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I've just found this information on a page I use to practice my scales. Is it true? What's the difference between a theoretical scale and a real one??? https://www.musicteacherguide.com/piano-melodic-minor-scales/

  • I don't consider this approach (train all scales in case one encounter them later) as efficient: playing scales is most useful, when you begin exercising a piece in the respective key. This has the advantage, that wil not loose time with hard-to-encounter key signatures. – guidot Jan 20 at 20:03
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The page itself tries to explain it. Quote with emphasis:

Double-flats and double-sharps are often used as accidentals but placing them in the key signature makes the music generally very hard to read. The Scales who use double-flats in the key signature (Db Minor, Gb Minor, Ab Minor) are just Theoretical Scales.

Such key signatures could theoretically exist, but you won't find them used in practice. For example, instead of Gb minor, F# minor with three sharps is used.

Here's another page that tries to explain it: https://www.basicmusictheory.com/g-flat-minor-key-signature

As noted by Rosie F, Ab minor (7 flats) shouldn’t be on the list. https://www.basicmusictheory.com/a-flat-minor-key-signature

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    Correction: A♭ minor's scale doesn't have any double-flats (it's all the single-flats). It's not just theoretical either -- composers have actually used it, usually with its complete key signature of 7 flats. – Rosie F Jan 20 at 19:03
  • @RosieF good catch. :) It’s a quote from the page linked by the OP. This other site doesn’t have that mistake basicmusictheory.com/a-flat-minor-key-signature – piiperi Reinstate Monica Jan 20 at 19:21
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Generally speaking, there are enough keys to cover all, using purely sharps or flats. With seven sharps, that takes us into C♯ major, which can, in 12tet, be re-written as D♭. The latter has five flats.

With seven flats, that takes us into C♭ major, which can be written as B major, with five sharps. There are very few occasions where a composer would need, or want to use more sharps/flats in a key signature, so going even further and using double sharps (x) or double flats (♭♭) is not going to be helpful to any instrument player. If particular scales have to use double either, it's due to particular notes needing to be written as such.

Having double either in a key signature is therefore somewhat pointless, as the 'simple' ones cover all that's needed. Thus, theoretical.

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Key signatures and accidentals are a form of conventionalised notation - with equal temperament tuning there are multiple ways of notating the same note and the same scale. Double sharps and flats aren't the limit, and a few composers have used triple accidentals.

But just because something is possible in this notation system doesn't mean it should be used. We could teach beginners to play piano in the B♯ major key, but that would be needless cruel when we could teach them to play in the C major key instead. Theoretical keys are allowed by the notation system but have a simpler equivalent notation which should be used unless you have an extremely good reason for putting such a burden on the performers of your music.

Wikipedia gives a few examples of compositions which have modulations from seven-accidental keys to their fifth, which therefore has eight accidentals, and where the composer then has to choose whether its simpler to switch from sharps to flats (or vice versa) or to use double accidentals.

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