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Page 106 from the book

This is from page 106 of The Complete Elementary Music Rudiments, 2nd Edition by Mark Sarnecki. It is in the section about enharmonic intervals

The question is asking for the interval from A# to E# (a perfect 5th), after the A# is changed enharmonically. The only notes enharmonic to A# are Bb and Cbb, and they would result in a double-augmented-4th or a triple-augmented-3rd, which aren't really proper intervals and were never mentioned in the book.

Is this a publication error? Or am I missing something?

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This would be a doubly augmented fourth. They're very rare, but we do encounter them.

It's hard to know if this is an error in publication or an error in writing the textbook itself. (In my opinion, a textbook should discuss doubly augmented and diminished intervals.)

The good news is that, based on this question, you seem completely solid with intervals. Only people that really know them inside and out could spot this as a doubly augmented fourth. Good work!

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  • Richard, did you mean "...textbook should not...? – Michael Curtis Jul 24 at 20:10
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    I didn't! (Perhaps I'm in the minority here...) I think a textbook should discuss them. Not while just introducing intervals, of course, but I think a good textbook would show at least one example, at the end of the chapter, just so students know they exist and how to think through them. – Richard Jul 24 at 20:26
  • Just making sure. It does seem like a good idea just as you explained. – Michael Curtis Jul 24 at 20:32
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    When a textbook introduces a question which involves points not covered already, it's falling short, surely. And, it is DOUBLY augmented, in preference to DOUBLE augmented - as quoted by Richard. – Tim Jul 25 at 6:01
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I agree with your interpretation that it's an error in the book. Give some thought to contacting the author to point out the mistake. The one time I did this, the next edition of the book was updated.

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