Interval arithmetic: Difference between revisions
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* name the intervals E–G and E–B, and identify the type of chord E–G–B forms | * name the intervals E–G and E–B, and identify the type of chord E–G–B forms | ||
A consistent interval arithmetic will produce 2nds larger than 3rds, 3rds larger than 4ths, etc. For example, 7/5 is logically a 5th because it's the sum of two 3rds, 7/6 and 6/5. This makes 10/7 a 4th. But since 10/7 is larger than 7/5, the 50/49 interval between them must be a negative 2nd. Some microtonalists notate 7/5 as a 4th, avoiding negative 2nds but abandoning consistency. | A consistent interval arithmetic will produce 2nds larger than 3rds, 3rds larger than 4ths, etc. For example, 7/5 is logically a 5th because it's the sum of two 3rds, 7/6 and 6/5. This makes 10/7 a 4th. But since 10/7 is larger than 7/5, the 50/49 interval between them must be a negative 2nd. Some microtonalists notate 7/5 as a 4th, avoiding negative 2nds but abandoning consistency. Some notations allow one to rename 7/5 as a 4th via accidentals that raise/lower by a pythagorean comma, providing both freedom and consistency. | ||
== Degree vs stepspan == | == Degree vs stepspan == | ||