Site hosted by Build your free website today!
Music theory instruction
 Music theory-Tone/Pitch
 Music theory-The twelve tone standard
 Music theory-Measuring the chromatic scale
 Music theory-Scales
      The natural major scale (Ionian)
      Understanding intervals in the major scale
      Playing intervals
      The natural Minor scale (Aeolean)
      What is a relative minor scale?  
      Pentatonic scales (5 notes)
 Music theory-Chord theory
      The major triad
      The minor triad
      The major third interval:King of notes
      Inverting and voicing chords
 Music theory-Complex chords
      Dominant seventh
      The important seventh interval
 Music theory: Chord progression theory
 Music theory: Exotic scales
 Music theory-Understanding modes
 Music theory-Applying the modes
Music links



I have put together this instruction series to teach beginners and as a guide for advanced students of music theory. This instruction covers a lot of ground and is presented in a very logical form and progression. Music theory is to be understood by all musicians. What instrument you play is irrelevant. When music theory is used to play an instrument it is called "applied theory". If you are a soloist/composer it is especially vital you have a good understanding of theory so that you can apply it to your instrument/compositions. I hope you enjoy this site will not hesitate to refer other musicians here. If you have any comments, questions, or additions to this material my email address is



When I refer to "tone" I am refering to a sound played at a certain pitch. "Pitch" is the frequency of that tone. If a sound is high it has a high frequency (many wave peaks per cycle). If the sound is low it has a lower fequency (fewer wave peaks per cycle). This frequency is measured in "Hertz" Hz. Up

The twelve tone standard: The foundation of music

Sound engineers found that virtually any music can be played when enough tones are available. They found that twelve tones was that magic number. It was sufficient enough to cover all common types of music worldwide. Therfore, it has become the standard. The formation of the intervals began by listening to a reference tone and it’s next higher tone. This tone sounds the same to the ear yet is just higher in pitch (frequency doubled). Next they broke the distance between the two tones into equal parts. The distance between any two tones is called an ‘interval’. Once the equal parts were tuned it was necessary to experiment with the pitch of that reference tone on which all the others tones were built.
After careful listening of the intervals based on different reference pitches, engineers determined that the pitch that produced the best sounding intervals between the 12 tones is 440 hz. The reference tone was named A. So today we have the standard tuning of A=440hz. There are other pitch tunnings that are popular yet are very close to the standard. Example A=338,339,441,442hz. Any of the twelve tones when doubled in frequency will produce it’s next higher tone. Likewise when any of these twelve tones frequencies are divided by 2 it’s next lower tone equivalant is produced. Example: the next higher tone of the ref tone A at 440 is 880hz, lower is 220hz. The twelve tones are known as the "Chromatic Scale". They are each given a letter reference and are called a ‘note’ A, A#, B, C, C#, D, D#, E, F, F#, G, G#. The (#) symbol means sharp. Note: Of the traditional instruments, the 88 key piano has the largest frequency range playing frequencies below 32hz and above 1,975hz!Up

Measuring the chromatic scale

Today a simpler measurement exists that divides each of the twelve intervals into one hundred equal units. "Cent" meaning one hundred is that measurement. Therefore, the distance between two chromatic tones is one hundred cents. All modern electronic tuning devices today will show this measurement. Up

Scales:The building blocks of music

Scales are merely a sequence of notes. The chromatic scale has all twelve of the available notes. From the chromatic scale we can pull notes out and create other scales. The chromatic scale should be thought of as our tool box. We can build our own scales from these twelve notes. Earlier we learned that the distance between any two tones (notes) is called an ‘interval’. With 12 tones available we will measure distances from one note to the next with 2 basic types of intervals ‘half step’ and ‘whole step’. A half step is a movement up(+) or down(-) one note from any note. A whole step is the movement up(+) or down(-) two notes from any note. All scales are based on a starting point known as the "root" note and have an ending point which is usually the higher root note. In scale formation this root note is also the ‘key’ name for the scale. For example, if our scales starting point is the C note then it’s a scale in the key of C. Now from the root, when we move up a half step we come to the next available note. Or we can move up a whole step (which is up two notes) or a whole step and a half step which is three notes etc. Again, a scale generally starts on a note and ends on it’s higher note. So when creating a scale we have a starting and ending point and we pick the notes we want to use in between. Then we write out a fomula based on intervals using variables; W=whole tone, H=half tone, W+=whole tone+half tone,2W=two whole tones.

