Math2Music is a C# console application that converts numeric sequences into rich musical sounds by mapping digits to frequencies with advanced audio processing capabilities. The application now supports both monophonic and polyphonic music generation, WAV file output, configurable sound settings, timber profiles, and multiple audio processing modes including multi-octave harmonics.
The application implements a sophisticated mathematical-to-musical mapping system:
- Each digit (0-F) is mapped to a frequency multiplier
- Configurable base frequency (default: 180 Hz) and duration (default: 300ms)
- Each digit creates a tone at
baseFrequency × digitValue - For example: digit '4' generates a tone at 180Hz × 4 = 720Hz
- Supports polyphonic music using
+operator (e.g.,123+456creates harmonic chords) - Multiple output formats: Console beeps, WAV files with stereo positioning
- Rich timber profiles simulate natural instruments (Piano, Guitar, Violin) and synthetic sounds
- Multi-octave processing creates harmonically rich compositions
Sources/MathToMusic/
├── Program.cs # Main application entry point with rich configuration UI
├── ExpressionParser.cs # Polyphonic expression parser (123+456 notation)
├── MathToMusic.csproj # Project configuration file
├── Contracts/ # Interface definitions
│ ├── ITonesProcessor.cs # Interface for tone processing logic
│ ├── ISequenceProcessor.cs # Interface for sequence processing
│ ├── ITonesOutput.cs # Interface for audio output + core data models
│ └── ITonesFileOutput.cs # Interface for file-based outputs
├── Models/ # Data models and enums
│ ├── NumberFormats.cs # Enum: Bin, Qad, Oct, Dec, Hex, Base32
│ └── TimberProfiles.cs # 18+ predefined timber profiles (Piano, Guitar, etc.)
├── Processors/ # Audio processing implementations
│ ├── SingleTrackProcessor.cs # Basic monophonic processing
│ ├── ReachSingleTrackProcessor.cs # Multi-octave harmonic processing
│ ├── MultiTrackProcessor.cs # Polyphonic music processing
│ ├── TimberSequenceProcessor.cs # Timber profile application
│ └── HarmonicCombiner.cs # Harmonic combination logic
├── Outputs/ # Audio output implementations
│ ├── BeepOutput.cs # Console.Beep audio output
│ ├── WavFileOutput.cs # Professional WAV file generation
│ ├── OpenFileOutput.cs # Auto-open generated files
│ ├── OpenFileLocationOutput.cs # Auto-open file locations
│ └── TestMelodyOutput.cs # Testing and demonstration output
├── Extensions/ # Fluent API extensions
│ └── FileOutputExtensions.cs # Chainable file output operations
├── Demo/ # Demonstration code
│ └── FluentApiDemo.cs # WAV output fluent API examples
└── Utils/ # Utility classes
├── CommonNumbers.cs # Mathematical constants (PI, E, Golden Ratio)
└── NumberConverter.cs # Base conversion utilities
Purpose: Rich interactive console interface with comprehensive configuration options
Key Features:
- Session Configuration: Configurable base tone frequency and duration
- Timber Profile Selection: Choose from 18+ predefined instrument profiles
- Multiple Number Formats: Binary, Quaternary, Octal, Decimal, Hexadecimal, Base32
- Polyphonic Processing: Support for
+operator notation (e.g.,123+456) - Processor Selection: Choose between simple or ReachSingleTrackProcessor
- WAV File Output: Professional audio file generation with auto-open capability
- Mathematical Constants: Easy access to predefined constants (PI, E, Golden Ratio)
Purpose: Converts numeric sequences to single-track musical tones
Key Properties:
baseToneHz: Configurable base frequency (default: 180 Hz)baseDurationMilliseconds: Configurable duration per tone (default: 300ms)toneMap: Dictionary mapping characters (0-F) to frequency multipliers
Purpose: Creates rich harmonic content by generating multiple octave groups
Key Features:
- Multiple Octave Groups: Low, MidLow, MidHigh, High frequency ranges
- Harmonic Richness: Distributes digits across different octave ranges
- Synchronized Timing: All octave groups maintain consistent duration
- Advanced Filtering: Smart digit distribution based on value ranges
Purpose: Handles polyphonic expressions with + operator for harmonic music
Key Features:
- Expression Parsing: Automatically detects and parses
123+456notation - Stereo Positioning: Places different sequences across stereo field
- Harmonic Combination: Synchronizes multiple sequences for chord creation
- Dynamic Scaling: Prevents clipping when mixing multiple sequences
Purpose: Applies instrument-specific harmonic profiles to generated sequences
Key Features:
- Overtone Generation: Creates realistic instrument sounds using harmonic series
- 18+ Predefined Profiles: Piano, Guitar, Violin, Flute, Trumpet, Saxophone, etc.
