User:Grady/Harmonic similarity: Difference between revisions

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As an important note, the concept of [[interval class]] is usually defined to refer to undirected interval class: for example, a major third and minor sixth would be considered the same interval class due to being octave complements. However, this theory requires establishing the concept of directed interval class, in which octave complements are separate classes. In order for this to work, we need to define intervals as being directed in general; in other words, that an upward major third and a downward major third be considered two separate intervals. The downward major third falls into the same directed interval class as the upward minor sixth, but the upward major third does not. If the upward major third can be thought of as the ratio 5/4, then the downward major third can be thought of as 4/5. In the absence of a specifier for upward or downward direction, it should be assumed that an interval points in the upward direction.

The theory of harmonic similarity provides credence to the idea that various intervals with the same interval quality specifier (e.g. major, minor, perfect, neutral, etc.) should actually sound similar in emotional character, since those interval classes are near each other on an interval-based circle or chain of fifths. In other words, just as the notes C4 and G4 sound related to each other since C4 relates to G5 by a tritave, and G5 relates to G4 by an octave, a [[5/4|major third]] and [[15/8|major seventh]] should be expected to sound similar in character to each other since the major third relates to the [[15/4|major fourteenth]] by a tritave, and the major fourteenth relates to the major seventh by an octave.

Revision as of 10:47, 4 August 2025 view source Grady (talk \| contribs) 55 edits →Other implications: Added interval quality section Tag: Visual edit ← Older edit		Revision as of 10:56, 4 August 2025 view source Grady (talk \| contribs) 55 edits →Interval quality: Added more info Tag: Visual edit Newer edit →
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	As an important note, the concept of [[interval class]] is usually defined to refer to undirected interval class: for example, a major third and minor sixth would be considered the same interval class due to being octave complements. However, this theory requires establishing the concept of directed interval class, in which octave complements are separate classes. In order for this to work, we need to define intervals as being directed in general; in other words, that an upward major third and a downward major third be considered two separate intervals. The downward major third falls into the same directed interval class as the upward minor sixth, but the upward major third does not. If the upward major third can be thought of as the ratio 5/4, then the downward major third can be thought of as 4/5. In the absence of a specifier for upward or downward direction, it should be assumed that an interval points in the upward direction.		As an important note, the concept of [[interval class]] is usually defined to refer to undirected interval class: for example, a major third and minor sixth would be considered the same interval class due to being octave complements. However, this theory requires establishing the concept of directed interval class, in which octave complements are separate classes. In order for this to work, we need to define intervals as being directed in general; in other words, that an upward major third and a downward major third be considered two separate intervals. The downward major third falls into the same directed interval class as the upward minor sixth, but the upward major third does not. If the upward major third can be thought of as the ratio 5/4, then the downward major third can be thought of as 4/5. In the absence of a specifier for upward or downward direction, it should be assumed that an interval points in the upward direction.

			The theory of harmonic similarity provides credence to the idea that various intervals with the same interval quality specifier (e.g. major, minor, perfect, neutral, etc.) should actually sound similar in emotional character, since those interval classes are near each other on an interval-based circle or chain of fifths. In other words, just as the notes C4 and G4 sound related to each other since C4 relates to G5 by a tritave, and G5 relates to G4 by an octave, a [[5/4\|major third]] and [[15/8\|major seventh]] should be expected to sound similar in character to each other since the major third relates to the [[15/4\|major fourteenth]] by a tritave, and the major fourteenth relates to the major seventh by an octave.