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If augmented fifths and minor sixths are enharmonically equivalent why does johan fux in his book study of counterpoint allow minor sixths but not augmented fifths if they sound the same? How does one distinguish between the two an augmented fifth and minor sixth when composing?

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Fux does allow them in counterpoint. As I pointed out in one of my comments, confusion comes from voice-relationships:

A minor-sixth is of course allowable between two voices because it is an imperfect consonant interval.

A minor-sixth is not allowable within the same voice because it is a leap greater than a perfect-fifth and is therefore inexcusable in strict counterpoint.

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That is partially wrong because octaves and major sixths are allowed –  Chris Olszewski May 21 '13 at 0:08
    
Your reasoning of why minor sixths is not allowed is wrong –  Chris Olszewski May 21 '13 at 0:09
    
Chris - with all do respect, I have been doing counterpoint for many years, and you are just beginning. It is hard to take seriously an unsupported assertion by someone - especially one who is just learning. I submit to you to refer to pg. 37, second paragraph of the Fux: a skip of a major-sixth is prohibited in strict counterpoint. Also refer to pg. 27, the footnotes: nor intervals larger than a fifth (except...minor sixth...employed only in an upward motion.) –  jjmusicnotes May 21 '13 at 1:10
    
Sorry I jumped the gun. –  Chris Olszewski May 21 '13 at 1:29
    
JJmusicnotes is there some way I can set up some sort of correspondence with you via some other medium. As you said before, you are occasionally on this site. Again I'm sorry for previously claiming that you were wrong. I commented without due respect. You are (which I've already guessed) very experienced and an authority on this matter. –  Chris Olszewski May 21 '13 at 1:32
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