Species Counterpoint (part 3 – First Species)

      First species counterpoint is a “note against note” style of polyphonic writing.  This means that each rhythmic value in the counterpoint matches the rhythmic values of the cantus firmus.  Since a cantus firms does not contain rhythmic variation, counterpoint in first species will also contain no rhythmic variation.  Since the rhythm of a work of first species counterpoint is identical to that of the cantus firmus, and neither melody contains rhythmic variation, this results in harmonic relationships that always arrive on strong beats.  Because of this, the harmonic relationship between each pitch of the cantus firmus and its corresponding pitch of counterpoint must be consonant.

                

      The same melodic rules for composing a good cantus firmus apply to composing a good work of counterpoint.  The two melodies should display melodic independence.  They should contain independent climaxes, independent melodic contours and no voice crossing.

Sequences should be avoided in first species counterpoint.  Although sequences and patterns play a large role in most forms of musical composition and improvisation, a primary part of their musical function is to flesh out an idea across a larger piece of music.  Counterpoint is a small and concentrated piece of music.  When composing such a piece of music, the entire piece should represent one independent melodic phrase. 

Some additional rules for first species counterpoint include the fact that the resolution should be reached by contrary stepwise motion.  The cantus firmus and counterpoint should be kept within a perfect 12th of each other.  Distances greater than this cause the harmonic connection between the two voices to become too weak.  Unisons should be avoided except for the first and last measures.  Unisons within the middle of the piece cause the second voice to seem to disappeared.    In addition to these rules, the basic rules of polyphonic motion that we discussed last week all apply.

When composing first species counterpoint, I suggest starting with the final cadence.  This interval must be either a unison or an octave.  Based on this choice, and the way the cantus firmus resolves, there will be only one solution for the pitch in the second to last measure of your counterpoint.  Now you have a target to aim for in your resolution. 

Next I would suggest considering which pitch you will start on, and where your climax will be.  Once these important points of the composition have been established, the rest of the measures can be filled in.  Try to use contrary and oblique motion as much as possible since direct motion requires more care to avoid issues.  Also, try to use a majority of imperfect consonances, so that your counterpoint contains an abundance of rich harmony. 

Try to maintain a smooth melodic line.  Use mostly stepwise motion.  Fill in skips (especially ones larger than a 4^th) with stepwise motion in the opposite direction.  Avoid repetitive sequences.  Remember, you are composing a concise melodic phrase.  Also, avoid crossing over the cantus firmus.  If you are writing above the cantus, remain above for the entire melody (and if below, remain below). 

Voice exchange is a beautiful effect that can occurs when the pitches of two melodies move in contrary stepwise motion in a fashion that causes the original pitches to exchange parts at the end.  This occurs most often in first species counterpoint between imperfect consonances.  Remember, imperfect consonances are the most desirable harmonic intervals in counterpoint.  Plus, voice exchange between imperfect consonances occurs after only two steps of contrary. 

Based on the rules and tips presented in this lesson, you should be prepared to compose your own first species counterpoint exercises.  For more guidance, please refer to the end of the accompanying video where I compose an example of first species counterpoint both above and below a cantus firmus.  Continued practice will grant you valuable insight into the nature of melodic motion and the way multiple melodies react harmonically.    

This Learning Music With Ray video discusses the topic of first species counterpoint.  In this video I discuss the rules that govern composing a work of first species counterpoint.  I also provide some helpful tips that will make your experience composing first species counterpoint easier.  Finally, I compose a line of first species counter point both above and below a cantus firmus in order to provide a live demonstration of the principles discussed in the video.   

  

Species Counterpoint (part 2 – Rules of Polyphonic Motion)

        Before studying the specific rules of each species of counterpoint, there are some basic principles of polyphonic motion that we should understand.  The first concept among these principals is the fact that there are three types of polyphonic motion.  They are direct motion, contrary motion and oblique motion. 

        Direct motion consists of two or more parts moving in the same direction (ascending or descending) by step or skip.  Whether the parts move in equivalent intervals (all steps, all skips, equal distances) is irrelevant.  The only relevant factor to qualify polyphonic motion as direct is that the parts move in the same direction. 

