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I'm asking for a textbook, website or whatever that is filled with "musical interval equations" to solve and that can check me.

By "musical interval equations" I mean something like:

  • You are given a note and an interval or amount of semitones. You need to sum or subtract them and write the resulting note. E.g. "D + 11 st. = *you write the resulting note(C#)*", "Bb - minor 6th = *you write the resulting note(D)*" and so on.
  • You are given two intervals or two notes. You need to find their difference in semitones or intervals. E.g. "A# - F = *you write the resulting interval(major 3rd)*", "tritone - major 7th = *you write the resulting interval(perfect 4th)*".
  • And so on...

Also, how useful is it to do such kind of exercise, will I be able to recognize intervals nearly without thinking in the same way that I add and subtract small numbers(like the ones up to 20). Is there the something like this but about chords or scales?

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    I believe your question about how useful such exercises are is more on topic for this website than your request for a textbook or website containing them, to the point that your request makes your text as a whole off-topic. I advise removing your request as a result.
    – Dekkadeci
    Oct 19, 2021 at 13:01
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    (To elaborate or clarify: requests for textbooks, websites, or other "external resources" are not covered here, so a "help me find a ___" question would be closed. However, your last paragraph is a valid question; you might also ask about other techniques for developing this skill.
    – Andy Bonner
    Oct 19, 2021 at 13:52
  • "how useful is it to do such kind of exercise". Probably less than practicing your instrument. I guess exercises like this may appear in some textbooks to aid in understanding of music theory, but I don't think solving this kind of riddles has much benefit for a musician or a composer. As Andy wrote, the question is off-topic. It could be on topic if you focused it around issues you would like to solve.
    – user1079505
    Oct 19, 2021 at 14:42
  • Not answering the first part - it's well off topic! However, I can see little to no advantage in being able to do the sort of calculations you describe: they will be of no use in just about anything you do. Recognition of intervals, however, will be very useful.
    – Tim
    Oct 19, 2021 at 14:46
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    For my two cents, see this answer. There is a reason to pair every analytical exercise with actual music-making; it will not only be easier but will settle into a different part of your brain, more permanently. In other words, the best way to learn that major 3rd plus minor 3rd equals perfect 5th is not by writing it down, closing the book and putting down the pencil, but by playing it thousands of times and engaging analytical inquiry of what you're doing.
    – Andy Bonner
    Oct 19, 2021 at 15:05

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