Pitch Class Set Improvisation
Sonic Resource Guide
The Sonic Resource Guide is a guide to pitch class set theory, providing a structure with which to organize music. When utilized, it will broaden your improvisational and compositional palette leading to a personal, and unique sound.
What is a Pitch Class Set?
Basically, a Pitch Class Set is just a fancy name for a scale. This scale can have between 2 and 12 notes. What makes it a bit different is that a Pitch Class Set also includes many groupings of notes that we don’t usually think of as a scale like a dyad or triad.
What sets a Pitch Class Set Apart from a Scale?
What sets a pitch class set apart from a scale is how these 2 to 12 notes scales are organized and categorized. A good example is a three note scale. A Major Triad could be thought of as a three note scale. If you consult the New York Guitar Method Volume One you will find a complete list of all the possible three note scales. There are 49 three note scales in total. These 49 possibilities are listed as degrees. For instance a Major Triad is 1,3,5 and we can then figure out the inversions from there i.e. 3,5 up to 1 is 1st inversion and 5 up to 1 up to 3 is 2nd inversion.
Let’s Dig a Bit Deeper
But this can be a very inefficient way to work with music. As you dig deeper through this list you also find 1,b3,b6. Well, that is actually the 1st inversion of a Major Triad in Ab right? Let’s think of both instances starting from the note “C.” If we take the 1st inversion of 1,3,5 the “3” is “E.” We have 3,5 up to 1 which is E,G,C. If we take 1,b3,b6 and make “1” an “E” we again have E,G,C. So both are the same. This can make processing a list such as the one you find in the New York Guitar Method Volume One tricky. If you aren’t a pretty advanced musician, organizing 48 three note combinations plus their inversions is a crazy amount of work. Besides, in some cases those inversions are already listed as other groups! In my opinion, this is not an effective way to practice with or organize sound. Not to mention that remembering 48 plus inversions is a daunting amount of material to put to memory.
Why Pitch Class Set and Prime Form?
Now let’s look at the difference if you think of scales as pitch class sets and establish their prime form. Go back to the New York Guitar Method Volume One list and this time choose 1,2,5. In “C” that would be C, D, G. But you would also find 1, 4, b7 and 1,4,5 in the list. But wait! Aren’t all three of these combinations the same things? 1,2,5 could be C D, G. If we make “1” a “D,” 1, 4, b7 would be D, G, C. Then if we made “1” a “G.” 1,4,5 would be G, C, D. Hopefully you are starting to see that we are running around in circles with this list and hopefully we could organize things more easily, so we aren’t always taxing our brains to make sure the information is not overlapping or redundant.
Enter Prime Form
With Pitch Class Sets there is a thing called “Prime Form.” The idea behind “Prime Form” is to reduce all scales (pitch class sets) into “one” grouping of notes so we don’t have to remember so many combinations as we have seen in the previous examples.
Example of Prime Form
“Prime Form” always reduces any group of notes into its smallest interval combination. For example C, D, G is already in Prime Form. You would find that if we called “C” “0” or the starting point and “D” “2′ because it’s two half steps above “C.” Then we called “G” “7” because it’s seven half steps above “C.” Using this system C,D, G can be reduced to a scale i.e. a pitch class set that is “027.” Let’s look at another example; what if we had D,G,C. If we start from “D” and make that “0” the D= 0, G is up a fourth so it’s “5” and C is up a minor 7th from “D” so it’s 10. So a D,G,C is a 0,5,10 but of course we can reduce this to 027. This is why changing your thought patterns over, so that you think of everything you play in its Prime Form, you have drastically reduced the number of things you have to remember.
Less is Best
When you are an improvisor the less you have to think about, the more spontaneous and creative you can be. So I call improvisation where pitch class sets are a part of your thinking “pitch class set improvisation.” This technique gives you a serious leg up on organizing improvisational ideas, not to mention creating some really awesome contemporary-sounding melodic and harmonic music.
Reducing our 48 Three Note Combinations
If we shrink all 48 three note scale down to their “Prime Form” we only have 12 three note combinations. OK now we are talking about something that is easy to remember. Anyone can remember 12 different groups of three notes. This is why working with The Sonic Resource Guide is so awesome. It shrinks every scale down to its smallest combination, which means in total there are only 220 possible scales that exist with all 12 notes.