  

      Contrary motion consists of two parts moving in opposite directions (ascending and descending) by step or skip.  Again the interval of movement is irrelevant since the classification of contrary motion is only contingent on the direction of the motion.  This type of polyphonic motion can only occur between two parts since there are only two directions of motion (ascending or descending).  A third part would have to duplicate one of these two types of motion, and thus be an example of direct motion with that part. 

        Oblique motion consists of one part moving (by step or skip) while the other part remains stationary.  The stationary part could be a single pitch with a rhythmic value that is longer than the pitches of the moving part, or it could be repeated rhythmic occurrences of the same pitch.  As we will discuss in future lessons, the rhythmic value of a piece of counterpoint may vary from that of the cantus firmus only in certain species. 

        Now that we understand the three possible types of polyphonic motion, we can discuss the four fundamental rules of polyphonic motion.  They are listed below:

1. From one perfect consonance to another perfect consonance one must proceed in contrary or oblique motion.
2. From a perfect consonance to an imperfect consonance one may proceed in any of the three motions.
3. From an imperfect consonance to a perfect consonance on must proceed in contrary or oblique motion.
4. From one imperfect consonance to another imperfect consonance one may proceed in any of the three motions.

These four rules can be boiled down to two basic principles.  When we are traveling to an imperfect consonance, we may use any type of polyphonic motion.  However, when we are traveling to a perfect consonance, we must avoid direct motion.      

        As a result of these rules, composers find it more desirable to utilize imperfect consonances in their polyphonic writing.  This results in less restriction on the types of motion that they can employ.  In addition, imperfect consonances are perceived to be more harmonious than perfect consonances.  The pure quality of perfect consonances cause them to sound hollow or empty.  The impure quality of imperfect consonances cause them to sound rich and full.    Therefore, the majority of harmonic consonances within a polyphonic work should be imperfect otherwise the work will seem to lack harmony. 

       However, a work of counterpoint must start and end with a perfect harmonic consonance in relation to the cantus firmus.  To be more specific, all works of counterpoint must end with either a unison or octave.  In addition, any work of counterpoint that is composed below the cantus firmus must begin with a unison or octave.  Works of counterpoint composed above the cantus firmus may also begin with a fifth. 

This cannot be done with counterpoint that is composed below the cantus firmus because a fifth below would result in an obscuring of the perceived key.  Another rule of polyphonic motion is that all counterpoint must remain in the same key as the cantus firmus.  A starting interval that is a fifth below the cantus firmus could be perceived as a Do – Sol relationship in which the counterpoint is starting on the tonic even though it is actually a Fa – Do relationship in which the cantus firmus is starting on the tonic.  This dilemma could obscure the perceived key of the polyphonic work, and is thus avoided. 

The perfect fourth is considered to be a consonant interval when examining two pitches outside of any other musical context.  Remember, the perfect fourth is an inversion of the perfect fifth, and is thus heard as a similar interval.  However, within various musical contexts the state of this interval is more complex.  The best way to understand consonance and dissonance in polyphonic music is to think of consonant intervals as stable in relation to the key, and dissonant intervals as unstable in relation to the key.  Therefore, any interval of a fourth that requires resolution is considered to be dissonant. 

Since the perfect fourth is and inversion of the perfect fifth, Do – Fa relationships can easily be misperceived as Sol – Do relationships (as discussed earlier).  Any polyphonic situation that obscures the identity of the key would be considered dissonant, and in need of resolution.  In works containing three or more voices, additional pitches may help to support the integrity of the key and cause an interval of a perfect fourth to be considered consonant.  However, in two part compositions the perceived dissonance of the perfect fourth would be unavoidable. 

Now that we have an understanding of the basic principles of polyphonic motion, we are better prepared to discuss the specific rules of each species of counterpoint.  In future lessons on each species, please review the principles of this lesson.  Once we apply these principles through the practice of polyphonic composition, they will become easier to understand and retain.   

       
         This Learning Music With Ray video gives an overview of the basic rules of polyphonic motion that govern all polyphonic composition. After gaining an understanding of these rules, one will be better prepared to study the specific rules of each species of counterpoint. The video starts by discussing the three types of polyphonic motion. I then cover the four fundamental rules of polyphonic motion. Next, I discuss the difference between perfect and imperfect consonance in polyphonic music. Finally, I go on to discuss other miscellaneous rules of polyphonic motion, and the dissonant nature of the perfect 4th in polyphonic music. 

Species Counterpoint (part 1 – Cantus Firmus)

What Is Species Counterpoint?