- Synthetic Sounds: Sawtooth, Square, Triangle, Sine wave profiles
- Custom Coefficients: User-definable overtone amplitude ratios
Purpose: High-quality stereo WAV file generation with advanced audio processing
Key Features:
- CD Quality Audio: 44.1kHz, 16-bit, stereo output
- Stereo Positioning: Automatic stereo field distribution for polyphonic sequences
- Dynamic Range Management: Intelligent normalization and amplitude scaling
- Frequency-Based Amplitude: Low frequencies receive appropriate boost for audibility
- Anti-Clipping Protection: Sophisticated multi-sequence mixing without distortion
- Results Directory: Organized output in
Results/folder with timestamped filenames
Purpose: Chainable post-processing operations for WAV files
Fluent Methods:
.OpenFile()- Auto-opens generated WAV file in default application.OpenFileLocation()- Opens Windows Explorer at file location- Chainable:
new WavFileOutput().OpenFileLocation().OpenFile() - Cross-Platform: Graceful fallback on non-Windows systems
Purpose: Immediate console-based audio feedback using system beeps
- Real-time playback during processing
- Windows-specific Console.Beep API
- Useful for quick testing and immediate feedback
Purpose: Represents a single musical tone with rich harmonic content
Duration: Precise timing control via TimeSpanObertonFrequencies: Array supporting multiple harmonics and overtonesBaseTone: Convenient access to fundamental frequency
Purpose: Represents a complete musical sequence with metadata
TotalDuration: Total playback duration for synchronizationTones: List of individual tone objectsTitle: Descriptive name for identificationTimber: Optional timber profile coefficients for harmonic shaping
Supported numeric systems:
Bin = 2(Binary)Qad = 4(Quaternary)Oct = 8(Octal)Dec = 10(Decimal)Hex = 16(Hexadecimal)Base32 = 32(Base32) - NEW: Extended support for Base32 encoding
Purpose: Provides predefined timber profiles for realistic instrument simulation
Natural Instruments (9 profiles):
- Piano, Guitar, Violin, Flute, Trumpet, Organ, Clarinet, Saxophone, Cello, Oboe
Synthetic Sounds (7 profiles):
- Sawtooth, Square, Triangle, Pulse, Bright, Warm, Metallic, Bell, Pad, Sine
Special Effects (4 profiles):
- Hollow, Nasal, Growl, Ethereal
Key Methods:
GetAvailableProfiles()- List all available timber profilesHasProfile(name)- Check if profile existsGetProfile(name)- Retrieve coefficients for specific profile
Purpose: Parses mathematical expressions with musical operators
Key Features:
- Plus Operator: Parses
123+456+789into individual sequences - Polyphonic Detection:
IsPolyphonic()identifies multi-track expressions - Clean Parsing: Handles whitespace and empty segments gracefully
- Array Output: Returns string array of individual numeric sequences
Purpose: Provides easy access to important mathematical constants
Available Constants:
- PI variations: PI100, PI1000 (π with 100 and 1000 digit precision)
- Golden Ratio: FI100 (φ with 100 digit precision)
- Euler's Number: E100, E1000 (e with 100 and 1000 digit precision)
- Square Roots: SQRT2, SQRT3 (√2 and √3)
- Additional: Various other mathematical constants in the collection
- Launch Application:
dotnet run - Configure Settings: Optionally customize base frequency and duration
- Select Timber Profile: Choose from Piano, Guitar, Violin, or 15+ other profiles
- Choose Processor: Basic SingleTrack or advanced ReachSingleTrack with harmonics
- Enter a number (e.g., "1234")
- Specify output formats (e.g., "2,8,16" for binary, octal, hex)
- Generated WAV files automatically saved in Results/ folder
- Files auto-open in default application (Windows)
- Use
+operator to combine sequences:123+456 - Create complex harmonies:
ABC+DEF+789 - Different sequences positioned across stereo field
- All sequences synchronized for harmonic chord progression
- Select "ReachSingleTrackProcessor" when prompted
