MidiToHzConvertor: Convert MIDI Notes to Hz in SecondsModern music production often mixes musical intuition with mathematical precision. Whether you’re designing synths, tuning samples, building audio plugins, or writing algorithmic composition code, converting MIDI note numbers to frequencies (Hz) is a foundational task. MidiToHzConvertor is a straightforward utility that makes that task immediate and accurate — converting MIDI notes to Hertz in seconds. This article explains the theory, common use cases, implementation approaches, and practical tips for integrating a MidiToHzConvertor into your workflow.
What is MIDI note numbering?
MIDI (Musical Instrument Digital Interface) encodes musical pitch using integer note numbers from 0 to 127. These numbers map to pitches spanning multiple octaves; for example:
- MIDI note 60 = Middle C (C4) by common convention.
- The standard reference pitch A4 (the A above middle C) is normally tuned to 440 Hz, though alternate tunings (e.g., 432 Hz) are sometimes used.
MIDI numbers are convenient for sequencing and digital instruments, but most audio processes require frequency values in Hertz. That’s where MidiToHzConvertor comes in.
The math behind MIDI-to-Hz conversion
The relationship between a MIDI note number and frequency is exponential: each increase of 12 MIDI numbers raises pitch one octave (frequency doubles). The standard conversion formula, using A4 = 440 Hz as reference, is:
f = 440 * 2^((m – 69) / 12)
Where:
- f is frequency in Hz,
- m is the MIDI note number,
- 69 is the MIDI number for A4.
This formula yields exact frequencies for equal-tempered tuning based on the chosen A4 reference.
Key features of an effective MidiToHzConvertor
- Instant conversion from a single MIDI note to frequency.
- Batch conversion for lists or arrays of MIDI notes.
- Support for custom reference pitches (e.g., A4 = 432 Hz).
- Support for microtuning via fractional MIDI values (e.g., 60.5 for a quarter-tone).
- High numerical precision and low computational overhead for real-time contexts.
- Simple API for integration into DAWs, plugins, synthesis code, and web pages.
Use cases
- Synthesizer oscillators: Calculate oscillator frequencies from MIDI input in a soft-synth or hardware emulation.
- Tuning sample playback: Resample or pitch-shift audio samples accurately for a given MIDI note.
- Frequency displays and visualizers: Show Hz values next to note names in music education tools.
- Audio plugin development: Map MIDI note events to parameter values (e.g., oscillator frequency, filter cutoff).
- Algorithmic composition and analysis: Convert between symbolic note representations and DSP processes.
Implementation examples
Below are concise, practical code examples for common environments.
JavaScript (browser / Node.js):
function midiToHz(midi, a4 = 440) { return a4 * Math.pow(2, (midi - 69) / 12); } // Examples midiToHz(69); // 440 midiToHz(60); // ~261.625565 midiToHz(60.5); // supports fractional for microtuning Python:
import math def midi_to_hz(midi, a4=440.0): return a4 * (2 ** ((midi - 69) / 12.0)) # Examples midi_to_hz(69) # 440.0 midi_to_hz(60) # ~261.6255653005986 C (for real-time/synth engines):
#include <math.h> double midi_to_hz(double midi, double a4) { return a4 * pow(2.0, (midi - 69.0) / 12.0); } Batch conversion is just mapping this function across arrays or buffers of MIDI values.
Handling alternate tunings and temperaments
- Change the A4 reference to shift the overall tuning (e.g., 432 Hz).
- For non-equal-temperament scales, use lookup tables or scale-specific formulas; MidiToHzConvertor can accept a mapping from MIDI to cent offsets and apply: f = a4 * 2^((m – 69 + cents/100) / 12)
Fractional MIDI numbers are useful for microtonal systems: 1 MIDI unit = 100 cents, so cents adjustments can be converted to fractional MIDI offsets.
Performance considerations
- The conversion uses a single pow() or Math.pow() per note — cheap enough for real-time on modern hardware.
- For very large arrays or extremely tight real-time constraints, precompute a lookup table (128 entries for integer MIDI notes) and interpolate for fractional values.
- Use single-precision floats in DSP code where acceptable to save CPU/cache bandwidth.
UX tips for tools and interfaces
- Show both the MIDI number, note name, and frequency (e.g., “60 — C4 — 261.63 Hz”).
- Allow users to change A4 and see live recalculation.
- Offer copy/paste and CSV export for batch results.
- Include toggle for equal-temperament vs. custom tuning modes.
Quick reference table
| Input | Output (A4=440Hz) |
|---|---|
| 69 (A4) | 440.00 Hz |
| 60 (C4) | 261.63 Hz |
| 0 (C-1) | 8.18 Hz |
| 127 (G9) | 12543.85 Hz |
Conclusion
MidiToHzConvertor encapsulates a tiny but vital piece of music technology: converting MIDI pitch numbers to audible frequencies. With a single-line formula, options for alternate tunings, and easy batching, it’s a tool that belongs in any developer or musician’s toolkit. Implementations in JavaScript, Python, C, and other languages are trivial and performant, making it simple to add accurate pitch-to-frequency conversion “in seconds.”
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