A whole tone scale would be writen simply W+W+W+W+W+W
In this example we chose a starting note and move in whole steps 6 times bringing us to the higher root note. This scale has six different notes. We call this a hexatonic scale, hex meaning six. When we play the scale from beginning to end we start on the root note and end on it’s next higher root note. So with this whole tone scale we play seven notes.

Once you have your scale formed you can start it from any of the twelve notes. The scale intervals do not change. The starting note will be key name of your scale.

Note: even though the intervals of one scale do not change regardless of where you choose to start your scale… each of the twelve keys have a uniqueness of their own. This is partly due to the fact that the ear is hearing the scale melody at different frequencies. That is why some songs are said to sound better in certain keys. However, this is all a matter of personal opinion.

The natural major Scale (Ionian)

There are many scales that have been created and used throughout history. Each one with it’s own unique sound (melody). Today, one such scale has become the reference scale used to compare all others. This scale is called the "natural major scale" (Ionian).

The natural major scale is made up of seven individual notes. The formula for the scale is W,W,H,W,W,W,H. As with all scales, this scale has a unique sound and is the most common scale in modern western music. Countless songs have been writen using this scale.
In modern music theory we know this all important scale as the "reference scale" by which we compare all the other scales. It is crucial that you memorize this scale and know it well.

Understanding intervals in the major scale

The "key" to understanding music well is to think in terms of intervals. Intervals in music theory are used to describe a few different things. We already know intervals are the distance between individual notes ie half step, whole step and used in scale formulas. Next comes the magic.

Now once we have a scale established we can number each note starting with the root note. This alows us to identify a notes position within the scale. In the case of the major scale we number one through seven. The eigth note is the same as the first only higher in sound.. Thefore, this note is called the "octave" ‘oct’ meaning eight. Later in chordal theory we will number past the octave to describe complex chords. But thats later. When playing any scale you should be aware of any notes position within the scale. This position of any note within a scale is also known as it’s ‘interval’ but now it is used to define a location within the scale. For example, if we are playing the natural major scale in the key of C the fifth interval(note) is G. C,D,E,F,G,A,B,C

Playing intervals

‘Playing intervals’ means that we sound two different notes at the same time. We start on any given note and construct the natural major scale. The root is the first interval, then we can choose any other note to play simultaneously with it whether it is related to the scale or not. For example: based on the C natural major scale, to ‘play a third’…we would play the C note and the E note together because E is third in line. To play a fifth interval we play C/G, fourth C-F and so on. Thirds are very often used in Spanish music and chromatically in polynesian music. Fifths are used to death! (rock, blues, country and middle eastern music.) Sixths are used heavily in country western music and ragtime.

The (#) designation seems to have derived from use of the popular scale of C major throughout history which has no sharps at all. C,D,E,F,G,A,B,C

The natural Minor Scale (Aeolean)

The natural minor scale is also a seven note scale. We could write the formula out for this scale using the scale formula above however, now that a reference scale has been established we use it instead. This is how it is done. We create the natural minor scale by altering the natural major scale (reference scale). We will use the terms "sharp"(#) or "flat"(b) meaning to chromatically go up or down a half step to alter the intervals of the natural major scale. Based on note intervals the minor scale is 1,2,d3,4,5,d6,d7. This means that we have altered the natural major scale by flatting it’s 3rd, 6th and 7th intervals. If a note is not changed it is said to be "natural". Here we have the 1st and 5th intervals natural also the 2nd.

