Talk:Theoretical key

Equal temperament

A note about today's equal temperament might help put this into context, as C# hasn't always been exactly the same as Db. A qualifier is needed about double flats being common enough for enharmonic changes, but rarely used in key signatures. --Alf ^melmac 14:39, 13 August 2006 (UTC)

Even today, with any musician who plays (or sings) any non-keyboard instrument, their c-sharp will not equal their d-flat. Equal Temperament is a sort of compromise, so that all notes are equally in tune. However, that also means that all notes are equally OUT of tune. So, therefore, c-flat minor and b minor, for example, are not always the same thing, and therefore, c-flat minor and its other 'theoretical' brethren do, in fact, exist.

--Irishmaestro 19.18, 8 February 2007 (BST)

Plus, harmonic progressions can strongly imply one enharmonic over another. Modulation and tonicization can give a strong impression of, for example, one key modulating to its subdominant key, which in turn could do the same, giving a sense of modulating into ever more flatted keys, even if equal temperament "magically" makes a Abbbb into an F, for example, it is possible to give the impression of a harmonic progression into a key like Abbbb, even if no sane composer would notate it that way. There's a Beethoven piece that does exactly this, although I forget which piece at the moment. ..but my point is that something like Abbbb is not an "impossible" or "theoretical" key except in terms of the music notation being too unwieldy to employ. Pfly 07:26, 20 March 2007 (UTC)

It's the Appassionata! :-) Double sharp (talk) 09:20, 5 July 2015 (UTC)

Equal Temperaments and Division of the Octave

I do not think it makes sense that in other equal temperaments, the normal conventional scales are built. For example, this article says that "in the 19 tone equal temperament, Bbb major is enharmonic to A# major". The normal major/minor scales are based on dividing the octave into 12 parts, not 19. So if we split the octave into 19 parts instead of 12, then the diatonic scales built on these pitches should also be completely different - a halfstep would be 1/19, not 1/12, of an octave, and a fullstep would be 2/19, not 1/6, of an octave. So, the scales would not be the normal major and minor - they will be totally different, because it would be a different key system (if it would proceed around a 'circle of fifths' at all).Majopius (talk) 01:02, 1 October 2009 (UTC)

I have no knowledge of non twelve-tone systems. But I strongly agree that the statements need supporting evidence. So I've tagged it 'Disputed-section'. (I've also tried to tidy up the article, but that's another story...) Feline Hymnic (talk) 19:11, 14 November 2009 (UTC)

It's fine. It links to the pages for 19-ET and so on so you can read more there. I'm removing the tag. —Preceding unsigned comment added by 170.170.59.138 (talk) 16:51, 13 March 2010 (UTC)

That's not how it works. In 19-tone equal temperament a perfect fifth is 11/19 of an octave. A whole tone is 3/19, a diatonic semitone is 2/19, and a chromatic semitone is 1/19. Assigning note names in the usual way then does indeed result in B being enharmonically equivalent to A♯. Double sharp (talk) 14:58, 14 May 2015 (UTC)

Can we not have a thumb?

It really undermines the point of having an example if it's so small that users have to click on it to see it. Anyway, what's so important about pointing out the nonstandard key signatures? —Wahoofive (talk) 00:37, 30 May 2013 (UTC)

The image has some sharps in the key signatures place in positions that everyone considers wrong today. Georgia guy (talk) 00:53, 30 May 2013 (UTC)

But that is hardly the point. The point is that the local key is E♯ minor, and instead of giving an 8♯ key signature or a 6♯ 1 key signature, a 7♯ key signature is used. In fact, I don't really find this a good example as E♯ minor is just one of the modulations the piece (in C♯ major) goes to, and is not the main key of the piece. A better example would be a piece that was really based in, for example, G♯ major, written in a (technically wrong) normal key signature like C♯ major (not A♭ major; F must be used clearly as rather than as , to show it is G♯ major), but good luck trying to find something like that. It would also be good to get an example from a piece that really does use a key signature specifically for a theoretical key (e.g. John Foulds' A World Requiem, G♯ major with 6♯ + 1 key signature near the end).