The Sonic Resource Guide is really a reference book that provides you with all kinds of information about chords and scales using Pitch Class Set Theory. This helps you to switch your organizational principle over to a pitch class set improvisation way of thinking. With this book, unlike others on the same subject, everything is presented simply and clearly, without advanced math or equations. In addition, unlike these other books which are targeted toward classical music, the Sonic Resource Guide is for any improvisor, no matter the genre. This makes it unique. Using it, you can organize all scales and chords into a system that is logical and shows you relationships that might have been previously unseen. Additionally, the Sonic Resource Guide reduces all possible scales down to a manageable 220 possible combinations.
Organization Principle = Pitch Class Set Improvisation
The Sonic Resource Guide‘s logical organizing principles allow a musician to see all of the possibilities behind any scale (Pitch Class Set) in a clear and concise way. So really we are switching over to a pitch class set improvisation way of thinking. If you are a musician who wants to explore new sounds for improvisation or composition then this book will be a great resource that you can refer for years.
Bridging the Gap
The aim of The Sonic Resource Guide is to bridge a gap in music education; it is a balance between the highly mathematical approach to pitch class theory and the often limited scope of jazz improvisational methods. By demonstrating numerous theoretical relationships that an improviser can use to create original musical content, the Sonic Resource Guide provides a breath of fresh air and sound to your musical expression.
Jazz Theory Within a Pitch Class Setting
Within the The Sonic Resource Guide you will find various melodic and harmonic relationships of each pitch class set listed. This makes it easy to locate and utilize these relationships within your own playing. Along with each pitch class set is a listing of possible related jazz chords so that you can plug these sounds into your playing immediately.
Sonic Resource Additional Content
Where appropriate a listing of all three and four note chords can be found to aid in creating varied and unique harmonic palettes, as well as three, four, six and eight note subset relationships to help in exploring subset based musical ideas. All musicians will find this book user friendly because all Pitch Class Set (Scales) relationships are listed as both pitch names and scale degrees. Set theory students will find each pitch class set is expressed in its prime form so it will be easy to navigate.
Using Pitch Class Set Improvisation as a way to Organize
Thinking and organizing via pitch class set improvisation will give your thought processes much more clarity. You will be able to create any scale on the fly and immediately discern their hidden relationships. You can investigate the common scales you know, or create new scales at your whim. All this can be done quickly by using the index which helps you locate any group of notes in its prime form, which will then be your guide to finding the scale within the book. There is also a brief theory section exploring some of the many uses of the information presented.
Think of the The Sonic Resource Guide as a reference book where you find cool relationships. But now that you’ve found some, how do you apply them? To that end I’ve created a series of books. Here is a list of them to check out, to help you develop pitch class set improvisation ideas.
Here are some Pitch Class Set Improvisation Books
- Tools for Modern Improvisation
- Ultimate Three Note Chord Lexicon
- Ultimate Arpeggio
- 013 Hexatonic Etudes
- ChopBusters Series of Books
- Set Theory for Improvisation 027 016
- Set Theory for Improvisation 027 027
- Symmetrical Trichord Pairs
- Tertial Intervallics
- Tertial Octatonics
- Time Transformation
- Scale Analysis
CD and DVDs where I use Pitch Class Set Improvisation
- A Few Dozen
- Blue Eleven
- Give Em Some
- Music of Webern
- Quartet for the End of Time Messiaen
- Blue Lotus
- Schoenberg Five Piano Pieces
- Bruce Arnold Trio Live DVD
- Heavy Mental
- Art of the Blues
- Vanishing Point
Pitch Class Set Improvisation is Not Style Specific
Many times people think that using Pitch Class Set Improvisation techniques means you are playing “avant garde” melodies and chords. This could not further from the truth. Pitch Class Set Improvisation can be used with any style.
Here are some examples:
- An example of a fusion style: A Few Dozen
- Classical Music Improvisation: Music of Webern
- An Example of using Pitch Class Sets to compose compositions: Duets
- Jazz Pitch Class Set Improvisation: Art of the Blues
- Rock/Heavy Metal Pitch Class Set Improvisation: Vanishing Point
Bruce Arnold Music Education Genealogy Chart
You might enjoy checking out the “Music Education Genealogy Chart” located on my artist’s site. You will clearly see the historic progression of pedagogy that is the basis for Muse Eek Publishing Products. Great musicians throughout history have been studying the ideas presented by Muse-eek.com which derives its content from a a lineage that stretches back to Scarlatti!