When fifth intervals are played either major or minor scales can be played over it since the 5th interval is natural in both scales. Therfore, playing fifths do not designate major/minor key. Rock/blues music is founded on this idea.

What is a relative minor scale?

The relative minor scale is simply the sequence of notes of the major scale that naturaly satisfies the 1,2,d3,4,5,d6,d7 minor scale formula. Any natural major scale has a relative minor scale and it always starts on the 6th interval. For example, the relative minor scale of C major is A minor. This is also known as the 6th ‘mode’ called the ‘aeolean’. Modes will be discussed later.
To better understand this lets look at the C major scale. This scale has notes CDEFGABC. When we build the minor scale we alter the natrl major scale which is our reference scale. So in building A minor we alter the A major scale. Using the WWHWWWH formula to build from the chromatic twelve tones we have A,B,C#,D,E,F#,G#,A. We can see that this A major scale has three sharped notes and that is exactly how this key is notated on the musical staff. When we now alter the scale with b3,b6,b7 we end up with A,B,C,D,E,F,G. Those are all natural notes in the C major scale! So whenever we start on a major scale’s sixth interval and play to it’s octave, we are playing it’s relative minor scale also known as the Aeolian mode.

Pentatonic scales

As mentioned earlier there have been many scales formed throughout time. In western music one scale has been used quite often in blues and rock-n-roll music and country music. It is a pentatonic scale consisting of five notes "penta" meaning five. Based on the major scale the formula for the major pentatonic is 1-2-3-5-6. The minor is 1-d3-4-5-d7. When playing over fifth intervals you can play either the major or minor pentatonic whichever you choose since fifths don’t dictate either minor or major key. Blues music often uses the minor. Country and rock-n-roll music tends to use both. Up

Chordal Theory

When we have a scale created we can then build chords from the notes contained within it.. Chords are generally constructed bye linking third intervals of the major scale and this creates harmony. A chord (triad) must have at least three different notes "tri" meaning three. The most important thing to remember in chordal theory is that chords are built from ‘natural’ or ‘altered’ notes of the natural major scale and are notated in relation to that scale.

The Major Triad

The major triad consists of three notes "triad" meaning three. The formula for a major triad is 1-3-5. This is the first, third and fifth intervals(notes) of the major scale. For example from the C major scale we would get C-E-G. This is the C major triad usually notated as just the letter C. The chord gets it name from the scale that it was formed from and the ‘major’ designation because everything is natural. No alterations.

The Minor Triad

The minor triad also consists of three notes. The formula for a minor triad is 1-d3-5. Again we always use the major scale as our reference. Just as we altered the major scale to create the minor scale so do we to create chords. We see that we use the natural 1st and 5th intervals of the major scale however we alter the 3rd interval by flatting it. So if we are using the C major scale as reference we have C-Ed-G because E is the 3rd interval of the C major scale. So we have a C minor triad. This chord is notated as Cmin or Cm. Again, it gets it’s name from the scale of which it was created and the ‘minor’ designations because of the flatted third interval. You can think of the flatted third as a "minored" third. Minor meaning lesser or flat.

The most important third interval:The King of notes

It can now be clearly seen that the third interval of the major scale is very important in chord construction. If it’s unchanged or "natural" it produces a major chord sound if it is flatted (or minored) it produces a minor chord sound. Two very different sounds. As we saw in scale construction it also dictates whether a scale is minor or major. This is the most important note in all music theory.