The octave displacement of the F♯ and G♯ (in the treble clef) and A♯ and B♯ (in the bass clef) is certainly useful and relevant content for the key signature article in describing the history of the notation of key signatures, but is not very relevant here. Double sharp (talk) 11:14, 5 June 2013 (UTC)

(BTW: not everyone. The Billaudot edition of the Alkan concerto still has the A♯ in the bass clef on the top line. While it is a reprint of the old Richault edition from the 19th century, given that it's easy to change this now, it is somewhat odd. I haven't checked if they did change the nonstandard key signature layouts for the Op. 35 études; given that some of the volumes in their selected Alkan works series are re-typeset using Sibelius, but not all, I suspect it was done, if they re-typeset that one.) Double sharp (talk) 11:17, 5 June 2013 (UTC)

The point of the example is that it doesn't use a weird key signature (other than the insignificant octave transpositions), but is a common-practice work in standard repertoire using standard notation, which still requires these "theoretical" keys. Admittedly, this particular example is a bit vague between G# major and E# minor and doesn't cadence in either key, so perhaps we could find a clearer example. —Wahoofive (talk) 15:26, 5 June 2013 (UTC)

This might be better:

—Wahoofive (talk) 15:39, 5 June 2013 (UTC)

Actually we should have both a piece in a theoretical key that doesn't use a weird key signature and one that does. Double sharp (talk) 13:03, 6 June 2013 (UTC)

the table

Originally it was up to 10 sharps or flats, because that's the most you can get out of parallel keys of non-theoretical keys. Someone added 11. Actually I think the best closure spot if you're unsatisfied with 10 would be 12, given that that is where the circle of fifths closes again (it first closes at 6 sharps or flats, where F♯ = G♭; now we have B♯ = C = D), so I added 12. The most you could legitimately go to is probably 14, as beyond that you need triple sharps and flats. (And also, I don't think anyone has used those keys, even transiently; at least B♯ major with its 12 sharps is transiently encountered, for example in one of Reicha's 36 Fugues, though not with its key signature.)

(Although with regards to avoiding triple sharps: you can't get completely away from the problem here. G minor has 12 sharps, and the ascending G harmonic minor scale would have to be: G, A, B♯, C, D, E♯, F♯, G.) Double sharp (talk) 13:44, 7 August 2015 (UTC)

Ah, OK: that someone was Georgia guy. Double sharp (talk) 13:52, 7 August 2015 (UTC)

"Impossible key" references inappropriate.

I think the references to the keys covered by this article being "impossible" should be changed. These keys are not in the least impossible; they are entirely possible, and I know of actual examples of pieces that use key signatures for G# major and Db minor for certain passages. So they are not even "theoretical keys", but actual keys, albeit it extremely scarce and outside the key limits conventionally taught in music theory books (which include keys up to 7 sharps and 7 flats, major and minor, and stop there without mentioning anything beyond that).

That is for passages using the actual 8-sharp or -flat key signatures that match. These keys are only slightly scarce when you take into account passages, sometimes of several bars' length, that are in one of these keys but without changing to the key signature that would match them. Chopin's Piano Concerto no. 1 in E minor, Op. 11, even contains a passage continuously in G# major for several pages of full score (complete with subsidiary modulation to its dominant, D# major); his Polonaise-Fantaisie in Ab major, Op. 61, contains a passage about 7 bars long in the key of A# major.

I'm not sure if this is a "be bold and do it" case, or whether I'd be going too far. I may think about it further, though - and would of course take note of any opinions offered here. M.J.E. (talk) 18:08, 20 November 2015 (UTC)

You go off on some tangents here, MJE, but if your main point is that the word "impossible" is inappropriate, I couldn't agree more. Basically all this topic concerns is "keys which don't have corresponding key signatures." Finding examples of musical passages in these keys is not that difficult. Abnormal key signatures (such as those using double accidentals) are an extreme rarity in notated music and that fact should be emphasized. —Wahoofive (talk) 16:42, 22 November 2015 (UTC)

In some editions of the Chopin concerto (e.g. Peters), the G-sharp major section is re-notated in A-flat major, with an editorial key signature change. I do not think that would count, although the original notation would.

