Semitone/Cents Ratio ↔ Playback Speed (Pitch/Time) Calculator

Inspectable records

Ledger state

The current ledger marks this instrument verified clean within the source-bound verification corpus.

Area

Audio, Music, Photography & Color

Tranche

tranche-5

Evidence ID

t5-124

Ledger rows

1

No ledger note is attached.

Review findings

The core semitone-to-speed formula is standard and correct, but the catalog entry is incomplete for its stated semitone/cents and bidirectional functionality. Add explicit cents and inverse formulas, define the speed-percentage convention, and enforce speedRatio>0. The honest-label limitation to simple speed-based pitch shifting is appropriate.

Formula and scope findings

• speedRatio=2^(semitones/12) is correct for equal-tempered, speed-based pitch shifting when semitones are measured relative to the source.
• The stated formula does not directly support cents, despite the instrument name and description. Cents require speedRatio=2^(cents/1200), or semitones=cents/100 before applying the stated formula.
• The vice-versa calculation is not specified. For a positive speed ratio, the inverse is semitones=12*log2(speedRatio) and cents=1200*log2(speedRatio).
• Resulting BPM requires the additional formula resultingBPM=sourceBPM*speedRatio, which is not stated.
• The input specification says semitone shift or speed percentage but does not explicitly define cents as an accepted input.

Unit assumptions

• One octave equals 12 equal-tempered semitones and 1200 cents.
• A speed percentage is interpreted as percentage change from nominal speed: speedRatio=1+speedPercentage/100. Thus +100% means 2.0x speed, while 150% absolute speed would also mean 1.5x but is a different convention.
• Source BPM is in beats per minute and resulting BPM is sourceBPM multiplied by the speed ratio.
• The formula models turntable, tape, or other speed-based pitch shifting, not independent time-stretching.
• Logarithms in inverse formulas are base 2.

Boundary hardening

BREAK_CLAIMED · SELF_FLAGGED

A speed input of -100% produces speedRatio = 0, making the inverse logarithm undefined. The instrument must reject this input or explicitly report an undefined semitone shift.

Errata and corrections

No applied erratum is attached to this unique-name record.

Inspectable example

4 review vectors are recorded. One source-bound sample is shown below.

{
  "inputs": {
    "semitone_shift": 0,
    "source_bpm": 120
  },
  "expected_outputs": {
    "speed_ratio": 1,
    "speed_percentage": 0,
    "resulting_bpm": 120
  },
  "working": "speedRatio=2^(0/12)=2^0=1. speedPercentage=(1-1)*100=0%. resultingBPM=120*1=120 BPM."
}

Related workflows

No source-defined multi-instrument workflow membership is recorded.

Sources and evidence

These pointers bind the page to evidence. They do not grant authority or collapse verification into deployment.

• VERIFIED_LEDGER.json · VERIFIED_CLEAN
• evidence-tranche5/tranche5-results.json
• BOUNDARY_HAZARD_CATALOG.json