Build a Scale from Supplied Offsets

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: Supplied major-scale semitone pattern from root 48 has offsets 0,2,4,5,7,9,11,12. Fill the missing pitch-number in [48, 50, 52, '?', 55, 57, 59, 60]. Supplied candidates: (A) 52 pitch-number (B) 53 pitch-number (C) 54 pitch-number (D) 55 pitch-number.
• Independent check: Supplied major-scale semitone pattern from root 49 has offsets 0,2,4,5,7,9,11,12. Fill the missing pitch-number in [49, 51, 53, 54, '?', 58, 60, 61]. Supplied candidates: (A) 55 pitch-number (B) 56 pitch-number (C) 57 pitch-number (D) 58 pitch-number.

Learn the idea

Inspect the relationships underlying a score. Group eighth-note subdivisions, construct the supplied major-scale pattern, apply a declared tonal return and schedule a delayed movement motif with complete duration accounting. The supplied Western major-scale pattern uses semitone offsets zero, two, four, five, seven, nine, eleven and twelve from the tonic. Add each offset to construct the numeric pitch collection.

Reason through the supplied case: The missing position uses offset 5 from the supplied pattern. Add it to root 48 to obtain 53. This models one Western major scale; other traditions can organize pitch differently.

Numeric pitch construction does not automatically determine correct letter spelling or a performed scale. This lesson establishes the supplied equal-tempered pattern; other musical systems have different frameworks.

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. Build a numeric major scale from root sixty and annotate the two one-semitone neighboring gaps.
5. Check your artifact against these explicit criteria: The offsets are applied consistently, and the gaps between degrees three/four and seven/eight are one semitone.

Check your reasoning

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Take it further

New-input analysis: Supplied major-scale semitone pattern from root 55 has offsets 0,2,4,5,7,9,11,12. Fill the missing pitch-number in [55, 57, 59, 60, 62, 64, '?', 67]. Supplied candidates: (A) 65 pitch-number (B) 66 pitch-number (C) 67 pitch-number (D) 68 pitch-number. Expected relationship: 66 pitch-number. The missing position uses offset 11 from the supplied pattern. Add it to root 55 to obtain 66. This models one Western major scale; other traditions can organize pitch differently. Create your own artifact: Build a numeric major scale from root sixty and annotate the two one-semitone neighboring gaps. Completion criteria: The offsets are applied consistently, and the gaps between degrees three/four and seven/eight are one semitone.

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