Is this Pitch-Class Set Calculator U.S.-focused?

Yes. U.S. units, terminology and rules are the primary defaults where location matters.

Pitch Class Set Calculator: Formula, Steps & Results

United States calculator

Analyze a pitch-class set, prime form and interval vector

Analyze a pitch-class set using modulo-12 arithmetic to find unique pitch classes, normal order, transposed form, inversion, prime form and interval-class vector.

Normal order • inversion • interval classes

Calculator inputs

Pitch classes (0–11)Display notation

Pitch-Class Set Calculator results

How this Pitch-Class Set Calculator works

The set is deduplicated modulo 12. Rotations are compared by compact span and left packing to obtain a normal order. The original and inverted normal forms are transposed to zero and compared for prime form.

Important: Set-theory conventions can differ in edge-case tie breaking. This calculator uses a transparent compact-span and lexicographic comparison method.

What assumptions should I verify?

In the Pitch-Class Set Calculator, this guidance applies to Pitch classes (0–11) and Display notation and the reported +a.map(r.show).join(, Unique set, and Normal order. The `pitch-class-set` workflow evaluates Ic = min(d,12-d) in the stated canonical units; verify the stated assumptions, domain limits and any professional requirements that apply. Verification context: abd681.

Is information sent anywhere?

No—the Pitch-Class Set Calculator does not infer conditions beyond Ic = min(d,12-d). It reports +a.map(r.show).join(, Unique set, and Normal order from the entered Pitch classes (0–11) and Display notation; verify the stated assumptions, domain limits and any professional requirements that apply.

Pitch-Class Set Calculator: formula-based step-by-step solution

This Pitch-Class Set Calculator worked derivation uses the published default state. Its live formula panel replaces these values whenever an input, unit, mode, date, material, or scenario changes.

Governing formula or algorithm — exact production relationships:

Ic = min(d,12-d)
D = (set[j]-set[i]+12)%12
J = i+1
No = normal(set)
Trans = zero(no)
Inv = zero(normal(invSet))
Prime = lex(trans,inv)<=0?trans:inv

1. Governing formulas and numeric substitution

Formula 1: Ic = min(d,12-d)
Default-value substitution: Ic = min(d,12-d) | current data: Pitch classes (0–11)=0,1,4,7 0–11; Display notation=numbers
Formula 2: D = (set[j]-set[i]+12)%12
Default-value substitution: D = (set[j]-set[i]+12)%12 | current data: Pitch classes (0–11)=0,1,4,7 0–11; Display notation=numbers
Formula 3: J = i+1
Default-value substitution: J = i+1 | current data: Pitch classes (0–11)=0,1,4,7 0–11; Display notation=numbers
Formula 4: No = normal(set)
Default-value substitution: No = normal(set) | current data: Pitch classes (0–11)=0,1,4,7 0–11; Display notation=numbers
Formula 5: Trans = zero(no)
Default-value substitution: Trans = zero(no) | current data: Pitch classes (0–11)=0,1,4,7 0–11; Display notation=numbers
Formula 6: Inv = zero(normal(invSet))
Default-value substitution: Inv = zero(normal(invSet)) | current data: Pitch classes (0–11)=0,1,4,7 0–11; Display notation=numbers
Formula 7: Prime = lex(trans,inv)<=0?trans:inv
Default-value substitution: Prime = lex(trans,inv)<=0?trans:inv | current data: Pitch classes (0–11)=0,1,4,7 0–11; Display notation=numbers

2. Variables and measurement units used

Pitch classes (0–11) = 0,1,4,7 0–11
Display notation = numbers

3. Pitch-Class Set Calculator final evaluation: this calculator’s production engine evaluates the substituted relationship with unrounded internal precision; its subject-specific result cards, table, and visual report the rounded final answer and verification quantities.

Formula-based calculator guide

Pitch Class Set Calculator: formula, steps, units and verification

pitch class set calculator is designed for a transparent calculation rather than a black-box answer. Pitch Class Set Calculator: calculate pitch class set with task-specific inputs, transparent formulas, intermediate steps, unit checks, validation.

How to use the pitch class set calculator in 5 steps

Choose the required mode. Select the calculation path that matches the quantity you know and the result you need.
Enter source values. Use measured, documented or assignment values rather than rounded estimates whenever possible.
Confirm every unit. The pitch class set calculator converts supported units before formula substitution, so each selector must describe the entered number.
Run the calculation. Review the displayed formula, normalized values and numeric substitution before accepting the final result.
Verify the answer. Reproduce the substitution manually and check whether the output is reasonable for the stated assumptions.

Pitch Class Set Calculator formula and unit checks

The pitch class set calculator keeps source inputs, canonical calculation units and displayed output units separate. This prevents a correct formula from producing a wrong answer because feet were treated as meters, percentages as decimals, or time values as the wrong interval.

For an independent check, copy the formula shown by the calculator, substitute the unrounded canonical values, preserve full precision through intermediate operations and round only the final result. The verified answer should match both the displayed number and its measurement unit.

How to interpret the pitch class set calculator result

A result is useful only when its assumptions match the real problem. Compare the answer with expected ranges, inspect any warning or boundary message, and test a nearby input to confirm that the output changes in the direction predicted by the governing relationship.

The pitch class set calculator provides an educational and planning result. For regulated, medical, structural, financial, laboratory or safety-critical decisions, verify the inputs and method against the applicable professional requirements before acting.

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Pitch Class Set Calculator quick verification checklist

Before saving or reporting a result from the pitch class set calculator, confirm the input source, unit selections, formula mode, intermediate substitution, final unit and rounding rule. These checks make the calculation reproducible and easier to audit.

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