Beginner's Primer

What Is This App, and Why Does It Exist?

Here's something most people don't know: the piano is always slightly out of tune. Not broken — deliberately, mathematically out of tune, as a trade-off that makes the instrument practical to play. Almost every keyboard, guitar, and digital instrument works the same way.

Singers don't have that limitation. Because your voice can land on any pitch — not just the keys on a keyboard — you have the ability to sing notes that are more pure, more resonant, and more satisfying to the ear than what a piano can produce. But only if you can hear the difference and train your voice to find those exact spots.

That's what Intonation Lab is for. It listens to your voice through your microphone and shows you in real time how close you are to a target pitch — not the piano's version, but the mathematically pure version. Then it gives you tools to train your ears and your voice until landing on those pure pitches becomes natural.

The Big Concepts

What Is a Pitch?

A pitch is how high or low a note sounds. When something vibrates — a guitar string, a piano string, your vocal cords — it pushes air back and forth in waves. The faster it vibrates, the higher the pitch sounds.

We measure vibration speed in Hz, which stands for Hertz and just means "times per second." The note called A4 (the A above middle C on a piano) vibrates 440 times per second — so we say it's 440 Hz. A higher note vibrates faster; a lower note vibrates slower.

What Is an Interval?

An interval is the gap — the musical distance — between two pitches. When you sing one note and then another, the relationship between them has a name. "Perfect 5th" and "Major 3rd" are just names for specific distances, the same way "one foot" and "one mile" are names for distances in space.

Some intervals sound open and stable, like the Perfect 5th. Some sound bright and warm, like the Major 3rd. Some sound tense and unresolved. The sound character of an interval comes directly from the physics of how the two pitches relate to each other — and that's where ratios come in.

What Is a Ratio?

A ratio describes a relationship between two numbers — specifically, how many times one is bigger than the other. In music, a ratio tells you how fast the upper note vibrates compared to the lower note.

For example:

• An Octave has a ratio of 2:1, meaning the upper note vibrates exactly twice as fast as the lower. They're the "same note" in different registers.
• A Perfect 5th has a ratio of 3:2, meaning for every 3 vibrations of the upper note, the lower one vibrates exactly 2 times.
• A Major 3rd has a ratio of 5:4.

The simpler the ratio, the more "pure" and locked-in the interval sounds. This is physics, not opinion — simple ratios produce sound waves that align in clean, repeating patterns. Complex ratios produce patterns that fight each other slightly, which is what gives dissonant intervals their tense, restless quality.

What Is Just Intonation?

Just intonation (often abbreviated JI) is a way of tuning where every interval uses those clean, simple ratios. When two notes are in a just intonation relationship, their sound waves line up so perfectly that the interval has no "wobble" — it's completely still and clear.

This is how instruments like the human voice, violins, and trombones naturally want to tune when skilled players listen carefully to each other. It's also why a great barbershop quartet or a cappella choir can produce that shimmering, almost supernatural resonance — all the voices are locking into just intonation together.

What Is Equal Temperament?

Equal temperament (ET) is the tuning system your piano uses. To understand why it exists, think about this problem: if you tune your instrument using pure just intonation ratios for one key — say, C major — then when you try to play in a different key, like F# major, the intervals sound wrong. The math doesn't work out evenly.

The solution, developed centuries ago, was to make a compromise: slightly adjust every interval so they're all a little wrong in the same way. Divide the octave into 12 exactly equal steps. Now every key sounds the same, and you can play in any of them without retuning.

This is brilliant for keyboard instruments. But it means the intervals are never quite pure. The Major 3rd on a piano is noticeably sharp of its pure version. The Minor 7th is quite far off. Intonation Lab trains you to hear and sing the pure versions instead.

What Is a Cent?

A cent is a tiny unit for measuring pitch differences — specifically, for measuring how far a pitch is from a target. Think of it like millimeters for pitch: useful precisely because it's so small.

Here's how it scales: there are 1,200 cents in one octave, and 100 cents between any two neighboring keys on a piano. So one cent is 1/100th of the distance between two adjacent piano keys — genuinely tiny.

Why do we need such a small unit? Because the difference between a pure just intonation interval and the equal temperament version of that same interval can be as small as 2 cents or as large as 31 cents. That range matters — a lot. The app shows you your cents offset at all times: positive numbers (+) mean you're sharp (too high), negative numbers (−) mean you're flat (too low). Getting to zero means you've hit the target.

What Are Beats?

This is the most important concept in the entire app, so it's worth taking a moment to really understand it.

