The following is the preface from Peacock’s Perfectly Complete Collection of All Possible Musical Scales:
This book is the product of three years of dedicated research and analysis of all known musical scales and theory of scales. For three years, I literally dreamed about scales every night! It is a “perfectly complete collection” because it contains every possible pentatonic (five-note), heptatonic (seven-note) and octatonic (eight-note) scale! The mathematics and matrices in Part Three prove, without a doubt, that I’ve included all four-hundred and sixty-two heptatonic, three-hundred and thirty pentatonic and three-hundred and thirty octatonic scales with no repeated scales. This is more than just a collection of scales, though . It’s also my arrangement of all possible scales. My arrangement includes technical analysis as well as historical context and my own personal organization from the perspective of a performer and a composer.
So what is this book? How does one use this book? This is a futuristic technique book for any instrument or voice: a path to the mastery of the music of the past, the present and even the music of the future! This book is not just a technique a book. But those who dwell in its pages will gain an advanced degree of mastery on any instrument as well as a sharper musical mind. For those with an open mind, it’s a book to inspire imagination and wonder too. For creative musicians, this book is full of strange new worlds to mine for rare musical metals: a kind of cookbook, prayer book, atlas and book of spells all-in-one. It’s also a source of comfort and music therapy: a place to meditate and appreciate logic; a place to get lost as well as a place to find yourself. I use this book to warm up and meditate with my horn every time I pick it up.
I also use it as a form of escape, as though it can take me to exotic vacation spots whenever I please. I even like to gaze into it like it is a crystal ball that shows me the future when I write.
More specifically, anyone using this book should start by studying the scales in Part One: Traditional Scales followed by Ferruccio Busoni’s kaleidoscopic variations on these traditional scales in Part Two. Then Part Three: Tetrachords is crucial for understanding the scales in the complete collections that follow. Each complete collection starts with variations on traditional scales followed by “Deviant” scales which do not compare to traditional scales and “Radical” scales which barely resemble a scale.
In his book, Sketch of a N ew Esthetic of Music (1911), Ferruccio Busoni describes all the paths of the modern music of his time as “leading so far afield – but none lead upward” [emphasis in the original]. He also describes the intervals within a heptatonic scale as being differently arranged in isolated passages by the likes of Liszt and Debussy, but claims “it does not appear to me that a conscious and orderly conception of this intensified means of expression has been formed by these composers.” From my perspective, over a century later, things have not changed. This book aims to change that with a systematic uncovering of all possible scales which offer a path upward to new and intensified means of musical expression.
While I can prove with mathematics that this book contains all possible pentatonic, heptatonic and octatonic scales, I did not use mathematics to generate these scales. I only used mathematics at the very end of the process to verify my findings. To uncover all possible scales, I developed my own unique system of tetrachord juxtaposition. With this system, every variation of each type of scale (pentatonic, heptatonic or octatonic) fits neatly into a matrix on only one page each! This is a testament to the simple elegance of my system. My matrices are included in this volume as well and I believe that with the use of my matrices, virtuosi of the future, including myself, could even play all these scales from memory simply by memorizing the order of tetrachords.
This book began when my wife, Lyndi, gave me a trumpet for Valentine’s Day 2019. With the addition of trumpet, I play every brass instrument as a multi-instrumentalist. My first thoughts about playing the trumpet were how easy and fun scales are on the trumpet. Without a doubt, the trumpet is the best brass instrument for scales. So as I began to play trumpet, I played all the common scales everyday. Then I started to write out these scales for my students and I thought it would be good to compile a more comprehensive book of scales for myself. When I began, I didn’t intend to write every possible scale. I merely intended to compile a more extensive book of scales for myself. But as I collected the scales, I put on a serious soundtrack of jazz and rock and went a little crazy. Then I added more and more until I exhausted all possible scales. So this book began as a scale book for trumpet, essentially. But it is now intended for serious musicians of any instrument or voice at any level and for creative musicians of any genre.