Ear trainer: higher or lower?

How this measures

The question

Two sounds, one after the other. The second is higher or lower than the first by the difference of that question. Which way it goes is picked at random each time, in your browser, so there is no pattern to learn. The first sound moves to a new pitch for every question, so you cannot learn one note.

The staircase

The first question is 100 cents apart: one semitone. After two right answers in a row the difference gets smaller. After one wrong answer it gets larger. At first each step halves or doubles the difference. From the second change of direction on, each step is one and a half times. The difference stays between 1 and 400 cents.

The number

A change of direction is a question where the run turns from getting harder to getting easier, or back. A run has 40 questions. The result is the average of the differences at the changes of direction, leaving out the first two (a geometric mean, the usual average for ratios; one more is left out if the count is odd). It needs 4 of them; with fewer, the page gives no exact number. A run with this rule settles near the difference you get right about 7 times in 10.

How repeatable it is

A run is short, so the number moves from run to run. In our simulation of a listener whose true value does not change, 8 runs in 10 landed between 0.51 and 1.58 times that value. That is where the range beside your result comes from: it runs from 0.63 to 1.96 times the result. Read one run as a rough reading, and the middle one of three runs as a better one. The simulated listener is a model; real ears tire and learn during a run.

Short runs and guessing

A run stopped before question 30 gives no number: in our simulation a run of 20 questions read about 1.2 times the true value. A run stopped from question 30 on gets a wider range, 0.55 to 1.96 times the result. When 6 answers in 10 or fewer were right, the page says that the answers were close to guessing and does not call the number reliable. Guessing gets about half right, and in our simulation this marked 9 in 10 of the guessed runs that gave a number. When you were right at 1 cent 8 times or more and wrong there at most once, and the run has too few changes of direction for an average, the result is given as 1 cent or less.

The sounds

Pure tone is a single sine wave made in your browser: 0.5 s long, fading in and out over 20 ms. Piano, guitar and flute are recordings of real instruments, one note for each range, loaded from this site when you choose them; each sound lasts 0.7 s. Both sounds of a question are the same recording played at two speeds, and the speed ratio sets the difference exactly. The two sounds are played at the same level, with 0.3 s of silence between them, and each starts and ends at silence, so there is no click.

Where the first sound falls

Pure tone: anywhere in the chosen range, Low 130 to 260 Hz, Middle 330 to 660 Hz, High 1000 to 2000 Hz. Instruments: up to 3 semitones above or below the recorded note. Piano: C3, A4, C6. Guitar: A2, C4, E5. Flute, played without vibrato: E4, D5, D6. Each new first sound is at least 2 semitones away from the one before.

Pure tone and instruments

A result taken with an instrument and a result taken with the pure tone are not the same number. A pure tone has one frequency. A note of an instrument has many at once: the note itself and its overtones, at about 2, 3, 4 and more times its frequency. A change of pitch moves every overtone with it, so the ear has more to compare. Playing a recording faster also makes the note die away a little sooner. Compare a result only with results taken with the same sound and range.

Cents

A cent is one hundredth of a semitone, and 1200 cents make an octave. The second sound’s frequency is the first one’s multiplied by 2 to the power of (cents / 1200). At 440 Hz, 10 cents is about 2.5 Hz.

Limits of your device

A phone speaker or small earbuds play low sounds weakly and can add a buzz of their own, and a noisy room hides small differences. Headphones or good speakers in a quiet room give a fairer reading. Sound clock on this device: read when the sound starts.

The recordings

The piano, guitar and flute notes come from the University of Iowa Musical Instrument Samples (the link opens in a new tab), created by Lawrence Fritts, Director of the Electronic Music Studios at the University of Iowa. That site says the recordings may be downloaded and used for any projects, without restrictions. For this page each note was cut to 1.1 s, mixed to one channel where the source has two, cleared of low rumble and set to one level. The list of files and what was done to each: /snd/SOURCES.txt.

Privacy

The pure tone is made in your browser. The instrument notes are sound files from this site, loaded when you choose that instrument; our server logs that request like any other (privacy notice). Your answers and your result are not sent anywhere or stored. The run is gone when you leave or reload the page.