harmonic series - 2026 ACF Regionals

Question

Answer the following about the intersection of mathematics and 20th-century music theory, for 10 points each.

[10e] Microtonal composer Harry Partch developed extended tuning systems using this series, which can be used to explain consonance. This divergent series consists of integer multiples of a fundamental frequency.

ANSWER: harmonic series [or overtone series]

[10h] David Lewin proved that two sets with identical examples of this object, called homometric, can be otherwise entirely unrelated. This mathematical object represents the intervals contained in a set of pitch classes.

ANSWER: interval vector [or interval-class vector or absolute pitch-class interval vector; accept APIC vector]

[10m] Students learning serialist composition create matrices in which transposition, retrograde, and this operation have been applied to tone rows. This operation names chord voicings denoted by figured bass symbols like “6 4.”

ANSWER: inversion [or word forms like inverted]

<DM, Classical Music>

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Summary


California (North)	Main Site	Y	3	16.67	67%	100%	0%
California (South)	Main Site	Y	4	17.50	100%	75%	0%
Canada	Main Site	Y	11	13.64	73%	64%	0%
Florida	Main Site	Y	3	16.67	100%	67%	0%
Great Lakes	Main Site	Y	5	16.00	80%	80%	0%
Lower Mid-Atlantic	Main Site	Y	8	10.00	63%	38%	0%
Midwest	Main Site	Y	8	17.50	88%	88%	0%
Northeast	Main Site	Y	5	14.00	80%	60%	0%
Overflow	Main Site	Y	3	16.67	67%	100%	0%
South Central	Main Site	Y	2	5.00	50%	0%	0%
Southeast	Main Site	Y	7	11.43	86%	29%	0%
UK	Main Site	Y	6	15.00	83%	67%	0%
Upper Mid-Atlantic	Main Site	Y	9	14.44	78%	67%	0%
Upstate NY	Main Site	Y	3	10.00	67%	33%	0%

Data


Berkeley A	Berkeley B	10	10	20
Berkeley C	Berkeley D	10	10	20
Stanford A	Stanford B	0	10	10
Arizona State	UCLA B	10	0	10
UCSD B	UCSD A	10	10	20
McGill B	Brock	10	10	20
Toronto E	Guelph	0	0	0
McGill A	Waterloo B	10	10	20
McMaster A	Queen's	10	10	20
Toronto B	Ottawa	10	10	20
Simon Fraser	Toronto C	10	0	10
Toronto Metropolitan	Toronto D	0	0	0
Toronto F	McMaster B	10	10	20
Waterloo A	UBC A	10	10	20
UBC B	Carleton University	10	10	20
Western C	Toronto G	0	0	0
UCSD C	UC Santa Barbara	10	10	20
Central Florida B	Florida C	10	0	10
Florida A	Central Florida A	10	10	20
Central Florida C	Florida B	10	10	20
UCLA A	UC Irvine	10	10	20
Michigan A	Ohio State B	10	10	20
Michigan State	Michigan B	10	10	20
Michigan C	CWRU A	10	10	20
Ohio State A	Ohio State C	10	10	20
CWRU B	Pittsburgh	0	0	0
Virginia Tech A	North Carolina C	10	10	20
North Carolina B	Liberty A	10	0	10
Liberty B	NC State A	0	0	0
Duke	North Carolina A	10	10	20
William and Mary	VCU	0	0	0
James Madison B	South Carolina B	0	0	0
Illinois A	Chicago B	10	10	20
Chicago A	Chicago E	10	10	20
Illinois C	Indiana C	10	10	20
Northwestern B	Indiana B	10	10	20
Notre Dame A	Northwestern C	10	10	20
Northwestern D	Chicago D	0	0	0
Purdue A	Notre Dame B	10	10	20
Purdue B	Chicago C	10	10	20
Brandeis A	Dartmouth A	0	0	0
Harvard B	Brandeis B	10	0	10
Brown	Dartmouth B	10	10	20
Harvard A	Southern Connecticut State	10	10	20
MIT	Yale	10	10	20
South Carolina A	Virginia Tech B	10	0	10
Carleton College	Missouri B	0	10	10
Georgia Tech A	Minnesota A	10	10	20
Washington B	Claremont	10	10	20
Murray State A	Texas A&M A	0	0	0
Texas B	Texas A	10	0	10
WashU A	Bruin	10	0	10
Georgia Tech B	Georgia Tech C	10	0	10
Alabama A	Louisville B	10	0	10
Mississipi State	Alabama B	10	0	10
Georgia Tech D	Tennessee A	0	10	10
Louisville A	Vanderbilt B	10	0	10
Kentucky	WashU B	10	10	20
Virginia	James Madison A	10	10	20
Cambridge B	City St. George's	0	10	10
Bristol	Edinburgh B	10	10	20
Oxford A	Imperial C	10	10	20
Durham	Oxford B	10	0	10
UCL	Imperial A	10	10	20
Catholic	Maryland B	0	0	0
Rutgers B	Columbia C	10	10	20
Georgetown	Swarthmore	0	10	10
Johns Hopkins B	John Jay	10	0	10
Columbia A	Johns Hopkins A	10	10	20
Maryland A	NYU A	10	0	10
Columbia B	NYU B	10	10	20
Rutgers A	Maryland C	10	10	20
Vassar	NYU C	10	10	20
Cambridge C	LSE	10	0	10
Cornell A	Cornell B	10	0	10
Cornell C	Rochester	0	0	0
Penn State	RIT	10	10	20