Musical Intervals

                As I mentioned last week I am writing a series of posts (accompanied by You Tube videos) geared toward musicians who desire to learn the basics of musical notation.  In last week's post one of the topics we discussed was the musical distance of a half step and a whole step.  In real music, the distance between pitches can extend beyond a whole step.  There is a musical unit of measure that we use to measure the distance between pitches.  That unit of measure is an interval, and it is the topic of today's discussion.

                As we mentioned last week, there are seven letters in the musical alphabet.  When measuring distances between these seven letters, we count the starting letter as one and then count our way to the destination letter.  So, the distance from A to C would be a third, because we count A as one, B as two and C as three.  This graphic helps to demonstrate all of the intervals between the seven letters of the alphabet.  

                We can count the same way on the musical staff.  Every line and space on the staff represents a letter.  We count the starting note as one, and then continue to count the lines and spaces up to (and including) the target note to determin the interval.  This graphic displays the musical intervals of one cycle of letters from C to C. 

                If you notice, that last graphic included an interval of an 8th.  Remember that the musical alphabet is a seven letter cycle that repeats back to A.  Since the letters repeat in a cycle, the interval of an 8th will always be a repeat of the letter you started on.  It is not an identical match of the starting pitch (which is called a unison).  It is the same letter in a higher or lower register.

                When two pitches are sounded at the same time they create harmony.  Harmonies that are pure and free from discord are called consonant.  There are two types of consonence in music, perfect and imperfect consonence.  The perfect consonent intervals in music are the unison, perfect fourth, perfect fifth and octive.  The imperfect consonences are thirds and sixths.  Harmonies that are discordant or clashing are called dissonant.  The dissonant intervals in music are seconds and sevenths. 

                The pairings of numbers mentioned in the last paragraph have an interesting relationship.  Each pair (2&7, 3&6, 4&5) are inversions of each other.  An inversion is the flipped version of an interval.  If a person plays a C and the E directly above it, this is the interval of a third.  If you then change the order of these two pitches by playing the E below the C (instead of the one above) you are playing the interval of a sixth.  You are still playing the same two pitches, but you have flipped the order of the pitches.  The same is true when flipping a second into a seventh, or a fourth into a fifth.

                Consonance and dissonance are used as tools by composers to create tension and release.  Any form of good entertainment (a book, a movie, a sporting event, a piece of music, ect.) will contain conflict that builds twoard a climatic moment and then resolves.  In music, this is accomplished by having dissonance resolve to consonance.  There are other tools used to compose great musical climaxes, but the most basic elements are dissonance and consonance. 

                Unfortunatly, musical intervals are not always just simple numbers.  Remember, there are actually 21 different pitches in music due to the sharps and flats.  This means that there are variations on each number when pitches are raised or lowered.  The unison and octive cannot be altered at all.  Once these distances are changed they are no longer a unison or octive.  The other perfect consonent intervals can be shortened (diminished) or lengthened (augmented). 

diminished 4th  / perfect 4th      / augmented 4th

diminished 5th  / perfect 5th      / augmented 5th

Imperfect consonent intervals and dissonant intervals have two versions, major and minor.  In addition, they can also be diminished or augmented.     

diminished 2nd / minor 2nd / major 2nd / augmented 2nd

diminished 3rd / minor 3rd / major 3rd / augmented 3rd

diminished 6th  / minor 6th / major 6th / augmented 6th

diminished 7th  / minor 7th / major 7th / augmented 7th

                All of these interval names can get confusing.  Remember the principal of enharmonic equavlince from last week's post.  Every sharp pitch can also be identified by a corrisponding flat (or in some cases natural) name.  This means that many of these interval names overlap each other.  A diminished 2nd, for example, is the same thing as a unison.  An augmented 4th is the same thing as a diminished 5th.  However, if you were measuring the distance from C to F#, you would call it an augmented 4th.  If you were measuring the distance from C to Gb (same pitch as F#), you would call it a diminished 5th. 

