Click or tap a spot to jump there.
Connect modules with cables and hear what comes out. To get started, listen to an example:
Or build your own: pick a module from the “Modules” list.
Calculators for the generator: work out pitches, chords, scales, rhythms, times and levels, then dial the values in there. “In the generator” names the modules and controls each tile refers to; click a name to see the module there.
Everything is computed in your browser and nothing is stored. “Randomize” supplies fresh example values. The same arithmetic without the sound — in check digits, ciphers and patterns — is in the Modulo tab.
What frequency is a note, and what note is hiding in a frequency? Useful for tuning oscillators and setting filters.
In the generator : frequency, detune · : cutoff
Spelling: C4 is middle C, accidentals as F#3 or Eb5; B is B natural, which German notation calls H. The formula: note name = MIDI mod 12, frequency = reference · 2^((MIDI − 69) / 12).
A chord built from several oscillators: gives the transposition in semitones for each, plus a hint for a wide, drifting sound.
In the generator : frequency, transpose, detune ·
The keys show two octaves from C, the root is orange. In brackets the frequency ratio to the root: the simpler it is, the calmer the interval sounds. The formula: note = (root + semitones) mod 12, frequency × 2^(semitones / 12).
Shows which notes belong to a scale. Handy for sequencer melodies that are not meant to sound off.
In the generator : root, scale, pitch per step
The twelve cells are the keys of one octave from C, the root is orange. The seven church modes share the same spacing, only started from a different degree. The formula: note = (root + sum of the intervals) mod 12.
Spreads beats as evenly as possible across a bar. Many traditional rhythms arise exactly this way – a good template for the step sequencer.
In the generator : number of steps, steps on/off
The ring starts at the top and runs clockwise. The formula: step i gets a beat when (i · beats) mod steps is smaller than the number of beats.
Converts a tempo into milliseconds, for a delay that echoes in time for instance. You can tap along to a song with “Tap”.
In the generator : BPM · : time · : frequency · : decay, release
| Note | plain | dotted | triplet | LFO |
|---|
Times in seconds, LFO in Hz (one cycle per note value). Highlighted: the sixteenth, which is one sequencer step. BPM = quarter notes per minute. The formula: quarter = 60 / BPM, dotted × 1.5, triplet × 2/3.
How much quieter is −6 dB? Converts decibels into factors and back, for volume controls, mixers and amplifiers.
In the generator : level A/B · : base level · : volume
Gain is the factor a control multiplies the signal by. The bar shows the value relative to digital full scale (0 dB); above that it clips. Rules of thumb: +6 dB ≈ twice the gain, +10 dB ≈ twice as loud to the ear. The formula: dB = 20 · log₁₀(gain) = 10 · log₁₀(power).
Modulo is the remainder of a division: 17 mod 5 = 2, because 17 = 3 · 5 + 2. That single operation is behind the check digits on books and bank transfers, old ciphers, rhythms and geometric patterns. Each tile shows one of them to try out.
Everything is computed in your browser and nothing is stored. Calculators for sound are in the Tools tab.
The remainder of a division on a clock face: count on from zero and start over at zero once you reach m. Programming languages disagree about negative numbers – here the three answers stand side by side.
The face shows the positions 0 to m−1, with zero at the top. Positive a runs clockwise, negative a backwards. The formula: a = q · m + r, and r is what we are after. The three conventions differ only in how the quotient q is rounded – towards zero, downwards, or so that r is never negative. The face only has positions from 0 upwards and therefore always shows the euclidean remainder.
The last digit of an ISBN, a barcode or an IBAN carries no information but a check: it is computed from the other digits. Mistype one and the arithmetic no longer works out.
Every method weights the digits and demands that the sum leave a particular remainder: EAN and ISBN-13 alternate between ×1 and ×3 and require remainder 0 modulo 10; ISBN-10 weights from 10 down to 1 modulo 11 (remainder 10 becomes X); Luhn doubles every second digit from the right; the IBAN travels via a number of more than twenty digits to remainder 1 modulo 97. That is how transposed neighboring digits and single typos give themselves away. Try it with the ISBN on the back of a book, the barcode on a package or your own IBAN – everything is computed in the browser, nothing leaves your device. The reverse does not hold: a well-formed number is not a real one. Luhn also checks card numbers, but says nothing about whether the card exists; the payment providers’ well-known test numbers such as 4242 4242 4242 4242 pass the arithmetic and belong to no account.
The two oldest ciphers in the history of writing, both nothing but an addition modulo 26: letter plus key, and when it runs off the end past Z you start again at A.
Every letter becomes a number: A = 0 up to Z = 25. The formula: new = (old + key) mod 26, and minus instead of plus to decipher. Caesar shifts every letter by the same amount; at 13 that is ROT13, which undoes itself. Vigenère takes a keyword and uses its letters in turn as the shift — so the same plain letter becomes a different cipher letter depending on where it sits. Neither is anywhere near secure any more: Caesar has only 25 possibilities, all of which can be tried, and with Vigenère the length of the key gives itself away through repeating patterns in the text. Digits, accented letters and punctuation are left as they are.
Two voices tapping at different spacings. Each one lands when the step is divisible by its cycle length – that is, when the remainder is 0. Together they only meet again after the least common multiple.
Voice A in orange above, voice B in turquoise below, outlined are the steps where both land at once. The formula: A strikes when step mod a = 0, B likewise at step mod b = 0. Both at once holds exactly when the step is a multiple of both lengths – for the first time after lcm(a, b) = a · b / gcd(a, b). If a and b share no divisor that takes a · b steps and the pattern sounds at its most interlocked; if they share a lot they meet early and it sounds orderly. The best-known example is 3 against 2, the hemiola.
The humble times table, arranged in a circle: n points, and from each one a line to its k-fold. Because the first point follows the last, nothing but straight lines produces curved figures.
The points are numbered from 0 clockwise, starting at the top. The formula: point i is joined to point (k · i) mod n. The curve that emerges from the chords is an epicycloid with k−1 cusps: at k = 2 the cardioid, the same heart shape that appears as a bright arc in a coffee cup, at k = 3 the two-cusped nephroid. Whether every point is hit exactly once depends on the greatest common divisor of k and n – if it is 1, multiplying merely reorders the points, otherwise gaps remain.
In Pascal’s triangle every number is the sum of the two above it. Color not the numbers themselves but only their remainders, and a pattern emerges that the numbers alone do not reveal.
The arithmetic is the same as in the familiar triangle, except that after every addition only the remainder is kept: cell = (cell above left + cell above right) mod m. That is allowed because remainders add just like the numbers themselves – so the enormous binomial coefficients never have to be worked out. At m = 2 remainder 0 simply means “even”, and the odd cells form the Sierpiński triangle: the same pattern repeats at half the size, and again within that. It looks the way it does because of Lucas’s theorem, by which the remainder can be read off the digits of row and column in base m. That only holds when m is prime – at 4, 6 or 12 the pattern visibly falls out of step.
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