Exporting Microtonal Tuning Files with Scala: A Practical Guide

Frequency is measured in Hertz (Hz), while pitch is measured in cents. One octave corresponds to a frequency doubling (2x), so for n octaves, the frequency multiplier is 2^n. One semitone corresponds to a frequency ratio of 2^(1/12), approximately 1.05946. For n semitones, the frequency multiplier is 2^(n/12). A cent is a unit of pitch measurement where one octave equals 1200 cents and one semitone equals 100 cents. To find the cent value for a frequency ratio, use the formula: cents = 1200 × log2(frequency ratio). For example, a frequency ratio of 3 corresponds to approximately 1902 cents. To find the frequency ratio for a given cent value, use: frequency ratio = 2^(cents/1200). This logarithmic relationship allows calculation of pitch intervals for any frequency ratio.

Cents provide a way to represent pitch height mathematically, with 1200 cents in one octave. Each standard piano semitone equals 100 cents (12 semitones × 100 = 1200 cents). Cents are easier to intuit because they directly explain pitch height. Every cent value corresponds to a specific frequency ratio and vice versa. Whole number ratios, known as just intonation, refer to frequency relationships—multiplying a frequency by an interval ratio raises it by that interval. For example, a 2:1 ratio produces an octave, 3:2 creates a perfect fifth, 5:4 forms a major third, and 6:5 produces a minor third.

Musical intervals can be measured in cents, a logarithmic unit where one octave (2:1 frequency ratio) equals 1200 cents; to convert a frequency ratio to cents, multiply 1200 by the base-2 logarithm of the ratio, or equivalently multiply 3986 by the base-10 logarithm of the ratio, and to convert cents back to frequency, multiply the base frequency by 2 raised to the power of cents divided by 1200.

The cent system provides a logarithmic measurement for musical pitch where one octave (2:1 frequency ratio) equals 1200 cents. The formula cents = 1200 × log₂(f₂/f₁) allows precise interval measurement. In natural tuning, intervals have specific cent values: perfect fifth at 702 cents, major third at 386 cents. This system enables precise comparison between natural and tempered intervals, revealing subtle acoustic differences that shape musical tuning systems.

Pitch perception works logarithmically—our ears perceive equal frequency ratios as equal distances. Doubling a frequency always produces the same perceived interval (an octave). This explains why we use cents (logarithmic units where 1200 cents = one octave) rather than linear measurements. Frequency ratios (like 9:8 for major second) describe how frequencies relate, while length ratios work inversely—for strings/pipes, achieving the same interval requires dividing by the ratio. In just intonation, intervals are fractions between 1 and 2; inverting an interval requires multiplying by 2/1 (an octave) and simplifying. The overtone series begins with the fundamental and includes harmonics at integer multiples: 2x (octave), 3x (perfect fifth), 4x (perfect fourth), 5x (major third). The major third in the overtone series is approximately 15 cents flat compared to equal temperament. Consonance produces an objective physical sensation where beats (rapid amplitude fluctuations from near-equal frequencies) disappear, creating stability. This differs from subjective judgments about musical taste.

The .scl file format is used to store scale definitions in the Scala file format. Users can import pre-created scales or create their own. The format supports 12 tones to cover an octave, with options to create scales with sharper sharps and flatter flats to add dissonance when coupled with MIDI notes.

The poly wave table mode on the listing ex supports non-equal tempered tunings through scala files, which can be loaded from a micro SD card. Two essential files are required: an SCL file that defines the relationships of notes and pitches within a scale, and a KBM file that maps the pitches in your scale to a MIDI keyboard or CV gate, effectively converting CV signals into note numbers to look up the correct pitch.

Custom tunings can be exported in multiple formats: Ableton Live Set (.als) for project-specific use, Ableton Scala file (.atn) for compatibility with Live 12, and original Scala file (.scl) for use with the Scala software. The Ableton Scala format includes both the tuning definition and keyboard mapping (kbm) files, with the reference pitch information stored in the second file. Users should choose the appropriate format based on whether they need standalone project files or interoperability with other software.

Max 8.5 introduced Scala scale support in M2F, enabling flexible scale definitions for non-Western music, microtonal compositions, and custom scales. Scala files define scales with name, description, length, and note offsets using either cent values (100ths of a semitone) or frequency ratios. The M2F object maps MIDI notes to frequencies according to the loaded scale, producing different frequencies for the same MIDI note depending on the scale. To implement custom scales, use Scale Workshop to create Scala files, then use a parser abstraction to convert them for M2F. The F2M object converts frequencies back to MIDI values, useful for verifying mappings or feeding MIDI-compatible instruments.

A MIDI synthesizer works by receiving digital messages (note on/off, velocity, controller values) from a MIDI device, which then generates sound through oscillators that produce waveforms at specific frequencies; the basic components include oscillators (waveform generators), amplitude modulation via velocity, and envelope generators (ADSR) that shape the sound's attack, decay, sustain, and release characteristics to create musical tones.

Software Instrument Tracks (green) enable playback of virtual instruments using MIDI controllers or GarageBand's Musical Typing feature. MIDI (Musical Instrument Digital Interface) transmits digital note data without carrying audio signals. MIDI controllers connect via USB and send information about which notes to play and how hard to play them. Musical Typing uses your computer keyboard (J=low C, K=middle C) as an alternative. This separation of control from sound enables flexible instrument switching and creative possibilities in music production.

Software instruments (MIDI/virtual instruments) are essential DAW components providing access to instruments unavailable physically. They operate through two methods: sample libraries (pre-recorded acoustic notes) and algorithmic emulations (mathematical sound generation). MIDI (Musical Instrument Digital Interface) is the protocol enabling communication between controllers and software, transmitting note data, timing, and velocity. These tools democratize music production by eliminating physical instrument limitations, allowing unlimited playback and portability across laptop-based workflows.

MIDI (Musical Instrument Digital Interface) is a communication protocol developed in the early 1980s by synthesizer manufacturers to create a universal standard for device communication. The protocol has remained largely unchanged for approximately 40 years. MIDI In receives information from computers or sequencers, telling synthesizers which notes to play and parameters to modify. MIDI Out sends information to other devices. Modern synthesizers often feature combined USB MIDI connections that transmit both MIDI data and audio, functioning as both MIDI and audio interfaces.

MIDI (Musical Instrument Digital Interface) is a communication protocol invented in the 1980s that enables different musical synthesizers and instruments to communicate and coordinate with each other. The protocol uses values from 0 to 127 and includes different message types such as Note On (which starts playing a note with a specific pitch and velocity), Note Off (which stops playing a note), and Control Change (which modifies parameters like filter frequency, resonance, and modulation). MIDI can be used to control physical synthesizers through computer software like Processing, enabling interactive musical applications, alternative interfaces for people with disabilities, and innovative musical experiences that go beyond traditional keyboard-based instruments.