                Some of the other examples, like the diminished 2nd mentioned above, occure rarely.  For this to take place, you would have to be measuring the distance between a C and a D double flat.  The term double flat means that you have lowered the pitch two half steps instead of one.  These types of musical concepts are too complex for this basic discussion, so we will leave them for a future date.  The most common musical intervals are listed in this figure.

                This concludes our discussion on musical intervals.  Please refer to the attached video for further understanding.  I also provide private music instruction online.  Private lessons can be booked from this page on my website (http://www.raymelograne.com/private-lessons.html).  I will be sharing more music lessons combined with videos (like this one) in future posts.

The Musical Alphabet

                As mentioned in the description, the posts in this blog are intermediate to advanced level music theory and performance discussions.  However, the ratings of intermediate and advanced are relative to the situation being rated.  I would consider the Beatles to be advanced song writers, but they did not know how to read musical notation.  Therefore, I am going to write a series of posts geared toward musicians who desire to learn the basics of musical notation.  They will be accompanied by You Tube videos that provide further explanation and visual aid.  Readers at advanced music theory levels may even find this material useful in teaching their own students.  I only request that you refrain from creating/distributing illegal copies of the You Tube videos.  If you would like to purchase personal copy, they are available on my website.

                The musical alphabet is composed of the first seven letters of the English alphabet (A-B-C-D-E-F-G).  Once you get to G, the group repeats over again.  Each repeat is a higher register of the same pitches.  This cyclical nature of the musical alphabet is easer seen when the letters are drawn in the manor displayed here.

                Musical notation is written on a collection of horizontal lines (and the spaces between those lines) called a staff.  There are five lines and four spaces on a single staff, although there are actually an infinite number of lines and spaces in music.  The specific five lines and four spaces being listed on a particular staff are identified by a special label which is placed at the front of the staff.  This label is called a clef, and there are several different types of clefs (more on this later).        

                Most music teachers like to use catchy phrases to aid students in remembering the names of musical pitches.  They accomplish this by separating the pitches which fall on the lines of the staff from those that fall on the spaces.  The figure shown here is an example of this teaching method.

                However, separating the lines and spaces makes it difficult to see the alphabet within the pitches.  Listing the pitches on the staff in a consecutive "line - space" fashion reveals the alphabet.  This way of listing the pitches also displays the cyclical repetition of the alphabet across registers. 

                Although there are seven letters within the musical alphabet, there are more than seven pitches.  For every letter there is a natural (regular), sharp (slightly higher) and flat (slightly lower) version.  That makes for a total of 21 pitches in music. 

                                A#          B#           C#           D#          E#           F#           G#

                                A             B             C             D             E              F              G

                                Ab          Bb           Cb           Db          Eb           Fb           Gb

                The distance from one of these 21 pitches to the very next pitch is called a half step.  The distance of two half steps equals one whole step.  The distance from a letter to its corresponding sharp or flat is a half step.  However, the distance between the letters of the musical alphabet is not always a whole step.  There are two groups of letters (B & C / E & F) which are actually a half step apart. 

                The final topic of this discussion is enharmonic equivalence.  This topic was already discussed in a previous post, so I will quote that post here for your convenience. 

                When a sharp is applied to a pitch it raises the pitch by a half step.  When a flat is applied the pitch is lowered by a half step.  This creates an interesting dilemma as is seen by the graphic below.

In this example, the pitches C# and Db end up residing on the same key of the piano keyboard.  These two names actually lable the same pitch. 

                This concept can be confusing at first.  How can one pitch have two different names?  When I am teaching my public school students I describe it this way.  I also have two names (a first and last name).  At home, my wife calls me Ray, but at work my students call me Mr. Melograne.

                                                               

I am the same person, but it is more appropriate to use my first name in some settings and my last name in other settings. 

                The same is true of musical pitches.  If you are raising a C it is more appropriate to call that pitch a C#.  If you are lowering a D the resulting pitch is the same.  However, in this case it is more appropriate to call that pitch a Db. 

