Who this is for
Curious learners who know intervals and wonder why they sound the way they do. No maths needed beyond counting. Already know the overtone series and equal temperament? Test out on Day 5.
Best done after: Intervals. It is advice, not a rule: every lesson has short "rusty on…?" boxes for anything you skipped.
Why learn this
Music theory can feel like a set of arbitrary rules: why a fifth, why twelve notes, why these chords. Sound gives answers. A single note contains a whole stack of higher notes, and the first few of them are an octave, a fifth, a fourth and a major third: the intervals music is built from.
This short program gives you the "why" behind the rules, and finishes with compound intervals, the bridge between simple intervals and the 9th, 11th and 13th chords.
What you will be able to do
- Frequency, pitch and the octave
- The overtone series
- Why perfect fifths and major thirds exist
- Compound intervals (9ths to 13ths)
- Equal temperament and cents
- Consonance and dissonance
The 5-day plan
- Frequency, pitch and the octave. Know that pitch is frequency and that an octave is a doubling.
- The overtone series. See where the octave, fifth, fourth and major third come from.
- Compound intervals. Name intervals bigger than an octave and reduce them to simple intervals.
- Tuning: equal temperament. Understand why the piano is tuned the way it is, and what a cent is.
- Consonance and dissonance. Explain why some intervals sound stable and others tense.
How each session works
Every day follows the shape of a workout. It starts with a warm-up that reviews earlier days, then technique: a short, plain explanation with a small interactive tool to try it on. Then come the working sets, drills with instant feedback, and a finisher, a short test with a pass mark so you only build on things you can do. A cool-down recaps the day and previews the next.
Choose your split
The daily split is a session a day: done in a week. The easy split is a session every other day, with rest days between: two weeks, and a gentler pace. On your own pace there is no schedule. Nothing is ever locked, and you can change split at any time.
What comes next
ii–V–I and Jazz Harmony: The 7-Day Program. See the whole training plan.
Frequently asked questions
What is the pitch of a note?
How high or low it sounds, set by its frequency: the number of vibrations per second (Hz). A (the A above middle C) is usually tuned to 440 Hz.
Why is an octave a doubling?
Double the frequency and the ear hears "the same note, higher". A is 220, 440, 880 Hz. That is why every octave contains the same twelve note names.
Why does the piano use equal temperament?
Pure ratios cannot all be true at once: twelve pure fifths overshoot seven octaves. Equal temperament makes every semitone the same size so all twelve keys work, at the cost of tiny impurities everywhere.
What is a cent?
One hundredth of a semitone. There are 1200 cents in an octave. A trained ear hears differences of five to ten cents.
Why are some intervals consonant?
Because their frequencies are in simple ratios (2:1, 3:2, 4:3) and their harmonics line up. The simpler the ratio, the smoother the sound.