Neo-Riemannian Theory for Epic Chord Progressions

This section explores the mathematical and theoretical extensions of tonics beyond traditional two-dimensional frameworks. Euler's 2D tonics is mathematically equivalent to a torus (the surface of a doughnut), representing the quotient space of a torus. Vogel pioneered extending this into three dimensions by adding a seventh-axis perpendicular to the traditional grid, creating a cubic structure where each vertex represents a different pitch class. Moving forward represents harmonic sevenths (ratio 7:4), while moving backward represents descending sevenths. The 2D Euler/Riemann grid represents five-limit tuning (ratios with 2, 3, and 5), while the 3D extension encompasses seven-limit tuning (including ratios with 7). Further dimensions could theoretically add eleven-limit tuning, though Vogel argued the ear cannot easily distinguish eleventh harmonics. This geometric expansion enables visualization of seventh chords and their relationships in ways impossible in two dimensions, providing rigorous frameworks for understanding complex harmonic structures.

The Tonnetz provides a comprehensive visualization of harmonic space by incorporating perfect fifths, major thirds, and minor thirds. On this grid, vertical columns represent circles of fifths (brightness increasing upward), while diagonal lines show third relationships. Major chords and scales appear on the right side (brighter), while minor chords and scales flip to the left (darker). This creates a vertical channel representing a harmonic continuum—a continuous path from brightness to darkness where all chords can travel. Extended chords (sevenths, ninths, thirteenths) follow the same progression, maintaining the relationship between harmonic luminosity and vertical movement on the grid.

Seventh chords (tetrads) add a fourth note (seventh) to triads. Find the seventh by counting backward from the root to the previous scale note. The complete seventh chord harmonic field: C major 7 (I), D minor 7 (ii), E minor 7 (iii), F major 7 (IV), G major 7 (V), A minor 7 (vi), B half-diminished 7 (vii°). The quality pattern: minor chords (II, III, VI) have minor sevenths; major chords (I, IV) have major sevenths; V has dominant seventh (major chord with minor seventh); VII is half-diminished. This enables harmonic analysis as numbers (e.g., 2-5-1 progression), allowing transposition to different keys and understanding harmonic relationships across musical contexts.

Chromatic mediant progressions carry specific narrative associations in film and opera music. Major triads separated by a major third evoke 'magic' responses, while those three semitones apart suggest 'hero' character pairs. Minor triads at four-semitone intervals receive labels like 'Vader' (eerie/sinister) from Star Wars music, and minor thirds at 'Palpatine' (uncanny/sorcerer) associations. These progressions appear extensively in Wagner's operas and film scores by Jerry Goldsmith, John Williams, Howard Shore, and Danny Elfman, becoming obligatory clichés in epic and dramatic film music. The systematic application of these transformations allows composers to trigger specific emotional responses from listeners through carefully chosen harmonic progressions.

The epic chord progression is a four-chord sequence (E minor, C major, G major, D major) commonly used in film scores by composers like Danny Elfman, John Williams, and Hans Zimmer; it creates a dramatic, cinematic sound through simple chord inversions in the left hand combined with either sustained octaves or arpeggiated patterns in the right hand, typically played in 6/8 time with pedaling on beats 1 and 4.

Chromatic medians are chords built a major or minor third away from the tonic that contain non-diatonic tones, creating tension commonly used in film and TV scores; they can be used by pinging between the tonic and a chromatic median, alternating between different chromatic medians, or mixing chord qualities to enhance dramatic effect.

This segment analyzes the solo's chromatic and triadic techniques. The presenter explains that the soloist moves up a semitone (side-steps) and then chromatically down to the first three notes of a D major pentatonic scale. This is followed by a C major triad, B augmented, G minor, D flat augmented, and F sharp major. The progression moves around A, decorating the sharp 11 in the key of G, demonstrating bluesy movement from flat third to major third over A. The presenter then analyzes the section over E flat minor, explaining that the soloist outlines a B flat major triad. The major third in relation to D becomes the major 7th of E flat minor. The presenter notes that the triads move around and resolve into the tonality, demonstrating how triads can be used to outline chord changes while maintaining harmonic coherence.

