Rhythm Grid Rotation Canonicalizer
Canonicalize a rhythm step mask by lexicographic cyclic rotation and retain every tied rotation offset.
Description
Canonicalize a rhythm step mask by lexicographic cyclic rotation and retain every tied rotation offset.
A cyclic rhythm can have several start positions yielding the same minimal bit spelling.
When to use this tool
Canonicalize a rhythm step mask by lexicographic cyclic rotation and retain every tied rotation offset.
- Prepare the supplied bits fields for this operation.
- Compare the complete example with the representation used by your own input before carrying the result into another step.
How to use the tool and how it works
- Enter bits. Use the exact text syntax, units and index conventions explained below.
- Run the tool. If input validation fails, correct the supplied fields before interpreting any result.
- Read result.canonical, result.offsets. Interpret false, null and empty lists using the distinctions below; they can be valid outputs.
Generate all left rotations of bits, choose the lexicographically smallest and return every offset producing it.1
| Input field | Meaning and representation | Accepted input |
|---|---|---|
| bits | bits. | Binary text containing only 0 and 1; at most 128 characters |
| Output field | Interpretation |
|---|---|
| result | Object containing the named outputs below. |
| result.canonical | The canonical value under the stated formula or text convention. |
| result.offsets | The offsets list in the ordering and representation described above. |
{
"input": {
"bits": "1010"
},
"output": {
"result": {
"canonical": "0101",
"offsets": [
1,
3
]
}
}
}Limitations and assumptions
- Leading zeros are meaningful. Empty input has one empty rotation at offset zero, and no reflection is included.
- Every declared top-level field is required and unexpected fields are rejected. Numeric inputs must be finite; ordinary text fields are bounded to 8,192 UTF-16 code units, with tighter operation-specific limits where stated.
- Lists are limited to 128 entries. JSON text must meet bounded size and depth checks, and numeric outputs beyond the safe finite magnitude are rejected. Exact large integers use decimal strings.
- Indexes are zero-based and spans have an exclusive end unless explicitly stated otherwise. A valid false, null or empty-list result is distinct from malformed input.
Alternative or Complementary methods
Retain the tick unit, channel numbering and event-pairing policy with the result. Use a MIDI-file parser or audio analysis when the task requires actual messages, playback behavior or recorded sound.
References
Similar or alternative tools
- Rhythm Grid Binary Decoder
Decode a binary rhythm step mask into onset indexes and explicit grid size.
- Rhythm Grid Binary Encoder
Encode bounded rhythm onset positions as a step mask, explicitly coalescing repeated onsets.