      Species counterpoint is a method that has been used for many years to teach polyphonic musical composition.  The method is modeled after the compositional works of Palestrina.  This method of study was propelled forward in our modern musical culture primarily by the Johann Joseph Fux’s book entitled Gradus Ad Parnassum.  The starting point for this method is creation of a fixed melody or cantus firmus.  Next, the student composes additional melodic lines as harmony parts to the cantus firmus.  Each species of counterpoint implements a different set of rules that the harmony line must follow in relation to the cantus firmus.

Why Study Species Counterpoint?

What makes a melody beautiful?  Why do certain harmonies sound nice, and others do not?  In tonal music, there are certain melodic and harmonic characteristics that are considered beautiful and expressive.  The study of species counterpoint helps composition or music theory students to understand, identify and replicate these characteristics. 

What Is A Cantus Firmus?

A cantus firmus is a pre-existing fixed melody that forms the basis or foundation of a polyphonic composition.  One of the best ways to familiarize yourself with the parameters of a well written cantus firmus is to study pre-existing examples.  Here is an example of a cantus firmus:

        

        

          There are several basic rules that we must follow when composing a cantus firmus.  These rules can be observed in the existing literature of great cantus firmi.  They are:

1. Cantus firmi do not extend beyond the range of a tenth, and they usually remain within the range of an octave.
2. Most cantus firmi are 8-16 notes in length,
3. Cantus firmi begin and end on the tonic.
4. Cantus firmi usually approach the final tonic by step.
5. Cantus firmi contain a single climax.
6. Cantus firmi contain no rhythmic variation (they are composed of all whole notes).
7. Cantus firmi contain mostly stepwise motion, but have some jumps (usually small).
8. Leaps larger than a fourth are followed by stepwise motion in the opposite direction.
9. Cantus firmi do not contain more than two leaps in a row, and consecutive leaps are usually in opposite directions.
10. The intervals between consecutive pitches in a cantus firmus are always melodic consonances.

Consonance & Dissonance

Webster’s defines consonant as:  being in agreement or harmony; free from elements making for discord.  It defines dissonant as:  a mingling of discordant sounds; especially: a clashing or unresolved musical interval or chord.  A simple explanation of these terms would be that consonant intervals create pure harmonies while dissonant intervals create impure or even clashing harmonies.

I covered the concept of consonance and dissonance in my Learning Music With Ray: Musical Intervals lesson.  However, the basic consonant and dissonant intervals discussed in that lesson are harmonic intervals.  A harmonic interval is the distance between two pitches that are heard at the same time.  A melodic interval is the distance between two pitches that are heard consecutively.  The rules for melodic consonance differ slightly from harmonic consonance.  Like harmonic consonance, melodic intervals that are perfect, major/minor thirds or major/minor sixths are considered consonant.  However, diatonic steps are also considered to be melodic consonance. 

When you watch a good movie, sporting event or read a good fiction, what happens?  It starts slow, then some issue develops that puts you on the edge of your seat.  Finally it reaches a climax and then resolves.  The same thing happens in good music.  Dissonance is used to create conflict, then consonance is used to resolve the conflict.  Learning to control the flow of tension and release in musical composition is an important key to creating beautiful and expressive music. 

The study of species counterpoint helps us to understand the nature of musical tension and release, in addition to other musical laws and tendencies.  To start studying species counterpoint, one must first study the nature and composition of a cantus firmus.  Continued study of existing cantus firmi, along with practice composing cantus firmi according to the rules listed above, will aid you in these studies.

       

          This Learning Music With Ray video discusses is meant to open a series I will be teaching on species counterpoint.  In this first lesson, I will give a brief description of what species counterpoint is.  I will also discuss the illusive concepts of musical expression and beauty.  I will explain how the study of species counterpoint can aid in understanding the construction of expressive and beautiful music.  Finally, I go on to discuss what a cantus firmus is, and the rules that form the basis for its composition.  

Approach Note Theory

                We have already studied the use of chord tones (triads, seventh chords and upper extensions) in musical improvisation.  Approach note theory is one way to derive additional pitches and create interesting and beautiful musical lines while traveling from one cord tone to the next.  Approach note theory establishes these chord tones as the target pitches of our improvised melodies.  Melodies travel from one target pitch to the next, using other pitches to fill in the gaps.  The other pitches are often non-chord tones (although they can also be chord tones).  These other pitches can be passing or neighbor tones.  They can be diatonic or chromatic.  Their primary melodic function is to facilitate traveling to the next target pitch. 

