, however, can just as easily spoil your song. You can use several methods to manage the tension in your song, including the clever usage of scale degrees, chording, dynamics, and variation. All of this will take some amount of practice; however, mastery of it can help you write better and more effective music.

_________________
"Pray, Mr. Babbage, if you put into the machine wrong figures, will the right answers come out?" ... I am not able rightly to apprehend the kind of confusion of ideas that could provoke such a question. -- C. Babbage


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 Post subject: Re: Music 101: A Primer
PostPosted: Mon Jun 11, 2018 9:48 pm 
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 Post subject: Re: Music 101: A Primer
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 Post subject: Re: Music 101: A Primer
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