Interval Transformations

<p><strong>Interval Transformations</strong> is the third and final chapter in a series of books devoted to melodic transformation. The journey began with <em>Octo Gradus Transformationis</em> which introduced scalar variation through the logic of eight structured contours. It continued with <em>Pentatonic Transformations</em> applying that same logic to five-note terrain. This volume completes the cycle turning fully toward interval. For the improviser composer and theorist it offers a terrain of angular possibility - a collection of melodic motion shaped by the <em>eight transformations</em> system. Across all three collections the question remains constant: what can we do with a simple melodic fragment once we begin to transform it?</p><p></p><p><strong>The System: Methodical Variation and Angularity</strong></p><p></p><p>This collection is built on the <em>Octo Gradus Transformationis</em> system - a framework for melodic variation that invites the player to stretch a single seed across eight distinct contours. The logic is methodical but the result is anything but smooth. These sequences are jagged spacious and deliberately angular. They move through <em>thirds</em> <em>fourths</em> <em>fifths</em> <em>sixths</em> and <em>sevenths</em> - not to flatten the terrain but to open it.</p><p></p><p>Unlike scalar lines which often flow predictably these intervallic shapes resist resolution. They demand attention. Even within diatonic terrain they create tension and surprise. The goal is not comfort - it's expansion. Each transformation offers a new way to inhabit the fragment a new shape toward which to tune the ear and hand.</p><p></p><p><strong>The Eight Transformations Explained</strong></p><p></p><p>At the heart of this collection are the <em>eight transformations</em> - structured contours that process a melodic seed into <em>eight</em> distinct shapes. These are not exercises in symmetry; they are invitations to move differently.</p><p></p><p>The first four transformations are directional. Even-numbered sequences ascend. Odd-numbered sequences descend. Each is treated as a sovereign phrase not a mirror image. This distinction matters: it trains the improviser to hear ascent and descent as separate logics each with its own emotional weight.</p><p></p><p>Transformations <em>five</em> through <em>eight</em> introduce compound motion. Retrograde inversion and layered shifts stretch the seed into its most unexpected forms. These are the most challenging contours in the collection - dense angular and often disorienting. They are designed not to be mastered but to be inhabited.</p><p></p><p><strong>Philosophy and Practice</strong></p><p></p><p>The philosophy behind this collection is simple: any melodic fragment can be transformed into compelling musical lines. Through systematic exploration even the smallest seed reveals unexpected shapes tensions and contours. The exercises in this book - and in the two companion collections - offer a way to experience that transformation directly.</p><p></p><p>By playing through these sequences students begin to hear how a fragment can be stretched inverted and reoriented. Over time the logic becomes familiar. Not through theory but through practice. The goal is not to memorize patterns but to develop a personal understanding of how melodic material behaves when placed under transformation.</p>