- Single input generates multiple octave groups (Low, MidLow, MidHigh, High)
- Rich harmonic content with frequency distribution across ranges
- Creates orchestral-depth sound from simple numeric input
Enter predefined constants by name:
- "PI100" - Plays first 100 digits of π (approximately 30 seconds)
- "PI1000" - Extended 1000-digit π sequence
- "FI100" - Golden ratio φ with 100 digits
- "E100" - Euler's number e with 100 digits
- "E1000" - Extended 1000-digit e sequence
- "SQRT2", "SQRT3" - Square root constants
- Set Input Format: Enter format number (2=Binary, 8=Octal, 10=Decimal, 16=Hex, 32=Base32)
- Enter Number: Input number in selected format (e.g., "1010" for binary)
- Select Output Formats: Specify multiple formats for comparison (e.g., "2,8,10,16,32")
- Base32 Support: Full support for Base32 encoding with characters 0-9, A-V
- Select Profile: Choose from 18+ available profiles during configuration
- Natural Instruments: Piano, Guitar, Violin, Flute create realistic instrument sounds
- Synthetic Waveforms: Sawtooth, Square, Triangle for electronic music
- Special Effects: Hollow, Nasal, Growl, Ethereal for unique textures
// Basic WAV output
var output = new WavFileOutput();
// With auto-open functionality (fluent API)
var output = new WavFileOutput().OpenFileLocation().OpenFile();- Professional CD-quality stereo WAV files (44.1kHz, 16-bit)
- Automatic file organization in Results/ directory
- Cross-platform compatible with graceful Windows-specific feature fallback
The application uses a configurable linear frequency mapping system with rich harmonic relationships:
| Digit/Character | Multiplier | Default Frequency (Hz)* | Harmonic State |
|---|---|---|---|
| 0 | 0 | 0 | Silence |
| 1 | 1 | 180 | Base Tone |
| 2 | 2 | 360 | Octave 1 |
| 3 | 3 | 540 | Quinta 1 |
| 4 | 4 | 720 | Octave 2 |
| 5 | 5 | 900 | Tertia 2 |
| 6 | 6 | 1080 | Quinta 2 |
| 7 | 7 | 1260 | Septima 2 |
| 8 | 8 | 1440 | Octave 3 |
| 9 | 9 | 1620 | Segunda 3 |
| A | 10 | 1800 | Tertia 3 |
| B | 11 | 1980 | Quarta 3 |
| C | 12 | 2160 | Quinta 3 |
| D | 13 | 2340 | Sexta 3 |
| E | 14 | 2520 | Septima 3 |
| F | 15 | 2700 | Septima Maj 3 |
| G | 16 | 2880 | Octave 4 |
| H | 17 | 3060 | Harmonic 17 |
| I | 18 | 3240 | Segunda 4 |
| J | 19 | 3420 | Harmonic 19 |
| K | 20 | 3600 | Tertia 4 |
| L | 21 | 3780 | Quarta 4 |
| M | 22 | 3960 | Harmonic 22 |
| N | 23 | 4140 | Harmonic 23 |
| O | 24 | 4320 | Quinta 4 |
| P | 25 | 4500 | Harmonic 25 |
| Q | 26 | 4680 | Sexta 4 |
| R | 27 | 4860 | Harmonic 27 |
| S | 28 | 5040 | Septima 4 |
| T | 29 | 5220 | Harmonic 29 |
| U | 30 | 5400 | Septima Maj 4 |
| V | 31 | 5580 | Harmonic 31 |
Default frequencies shown with 180Hz base frequency. Both base frequency and duration are user-configurable.
Perfect Octaves - Clean doubling of frequency:
- Octave 1 (2): Double the base frequency
- Octave 2 (4): Quadruple the base frequency
- Octave 3 (8): Eight times the base frequency
- Octave 4 (16): Sixteen times the base frequency
Harmonic Intervals by Octave:
- Octave 1: Quinta 1 (3)
- Octave 2: Tertia 2 (5), Quinta 2 (6), Septima 2 (7)
- Octave 3: Segunda 3 (9), Tertia 3 (10), Quarta 3 (11), Quinta 3 (12), Sexta 3 (13), Septima 3 (14), Septima Maj 3 (15)
- Octave 4: Segunda 4 (18), Tertia 4 (20), Quarta 4 (21), Quinta 4 (24), Sexta 4 (26), Septima 4 (28), Septima Maj 4 (30)
- Complex Harmonics: Harmonic 17, 19, 22, 23, 25, 27, 29, 31 - intermediate tones between main intervals
Frequency Calculation: frequency = baseFrequency × digitValue
Example: With base frequency 180Hz:
- Digit '1' → 180Hz (Base/Fundamental)
- Digit '2' → 360Hz (Octave 1)
- Digit '3' → 540Hz (Quinta 1)
- Digit '4' → 720Hz (Octave 2)
This harmonic structure creates naturally consonant musical relationships between digits, making mathematical sequences sound more musical and pleasing to the ear.
