Interval arithmetic

Interval arithmetic systems refer to sets of rules regarding the names and qualities of stacked intervals.

Diatonic interval arithmetic

Diatonic interval arithmetic is a set of rules governing diatonic notation systems, which says that the degrees of stacked intervals should always follow arithmetic if 1 is subtracted from all degree numbers. For example, a stack of two thirds is always a fifth, since (3-1)+(3-1)=(5-1).

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	d2	m2	M2	A2	d3	m3	M3	A3	d4	P4	A4	d5	P5	A5	d6	m6	M6	A6	d7	m7	M7	A7
d2	ddd3	dd3	d3	m3	ddd4	dd4	d4	P4
m2	dd3	d3	m3	M3	dd4	d4	P4	A4
M2	d3	m3	M3	A3	d4	P4	A4	AA4
A2	m3	M3	A3	AA3	P4	A4	AA4	AAA4
d3	ddd4	dd4	d4	P4	ddd5	dd5	d5	P5
m3	dd4	d4	P4	A4	dd5	d5	P5	A5
M3	d4	P4	A4	AA4	d5	P5	A5	AA5
A3	P4	A4	AA4	AAA4	P5	A5	AA5	AAA5
d4
P4
A4
d5
P5
A5
d6
m6
M6
A6
d7
m7
M7
A7