> ## Documentation Index
> Fetch the complete documentation index at: https://docs.nomn.jp/llms.txt
> Use this file to discover all available pages before exploring further.

# Pitch Logic

> 12 pitch selection algorithms and 100+ scale library

# Pitch Logic

The Pitch Logic card determines *what* notes play. It combines a **scale selection** system (100+ scales) with a **pitch pattern algorithm** (12 methods) that decides how pitches are chosen from the scale.

All 12 pitch patterns are streaming — they maintain internal state and produce the next pitch in O(1) time.

## Pitch Pattern Algorithms

| Algorithm            | What It Does                                                                                                                                                                                                                                                                                                             | Lineage                                                                                                                                                               |
| -------------------- | ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ | --------------------------------------------------------------------------------------------------------------------------------------------------------------------- |
| **Sequential**       | All pitches in the set must sound before any can repeat (with octave displacement allowed). Ensures chromatic completeness within each cycle. Each pattern parameter controls the spread of octave displacement.                                                                                                         | *Schoenberg, twelve-tone technique (1923). Serial exhaustion — aggregate completion as structural principle. Extended here to any pitch set, not just the chromatic.* |
| **Spiral**           | Spirals outward from a center pitch, alternating above and below in expanding intervals. Creates a widening melodic cone. The center pitch is configurable.                                                                                                                                                              | *Xenakis, arborescences — tree-like branching pitch structures (Evryali, 1973). Spiral motion as generative principle.*                                               |
| **Fibonacci**        | Next pitch determined by Fibonacci interval sequence (1, 1, 2, 3, 5, 8, 13, 21 semitones). Direction reverses when pitch boundaries are reached. Pattern parameter scales the interval magnitudes.                                                                                                                       | *Fibonacci sequence. Bartók's intervallic proportions. Lendvai's golden section analyses of Bartók's pitch structures.*                                               |
| **Register**         | Systematic traversal through octave registers — plays through all pitches in one octave before moving to the next. Traversal order varies from sequential to shuffled based on the pattern parameter.                                                                                                                    | *Messiaen's modes of limited transposition — systematic register exploration. Registral stratification in Webern.*                                                    |
| **Probabilistic**    | Weighted probability transitions where closer intervals have higher probability. Pattern parameter (Leap) shifts the bias from stepwise motion toward large leaps.                                                                                                                                                       | *Xenakis, Markov chains in music (Analogique A, 1958). Hiller & Isaacson, Illiac Suite (1957) — first computer-generated composition using Markov chains.*            |
| **Golden Ratio**     | Divides the pitch set at the golden ratio point (φ ≈ 0.618), creating two subsets. Alternates between subsets, cycling through each independently. Pattern parameter adjusts the split point.                                                                                                                            | *Golden section applied to pitch-space partitioning. Proportional subdivision as melodic generator.*                                                                  |
| **Interference**     | Constructs a pitch set from the interference of two interval generators. All pitches satisfying (root + n×A + m×B) mod 12 are collected, producing combination-tone-derived scales. Pattern parameter adjusts the generating intervals.                                                                                  | *Grisey and Murail, spectral music (Partiels, 1975). Combination tones and resultant pitch sets from interval interference.*                                          |
| **Mirror**           | Alternates between original pitches and their inversion around a configurable axis pitch (2×axis − pitch). Creates palindromic pitch contours. Pattern parameter sets the axis.                                                                                                                                          | *Serial inversion technique (Schoenberg, Webern). Symmetric pitch structures — Bartók's axis of symmetry system.*                                                     |
| **Permutation**      | Systematic reordering of the pitch set through circular rotations, retrograde, retrograde-inversion, or all transformations. Pattern parameter selects the variant.                                                                                                                                                      | *Combinatorial twelve-tone technique (Babbitt). Permutation groups applied to pitch ordering — exhaustive traversal of set transformations.*                          |
| **Corpus**           | Pitch transitions learned from a statistical pitch-class transition model. The 12×12 transition matrices bias note choice toward musically natural successions. Context parameter biases toward ascending motion, stepwise motion, or large leaps. Falls back to Probabilistic behavior if no corpus data is loaded.     | *Statistical learning of pitch transitions from symbolic-music corpora.*                                                                                              |
| **Arpeggiator**      | Classical arpeggiator over the active pitch set with configurable order — up, down, up-down, down-up, random, and converging/diverging variants. Pattern parameter selects the order. Useful under [Layers > Monophonic](/reservoir/features/layers) for single-line sequencing.                                         | *Arpeggio as melodic primitive. Sequencer arpeggiator tradition (Roland TB-303, classical synth design).*                                                             |
| **Harmonic Gravity** | Pitch choices biased toward chord-tone targets defined by the [Harmonic Conductor](/reservoir/features/capture). Notes resolve toward the active chord's strong tones (root, third, fifth) over time, with strength controlled by the pattern parameter. Falls back to Probabilistic when no chord vocabulary is active. | *Tonal gravity (Lerdahl, Tonal Pitch Space). Schenkerian prolongation — surface notes pulled toward structural tones.*                                                |