Inverting and voicing chords

When playing a chord we can change the sound to some extent without adding or deleting notes which would produce a different chord.
"Inverting" the chord is one way. This means instead of playing the chords’ root note first we start the chord with one of it’s other intervals. However, with inversions we are not changing the sequence of the notes. For example, if we want to invert a C major triad we can play G-C-E or E-G-C. As you can see the sequence of the notes don’t change… only the starting point. The sound will be slightly different particulary if a bass instrument is playing the inverted bass note.
"Voicing" a chord is one other way. With "voicing" we do change the sequence order the notes are played. Again we aren’t adding any new notes or removing any essential notes. We are merely arranging them in a different order. When we do this the ear hears some differnent intervals it didn’t before. For example, we could play that same C major triad like this G-E-C-G-C. Not only did we change the order of the three notes but this chord spans two and a half octaves! The sound is a bit different and is spread out more. A chord can span as many octaves as you like using inversions or different voicings however, as long as the foundation notes(in this case the triad notes) are the only notes, the chords’ name doesn’t change.Up

Complex chords

Now that we understand triads we can build upon them further. We can add more notes. We call these "complex chords". When we build upon a major triad there are rules that we need to memorize to do it properly and also to understand chord notation.

Major chords

When we add the seventh interval to the major triad we add "maj" and the interval that is added to the chord notation. For example, when we add the B note (seventh interval) to a C major triad we now note it as Cmaj7. So 1-3-5-7 is the formula for any maj7 chord. A 6th chord is major but is notated with merely a 6 extension. Example a C chord with notes 1-3-5-6-9 would be notated as C6/9

When intervals are added above eight (the octave), they are counted 9,10,11,12,13,14… However, we know that the eigth, tenth, and twelth note are merely repeats of the triad notes an octave lower and if it’s a maj7 chord the fourteenth is a repeat of the seventh so we don’t need to count them again. So the only new notes that can be added from the major scale are the 2nd, 4th and 6th intervals respectfully 9,11,13. Most commonly complex chords are voiced using these 9,11,13 intervals to spread the sound out more so they notes don’t tonally clash with the the other notes by being all in the same octave. No matter how you decide to voice a maj7 or min7 chord it should be notated with the 9,11,13 extensions. The seven is often dropped because when the "maj" is notated it means the seventh is present. So a C chord with 1-3-5-7-9-11-13 contains all the notes of the major scale and would be written as Cmaj9/11/13.

When the seventh is not present we notate "add" and then the interval. ie 1-3-5-9 is notated Cadd9. We can even add more dissonance to any chord by sharping or flatting any of the extensions. For example 1-3-5-7-#9-#11-#13 based on the C major scale is a Cmaj#9/#11#13. We know it’s a major chord because the natural third and then we notate it with "maj" because the seventh is also present and finally we notate the sharped extensions.

Dominant seven chords

A dominant seven chord is a major triad with a flatted seventh interval. The formula for a dominant seven chord is 1-3-5-d7. By flatting the seventh interval we create tension in the chord. Dominant seven chords are notated as merely a 7 added to the root note. If we build on dom 7 chords we merely add the new higher interval to the root note and drop the 7. Example, a C7 chord with the 9th interval added would be notated as C9. If we also add an 11th we drop the 9th and note it as C11 and so forth. So it is understood in chord notation that all the dom. intervals preceding are present. Any sharped extensions to the 9th and 11th or 13th intervals must be notated. Reminder, if the natural seventh (14th equiv.) is also present it should be notated with "maj" ofcourse. Lastly, if we want to add any interval not consecutive to the flatted seventh we add it on ie. C7/11. Dominant seven chords are still major in sound because the third interval is natural.

Minor chords

Most notation rules that apply to major chords apply to minor except when noting extensions we never drop the seventh because it is not implied. Remeber a chord is minor when the third interval is flatted. We notate minor chords with "min" or "m". When we add the natural seventh like in the maj7 chord we must note it min/maj7 because the natural seventh interval is present. Therfore, if a C chord has 1-d3-5-7 it would be notated Cmmaj7. This chord is still ultimately minor in sound because of the flatted third but with a slight major sound. If the seventh is ‘flatted’ it is notated with the 7 extension just as are dominant chords ie. Cmin7. Again, we must use "min" or "m" to show that the third is flatted making the chord minor. Here is an example of a chord that uses all the notes of the minor scale Cmin7/9/11/d13 remember the 7th is flat.