                In general, approach notes tend to have shorter rhythmic values and are placed on weak beats.  Of course there are always exceptions to the rules.  Approach notes can also be placed on strong beats for brief moments within some musical contexts.  In addition, this rule does not mean that all target notes must be long in duration.  Some intricate lines may contain several eighth or sixteenth notes that are a mix of approach notes and target notes.  However, these types of lines usually resolve with a longer tone that is a target note.  

                Another exception would be the use of a longer tone that is held over from a weak beat to a strong beat as an anticipation.  In this instance, the pitch would be a non-chord tone in relation to the harmony on the weak beat but a chord tone in relation to the new harmony on the strong beat.  It functions as an incomplete approach that anticipates the new harmony and transforms into a target note. 

Passing tones and neighbor tones are the two basic types of non-chord tones used in approach note theory.  A passing tone is a pitch that lies between two chord tones in a melodic phrase.  When traveling from the first chord tone (target pitch) to the next chord tone (target pitch), the passing tone serves to create a smooth melodic line (stepwise motion). 

A neighbor tone is a pitch that lies directly above or below a target pitch in a melodic phrase.  There are two types of neighbor tones: complete and incomplete.  A complete neighbor tone phrase travels from a chord tone, up or down to the neighbor tone and then returns to the original chord tone.  An incomplete neighbor tone phrase jumps to a neighbor tone and then travels to the intended chord tone.  Usually, incomplete neighbor tone resolutions travel in a direction that is contrary to the way they are arrived upon.  In other words, a jump up to an incomplete neighbor would usually be resolved down to the target pitch, and a jump down would usually be resolved up.

Based on this knowledge of passing and neighbor tones, here are some guidelines for the application of approach note theory in musical improvisation.  First, select target pitches to focus on when traveling from one chord to the next in a piece of music (can be any chord tone).  Next, create melodic phrases that travel from one target pitch to the next.  While creating these phrases, alternate between passing tones, complete neighbor tones and incomplete neighbor tones to create a skillful variety of stepwise motion, static motion and musical jumps.  Embellish you musical phrases with additional diatonic and/or chromatic pitches.  Use variations in rhythm and the number of pitches to skillfully arrive at your target pitch on the appropriate beat of the measure (as indicated by the chord changes). 

One practice method for studying the application of approach note theory would be to create and practice performing all of the possible approach phrases for traveling between two specific target pitches.  Once these approach phrases are mastered, the performer can transpose them to apply to a new set of target pitches.  This style of practice aids in mastering a wide variety of approach phrases in a shorter period of time.

Another practice method would be to create 2 – 4 approach phrases for each chord change within a section (verse, chorus or bridge) of a song.  Practice playing through the changes of the song applying these approach phrases in various patterns.  For example, one performance could consist of playing approach phrase number one that you created for each change.  After each approach is mastered in this way, another performance could consist of alternating between approach phrase number one and phrase number two while playing through the chord changes.  Although this style of practice may not cover as wide of a variety of approach phrases, it does aid in mastering direct application to actual songs.  Some people prefer playing actual music to rehearsing exercises.  This method would help such individuals to remain engaged in the practice session.       

When stringing various approach phrases together to create a musical improvisation, it is important to remember that recognizable melodic patterns help to orient and ground the listener.  If a listener is bombarded with a collection of random melodies that are not related to each other in any way, he/she can become overwhelmed and lost in the music.  Melodic patterns serve to provide structure and order within the music.  In addition, melodies communicate ideas and feelings.  Recognizable patterns aid in clarifying the melodic communication.  Some composers have even used certain recognizable melodic patterns to personify different characters in plays, operas and movies.  

      

          In this Learning Music With Ray video I discuss the concept of approach note theory and explain how it can be applied to musical improvisation.  I define the terms target pitches, passing tones and neighbor tones; and I explain the roles they all play in approach note theory.  Finally, I provide musical examples of approaches derived from the chord changes of a song.  I explain how these examples can be used to practice the skill of musical improvisation.    

