musicbasics

Music has parts, alot of parts. A well crafted composition consists of hundreds or perhaps thousands of individual ideas. And the grand total of the ideas expressed is much more than just the sum of all those parts. Knowledge is power, alot of power. If you develop your knowledge of music's fundementals, you stand a much better chance at achieving your compositional goals.

This article will attempt to explain the basic elements that form the foundation of many of today's music compositions. Much of today's music is based on the Diatonic scales. The scales are simply the arrangement of notes and the intervals between notes that form a regular pattern. Chords may be calculated using the intervals so that their pitches fall within these patterns. In this way, you'll compose with a scale and key signature. It's alot of information but music is an efficient language. It won't take very long to learn it if you keep with it.

This article is about western music. Many of the concepts may apply to the music of other cultures but this article is specifically written to describe primarily the music structures and concepts of European and American popular compositions.

Notes

The structure of music builds on very simple concepts. Just as in mathmatics, as you become familiar with very elementary concepts, (1+1=2), you can learn new ideas, (2*2=4), and build upon the more simple to arrive at the more complicated, ((2*2)+1=5). At its most simple, the fundemental concept in music is the tone. A tone is a sound that occurs as waves move through the air. The waves move at specific rates and the ear hears these rates as tones having specific frequencies.

Figure 2 - The Note A

The human ear can hear a very wide spectrum of frequencies. Rather than accounting for every possibility, the modern system of musical classificiation and terminology places strict limitations on which frequencies to use during composition. Certain frequencies have become part of the system while all the other possibile frequencies are simply ignored. For instance, when we hear sound waves that move through the air at precisely 440 times a second, music assigns the name "Note A" to that sound.

The Nature of Vibrations

Consider a very tight string, such as that on a guitar. When the string is plucked, it vibrates. This vibration causes the air around the string to vibrate and we hear the sound waves of the string. On a guitar, we can shorten and lengthen the string by holding down the string with a finger. It turns out that if you shorten the string by exactly one half, the string will vibrate exactly twice as fast. If we play the Note A that vibrates at exactly 440 times a second (hz) and then shorten the string by half, we'll hear a tone that is 2*440 or 880 times a second.

Figure 3 - The Note A One Octave Up

As the string is shortened by half again, we hear the vibrating sound waves at 1760 times a second. Under ordinary circumstances our ears find it difficult to tell the difference between these sounds as they are very closely related. Rather than giving these sounds a different name and because they sound so similar, music gives these sounds the same name but assigns a new idea to their different rates (frequencies) called the Octave.

Naming the Tones

So, an A1 at 440 hz, an A2 at 880 hz and an A3 at 1760 hz all sound very similar as compared to the infinite number of other possible frequencies. Now, you don't always have to divide the string in half, you can divide the string in any number of ways to arrive at any number of frequencies. To keep things from becoming overly complicated, music divides the range of all possible frequencies amoung 12 separate tones, each with their own set of octaves. These tones are called notes.

Each note in music is calculated by increasing the pitch (multiplying its frequency) of the previous note by the 12th root of 2, in other words 12 divisions of the one half division that forms an octave. Historically, the full range of calculated notes starts from the 440 hz note A. Orchestras use this A440 reference note to do a final tuning before a performance. A440 is the note you hear played on the piano just before the performance begins.

The names given to each of the 12 notes and their frequencies are listed in following table.

Figure 4 - Tones' Hz Increase Exponentially

Notice in the table that as you read across a row, the numbers are merely doubled (there is some rounding). The rate at which sound waves reach your ears increases by a factor of two as the octave is increased. As you read down a column, the frequency increases by the 12th root of 2. The frequency of the next note after the C of the Octave -2 is calculated as 32.70 hz * 1.05946309436 or 34.644443185572 hz which rounds to 34.65 hz. So the next note after C-2 is C#-2 having a frequency of 34.65 hz. To calculate the frequency of the next notes requires the multiplication of the factor times the previous note. The overall increase in frequency is therefore not a linear series of gradual steps. Rather, the steps get increasingly larger as we move up the spectrum. Subsequently, the frequency of musical tones is said to be exponential.

In acoustics theory, the distance between any two notes is calculated using a unit of measure called "cents". The distance between two notes is calculated using numbers from 0 to 1200, where 1200 equals an octave. 0 is the fixed lower note (tonic) and 1200 is the first octave of the tone 0. Using cents units, 100 cents equals one semi-tone. For example, 700 cents would be equivalent to 7 semi-tones (A to E). Cents are a useful measureing unit for tuning instruments.