                This concludes our discussion on the musical alphabet.  Please refer to the attached video for further understanding.  I also provide private music instruction online.  Private lessons can be booked from this page on my website (http://www.raymelograne.com/private-lessons.html).  I will be sharing more music lessons combined with videos (like this one) in future posts. 

Long Tones

                Last week we discussed the topic of overtones, and we mentioned the use of long tones when practicing overtones.  This week I would like to spend some more time discussing the importance of overtones in an instrumentalist's practice routine.  This discussion may not be applicable to the study of instruments that are not capable of sustaining their tone (like many percussion instruments).  However, the study and use of long tones is a vitally important, and often overlooked topic in the study of instrumental performance.

                Long tones are exactly what the name suggests them to be.  They are tones that are sustained for a long period of time.  As I mentioned, they are often overlooked in instrumental studies.  This occurs because most students desire to obtain speed in their playing.  The reason we all strive to learn how to play an instrument (or sing) is to impress others.  Performing passages with fast, flashy and elaborate notes always seem to be the best way to impress others.  Long tones seem easy to achieve and boring to perform.  However, long tones that are executed correctly are both challenging and constructive tools for increasing one's performance level.

                Tone quality is just as important of a performance quality as flash and speed.  Without a desirable tone the fastest notes in the world will still be perceived as annoying instead of being entertaining.  Developing your tone as a performer should be accomplished in two stages.  First, one should look to develop a tone that is consistent, neutral and controlled.  This will allow for the performer to achieve changes in pitch, rhythm, dynamic, and articulation while maintaining a consistent tone.  Developing a consistent tone quality with long tones is the first step in this process.  Then a performer can gradually increase the fluctuation of musical elements within his/her playing while striving to maintain a consistent tone.

                Consistent long tones also help to improve intonation on instruments where intonation can fluctuate due to performance technique.  Many performers practice long tones in front of an electronic tuning device to have a visual display of their intonation.  Repeated practice in this manor causes the performer to remember what it feels like to play in tune.  Eventually this type of tone production become second nature.  

                The second stage of tone production is developing one's own unique sound.  Each performer's tone is unique, since it is shaped by specific details of his/her playing style.  The unique quality of a performer's tone is even more relevant with instruments which require breath, because the tone is shaped by both the instrument and the performer's body.  Finding and perfecting your unique tone is a performance quality that will distinguish you from other performers.  Being identifiable and unique is often a beneficial quality in musical performance. 

                One of the best ways to develop your unique and identifiable tone is through the use of long tones.  After a musician has developed a consistent and controlled tone, he/she can begin to listen to an examine the unique qualities of that tone.  While holding out long tones, desirable tone qualities can be accentuated through experimentation.  The result will be a signature tone that is unique to the performer.

                I hope that this discussion has helped you to recognize the importance of long tones in the study of musical performance.  A well rounded musician develops every aspect of their performance ability, including tone quality.  I still incorporate long tones into my practice routine regularly.  The results of long tone studies are noticeable and valuable.   

Overtones

                What are overtones?  Every musical pitch is actually composed of a mixture of many different pitches or frequencies.  To avoid confusion I will use the term pitch to refer to a melodic note and frequencies to refer to the pitch elements which compose that melodic note.  The lowest frequency within a pitch is called the fundamental.  The additional frequencies present within the pitch are called overtones.  The first overtone is always one octave above the fundamental.  The second overtone is a fifth higher than the first overtone, and the next one is a fourth higher than that.  The interval of each overtone gets closer as one travels up the series.  This mixture of tone colors gives each pitch it's unique tone color.

                This post applies most directly to wind players, although knowledge in this topic can be applicable to other areas of musical performance.  Wind players blow air into their instrument to cause the vibration that produces sound.  By making slight modifications in the way we blow, we can emphasize certain overtones more than others.  Varying the emphasis of different frequencies across the overtone spectrum can change the color of a wind performer's tone.  Skilled musicians use this technique to adapt their tone to the musical style that they are performing.