The important seventh interval

As we can now see, the seventh interval is also very important in chord building. When it is added, depending on it being left natural or flatted, will determine whether a major triad will be major or dominant in sound. In a minor triad it will determine whether it is minor or partially major in sound. In addition to the root note and third, the seventh interval is the most important note in complex chord building. Because the third and seventh intervals dictate the type and sound of a chord they are called "color tones" In major/minor chords the fifth interval doesn’t dictate major or minor sound at all and because the other extensions all create tension/dissonance and character… the fifth is the least important note and can even be left out. It merely strengthens the existing sound by completing the triad. However, in the last two chords we will discuss the 5th is quite significant.

Diminished Chords

A diminshed chord creates tension because it is minor in sound and the fifth interval is flatted(diminished). Because it also has a flatted third we might think of it as a minor chord however, it isn’t a minor triad because the fifth is flatted so it is in a category all it’s own. Diminished chords have a unique sound. This chord is notated "dim" or "0". ie Cdim/ C°

Augmented chords

Augmented chords create tension because it’s major in sound and has the fifth interval sharped#. Because it has a natural third it is major in sound but the sharped fifth creates dissonance. Likewise we might think of this as major chord because of the natural third however the fifth is altered so it is in a category all it’s own. This chord is notated "aug" or "+". ie. Caug/C+Up

Chord Progression Theory

As mentioned earier, when we have a scale we can build chords from the notes therein. We have covered all the chords and now we want to see what kinds can be built using only the natural notes of a scale. Using the C major scale as our reference we find we can build these triads off of the notes of the scale:

C Major, D minor, E minor, F Major, G Major, A minor and Bdim

These triads are numbered numbered according to their roots position in the scale. For example the F note is the fourth interval in the major scale so this is the fourth triad. We us roman numerals to notate these chords. We can see this fourth interval triad is major so we use upper case IV. The second interval triad is minor so we use lower case ii. If we want to add extensions we can add on the interval number like so ii7. For dominant chords just write dom before the roman numeral example: domI, domIV, domV. Chord progressions are written this way. Musicians need only know the chord progression in this way to easily play in any of the 12 keys. This is because the order of the progression doesn’t change. That’s why thinking musically in terms of intervals is the "magic key" to understanding and playing music well.

Once we have the triads we can add extensions onto them, creating complex chords into our progression using the things learned from the section on "chord theory".Up

Exotic scales

For myself, one of the most exciting discoveries in music is playing foreign scales. When you have played with western scales for a long time the chord progressions become kind of old and you use the same ones over and over. When we study a foreign scale we find different intervals and therfore a different melody. These scales have their own unique sound and it is when we start to build chords from their intervals that we see the magic. We find ourselves creating different chord progressions than we were with the western scales because the different intervals dictate this. We sometimes also find ourselves using chords that we wouldn’t normally use also and in different places as well.
When building chords from new scales follow the same procedure as above but first determine whether it is a major or minor scale by looking at the important third interval. Start with each interval and based on the natural notes, try to build triads, diminished or augmented chords or merely fifths (common with many eastern scales). When you have many chords built we can then build a progression. Once a progression is built we can create melody over the top and suddenly a foreign music we have never ever played before starts to develop and it sounds fluent!Up

