Just Intonation vs Equal Temperament: Visual Demonstration

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.

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.

Microtonal scale design involves arranging pitches in specific sequences to create unique emotional palettes, and modern tools like Wilsonic MTS-ESP now enable real-time tuning across multiple software synthesizers in a DAW by implementing a shared library system where one plugin acts as a master that owns the global tuning state (mapping 128 MIDI note numbers to frequencies) while other plugins register as clients to pull the correct frequencies, significantly reducing the friction of using microtonality compared to previous methods that required manual configuration for each synthesizer.

Microtones are musical intervals smaller than the standard semitones found in the twelve-tone equal temperament system, such as the note between F and F sharp. Microtonal music is based on pitch frequency ratios rather than the standard twelve-tone system, with a major third corresponding to a 5:4 ratio and a major ninth to a 9:8 ratio. The twelve-tone equal tempered system differs significantly from these natural harmonic ratios. For composition, additive loop composition involves starting with a simple loop and gradually adding parts to fill space, either by writing parts that flow with the beat or identifying interesting gaps. The tools used to create music significantly influence the resulting output, with music written in digital audio workstations sounding different from music written at a piano.

This segment demonstrates the complete intonation adjustment process. The process involves: (1) Tuning the open string to perfect pitch, (2) Checking the 12th fret note, (3) If sharp, moving the bridge back to lengthen the string, (4) If flat, moving the bridge forward to shorten the string, (5) Re-tuning and re-checking after each adjustment, (6) Continuing until the 12th fret note is within a few cents of perfect pitch. The segment also covers checking both treble and bass sides separately, and notes that middle strings are typically not intonated as they are compensated by the bridge.

Good intonation requires a well-trained ear developed through active listening—paying attention to bass lines, chord progressions, and harmonic context beyond melodies. Each interval and chord has unique tendencies requiring adjustment. A tuner helps develop muscle memory for positions, but ensemble intonation demands a developed pitch sense because positions alone don't ensure proper harmony. Practice chord locking exercises: B-flat major chord (Bb, F, D) locks when F raises slightly and D lowers slightly. Moving to B-flat minor chord requires the minor third to pull up. Diminished chords and returning to major chords develop sensitivity to ensemble tuning requirements.

Intonation refers to pitch accuracy, and in ensemble playing, musicians must match each other's intonation rather than achieving perfect individual pitch. When breath pressure increases for louder sounds, intonation naturally becomes flatter, requiring embouchure adjustments. Articulation—the precision of note attacks—creates section tightness when all musicians start notes simultaneously. Altissimo notes require specific fingerings, even finger movement, and proper voicing. The only way to improve consistency is through repeated performance attempts, accepting that failure in front of audiences is necessary for growth. Active listening during performance—focusing on hearing underlying changes rather than visual references—creates deeper musical memory encoding.

Before executing a note, performers must have their embouchure correctly positioned - they cannot 'attach' to a note but must be precisely positioned beforehand. When performing messa di voce, performers must maintain consistent intonation throughout dynamic changes. Different notes require different embouchure positions, particularly when moving between registers. Performers should create clear dynamic differences between similar notes, particularly when one note arrives from a crescendo and another requires more intensity. This differentiation creates musical interest and prevents the performance from becoming monotonous.

This section covers action height measurement and adjustment, along with the principles and techniques of intonation adjustment. Action height is measured from the top of the fret to the bottom of the string at the 12th fret, with typical values ranging from 1.4mm to 1.7mm depending on the guitar's neck camber and the player's preference. The section explains that action should be measured at multiple points across the fretboard to ensure consistency. Intonation is defined as the guitar's ability to play in tune across the fretboard, with the goal of making fretted notes match harmonics at the same fret. The section details the adjustment process: if the fretted note is sharp, move the saddle back (away from the bridge) to lengthen the string and flatten the pitch; if the fretted note is flat, move the saddle forward (toward the bridge) to shorten the string and sharpen the pitch. The section emphasizes that intonation can be adjusted by ear, which is just as effective as using electronic devices.

The Pythagorean comma proves that perfect fifths and octaves cannot both be perfectly tuned simultaneously. Using proof by contradiction: assume X octaves = Y perfect fifths. This implies 2^X = (3/2)^Y, which simplifies to 2^(X+Y) = 3^Y. Since one side is always even and the other always odd, they can only be equal when X=Y=0. Once moving, these streams never cross again, proving perfect tuning of both intervals is impossible.

Repeatedly going up in perfect fifths (12 times) does not reach the same note as going up seven octaves, creating the Pythagorean comma. Mathematically, (3/2)^12 ≈ 129.746 while 2^7 = 128, showing they never converge. This occurs because 3^a = 2^(a+b) is impossible for integers a and b (odd vs. even). This fundamental incommensurability between octave and fifth intervals means pure tuning cannot work across all keys, requiring compromise solutions.

Pythagorean tuning stacks perfect fifth intervals (3:2 ratio) to build a 12-tone scale, using octave reduction to align values with the reference octave. An alternative method descends by stacking perfect fourth intervals (2:3 ratio) backwards. Both methods yield 12 stacks corresponding to a 12-tone scale. However, stacking 12 perfect fifth intervals to return to the same pitch as seven octaves creates the Pythagorean comma—a mathematical impossibility. The closest value equals a monstrous fraction representing B#'s interval or half D flat flats. This discrepancy causes the wolf fifth problem: the F# to C# or G flat to B flat interval doesn't perfectly line up with a 3:2 ratio, being 23 cents flat and sounding dissonant. The system assumes sharp inharmonics from perfect fifth stacks equal flat inharmonics from perfect fourth stacks, which they clearly do not.

The problem of creating musical instruments dates back approximately 2600 years to Pythagoras. Sound is a vibratory phenomenon, with musical notes being vibrations of strings, air, or metal. The Greeks discovered that different lengths of tubes or strings produce different pitches, but they did not understand the wave nature of sound or how to measure frequency. Equal musical intervals require equal ratios, not equal differences in physical dimensions. The solution is to use ratios: 20/10 = 2 and 40/20 = 2, both producing an octave. To divide an octave into 12 equal parts, one must find a number (r) such that r^12 = 2, meaning r is the 12th root of 2. The Pythagoreans faced this problem in the 5th century BCE, but they only knew whole numbers (1, 2, 3, 4, 5...) and did not understand decimals or fractions. Since no whole number raised to the 12th power equals 2, this posed an unsolvable problem for them. It is mathematically impossible to find two integers whose 12th power ratio equals exactly 2. The Pythagoreans found two approximations for the 12th root of 2: 2187/2048 (called the 'apotome') and 256/243 (called the 'limma'). By combining these intervals, they could create an octave that is exactly 2:1. When constructing the scale by ascending 12 perfect fifths and descending 4 octaves, the resulting note is extremely close to but not exactly 'do'. The ratio is 1.0135, which is almost exactly 1. This tiny interval is called the 'Pythagorean comma.' The Pythagoreans chose 12 notes because after 12 fifths, they almost return to the starting note, making it practical to stop there. This creates two different types of semitones: one from 7 fifths and one from 5 fifths, differing by exactly one Pythagorean comma. This explains why the octave is divided into 12 parts in Western music.

It is mathematically impossible to find whole numbers x and y such that (3/2)^x = 2^y. This means that generating a scale from fifths will never perfectly align with octaves. While systems with 665 notes per octave can approximate this better than 12-note systems, they become impractical because the differences between adjacent notes become too subtle for human ears to distinguish. Twelve notes per octave represents the best compromise between mathematical precision and musical usability.