Subtract Ordered Pitch Positions

Supplied materials

• Paper and a pencil, typed notes or a browser scratch area. Color names can replace colored supplies; drawn figures and timelines can replace performance.
• Complete teaching inputs: In a supplied twelve-equal-step pitch-number model, pitches are 48 and 50; one number step is one semitone. What is the upward distance? Supplied candidates: (A) 1 semitone (B) 2 semitones (C) 3 semitones (D) 4 semitones.
• Independent check: In a supplied twelve-equal-step pitch-number model, pitches are 49 and 52; one number step is one semitone. What is the upward distance? Supplied candidates: (A) 2 semitones (B) 3 semitones (C) 4 semitones (D) 5 semitones.

Learn the idea

Move from labels to transformations and reasons. Calculate dotted durations, compare semitone positions, reverse an ordered movement motif and connect a fictional character’s goal and obstacle to a playable action. Supplied equal-step pitch numbers rise by one semitone per unit. Subtract the lower position from the higher to calculate their distance without confusing it with letter spelling.

Reason through the supplied case: The interval distance is the pitch-number difference: 50−48=2 semitones. This chromatic distance differs from a generic letter-name interval and says nothing about the performer’s loudness or instrument.

The numeric model describes pitch distance. It does not by itself identify a written interval’s generic number or quality, which also depend on note-letter spelling.

1. Read the complete teaching inputs and mark the feature, rule or constraint being tested.
2. Compare the model decision with one rejected candidate; state the visible evidence or calculation that distinguishes them.
3. Solve the independent check and the three changed-input practice cases before reading feedback.
4. Choose pitch positions fifty-eight and sixty-three and record their upward semitone distance.
5. Check your artifact against these explicit criteria: The difference is five and the explanation does not invent a note-name interval from numbers alone.

Check your reasoning

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Take it further

New-input analysis: In a supplied twelve-equal-step pitch-number model, pitches are 55 and 58; one number step is one semitone. What is the upward distance? Supplied candidates: (A) 2 semitones (B) 3 semitones (C) 4 semitones (D) 5 semitones. Expected relationship: 3 semitones. The interval distance is the pitch-number difference: 58−55=3 semitones. This chromatic distance differs from a generic letter-name interval and says nothing about the performer’s loudness or instrument. Create your own artifact: Choose pitch positions fifty-eight and sixty-three and record their upward semitone distance. Completion criteria: The difference is five and the explanation does not invent a note-name interval from numbers alone.

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