The Whole Tone Scale

                The whole tone scale is a six pitched scale composed of six consecutive whole steps.  Remember that there are only 12 chromatic pitches in music.  Therefore, the six symmetrical whole steps of this scale represent half of the 12 chromatic pitches found in music.  This means that there are only two whole tone scales. 

                One of these whole tone scales contains the pitches C-D-E-F#-G#-Bb.  The other scale contains the pitches Db-Eb-F-G-A-B.  I happened to start these two scale examples on C and Db, but any pitch in the scale can be considered a valid starting point.  Other starting points are just inversions of the same group of six pitches. 

                There are no official rules for properly spelling the pitches of a whole tone scale.  There are, however, some helpful tips to consider.  First, use a spelling that will make the scale easiest for the performer to read.  Your spelling may vary based on the tonal context of your musical application.  For example, the starting pitch you select for the scale or the key of the piece you are applying the scale to may cause variations in the spelling you use.  Next, try to maintain a consistent spelling within the same musical phrase or section.  Finally, try to avoid double flats, double sharps and white note sharps/flats (Cb, B#, Fb and E#). 

               Due to the number of variables in spelling (depending on the musical context) I will not attempt to provide a sheet music scale listing for practice purposes.  Writing out your own scales and spellings based on the musical context of your application would be a much better practice exercise.  Once you are proficient in performing the scale with various starting points, then concentrate your efforts on studding the proper musical application of the scale.

                The whole tone scale is often used to create a floating or ethereal effect within the music.  It can be found in many musical genres, and is used heavily in impressionistic music.  The tasteful use of this scale in musical improvisation helps to add more variety and color to your musical pallet.  However, the sound created by this scale does not apply to every musical context.  The whole tone scale lends itself to being played over chords with a raised 5^th.  The ideal chord for this scale is the dominant 7+ which contains a raised 5^th and raised 11^th.         

                 In this Learning Music With Ray video I discuss the definition and composition of the whole tone scale.  I discuss the number of pitches that a whole tone scale is composed of, and the fact that there are basically only two whole tone scales to learn.  Finally I cover tips on how to use this scale in musical improvisation. 

 

The Diminished Scale

        Like the bebop scale that we discussed last week, the diminished scale is composed of eight pitches.  Remember, most of the music of bebop jazz era is composed in a 4/4 shuffle feel that is complemented by flowing eighth note patterns.  A 4/4 measure can contain a maximum of 8 eighth notes, so an 8 pitch scale would be the optimal tool for musical improvisation in this musical style.  The bebop scale introduced a chromatic pitch to add interest.  The diminished scale includes several chromatic pitches and adds even more variety. 

    

       The diminished scale is composed of alternating intervals of whole and half steps.  The scale can either start with a half step or a whole step (depending on the chord it is being applied to).  So, the interval pattern used to compose a diminished scale is either W-H-W-H-W-H or H-W-H-W-H-W. 

   Since the diminished scale is based on an alternating whole step / half step pattern, there are only 3 diminished scales to learn.  Tonics that are a minor third apart share the same diminished scale.  The tonics of C, Eb, Gb, and A share the same diminished scale, and they can be thought of a group 1 of the diminished scales.  The next group of tonics that share the same diminished scale are C#, E, G and Bb (group 2).  The final group (group 3) is composed of the tonics D, F, Ab and B.  Included in the video are slides in which the scales of each of these groups are written out (in both whole/half and half/whole form).  Practicing these scales in light of the three groups will aid in both understanding and memorization. 

   Due to the alternating whole and half step pattern of the diminished scale, the rules for proper pitch spelling are ambiguous.  There are three main methods commonly applied among music theorists to achieve uniform pitch spelling.  One is the fraternal neighbors method.  In this method, the eight pitches are paired in groups of two, and neighboring chromatic pairs are given different letter names.  An example of this in the C (half/whole) diminished scale would be / C Db / D# E / F# G / A Bb /.  The second method involves stacking two diminished tetrachords separated by a whole step.  This results in the same spelling as the fraternal neighbors method, and only differs in the mental grouping of the pitches (example: C (half/whole) diminished scale: / C Db D# E / F# G A Bb /).  The third is the identical neighbors method.  Just like the fraternal neighbors method, the eight pitches are paired in groups of two.  However, now the neighboring chromatic pairs are given the same letter name (example: C (half/whole) diminished scale / C C# / Eb E / Gb G / A A#/).  For the scale examples given in this lesson, I have used the fraternal neighbors method. 