When two pitches that are close but not quite the same play at the same time, something interesting happens. Their sound waves take turns being in sync and out of sync with each other. When they're in sync, the sound gets a little louder. When they're out of sync, it gets a little quieter. And because this happens over and over in a regular rhythm, you hear a pulsing, wobbling, throbbing effect in the sound.

That's called acoustic beating — or just "beats." And here's the key fact: the speed of the beats tells you exactly how far apart the two pitches are. Specifically, the beat rate equals the difference in Hz between them.

Simple example: if you sing 441 Hz against a reference tone of 440 Hz, you'll hear 1 beat per second. If you're at 443 Hz, you'll hear 3 beats per second. As your pitch gets closer to 440 Hz, the beats get slower. At exactly 440 Hz, they stop completely — and the sound becomes perfectly still and clear.

That stillness is just intonation. And slowing down the beats until they stop is how singers, string players, and instrument tuners have been tuning by ear for hundreds of years. Intonation Lab makes those beats visible as a pulsing circle, so you can see what you're hearing — which makes learning much faster.

The Intervals the App Uses

All 13 intervals in order from closest together to farthest apart, with simple descriptions and their JI ratios:

The Major 3rd — at almost 14 cents flat of equal temperament — will likely surprise you most when you first sing it pure.

What the App Shows You

The Beat Circle

The most important thing on the screen. It pulses at the same rate as the acoustic beats between your voice and the reference tone — what you're hearing, made visible.

• Fast pulsing, red — you're far from the target; the beats are rapid
• Slower pulsing, amber — you're getting close; keep adjusting
• Still and glowing green — beats have stopped; you're in just intonation

Rings also expand outward with each pulse, so you can track the rhythm in your peripheral vision while focusing on singing. Over time, the goal is to not need the circle at all — to hear the beats directly and control them with your voice alone.

The Singing HUD

HUD is short for Heads-Up Display — a term borrowed from fighter pilots. In the app, it's the central panel you watch while singing. It shows your current target note, your cents offset, a needle gauge that swings left when flat and right when sharp, and your microphone input level.

When you're within the target zone, the whole HUD glows green.

The Cents Gauge

A needle gauge — like a fuel gauge, but for pitch. The needle sits in the center when you're on target, swings right when you're sharp, and swings left when you're flat.

The Pitch Tracker

A scrolling line chart that records your pitch over time. The target sits at the center line; your voice is drawn as a moving line above or below it. Useful for spotting patterns — do you approach from above or below? Do you overshoot?

The Cymatics Mandala

A decorative, geometric visualization inspired by cymatics — the study of how sound physically organizes matter into patterns. When you're in tune, the mandala is symmetrical and stable. When you drift, it rotates and distorts. Think of it as a bonus view rather than a primary tool.

The Hold Bar and Stability Indicator

During training exercises, the hold bar fills up as you sustain your pitch within the target zone. Required hold times range from 2 seconds at Beginner level to 4 seconds at Expert. A 0.5-second grace window means a single momentary wobble won't reset everything.

The stability indicator tells you whether your pitch is Steady (green), Wobbly (amber), or Unstable (red). This is separate from whether your pitch is correct — you could be singing the right pitch unsteadily, or the wrong pitch very steadily.

Recording and Playback

The Record button in the Singing HUD captures your pitch data as you sing. When you stop recording, press Playback to watch your performance replayed on the Pitch Tracker — a great way to review patterns, see where you drifted, and track improvement over time.

AI Coaching Feedback

Below the recording controls, the app displays real-time coaching tips based on your pitch patterns. It detects whether you're trending sharp or flat, whether your pitch is stable or wavering, and gives specific advice — like "Engage more breath support" or "Focus on steady airflow." The feedback updates every few seconds while you sing.

The Settings and Modes

Basic vs. Advanced Mode

Basic mode shows only what a beginner needs: the interval selector, the microphone input, the beat circle, and the reference tone player. Advanced mode adds chords, all three visualization views, the training curriculum, and all the settings described below. Switch anytime with the Adv toggle in the header.

Free vs. Train Mode

In Advanced mode, Free mode lets you practice any interval or chord you want, whenever you want, with no structure. Train mode enters the guided curriculum — 52 exercises in a specific order designed to build skill progressively.

Voice Range (Lo / Mid / Hi)

Shifts the reference tone into a lower, middle, or higher octave so the pitches sit comfortably in your own voice. Use whichever keeps you from straining.