Figure 3 - The Note A Two Octaves

After carefully studying the motion of a plucked string, the ancient Greek, Pythagoras discovered that a string's motion was much more complex than a simple up and down motion. In fact, a string not only moves up and down across the entire length but also to a lesser extent across many fractions of the string. A string vibrates across each half of the string and many other fractions of the string, thirds of a string, fourths, etc. The basic pitch of the string is called the fundemental and the additional higher order vibrations are called harmonics.

The harmonics of a string represent nature's tendency towards the 12 tones we are used to hearing in modern music. The harmonics are defined in terms of simple ratios such as 1:2, 3:2 and 5:4. Calculating a set of frequencies based on these simple ratios produces results that are very close to the frequencies of the standard tones described earlier in this article. The actual frequencies we use are different, however. And, although the simple ratio based calculation of the frequencies theorectically produce perfectly in tune vibrations, the resulting tones do not fall neatly into divisions of an octave. Over the years, music theorists decided to adjust these "perfect" frequencies to allow for fixed pitched instruments such as the piano and flute. Such instruments need to have a complimentary set of frequencies for the repeating set of 12 tones. With such a set, the performer can play from octave to octave in any key without retuning.

Figure 3 - The Note A Two Octaves plus a 5th

The adjusted frequencies of the standard tones are therefor based on equal divisions of 12. This method for tuning is called 12-Tone Equal Temperament.

In looking at the Division column in the above table, you can kind of see where the 12th root of 2 business comes from.

Intervals

In music theory, the distance between any two notes of a scale is called an interval. If the two notes are sounded sequentially one after the other, the notes form a "melodic interval." When the notes sound together at the same time, they form a "harmonic interval." If the two notes are the same, the interval is called a "unison." The smallest interval above a unison is a "half step" or "semi-tone". An interval of two half-steps is called a "whole-step" or a "tone". An interval of 12 half steps or 6 whole steps is called an "Octave".

How It Sounds

Music is not in the notes being played, it is in the relationship between notes being played.

A tone chromatically raised aquires a tendency to continue upward, whereas a lowered tone is given a downward tendancy. Thus the forward motion of music is aided by chromaticism, although too much melodic movement by halfsteps is likely to impair the individuality and strength of the melodic lines. Chromatic tones may move in either direction before resolving to the principal tone, although modern idioms prefer the descending form.

Ear Training

Learning the difference between the intervals is the first step in understanding how music works. Ear training software is available that plays the intervals via your computer's sound card. You practice by identifying the intervals. When you are beginning, your initial goals should be very modest. Set the application up so that it only plays octaves and perfect 5ths. Practice learning to identify just these two intervals until you no longer make a mistake before adding additional intervals such as a perfect 4th.

Resist the temptation to jump ahead by learning to identify all of the intervals, or even scales and chords. Take a slow systematic approach. Learn each interval in relationship to other intervals first. Then proceed gradually to the ever increasing complexity of scales and chords.

Also, remember that the goal is not to aquire "perfect pitch" which is the ability to identify the name of a single tone sounded in isolation. Very few people have this ability. However, everyone has the ability to recognize tones sounding in relation to other tones. It turns out that having the ability of perfect pitch doesn't really make for a better composer or musician. Music is all about the relationship between tones (intervals and chords, melody and harmony) and not about solitary tones.

Two popular ear training applications are described next.

Free ear training software is available at www.musictheory.net. Download the latest version of the Music Trainers and Utilities. After launching the program, select the Interval Ear Trainer. Beginners should click off all of the check marks for all of the intervals except the Perfect 5th and the Octave. As you gain the listening skills, click the Play Mode button and learn to identify the intervals played melodically, harmonically and both melodically and harmonically.

Teoria offers a sophisticated and very affordable music training software application. To learn to identify intervals with Teoria, launch the program and then select the Intervals menu item. Choose the Ear Training menu item and then select either Melodic Intervals or Harmonic Intervals. Teoria will display the Intervals Ear Training Options dialog. Click the None button to turn off all of the intervals. Then click just the Octave and Perfect 5th options. As you listen to the intervals, you respond by either clicking on the interval identification buttons or by entering the notation by double clicking the staff. You can also use the right mouse button to view the name of the note under the mouse. Teoria keeps track of your progress. When you close the Teoria software, you will be asked to save your scores. If you save your scores, you can review them later by selecting the Database main menu and then select Browse Database. When you see the database browser, double click one of the previously saved exercise to view the details of the scoring.