                The modifications in mentioned in the last paragraph are made through slight adjustments in a performer's throat, tongue, mouth and jaw.  Through experimentation with long tones, a performer can  discover how to produce the tone that they desire with accuracy and consistency.  Many wind players disagree over how many of the body parts listed above should be used in shaping ones tone and to what degree they should be manipulated.  However, most agree on the concept of hearing the desired tone in one's mind and then experimenting to achieve it.

                I cannot speak specifically on this topic for every wind instrument.  I can, however, add specifics about the study of overtones in saxophone performance.  Saxophone players often practice shifting between the overtones of a particular note while fingering the fundamental on a long tone.  In addition, we practice overtone scales by using the fingerings of lower fundamentals to produce the pitches of higher notes within the sequence of a scale.  The ability to eliminate lower frequencies within a pitch and bring out a certain overtone as if it is the fundamental is helpful.  A saxophone player can use this ability to gain more control over the shape of their tone.  We can also use this ability to increase the range of our instrument by playing harmonic pitches. 

                As a student, I always found it helpful to understand the application of the elements I was practicing.  Overtones are one of those elements that many people include in their practice regiment without understanding the application.  I hope that this post will help you to understand the significance and use of overtone studies in your practice time.  

Rhythm In Improvisation

                We've spent the last two weeks discussing approach note theory and how it relates to improvisation.  Rhythm has not entered into the discussion much since approach note theory is centered around pitch.  As I reflected on this week's discussion, I thought about the fact that rhythm is often neglected in improvisation.  Many beginning improvisers yearn to play the blazing phrases that they have heard on their favorite recordings.  The mentality is to fit as many pitches as humanly possible into each measure and display one's technical dexterity. 

                True music, however, is about contrast.  Beautiful pieces of music contrast multiple musical elements, including rhythm.  Once the human ear has heard too much of any one thing it becomes bored and begins to tune out the content.  Constant contrast hold the listener's attention and challenges him or her to discover what will happen next.  These facts hold true for improvisation also, since it is a form of musical composition (the variation being that it is spontaneous).

                Attention to rhythm in improvisation can fulfill more than just the role of achieving rhythmic contrast.  In addition, motifs can be expressed through rhythm as easily as they are expressed through pitch.  A particular rhythmic motif can be expressed across phrases of static pitch, stepwise motion or leaps in pitch.  In these instances the rhythmic motif can be a commonality guiding the listener's ear through phrases of varying  pitch content.

                In my own practice, I use two methods to attempt to enhance my expression of rhythm through improvisation.  For practice in rhythmic variation, I rehearse using only one pitch per chord while improvising.  With this method, I force myself to use only rhythm for my source of variation.  This method is also useful when rehearsing dynamic and other elements of variation.  I gradually expand by introducing two pitches to my pallet, and then three.  The whole time I maintain focus on rhythm as the primary element of contrast.

                When practicing the development of rhythmic motifs, I write out one or two rhythmic motifs and try to implement the in improvisation across a wide range of pitch content.  I usually start with a narrow pitch range (even static motion) and then expand to a broader range of motion.  I save these rhythmic motifs as content that can be used in future performances.  I also listen for interesting rhythmic motifs in other people's performances and try to write them down.  This is easier to do with recordings, but I have walked away from concerts with napkin notation in my pocket (whatever works).  The main idea is to constantly be expanding our ability to express music through every element instead of just focusing on just one like pitch.  

Approach Note Theory

                Two weeks ago we discussed the use of scales and chords as content for improvisation.  This technique leads to the creation of basic improvised melodies that are diatonic to the harmony.  To further explain that statement, all songs possess a key signature which defines their diatonic boundaries.  However, some forms of music contain chords with pitches that are outside the diatonic boundaries of the key signature.  These chords tend to suggest other temporary key centers.  For this reason, it is easier to address the diatonic boundaries of the present harmony when analyzing improvisation over these types of chords.  The variety of pitches available and the temporary key centers introduced by the harmony provide the performer with a wealth of selections. 

