The Perfect Semitone: 5- and 7-Limit Just Intonation Explained

This tutorial demonstrates how to use the Vienna Synchron Player software to implement microtonal tuning, including features like cent deviation adjustment on the piano roll, support for various tuning systems (22 EDO, just intonation), and keyboard mapping for non-standard scales. The presenter shows practical techniques such as applying the same cent deviation across all octaves of a note, creating custom Scala files for scales like 22 EDO, and combining multiple software instances to create interesting microtonal effects.

Modern digital audio software typically uses the 12-tone equal temperament scale by default. To accurately reproduce the sounds of microtonal instruments like the chipi, software must support custom tuning systems. This requires implementing microtuning features that allow users to load scale files (such as those in Scala format) and apply them to sampled instruments. Once implemented, users can drag scale files onto the sampler window to make notes play according to the specified microtonal system rather than the standard chromatic scale.

This video explains how modern software synthesizers like Surge implement microtonal tuning systems through Scala (.scl) tuning files and keyboard mapping (.kbm) files, enabling musicians to explore alternative tunings beyond the standard 12-tone equal temperament; the implementation allows for both monotonic and non-monotonic keyboard mappings, though users must adjust synthesizer parameters like LFO amplitude and envelope settings when using non-standard tunings to achieve desired sonic results.

Scale Workshop enables users to implement custom microtonal tunings across major digital audio workstations and synthesizers. The application supports exporting to multiple formats including Anna Mark Tune files for Omnisphere, Native Instruments, and Serum; Scala files for Arturia synths and GPO 4; Carla files for open-source synths like ZynAddSubFX and Absynth; Max/MSP text files for Max/MSP and Pure Data environments; and Kontakt scripts for Native Instruments Kontakt instruments. This comprehensive compatibility allows musicians to experiment with microtonal tunings across their entire software synthesizer collection.

This concluding segment addresses the philosophical and practical dimensions of engaging with microtonal music. The presenter shares personal experience of how microtonal exploration shatters conventional musical worldviews while revealing new harmonic possibilities. Drawing on Mark Applebaum's philosophy, the video argues against rigid definitions of music, suggesting instead that the crucial question is whether something is interesting rather than whether it conforms to traditional notions of being 'in tune.' Practical advice includes embracing initial strangeness, as repeated exposure makes unfamiliar tunings feel natural. The presenter recommends avoiding preconceptions about tuning correctness and following music with openness. Finally, the video offers accessible entry points through digitized tuning files for virtual synthesizers, making microtonal experimentation achievable for home musicians without specialized equipment.

Martin Vogel pioneered the extension of tonics into three dimensions by adding a seventh-axis perpendicular to the traditional grid. This creates a cubic structure where each vertex represents a different pitch class. Moving forward represents harmonic sevenths (ratio 7:4), while moving backward represents descending sevenths. The 2D Euler/Riemann grid represents five-limit tuning (ratios with 2, 3, and 5), while the 3D extension encompasses seven-limit tuning (including ratios with 7). Further dimensions could theoretically add eleven-limit tuning, though Vogel argued the ear cannot easily distinguish eleventh harmonics. This geometric expansion enables visualization of seventh chords and their relationships in ways impossible in two dimensions.

This segment demonstrates the Pitch Grid software's core interface, which uses a two-dimensional regular lattice to visualize pitch relationships. The software functions as a MIDI effect that converts untuned MIDI signals into precisely tuned output. The lattice visualization shows how scales appear as paths, with the western scale pattern consisting of five large steps and two small steps. The skew parameter (generator) controls the fundamental interval size, allowing users to explore different tunings by simply turning a knob. The segment demonstrates how changing the skew from 12-EDO to Pythagorean tuning (where the fifth fits the 3:2 ratio) and then to mean tone tuning (with a cleaner major third) reveals the trade-offs between different tuning systems.

A harmonic lattice can be constructed by starting with a root note and adding notes derived from the third and fifth partials. From C, adding G (fifth) and F (fourth) creates the spine of fifths. Adding E (third above C) and B (third above G) creates the spine of thirds. This visual representation shows the quickest paths to all 12 equal-tempered pitches.

The Space of Multiples (ПК) is a three-dimensional coordinate system that visualizes musical harmony by representing sounds as points, where the fundamental tone is at the origin and each axis represents multiplication by 2 (octaves), 3 (fifths), and 5 (fourths). This geometric representation, derived from the physics of sound harmonics, shows that consonance corresponds to proximity in this space—closer points share more harmonics and sound more harmonious. The model provides a scientific foundation for understanding major/minor triads, tonal structures, and enables the construction of new musical systems including microtonal music.

Temperaments are systems that define the exact sizes of musical intervals; historically, they evolved from Pythagorean tuning (pure fifths creating a 'wolf' interval) to meantone temperaments (prioritizing pure major thirds), then to irregular/well-tempered temperaments (offering some pure intervals while others sound tense), and finally to equal temperament (where all 12 fifths are equally tempered to close the circle, becoming the dominant system by the 19th century despite being technically achievable only with modern tuning machines).

In most of Western Classical music history, enharmonics (notes like G# and Ab) were not actually the same pitch due to tuning systems like quarter-comma meantone temperament, which prioritized pure major thirds over equal semitones, resulting in a 'wolf fifth' and requiring musicians to choose between different pitches for enharmonic equivalents; this contrasts with modern equal temperament where all semitones are equal and enharmonics truly coincide.

Microtonalism uses intervals smaller than semitones, the smallest perceptible distance in Western music. Indian classical music uses 22 shrutis (versus Western 12 semitones) organized into ragas, with the first and fifth degrees fixed while other notes vary. The cent system measures pitch differences (100 cents per semitone). Arabic music uses 24 altitudes organized into seven maqams, with similar fixed tonic and fifth principles. The fifth interval's universal importance stems from harmonic series physics—every sound contains overtones forming predictable patterns, making the fifth naturally consonant across all cultures.

Equal temperament, the most prominent temperament of the 20th century, aims to make every tonality playable but creates disadvantages: no pure intervals, all fifths slightly narrower than pure, and all major thirds much wider than pure. Since all intervals are equally tempered, there is no key color—all major tonalities sound exactly the same. Quarter comma meantone emphasizes retaining pure major thirds (eight pure thirds) but creates a 'wolf fifth' between G-sharp and E-flat, and only limited tonalities are playable. Rameau temperament addresses these compromises with four pure major thirds, no very wide thirds, and no wolf fifth. Circulating unequal temperaments (Kirnberger III and Werckmeister III) allow playing in all tonalities with a mixture of pure and tempered fifths, giving each tonality a distinctive personality or color. The demonstration shows that historical temperaments can be used for complex jazz music, adding harmonic color missing from equal temperament.

Some musical traditions use microtones—notes that fall between the standard half tones of the chromatic scale. The video creator explains that while the chromatic scale consists of 12 notes per octave, gypsy (flamenco), Indian, and Mongolian music divide notes even further, creating sounds that standard pianos cannot reproduce. These microtonal notes are technically outside the chromatic scale, yet they create authentic, human sounds that cannot be replicated by conventional instruments. This demonstrates that musical expression can transcend conventional scales and that different cultures have developed unique approaches to pitch and sound.