Film music relies on interválica relationships rather than traditional harmonic relationships. The chromatic mediant progression creates epic, dramatic sounds by moving between chords a third apart that don't belong to the original scale. Starting from the root, you move up a major third, down a minor third, and down another minor third. For example, in C major: C → E major → Bb major → Ab major. This progression is called 'chromatic' because it moves to chords outside the original scale, creating tension and drama. The piano's symmetrical construction makes this easier to visualize and practice, as you can clearly see how the notes combine to create the overall harmonic effect.

Scaler 3 syncs with DAWs like Ableton Live, where bar numbers in the plugin correspond to bar numbers in the DAW. Chord progressions can be exported as MIDI files, preserving articulations like strummed patterns. The plugin includes mixing tools for adding effects and audio processing directly within the interface. The sketch page allows building multiple song sections with variations, suggesting new progressions based on existing chords. Voice leading refers to how individual notes move between chords, with natural voice leading keeping notes within a comfortable range. Scaler 3's auto voice leading function automatically adjusts notes to create smoother transitions. Density control determines how many notes are included in each chord, while open voicings spread notes with space between them for more resonant sounds.

Midinous presents a revolutionary non-linear sequencer interface featuring virtual MIDI ports for DAW/hardware integration, a toolbox displaying primary values and pathways, quantization options, and clock settings. Note blocks place configurable MIDI notes with parameters including pitch, velocity, probability, channel assignment, duration, repeat, and scale constraints. The relative changes feature enables automated semitone adjustments per trigger with randomization options. Three path types exist: vertical/horizontal (grid-aligned) and straight (grid-independent). Three impulse distribution modes determine routing behavior: single-point emission, multi-point emission, and random-path selection. Path weighting assigns probability values to connections, enabling probabilistic routing where weighted paths are more likely to be selected. Together, these systems create dynamic, evolving musical patterns through algorithmic generation rather than manual programming.

Applying Neo-Riemannian techniques requires systematic experimentation with chord connections. Start with a home chord and apply transformations sequentially, ensuring each new chord shares common tones with the previous one for smooth transitions. Build progressions by alternating between parallel motions, relative changes, and leading tone exchanges. Use software tools to explore multiple possibilities simultaneously. Consider chord inversions, voicings, and voice groupings to refine the sound. Finally, apply performance practices including instrumentation choices and common performance patterns to bring harmonic ideas to life effectively.

MIDI (Musical Instrument Digital Interface) is a set of instructions that control musical instruments, unlike audio which contains actual sound. MIDI files cannot be burned to audio CDs. The most basic MIDI messages are note messages containing information about what note to trigger, at what velocity, pitch, channel, and duration. Other message types include continuous controllers, pitchbend, and program changes. DAWs (Digital Audio Workstations) combine audio recording with MIDI sequencing. To record MIDI, configure input devices under Setup > MIDI, enable MIDI Through under Options, and set up MIDI input/output routing on tracks. Tracks serve dual purposes as hosts for software instruments and as tracks to record/playback MIDI data.

Mini News represents a paradigm shift in music composition by implementing a grid-based, non-linear MIDI sequencing approach. The software utilizes MIDI (Musical Instrument Digital Interface), a universal digital music format established over 30 years ago that enables seamless communication between music software and hardware devices. Users interact with a visual grid where each point represents a beat, and note distances determine playback timing. The interface supports three primary modes (selection, placement, pathing) controlled by keyboard shortcuts. Key features include pathing modes (Round Robin, Random with weighted probability, Instantaneous), channel routing (MIDI channels 1-16), and global controls for tempo, scale, and grid resolution. The software integrates with any DAW (Cakewalk, FL Studio, Reaper, LMMS) via standard MIDI output, functioning as a virtual MIDI keyboard. Built-in templates demonstrate advanced capabilities including fractal patterns and clock-based sequences. This approach removes the tedium of manual keyboard input, enabling algorithmic and probability-based composition accessible to users without physical keyboard access.