                However, this style of improvisation can begin to feel limited or restrictive after a while.  Musicians who have been improvising for some time may find themselves desiring a wider range of pitches to add to their vocabulary.  They desire to introduce pitches that are chromatic to the harmony they are improvising over.  One way to accomplish this is through the use of approach note theory.

                Last week we discussed neighbor tones, passing tones and how they relate to target notes.  These concepts form the fundamental ingredients of approach note theory.  The chord and scale tones that we were using in our beginning level of improvisation become the target notes for this style.  Instead of stringing diatonic pitches together to form melodies, we approach these pitches with chromatic neighbor and passing tones.  The root, third, fifth and seventh tend to work best as target notes since they are strongly related to the harmony and balance out the sound of the unrelated chromatic pitches.  However, the other pitches of the scale can also be used depending on the context.  Repeating motifs and other elements that have strong melodic pull can often compensate for weaker harmonic relations.

                There are two additional factors that govern the successful use of approach notes.  They are rhythmic duration and beat placement.  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 chromatic to the harmony on the weak beat but diatonic 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. 

                There are many possibilities, and it would be exhaustive for me to attempt to describe them all.  The point is to start our journey into this type of improvisation with following the rules, and once we are grounded in basic approach note theory we can look for ways to expand by bending the rules.  With the introduction of approach notes to the vocabulary of improvisation, we will find access to a vast variety of melodic expression.

Neighbor Tones & Passing Tones (a prerequisite to Approach Note Theory)

                I want to start discussing approach note theory as it relates to melodic improvisation.  In preparation for that discussion, I am using this week to explain neighbor tones and passing tones.  These two types of melodic ornaments are the fundamental ingredients in approach note improvisation. 

                The main concept to grasp in this discussion is the difference between a target pitch and a ornament or traveling pitch.  A target pitch is the primary pitch of the melodic passage.  It is both related to and supported by the overall harmony in that section of the music.  I say "that section" because music can often contain harmonic moments that travel outside the main key signature to introduce leading tones or suggest other temporary key centers.  The most basic target pitch of a given melody would be either the 1st, 3rd or 5th interval of chord at that moment of the music.  More complex styles of music also incorporate target pitches that are the 7th, 9th, 11th or 13th of the chord. 

                Ornament or traveling pitches are pitches that are outside of the overall harmony in that section of music.  The strongest examples are chromatic in relation to the intervals of the present harmony.  For this reason, they cannot be utilized as foundational pitches within the melodic passage.  Instead, they act as additional melodic dressing around the target pitches, and provide fleeting moments of melodic variation.  Pitches that are diatonic to the present harmony, but weaker in relation when compared to the focus pitch can also be used (such as 9ths, 11ths and 13ths). 

                Neighbor tones are ornaments that are related to one target pitch.  There are actually two types of neighbor tones, complete and incomplete neighbors.  A complete neighbor tone starts on the target pitch, travels (a half or whole step up or down) to the neighbor tone and then returns to the target pitch.  An incomplete neighbor tone starts on the neighbor tone (a half or whole step above or below) and then travels to the target pitch.  The mindset is that the target pitch is the melodic goal and the neighbor tone is a fleeting pitch that leads to the goal. 

                Passing tones are ornaments that are related to two target pitches.  They are melodic content used to travel from one target to the next by filling in the gap.  For example, if a melodic passage contained the pitches E - D - C over a C major harmony, the D would be considered a passing tone traveling from the 3rd interval (E) to the 1st interval (C) of the chord.  When traveling between the 5th and root of a chord the gap is filled with two passing tones. 

                Next week I will discuss approach note theory in melodic improvisation.  I will expound on this discussion and show how the concept of target notes can be used to introduce additional pitches and chromaticism into your improvisation.  Please comment with any questions you may have in preparation for next week!