Voicing Mode

Controls what you hear when the reference tone plays:

• Just my note — only your target pitch plays; good for basic interval matching
• Chord without me — all other chord notes play except yours; you supply the missing voice (the most musically realistic practice)
• Full chord — every note plays including yours; useful for hearing how your voice fits

Sensitivity Levels

Controls how accurate you have to be to register as "in tune." The green zone narrows at each level:

Start at Beginner. Even experienced singers are often humbled by Intermediate.

Octave-Agnostic vs. Absolute Mode

In Octave-Agnostic mode (the default), you can sing your target note in any comfortable octave. In Absolute mode, you have to match the exact octave. Octave-Agnostic is the practical choice for most training.

Concert Pitch (A4 Tuning)

440 Hz is the international standard pitch. European orchestras often tune to 442 Hz; baroque musicians use 415 Hz. The app lets you adjust from 415 to 466 Hz.

Vibrato Smoothing

Vibrato is the natural, slight wavering in pitch that trained singers develop. Smoothing averages it out so the app reports the center of your vibrato. Leave it on while training.

Input and Output Dropdowns

If you have a USB microphone or external audio interface, these dropdowns let you choose which device to listen to and which to send the reference tone to. Set your USB mic as input and your headphones as output so the reference tone doesn't feed back into the microphone.

Dark Mode

Click the sun/moon icon in the header to toggle between light and dark themes. Your preference is saved automatically. The app also respects your system's dark mode setting on first visit.

Drone Mode

The Drone control in the Tone card plays a continuous reference pitch in the background. Choose Root for the root note alone, or Root+5th for a richer drone that includes the pure perfect fifth (3:2 ratio). The drone restarts automatically when you change the reference note.

JI vs ET Comparison

The Compare JI / ET button plays the current interval first in just intonation, then in equal temperament, with a brief pause between. This makes the acoustic difference between the two tuning systems immediately audible — especially on intervals like the Major 3rd where the gap is largest.

Arpeggio Speed

When playing chords, the Arpeggio control staggers the notes so they sound one at a time (arpeggiated) rather than all at once. Choose Off (simultaneous), Fast, Medium, or Slow.

Snap Chime

When enabled, a brief chime sounds the moment your pitch enters the green (in-tune) zone. This gives you immediate audio confirmation without needing to watch the screen.

Fullscreen Visualization

Click the expand icon next to the visualization tabs to enter fullscreen mode. The active visualization fills your entire screen — useful for focused practice or when projecting for a group. Press the icon again or hit Escape to exit.

The Training Curriculum

The 52 exercises progress from easiest to most challenging — 13 intervals, each trained at all four sensitivity levels. The order follows the logic of how the ear develops: you start with intervals whose beats are easiest to hear (Unison, Octave, Perfect 5th), then work toward more subtle intervals.

Each exercise follows the same flow:

1. Prep countdown — a 3-2-1 countdown plays the reference tone so you hear the target before you sing
2. Singing phase — you sing while the hold bar fills; stay in the green zone continuously until it's full
3. Success — the app moves to the next exercise after 2 seconds
4. Timeout — if 45 seconds pass without success, the app analyzes your attempt and tells you specifically what went wrong

The timeout feedback is one of the most useful features. Rather than just failing, you learn whether you had no detectable pitch, were hitting the target but couldn't hold it, had an unsteady pitch, or were consistently sharp or flat by a specific amount.

Your progress is saved automatically and persists between sessions. The mastery grid shows at a glance where you've been and where you're headed.

Practical Tips

Wear headphones. Without them, the reference tone from your speakers leaks into the microphone and creates false pitch readings.

Sing a pure, open vowel. "Ah" or "oo" (as in "food") give the pitch detector the clearest signal. Avoid consonants, breathiness, and heavy vibrato while first learning.

Approach from both sides. Deliberately sing a little too high, then a little too low, and pay attention to how the beats change. They speed up in both directions and slow down as you approach center.

Trust the stillness, not the numbers. When the beats stop and the circle goes green, something in the sound changes — it opens up, it clears, it resonates. That sensation is your real goal.

The Major 3rd will feel flat at first. The just Major 3rd (5:4 ratio) sits almost 14 cents below where a piano plays it. After a lifetime of hearing piano tuning, that lower pitch will feel wrong. Listen for the beats to stop — notice how the sound fills out compared to the piano version.

Record yourself. Use the Record button during a practice session, then play it back on the tracker. You'll often spot patterns — like consistently approaching from sharp — that you can't notice in real time.