Elementary Music Theory

by Reed W. Robins

PART 1 ACOUSTICS and PROPERTIES OF SOUND

Sound is Produced by Vibration With a Guitar, for example: THE VIBRATING STRING(vibrates) THE AIR(vibrates)THE EARDRUM the vibration of the eardrum produces the sensation of sound Noise is the result of irregular vibration patterns Tones are the result of regular vibrations Tones have 4 basic characteristics Pitch: high or low Duration: length of the sound Intensity: volume or loudness Timbre: "color" of the sound Let's examine further the action of a plucked string (the principle is, of course, the same for a vibrating column of air, or a vibrating membrane, etc.):

When you pluck the string from it's resting point (a) it goes up to (b), back past (a) to (c), and then back to (a), it has completed one cycle. Nodes are points of no pratical vibration (in this case, at each end of the string). The greater the distance between (b) and (c), the louder the tone-in other words-wide vibration = loud tone/narrow vibration = soft tone. The Number of cycles per second (hertz-abbreviated Hz.) is the frequency of the tone. the A a 3rd below middle C is 440 Hz. (440 cycles per second)

OVERTONES:

One aspect we have yet to discuss about the properties of a tone is it's overtones-just as white light is made up many different colors of the "spectrum" (ever seen sunlight through a prism?) The "spectrum" of a tone is it's overtone series. You see the string we just talked about also has vibrations other than the fundamental vibration we've already spoken of. It also vibrates: In Halfs

In Thirds

In Quarters

Etc. Each of these produces a pitch called an overtone or partial which is heard (although less loudly) along with the fundamental pitch. These together produce a composite sound which give a particular instrument its characteristic sound.

So, for a low C on a typical soundmaking device the overtone series would look like this:

Some observations about the properties of overtones: In general, the lower the partial the louder it is- the fundamental is loudest-higher overtones are fainter in volume the overtone series continues on up in finitum The spacing of the overtone series is widest at the bottom, becoming gradually narrower as it goes higher in range the mix of the particular overtones is the principle determiner of the sound quality or "color" of a musical instrument* * (for instance, one might find in a sonic laboratory the human vocal sound is highly rich in overtones, or the oboe's sound tends to emphasize odd number partials, or the sound of a woodblock tends to be lacking in midrange overtones) -Being fully aware of the scope of this topic can greatly enhance writing and arranging abilities-for example the same chord will have quite a different effect if arranged for 4 vocalists instead of 4 trumpets. A Word About Pythagoras: For musicians Pythagoras's name should have a great deal more significance than that painful memory of 2nd semester high school geometry. Pythagoras made important discoveries about pitch, discoveries that brought about both the development of our system of twelve tones and the development of our understanding of the basic natural properties of sound. Get Ready, Here it is in a nutshell: The pitches sounded by a musical instrument are related to the length of the strings * * (Keep in mind that while this doesn't sound like much now, this was quite the discovery in the 6th century B.C.) * (Also note that this is again the same principle with a column of air, streched membrane, etc.-Pythagoraras, however; is said to have done the original experimentation with a string.) You See, Pythagoras stretched a string of a given length across a sounding board-and made the following discoveries: When divided in half (ratio of 2:1)-An octave above the string's original pitch was produced When divided in thirds (ratio of 3/2:1)-A fifth above the string's original pitch was produced When divided in quarters (ratio of 5/4:1)-A third above the string's original pitch was produced Continuing in this manner the entire overtone series was eventually produced. and the first 16 partials were used to devise a scale * * (This produced the first system of tuning. Ancient music tended to seldom modulate and was in a small range. Common beliefs hold that the use of wider ranges, contrupuntal textures and modulation in music are fairly new devices in the total history of music (although the earliest music is scantily documented). If the piano in your 20th century living room was tuned this way, however; the lowest and highest C's would sound out of tune with one another (the highest sounding flat in relation to the lowest). This phenomenon is called the pythagorean comma, and occurs in the tuning system that is derived in nature through the aformentioned method. Twenty centuries of calculations have produced a system in the western world which solves this problem by dividing the octave into twelve equal parts. This system is called Equal Temperment Tuning. it's precursor (Well Temperment tuning) was in common use by the time of Bach. This system of tuning, which allowed for free chromaticism and modulation, was the inspiration of Bach's Well Tempered Clavier, which is a book of preludes and Fugues in all 24 Keys -major and minor.) for a look at the many types of tuning systems used throughout history (many of which can be dialed up for interesting effect on your synth), look up "Tuning systems" in the Harvard Dictionary of Music. As you will see in the course of this study, these notes are not only the the first partials of the overtone series of any given note, but also the notes which comprise the most basic of all chords, the major triad. This is profound evidence of the effect of the natural laws of sonics and thier relationship with the development of harmony in music in cultures all over the world. Here's how they are arranged on the keyboard:

THE SOUND ENVELOPE: The sound envelope is a visual representation of the contour of a sound.: There are 4 ingredients of the basic sound envelope: 1) attack 2) sustain 3) decay 4) release A typical envelope might look like this:

Almost all synthesizers today have envelope generators which give the musician control over these parameters and allow shaping of a sound. Often they also have several other parameters added to the envelope for even greater control over the sound. -being aware of the differing shapes of sound envelopes of different instruments can also add to writing and arranging skills- For example: A woodblock's envelope might look like this:

While a bowed violin might look like this:

or a guitar:

Keep in mind that the same instrument can have many different types of envelopes depending on how it is played at any given moment (soft/loud, staccato/legato, pizz./Arco, etc.)