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Why does an authentic cadence sound pleasing to the ear? What makes an interval "Consonant" or "Dissonant" and why are there only two categories for intervals?

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    music.stackexchange.com/questions/4439/… may be relevant. Incidentally, although many books use phrases like "pleasing to the ear" when talking about intervals, it's probably best not to think of 'pleasing' and 'consonant' as having the same meaning; typically, a composer achieves a pleasing result through a progression of consonances and dissonances. – topo Reinstate Monica Oct 23 '18 at 16:47
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    related - music.stackexchange.com/questions/34253/… – Neil Meyer Oct 24 '18 at 11:49
  • "Consonant" means a good sound, while "dissonant" means a displeasing sound. – user53472 Feb 25 '19 at 5:15
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The notion of consonance/dissonance depends on the tradition or style used.

In European common practice perfect unions, octaves, fifths and major/minor thirds and sixths are consonant while seconds, fourths, tritones, sevenths and imperfect intervals are dissonant.

Some try to explain that arrangement acoustically by calling simpler ratios being more consonant. So an octave's ratio is 2:1 simpler and more consonant than a minor sixth with ratio 8:5.

The perfect fourth is interesting in this context, because sometimes it is considered dissonant other times consonant.

This doesn't explain the part of your question about perfect cadences. But that is a different question.

I would caution against thinking of intervals fitting into only two categories. There are several other categories/descriptors which can be reviewed here https://en.wikipedia.org/wiki/Interval_(music).

Perhaps you meant: why is there only a two-part consonant/dissonant duality? Some things can be though of in a dualistic way - light/dark, inhale/exhale, up/down, etc. - but sometimes you can or should reject dualistic thinking. There is music that doesn't work around notions of consonance/dissonance.

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Intervals aren't necessarily consonant or dissonant in themselves, it depends to an extent on where they are and what they're doing in the music.

There are not only two intervals per se. There are major, minor, augmented and diminished in most music.

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    I think his two categories are 'consonant' and 'dissonant', not major, minor, augmented... – Laurence Payne Oct 23 '18 at 17:26
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    You may well be right. To get an accurate answer, I've found one needs to ask accurate questions... – Tim Oct 23 '18 at 17:28
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It all depends on mathematical relationships. An octave is easy on the ear since it is a 2:1 relationship. A fifth likewise is an easy fraction. A third is more complex and thirds were for a long time considered dissonant. Then along came the 'consonance Angloise' and thirds became acceptable as consonances. Minor seconds have a relationship that is hard for the auditory system to analyse or relate mathematically so are heard as dissonant. It's all about the harmonic series.

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