Northern Shaanxi vs Jiangnan 4-vs-4 interval statistics

Four ι™•εŒ— (Northern Shaanxi) tunes β€” δΈ‰ει‡Œι“Ί, ε±±δΈΉδΈΉεΌ€θŠ±ηΊ’θ‰³θ‰³, ε…°θŠ±θŠ±, θ„šε€«θ°ƒ β€” against four ζ±Ÿε— (Jiangnan) tunes β€” θŒ‰θŽ‰θŠ±, η΄«η«Ήθ°ƒ, ζ— ι”‘ζ™―, 牧η«₯ηŸ­η¬›. Every consecutive interval is measured in semitones; the panels below aggregate and test the two sets. (Interval stats are pitch-only.)

Headline finding

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Per-tune statistics

mean |leap| = mean absolute interval (semitones); % β‰₯ P4 = share of intervals a perfect 4th or wider (β‰₯ 5 st); % ≀ M3 = share that are 3rds or smaller steps (1–4 st); osc = chained direction-reversing wide leaps. Remainder to 100% = unisons (repeated notes).

Significance tests

Aggregate interval distribution (ι™•εŒ— vs ζ±Ÿε—)

Each bar = that interval's share of the region's intervals. The crossover is the whole story: ζ±Ÿε— peaks on 3rds (m3/M3), ι™•εŒ— peaks on 4ths/5ths (P4/P5).

Wide-leap share by tune

Mean leap vs wide-leap %

Each point is one tune. The clusters separate on the vertical axis (how often wide leaps occur), far more than on the horizontal (average leap size).

Oscillating leaps β€” the ι™•εŒ— saw-tooth

A leap up answered by a leap down (both β‰₯ P4). This chained, direction-reversing motion is the ι™•εŒ— signature and is almost absent in ζ±Ÿε—.

Interval lines on the 12-tone clock β€” 4 vs 4, pooled

Every consecutive interval drawn as a chord on the 12-tone clock (tonic C at 12 o'clock; all tunes normalized to 1 = C). Line darkness is normalized by interval count, so the two wheels compare fairly: ι™•εŒ— rides the orange 4th/5th crossings, ζ±Ÿε— the blue-green stepwise rim. Interactive play-&-trace versions live on the landing page and each melody page.

3-mer triangles β€” 4 vs 4, pooled

Every run of three consecutive notes drawn as a triangle between its pitch classes, colored by its widest interval; oscillating-leap triplets (both β‰₯ P4, direction reversed) are outlined boldly β€” 21 in ι™•εŒ— vs 2 in ζ±Ÿε—, matching the oscillation counts above.

3-mer chord histogram β€” which triangles each region rides

Each 3-mer reduced to the chord it outlines (1 = C; ⇄ = a 3-mer confined to two notes, e.g. D⇄G covers Dβ†’Gβ†’D and Dβ†’Dβ†’G). Note the near-disjoint vocabularies: ι™•εŒ— on the suspended/quartal Csus2, D⇄G, D⇄A, Gsus2; ζ±Ÿε— on the tertian Am7(no5), Em7(no5) and stepwise G⇄A. Unlike the interval distribution above, the unit here is a whole three-note window β€” it measures what the melody camps on, not single steps.