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I'm studying from Walter Piston's book Harmony (5th Ed) so that I'm prepared before the semester starts at UNA.

Exercise 6.D asks: "For each one of the following intervals, name at least two scales that contain both notes", the notes given are E# & A#.

My problem is the following: Should I respond with the original interval, with its enharmonic equivalent F & Bb, or with both?

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  • 1) Congratulations! You're very smart to do a little music theory study in advance. Before my undergrad, I found a local professor who let me just listen to his Introduction to Music Theory class. Once I got to university, I still took the official Introduction to Music Theory course, didn't try to skip it, but I had a much easier time since I'd already heard some of the ideas. 2) Looking at some of the questions you've asked later, I feel like this sentence from the book is the source of some of your confusions. It uses the word "interval," but then names specific pairs of pitches. ...
    – Andy Bonner
    Jan 31, 2022 at 19:14
  • ... In general, an "interval" is simply a distance. Like, "700 km" is a distance, but "Buenos Aires and Córdoba" is not. In musical contexts, "interval" is more often used for a certain distance, like "fourth," that could be found between many different pairs of notes. I can't explain why Piston used the word here as if it referred to a collection of two specific pitches.
    – Andy Bonner
    Jan 31, 2022 at 19:18

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You should respond according to the original interval. Responding according to the enharmonic equivalent will give an enharmonically equivalent answer, so nothing is gained in that sense. Piston is intentionally giving two "difficult" notes to deal with to encourage thinking in those terms.

Of course, as a convenient "cheat", you could solve the problem using F and Bb, then convert it to the enharmonically "correct" answer.

I don't think I'm giving anything away by saying that F and Bb immediately conjure F major, which I can quickly "convert" to E# major for the purposes of answering the question.

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  • 1
    The next possible answer has only one more sharp than F# major! And is not THAT uncommon.
    – Laurence
    Jan 26, 2022 at 17:51
  • 2
    …not to mention relative minors…
    – John Belzaguy
    Jan 26, 2022 at 18:06
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    I would go so far as to suggest, that a grader would/should mark an enharmonically equivalent answer as incorrect (or at least only worth half-marks).
    – Elements in Space
    Jan 26, 2022 at 18:07
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    @Aelianus_Adolphus I think you can give the required 'at least two' answers without needing theoretical scales.
    – Laurence
    Jan 29, 2022 at 16:08

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