Table 2 - Tones

C	G	E	D
	5th Above	3rd Above	2nd Above
Tonic	Dominant	Mediant	Supertonic
Tonic	Subdominant	Submediant	Leading Tone
	5th Below	3rd Below	2nd Below
C	F	A	B

First, intervals which we consider concordant (pleasant-sounding) have simpler ratios than discordant (harsh-sounding) ones.

Table 3 - Resolving Intervals

Perfect 5th	Minor 6th	Major 6th	Minor 7th	Major 7th	Root	Minor 2nd	Major 2nd	Minor 3rd	Major 3rd	Perfect 4th	Perfect 5th
Consonant	Consonant	Consonant	Dissonant	Dissonant	Consonant	Dissonant	Dissonant	Consonant	Consonant	Consonant	Consonant
Majestic	Sinister	Happy	Cool	Sweet	Home	Tension	Anticipation	Sadness	Bright	Vague	Majestic

How It Looks

The intervals within one octave are called "seconds", "thirds", "fourths", "fifths", "sixths", and "sevenths". Unisons, fourth, fifths, and octaves are called "perfect" intervals. Seconds, thirds, sixths and sevenths can be either "minor" or "major". Minor intervals are a half step less than the major interval. Between the perfect fourth and the perfect fifth is an interval called the "tri-tone", the distance of which is three whole steps.

Table 2 - Intervals

Full name and Alternate	Short Name	Width	Piano	Notes	Interval	Diminished	Augmented	Inverted Interval
Perfect Unison, Diminished 2nd	P-1st	None		C to C same octave
Minor Second	P-1st	One Half Step		C to D flat				Major 7th
Major Second, Diminished 3rd	M-2nd	One Whole Step		C to D, C to E double flat				Minor 7th
Minor Third, Augmented 2nd	P-1st	One Whole and One Half Steps		C to E flat, C to D Sharp				Major 6th
Major Third, Diminished 4th	M-3rd	Two Whole Steps		C to E, C to F Flat				Minor 6th
Perfect Fourth	P-4th	Two Whole and One Half Steps		C to F				Perfect 5th
Tritone, Diminished 5th, Augmented 4th	P-1st	Three Whole Steps		C to G Flat, C to F Sharp
Perfect Fifth	P-5th	Three Whole and One Half Steps		C to G				Perfect 4th
Minor Sixth, Augmented 5th	P-1st	Four Whole Steps		C to A Flat, C to G Sharp				Major 3rd
Major Sixth, Diminished 7th	M-6th	Four Whole and One Half Steps		C to A, C to B double flat				Minor 3rd
Minor Seventh, Augmented 6th	P-1st	Five Whole Steps		C to B flat, C to A Sharp				Major 2nd
Major Seventh	M-7th	Five Whole and One Half steps		C to B				Minor 2nd
Perfect Octave	P-8th	Six Whole Steps		C to C one octave up

The numbers that are used to name the intervals refer to the relative positions of tones within seven tone scales. They are not a measure of distance. They are a measure of degree. When the intervals fall within one of the major or minor scales, the intervals are called "diatonic". Intervals involving notes that do not belong to one of these scales are called "chromatic". The rule is that each degree of a major or minor scale must have a different note name. Because the interval C to F have different note names and are degrees of the C Major scale, the interval is diatonic. Whereas, the interval C to C# have the same note name and subsequently cannot belong to the same scale. The interval C to C# is chromatic.

This section will not describe the way intervals sound but rather the way intervals appear on a page of musical notation. Closely inspect the table of intervals listed above and review the alternate notations for what are essentially the same notes on the piano. The interval C to A, for instance, is a major sixth while the interval C to B double flat is a diminished seventh. But in both cases, both intervals sound the same when played on the piano.

When calculating intervals, the lower note is always considered fixed, while the upper note is considered variable. Intervals are named from the lower note to the upper note, in the key of the lower note. For example, the intervals from C to B double flat and from C to B flat are both sevenths because the interval from C to B is a seventh.

When you decrease a perfect interval (unisons, octaves, fourths and fifths) by a semitone, the interval is refered to as diminished (the distance of the interval becomes smaller). When you increase a perfect by a semi-tone, the interval is refered to as augmented (the distance of the interval becomes larger). The sequence is therefore: diminished - perfect - augmented.

When you decrease a major interval by a semi-tone, the interval is refered to as a minor interval. When you decrease a minor interval, the interval is refered to as a diminished interval. When you increase a major interval by a semi-tone, the interval is refered to as an augmented interval. The sequence is therefore: diminished - minor - major - augmented.

Chords

Scales

Putting it All Together