Understanding Modes

A scale that is built from the natural notes of one scale is called a mode of that scale. If there are seven notes in a given scale then there will be seven modes available. Each mode has a unique melody because of the different intervals. The most commonly used are the modes of the natural major scale. However, every scale has modes whether it be the natural major scale or a foreign scale like the spanish gypsy (one of my favorites). Remember they are technically each a different scale. Since we are starting at different points within the reference scale and playing to it’s octave, each modes interval formula (ie. whole step, half step) are different. For the natural major scale there are 7 modes… one for every note of the major scale. Earlier we talked about the relative minor scale. It is the sixth mode of the major scale, called the ‘aeolean mode’. We started on the sixth interval. A mode is referenced according to it’s root note just like any other scale. The mode name is based on the notes position within the reference scale. Based on the triads built off each interval we can know whether a mode is minor or major quickly. So, using the C natural major scale as our reference scale we have these modes naturaly associated with their root triads: C Major(Ionian mode), D minor(Dorian mode), E minor(Phrygian mode), F Major(Lydian mode), G Major(Mixolydian), A minor(Aeleon mode) and Bdim(Locrian mode)

Here are all seven of these modes according to their position in the major scale and their formulas based also on the major scale from which each was formed and whether it is major or minor.

Root- Ionian Mode (natural major scale)
2nd- Dorian (minor) 1-2-d3-4-5-6-d7
3rd- Phrygian (minor) 1-d2-d3-4-5-d6-d7
4th- Lydian (major) 1-2-3-#4-5-6-7
5th- Mixolydian (major) 1-2-3-4-5-6-d7
6th- Aeolean ( natural minor) 1-2-d3-4-5-d6-d7
7th- Locrian (dim minor7) 1-d2-d3-4-d5-d6-d7


Applying the modes

So how do we use the modes? Easy. Look the chord progression! You can play a different mode over every chord change. For example the Dorian mode is minor because it has a flat third and natural fifth so we can play over a basic minor triad and also minor7 chords because it has a d7 also. Even if we have a progression using min7 chords like iv7,v7,i7 we could play a Dorian mode over each chord change and still be ok because our modes have the essential triad notes of each chord. For example if this progression is in A minor we have: Dmin7, Emin7 and Amin7. So we would play D dorian, E dorian and A dorian scales. However, if we wanted to stay entirely key related (meaning not using any modes with unnatural notes of the A minor scale) we could simply play the modes associated with each chord interval; D dorian, E phrygian and A aeolean scales. How did I determine this? Because the the A minor scale’s relative major scale is C major. All the chords in the progression are centered around the C major scale so it is the reference scale we use know what modes naturaly relate to the progression.

As long as you are following the basic rules you can do what you want. Jazz players do this a lot. For example, if I wanted to get Jazzy using the dorian minor mode, I might create a progression like i7,iv7,v7. This is a minor 1-4-5 progression using min7 chords. I might play a dorian mode over each change. For a jazy mixolydian sound… mixolydian modes over each change of a I9-IV9-V9 progression. Make sense?

Vintage blues was 12 bars of domI, domIV,domI, domV, domIV,domI. The fifth mode the Mixolydian has the flat seven and is major so we can think of it as the dominant mode. So we could play this mode over each chord change. Ofcourse, you might play a minor pentatonic scale or ever change for the vintage blues sound. I like to mix things up and use both.

If you want to play certain modes you should write chord progressions based on the modes you want to play. As with the blues example above; the primary mode would be the mixolydian. Jazz does this quite often- playing modes over each chord and changing keys often also. In conclusion, each mode has a unique melody and is to be used over the chord(s) they can form.

Solo tip; When playing modes over each chord change in a progression I like to use "chromaticism"(moving up or down in half tones) and quite often it sounds cool. Look for those opportunities. Like in 12 bar blues I use chromaticism when the V-IV change occurs. When playing the minor or major pentatonic I like to use chromaticism between the 4-5, d7-1, d3-4 and 2/3, 5-6, 1-2 intervals respectfully.

I hope all this material helps many of you out there to become better musicians.
Audios. Written by: Michael Park

Links to great music sites

Harmony Central-great music site! musician discussion forums,new gear articles, guitar tab etc. check it out!

Synth Zone-all the latest in keyboards,sounds etc.

Lyrics World-great lyrics site

Lyrics Cafe-huge site! full albums w/lyrics check it out!

Songsearch-find any song on earth here!!