A captured MIDI performance via [MIR Capture](/reservoir/features/capture) can additionally morph any of the twelve algorithms toward your own pitch habits — the Pitch Shape slider blends between the algorithm's choices and the captured PPM-Decay model. This is a morph mode, not a separate algorithm.

## Parameters

| Parameter            | ID                   | Range   | Default | Description                                         |
| -------------------- | -------------------- | ------- | ------- | --------------------------------------------------- |
| Pitch Selection      | `pitchPatternType`   | 0–11    | 0       | Algorithm selection                                 |
| Pitch Pattern Shape  | `pitchPatternParam`  | 0.0–1.0 | 0.5     | Algorithm-specific control (see table below)        |
| Scale                | `scaleIndex`         | 0–150   | 0       | Scale selection from library                        |
| Root Pitch Class     | `pitchClass`         | 0–11    | 0 (C)   | Root note (C, C#, D, ... B)                         |
| Starting Octave      | `octave`             | −1–9    | 3       | Base octave for pitch set                           |
| Octave Span          | `octaveSpan`         | 1–10    | 4       | Number of octaves to span                           |
| Custom Pitch Classes | `customPitchClasses` | 0–4095  | 4095    | Bitmask for custom scale (bit 0=C through bit 11=B) |

### Pattern Parameter Meanings

The `pitchPatternParam` slider controls different aspects depending on the active algorithm:

| Algorithm        | Parameter Label | Effect                                            |
| ---------------- | --------------- | ------------------------------------------------- |
| Sequential       | Spread          | Octave displacement range                         |
| Spiral           | Center          | Center pitch position                             |
| Fibonacci        | Range           | Interval magnitude scaling                        |
| Register         | Order           | Sequential ↔ shuffled traversal                   |
| Probabilistic    | Leap            | Stepwise ↔ leaping bias                           |
| Golden Ratio     | Split           | Split point adjustment                            |
| Interference     | Interval        | Generating interval adjustment                    |
| Mirror           | Axis            | Inversion axis position                           |
| Permutation      | Variant         | Transformation type selection                     |
| Corpus           | Context         | Motion bias (ascending / stepwise / leaping)      |
| Arpeggiator      | Order           | Up / down / up-down / random / converge / diverge |
| Harmonic Gravity | Pull            | Strength of resolution toward chord tones         |

## Scale Library

RESERVOIR includes 100+ scales spanning:

* **Western modes** — Major, Natural Minor, Dorian, Phrygian, Lydian, Mixolydian, Locrian, Harmonic Minor, Melodic Minor, Harmonic Major
* **Pentatonic and blues** — Major Pentatonic, Minor Pentatonic, Blues, Major Blues
* **Symmetric** — Whole Tone, Chromatic, Diminished (Whole-Half), Diminished (Half-Whole)
* **Japanese** — Kumoi, Iwato, Hon-Kumoi-Joshi, Banshiki-Cho, Naka Zora, Noh, Kokin-Choshi, Shimo-Chidori, and more
* **Indian ragas** — Raga Yaman, Raga Bhairavi, Raga Todi, Raga Marwa, Raga Lalit, Raga Hindol, Raga Kafi, and more
* **Synthetic** — Mono-quality triads, quartal formations, hetero-quality triads, mutated hexadic scales, intervallic mutations, and other constructions from the mid-20th-century jazz-modal tradition
* **Microtonal** — Just-intonation tunings (Septimal JI, Tonality Diamond, Pythagorean), historical temperaments (Werckmeister III, Kirnberger III, Quarter-Comma Meantone), and gamelan-derived sets
* **Custom** — User-defined pitch class set via bitmask

See [Scale Reference](/reservoir/reference/scales) for the complete list with descriptions.