Enhanced Pattern Database with Perfect Balance Explorer

🎵 Universal Pattern Input

Supported Formats:
• Polygons: P(vertices,offset) → P(3,1)+P(5,0) = Auto-expansion to LCM
• Single Polygons: P(vertices,offset,expansion) → P(3,1,4) = Explicit expansion
• Euclidean: E(beats,steps,offset) or E(beats,steps) → E(5,8,0) or E(5,8)
• Random: R(onsets,steps) or R(r,steps) → R(3,8) = Random 3 onsets in 8 steps, R(r,8) = Bell curve distribution
• Morse Intervals: -.-- (dots=short, dashes=long intervals) → Creates rhythmic patterns based on interval timing
• Morse Characters: M:C, M:SOS, M:HELLO → Converts Morse code characters to rhythmic patterns
• Shorthand: tri, pent, hept, oct → triangle, pentagon, heptagon, octagon (tri@1 for offset)
• Subtraction: P(3,0)+P(5,1)-P(2,0) = Perfect balance via subtraction
• Transformations: ~pattern (invert), rev pattern (retrograde), comp pattern (Euclidean complement)
• Stretch/Squeeze: S:2 pattern (stretch by 2x), Q:0.5 pattern (squeeze to half size)
• Custom Durations: D:1,5 pattern (short=1, long=5), D:3,1 pattern (reverse short/long)
• Pattern Stringing: pattern1, pattern2, pattern3 → Concatenates patterns with visual dividers
• Pattern Quantization: pattern;newSteps → E(3,8);12 (clockwise), pattern;-newSteps → 0x92;-6 (counterclockwise)
• Named Patterns: tresillo=E(3,8), mypattern=P(3,1)+P(5,0)
• Binary: b101010 or 101010
• Hex: 0x92:8 → Tresillo
• Octal: 0o111 → Ternary rhythms
• Decimal: 73 or d73 (prefix disambiguates from binary)
• Onset Arrays: [0,3,6]:8 → Onset positions with step count
• Rotation: pattern@steps → 0x92@3, P(3,1)@2
• Progressive Transformers: patternB>target, patternW>target, patternE>target, patternD>target
• Progressive Examples: E(1,8)B>8 (Barlow 1→8), E(5,16)W>3 (Wolrab 5→3), P(3,1)E>12 (Euclidean), 0x92D>1 (Dilcue) - Enter repeatedly steps through
• Multi-combinations: P(3,1)+P(5,0)+P(2,5) → Proper LCM(3,5,2)=30
• Keyboard: Enter = Parse, Cmd+Enter = Parse & Add to Database
• Buttons: "Add to Database" button available for any current pattern

🎨 Pattern Creation

Euclidean Dilcue Barlow Wolrab Random Polygon

Onsets:

Steps:

Offset:

Target:

Onsets:

Steps:

Style:

Intensity: 50%

Vertices: △

Offset:

Multiplier:

Vertices: ⬟

Offset:

Multiplier:

Vertices: ⬢

Offset:

Multiplier:

Step 1 of 5: 3 → 4 onsets

Pattern Creation:
• Euclidean: Distributes onsets as evenly as possible using Euclidean algorithm
• Dilcue: Anti-Euclidean using complement patterns for anti-rhythmic effects
• Barlow: Uses indispensability theory to generate patterns by onset priority
• Wolrab: Anti-Barlow with reversed indispensability for syncopated patterns
• Random: Creates varied patterns using distribution styles - Bell Curve (balanced), Syncopated (off-beat emphasis), Balanced (even spacing), Clustered (grouped onsets), or Uniform (pure random). Use 'r' for random onset count
• Polygon: Combines up to 3 regular polygons with +/- operations. Shows polygon icons and names. Optional offset and multiplier parameters for each polygon
• Progressive Mode: Fill in Target to step through from current to target onset count
• Keyboard: Enter = Generate/Step, Cmd+Enter = Add to Database

📊 Analysis

Ready

Tempo: 120

Volume: 50%

MIDI: Not connected

🎭 Rhythm Mutator

Style:

Amount: 30%

Original: Parse pattern first

Rhythm Mutation:
Transform rhythms by displacing onsets while preserving character.

