Random Tuning System Comparison Set Generator

Description

Sample supplied rational intervals and matched 12-TET steps into frequency and cents comparisons at an explicit reference frequency.

A musical fixture expresses pitch or timing through explicit numeric conventions such as MIDI numbers, semitone intervals, beats, and durations. A reproducible symbolic sequence is separate from a performed sound or a judgment of musical quality.

Sample supplied rational intervals and matched 12-TET steps into frequency and cents comparisons at an explicit reference frequency.

When to use this tool

Use this generator to create reproducible tuning system comparison set cases from the supplied model or bank. Inspect the returned evidence before using cases in a test or exercise.

How to use the tool and how it works

Supply count, intervals, referenceHertz in the field shapes below. Set seed when you need an explicit replay.
Run the tool and correct any input error. For generated controls, distinguish a successful fixture containing an invalid case from failure to generate the fixture.
Read referenceHertz, comparisons. Use the conventions below and keep answer-bearing fields separate when presenting an exercise.

Preflight all distinct supplied rational intervals, compare each numerator/denominator ratio with its matched 12-TET semitone ratio at referenceHertz, and calculate frequencies and signed just-minus-equal cents differences. Draw comparison records with replacement.^[1]

Delegated operations used for this result: just intonation ratio to cents; equal temperament ratio from semitones. Their calculation or parsing conventions apply to the corresponding result fields.^{[2, 3]}

Input field	Meaning and units	Accepted input
count	Requested count; the mechanics explain whether one draw expands into several returned records.	Required. Safe integer; minimum 1; maximum 128.
intervals	Intervals	Required. Array of Object; no unknown keys.; minimum items 1; maximum items 64.
intervals[].id	Literal identifier used to match records, independently of their display labels.	Required. Text; minimum UTF-16 length 1; maximum UTF-16 length 64.
intervals[].numerator	Numerator	Required. Safe integer; minimum 1.
intervals[].denominator	Denominator	Required. Safe integer; minimum 1.
intervals[].matchedSemitones	Matched Semitones	Required. Finite number.
referenceHertz	Reference Hertz	Required. Finite number; strictly above 0.
seed	Optional numeric seed; takes precedence over context randomness. Without either, use the fixed tool.io default seed.	Optional. Safe integer.

Output field	Interpretation	Returned shape
referenceHertz	Reference Hertz	Required. Finite number; strictly above 0.
comparisons	Comparisons	Required. Array of Object; no unknown keys.; minimum items 1; maximum items 128.
comparisons[].intervalId	Interval Id	Required. Text.
comparisons[].numerator	Numerator	Required. Safe integer.
comparisons[].denominator	Denominator	Required. Safe integer.
comparisons[].matchedSemitones	Matched Semitones	Required. Finite number.
comparisons[].justRatio	Just Ratio	Required. Finite number; strictly above 0.
comparisons[].equalRatio	Equal Ratio	Required. Finite number; strictly above 0.
comparisons[].justHertz	Just Hertz	Required. Finite number; strictly above 0.
comparisons[].equalHertz	Equal Hertz	Required. Finite number; strictly above 0.
comparisons[].justCents	Just Cents	Required. Finite number.
comparisons[].equalCents	Equal Cents	Required. Finite number.
comparisons[].differenceCents	Difference Cents	Required. Finite number.
randomness	Replay metadata: source is seed or context; seed is the normalized 32-bit seed or null for a context source.	Required. Object; no unknown keys.
randomness.seed	Optional numeric replay seed; normalization and precedence are explained below.	Required. Safe integer. or Null.
randomness.source	Source	Required. Text; one of "context", "seed".

An explicit safe-integer seed takes precedence over injected context randomness and is normalized to an unsigned 32-bit integer. With no seed and no context source, replay uses the fixed tool.io default seed. A context source must return finite values from zero inclusive to one exclusive; its advancing state must be retained separately. randomness records the source and normalized seed, or null for context. These generators are not cryptographic random sources.

json

{
  "input": {
    "count": 2,
    "intervals": [
      {
        "id": "fifth",
        "numerator": 3,
        "denominator": 2,
        "matchedSemitones": 7
      },
      {
        "id": "major-third",
        "numerator": 5,
        "denominator": 4,
        "matchedSemitones": 4
      }
    ],
    "referenceHertz": 440,
    "seed": 42
  },
  "output": {
    "referenceHertz": 440,
    "comparisons": [
      {
        "intervalId": "major-third",
        "numerator": 5,
        "denominator": 4,
        "matchedSemitones": 4,
        "justRatio": 1.25,
        "equalRatio": 1.2599210498948732,
        "justHertz": 550,
        "equalHertz": 554.3652619537442,
        "justCents": 386.3137138648348,
        "equalCents": 399.9999999999997,
        "differenceCents": -13.686286135165112
      },
      {
        "intervalId": "fifth",
        "numerator": 3,
        "denominator": 2,
        "matchedSemitones": 7,
        "justRatio": 1.5,
        "equalRatio": 1.4983070768766815,
        "justHertz": 660,
        "equalHertz": 659.2551138257398,
        "justCents": 701.9550008653874,
        "equalCents": 700,
        "differenceCents": 1.9550008653876136
      }
    ],
    "randomness": {
      "seed": 42,
      "source": "seed"
    }
  }
}

Limitations and assumptions

The interval correspondence is caller-supplied and frequencies must remain positive and finite. This is a tuning comparison rather than a claim that one tuning is perceptually or musically optimal.
A replay requires the same complete input and implementation. Randomized construction does not guarantee uniform coverage of every feasible output; finite samples can repeat unless a distinct-selection rule is explicitly stated.
The field tables state structural bounds; cross-field constraints and bounded search or output budgets also apply. Unknown keys are rejected where the object contract disallows them. Input errors are distinct from null fields and deliberate invalid controls in a successful output.

Alternative or Complementary methods

For a supplied example, inspect the returned construction or delegated check directly. To evaluate a consumer, also test cases chosen for its own boundaries; a generated finite corpus does not establish exhaustive coverage.

References

Tool behavior and example: Random Tuning System Comparison Set Generator — tool.io
Calculation or validation: music/just-intonation-ratio-to-cents — tool.io
Calculation or validation: music/equal-temperament-ratio-from-semitones — tool.io

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