- Windows: Full functionality with Console.Beep + WAV file generation
- Linux/macOS: Complete WAV file generation, limited console beep capability
- Cross-Platform: WAV output works identically across all platforms
- Windows-Specific Features: Auto-open files and file locations (graceful fallback on other platforms)
- Memory Usage: Linear O(n) scaling with input length
- Audio Processing: Real-time generation with professional quality output
- File I/O: Efficient WAV file generation with configurable sample rates
- Timing Precision: Accurate duration control via TimeSpan objects
- Polyphonic Processing: Intelligent stereo field distribution and anti-clipping normalization
- Professional Output: CD-quality 44.1kHz, 16-bit stereo WAV files
- Dynamic Range Management: Automatic normalization prevents clipping in polyphonic mixes
- Frequency-Based Amplitude: Lower frequencies receive appropriate boost for audibility
- Stereo Positioning: Polyphonic sequences distributed across stereo field for clarity
- Timber Processing: Realistic instrument simulation through harmonic coefficient application
- Multi-Octave Generation: ReachSingleTrackProcessor creates harmonically rich compositions
- Polyphonic Synchronization: Multiple sequences precisely time-aligned for harmonic music
- Configurable Parameters: User control over base frequency, duration, and timber profiles
- Expression Parsing: Robust parsing of complex polyphonic expressions with + notation
- Format Flexibility: Seamless conversion between all supported numeric formats including Base32
- ✅ Multi-Platform Audio: WAV file output works across all platforms
- ✅ Configurable Parameters: User-adjustable tone duration and base frequency
- ✅ Rich Harmonic Content: Full timber profile support with overtone generation
- ✅ Polyphonic Processing: Multi-track harmonic music generation
- ✅ Professional Output: High-quality stereo WAV file generation
The application features a sophisticated, extensible architecture with multiple extension points:
ITonesOutput: Implement for new audio output methods (MIDI, MP3, etc.)ITonesFileOutput: Extend for new file-based outputs with return path capability- Fluent API Pattern: Easily chainable post-processing operations via extension methods
ITonesProcessor: Create new conversion algorithms and processing logicISequenceProcessor: Implement custom sequence processing pipelines- Timber Profiles: Add new instrument profiles to
TimberProfiles.cs - Expression Parsing: Extend
ExpressionParserfor new musical operators
- Multi-Octave Processing:
ReachSingleTrackProcessordemonstrates sophisticated harmonic generation - Polyphonic Composition:
MultiTrackProcessorshows multi-track synchronization - Harmonic Infrastructure: Full overtone support in
Tonestruct enables rich harmonic content - Mathematical Constants: Easily extend
CommonNumberscollection
- Platform-Specific Features: Graceful fallback for Windows-specific functionality
- File System Integration: Configurable output directories and file management
- Audio Format Support: Professional WAV generation with configurable parameters
# Clone the repository
git clone https://github.com/BalancingRay/Math2Music.git
# Navigate to project directory
cd Math2Music/Sources/MathToMusic
# Build the project
dotnet build
# Run the application
dotnet run- .NET 8.0: Modern C# features and performance optimizations
- No External NuGet Packages: Self-contained with built-in .NET capabilities
- Built-in Audio APIs: Uses Console.Beep for immediate feedback (Windows)
- Native File I/O: Professional WAV file generation using standard .NET libraries
- Cross-Platform Compatibility: Runs on Windows, Linux, and macOS
Cross-platform audio→ WAV file generation implementedConfigurable parameters→ Base frequency and duration now user-configurableHarmonic generation→ Full timber profile system with 18+ instrumentsFile output→ Professional WAV file generation with fluent API
- MIDI Output: Generate MIDI files for use with external music software and DAWs
- Additional Audio Formats: MP3, FLAC, OGG export capabilities
- Advanced Musical Features:
- Musical scale mapping (Pentatonic, Chromatic, etc.)
- Time signature support and rhythmic patterns
- Chord progression analysis
- Visualization Components:
- Real-time frequency spectrum display
- Waveform visualization
- Musical notation export
- Advanced Expression Language:
- Mathematical operators beyond
+(-, *, /, ^) - Conditional logic and looping constructs
- Variable assignment and function definitions
- Mathematical operators beyond
- Performance Optimizations:
- Multi-threaded audio generation
- GPU-accelerated processing for large datasets
- Streaming audio for very long sequences
- Educational Features:
- Interactive tutorials for mathematical concepts
- Integration with educational platforms
- Real-time parameter adjustment during playback