Contents Preface 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 Major Dominant seventh Minor The important seventh interval Diminished Augmented Music theory: Chord progression theory Music theory: Exotic scales Music theory-Understanding modes Music theory-Applying the modes
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 firstname.lastname@example.org
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
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 its 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.
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 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 its 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 its 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
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 its 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
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 its 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 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 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 its 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
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 dont dictate either minor or major key. Blues music often uses the minor. Country and rock-n-roll music tends to use both. Up
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 its 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 its 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.
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.
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 its a maj7 chord the fourteenth is a repeat of the seventh so we dont 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 dont 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 its 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.
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 doesnt 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.
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 isnt a minor triad because the fifth is flatted so it is in a category all its own. Diminished chords have a unique sound. This chord is notated "dim" or "0". ie Cdim/ C°
Augmented chords create tension because its 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 its own. This chord is notated "aug" or "+". ie. Caug/C+Up
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 doesnt change. Thats 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
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 wouldnt normally use also and in different
places as well.
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 its 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 its 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
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 scales 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.