• Balanced: Random displacement in both directions
• Syncopate: Move toward off-beat positions
• Straighten: Move toward strong beats
• Groove: Bias toward groove positions
• Swing/Shuffle: Create swing or shuffle feel

Amount: 0% = original, 100% = maximum displacement
Preserves onset count and rhythm character!

🎶 Funky Generator

Type:

Steps:

Density: 60%

Style:

Funkiness: 50%

Funky Rhythm Generators:
Create new rhythms from scratch using musical algorithms.

• Groove: Template-based (funk, latin, afro, house)
• Funky Euclidean: Euclidean + groove deviations
• Probabilistic: Beat-strength based generation
• Polyrhythm: Layered rhythmic cycles

Try: Funk style, 60% density, 70% funkiness
Generates completely new patterns from algorithmic rules!

🎯 Barlow Transformer

Current Onsets: Parse pattern first

Target Onsets:

Operation:

🙃 Wolrab Mode (Reverse indispensability)

Barlow Indispensability Transformer:
Intelligently add or remove onsets based on Clarence Barlow's rhythmic indispensability theory.

• Dilution: Removes least indispensable onsets
• Concentration: Adds most indispensable positions
• Progressive: Multiple variations with gradual changes
• 🙃 Wolrab Mode: Reverses the logic - dilutes by removing MOST indispensable onsets, concentrates by adding LEAST indispensable positions

Theory: Positions are ranked by their metrical importance
Maintains rhythmic coherence while changing onset density!
Wolrab mode creates surprising, anti-metrical patterns!

🌀 Euclidean Transformer

Current Onsets: Parse pattern first

Target Onsets:

Operation:

Mode:

Euclidean Transformer:
Add or remove onsets using Euclidean distribution principles for mathematically optimal spacing.

• Dilution: Removes onsets while maintaining Euclidean spacing
• Concentration: Adds onsets using Euclidean distribution
• Progressive: Multiple variations with gradual changes
• 🙃 Dilcue: Uses complement patterns for unexpected rhythms

Theory: Uses Bjorklund's algorithm for optimal onset distribution
Creates mathematically perfect rhythm spacing!
Enter key on target onsets box steps through progressive transformations!

🔄 Progressive Offsets

Current Pattern: Parse pattern first

Forward Step:

Backward Step:

Current Offset: 0

Progressive Offsets:
Rotate patterns progressively by custom step increments in either direction.

• Forward Step: Press Enter to offset by +1, +2, +3... (or custom increment)
• Backward Step: Press Enter to offset by -1, -2, -3... (or custom increment)
• Reset: Return to original pattern position (offset 0)
• Manual: One-time offset by current values

Use Cases: Pattern variations, rhythm displacement, groove exploration
Works with any pattern - Euclidean, polygons, custom rhythms!
Enter key in number boxes for progressive stepping!

📏 Progressive Lengthening

Current Pattern: Parse pattern first

Steps to Add:

Current Length: 0

Extensions: 0

Progressive Pattern Lengthening:
Extend patterns by appending random steps with bell curve onset distribution.

• Steps to Add: Press Enter to progressively append this many steps
• Bell Curve Distribution: Uses same logic as R(r,n) - avoids empty or full sections
• Progressive Mode: Each Enter press adds another extension
• Reset: Return to original pattern length

Musical Use: Phrase extension, pattern development, compositional expansion
Creates musically intelligent random extensions!
Enter key in Steps to Add box for progressive lengthening!

Parse a pattern using the universal input above to see comprehensive mathematical analysis.

🎛️ Database Controls & Statistics

0 Total

0 Perfect

0 Favorites

0 Polygons

0 Euclidean

0 Combined

🔍 Perfect Balance Explorer

Milne's Perfect Balance Theory:
A pattern is perfectly balanced when: $$\sum_{j=1}^{k} e^{i2\pi k_j/n} = 0$$

Where: $k_j$ are the onset positions, $n$ is the total number of steps, $i$ is the imaginary unit

Key insights: Coprime polygon sides, strategic offsets, and subtraction operations can achieve perfect balance.

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Step Count Range: -