   Certain harmonies lend themselves to the use of the diminished scale in musical improvisation.  In addition, certain forms of the scale (whole/half or half/whole) are more appropriate depending on the harmony being improvised over.  When improvising over major triads and dominant 7b9 chords; the half/whole diminished scale that shares the tonic of the current chord can be used.  When improvising over minor triads, minor 7^th chords and diminished 7^th chords (fully diminished 7^th); the whole/half diminished scale that shares the tonic of the current chord can be used.  The tasteful use of these scales, in combination with the other scales we have studies, helps to provide a broader musical pallet for improvisation.  This leads to the creation of more interesting and varied melodies. 

        In this Learning Music With Ray video I discuss the definition and composition of diminished scales.  I cover the whole and half step pattern that is used to create this scale, and the proper way to spell the pitches of the scale.  I also explain why there are basically only three diminished scales to learn, and how all the other keys are related to these three.  Finally I cover which chords compliment the use of the diminished scale in musical improvisation.  

The Bebop Scale

                As we have discussed in past lessons, our Western musical system is based off of a seven letter musical alphabet.  This results in major and minor keys/scales that are composed of seven pitches.  In addition, even the modal scales are composed of seven pitches.  Pentatonic scales are only composed of five pitches, but they are based more on the concepts of Eastern and folk music. 

                When looking to compile a collection of pitches for musical improvisation, the music of bebop jazz era lends itself to a particular type of rhythmic feel and flow.  Most of this music is composed in a 4/4 shuffle feel that is complemented by flowing eighth note patterns.  A 4/4 measure can contain a maximum of 8 eighth notes, so an 8 pitch scale would be the optimal tool for musical improvisation in this musical style.

                The bebop scale is an eight pitch scale composed by introducing one addition chromatic pitch to a modal scale.  There are four types of bebop scales based on the four most common jazz seventh chords.  The four most common jazz seventh chords are the four chord qualities found in the diatonic seventh chords of the major and minor keys.  They are the major 7^th, minor 7^th, dominant 7^th and the half diminished 7^th chords.  This is demonstrated below by the included graphics that display the major and minor diatonic seventh chords.

                The bebop scale that is based off of the major 7^th chord is the called the major bebop scale.  A review of the modal scale relations to chords and improvisation reveals that the Ionian mode/scale is often used for improvisation over the major 7^th chord.  The major bebop scale is composed by adding a raised 5^th between the normal 5^th and 6^th of the Ionian scale.  The graphics below display both the formation of the major bebop scale and its written form in all 12 keys.

                The bebop scale that is based off of the dominant 7^th chord is the called the dominant bebop scale.  A review of the modal scale relations to chords and improvisation reveals that the Mixolydian mode/scale is often used for improvisation over the dominant 7^th chord.  The dominant bebop scale is composed by adding an interval that is a major 7^th from the root after the minor 7^th that is normally found in the Mixolydian scale.  The graphics below display both the formation of the dominant bebop scale and its written form in all 12 keys.

The bebop scale that is based off of the minor 7^th chord is the called the minor bebop scale.  A review of the modal scale relations to chords and improvisation reveals that the Dorian mode/scale is often used for improvisation over the major 7^th chord.  The minor bebop scale is composed by adding an interval that is a major 3^rd from the root between the minor 3^rd and the perfect 4^th that are normally found in the Dorian scale.  The graphics below display both the formation of the major bebop scale and its written form in all 12 keys.

The bebop scale that is based off of the half-diminished 7^th chord is the called the half-diminished bebop scale.  A review of the modal scale relations to chords and improvisation reveals that the Locrian mode/scale is often used for improvisation over the half-diminished 7^th chord.  The half-diminished bebop scale is composed by adding an interval that is a perfect 5^th from the root between the diminished 5^th and minor 6^th that are normally found in the Locrian scale.   The graphics below display both the formation of the major bebop scale and its written form in all 12 keys.

                In this Learning Music With Ray video I discuss the definition and composition of the bebop scale.  I cover a brief description of the overall concept of the bebop scale being an eight pitch scale, and why eight pitches are conducive to jazz improvisation.  I then go into a more detailed discussion on the four types of bebop scales and how they are derived.  Finally I cover tips on how to use these scales in musical improvisation.