## music theory – A maths / beauty question

I am an aspiring philosopher, not qualified in mathematics. There is one question that obsesses me for some time:

The musical melody is a structure composed of a series of two types of entities: sounds and pauses. Each tone has two properties: height and duration; each break has a property – the duration. According to these properties, they can be compared. The result of a comparison can be an identity or a difference.

Hypothesis: a combination of tones and pauses gives us a feeling of beauty, others do not. Suppose that beauty is proportional to the quantity and variety of identity relations contained in the melodic structure (1).

Question: How can we determine the quantity and variety of identity relationships in a given melodic structure if we know that there is:

1. identity relationships between individual sounds and breaks;
2. identity relations between relationships. (example: A and B are different in the same way (identical) as B and C, the duration of A is half the duration of B, just as (in the same way) the duration of C corresponds to half the duration of D, etc.) (2)
3. between groups of sounds (and pauses).

And a second question: by what method can we create structures that contain a maximum and a variety of identities?

(1) On the reasons for this assumption, see https://www.researchgate.net/publication/332382681_The_Reason_as_an_ability_for_identification_and_differentiation_updated
part 3.

(2) The structure must be observed projection time. If we play the tones and pauses of a beautiful melody in a random temporal order, the beauty will be lost. These types of relationships allow us that.

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