Here is another conundrum: Kuzka's song in Musorgsky's Khovanshchina. We start in A minor for the introduction (fine), and modulate to C major (also fine). This then becomes the dominant of F minor (still OK, but rapidly flattening), and we then encounter a D♭7 chord. The first time this acts as an augmented sixth; the second time as a dominant seventh, which then resolves to a minor tonic. Literally we have entered G-flat minor (where we stay for the next eight pages), though of course Musorgsky writes it as F-sharp minor to be sane. So perhaps this does not count. But then what happens is that the tonic F-sharp is then reinterpreted again as G-flat and we enter E-flat minor for the Scribe's entry (where we stay for the entire rest of the scene). Both entering and exiting, the tonic has been G-flat, not F-sharp. Does this count? David Brown seems to think it does, calling the Revolutionary Chorus in Boris G-flat minor (essentially the same thing happens; we enter G-flat as the Neapolitan of F minor, and leave it as the mediant of E-flat minor, which immediately turns major in this case). But we could easily argue that when push comes to shove Musorgsky has switched the tonic from G-flat to F-sharp and back simply to avoid theoretical keys, so that G-flat minor was not actually used, only theoretically implied. Double sharp (talk) 04:22, 4 January 2016 (UTC)

I agree entirely. The phrasing is bad. "Theoretical" is apposite - these keys exist in theory and it is their impracticality that means they are not used for performance. However, they are not impossible at all and are used in classrooms around the world - in fact I use theoretical key exercises with my students for some harmony tasks, and transcription too. It is not "being bold", it is simply wrong to say they are impossible. Knucmo2 (talk) 23:37, 14 January 2016 (UTC)

Uh oh!

I can find no attestation of "theoretical key" being used as a term in any reliable source. Firstly, those cited in the article presently do no such thing. Initial Google searches just return forum posts, Wikipedia, and Wikipedia ejecta.

So far, the Chambers Dictionary of Music, New Penguin Dictionary of Music, Oxford Dictionary of Music, and Harvard Dictionary of Music do not mention this term nor the concept, but that's not a smoking gun, this might be too silly a term to be there. JSTOR has nothing. I have now busted out the big guns and searched Oxford Music Online through TWL.

Nothing! Uh oh! I think we might have made this one up! I'm looking through various other music theory textbooks now, but I'm worried to say the least

(It's also perfectly possible it's simply a non-verifiable colloquial term, but I didn't find any internet results that implied its use before this article was created, so.) Remsense诉 11:15, 3 May 2024 (UTC)

Well this is interesting. I don't see it in any of my (practical, non-scholarly) books- Kurt Stone, Kostka/Payne, Schoenberg, Rimsky-K, Adler's or Kennan's orchestration books. - Special-T (talk) 19:12, 3 May 2024 (UTC)

What's more—there doesn't seem to be any term for this in the literature, so I think if we can't find anything we'd have to trim most of the article and merge what's left and citable into another. Remsense诉 22:27, 3 May 2024 (UTC)

Pinging @Double sharp as a veteran editor who might know where this term would be verifiable? Remsense诉 22:30, 3 May 2024 (UTC)

@Remsense: Bravo to your efforts. I can't find it anywhere either. It's admittedly also true that the term doesn't stand out: I could easily see myself explaining things along the lines of "okay, theoretically we should now be in D-sharp major, but in practice that's only a theoretical key because nobody wants to read double accidentals in the key signature, so instead we use the enharmonic equivalent E-flat". But that's not so much a term but an adjective-noun combination. As I linked above, in this actual theoretical discussion of this kind of thing the term "theoretical key" does not appear at all.

In any case, there's little to say about this concept in the first place. Probably it could simply be merged into Key signature to discuss the extreme rarities when double accidentals appear there. Double sharp (talk) 05:22, 4 May 2024 (UTC)

Agreed that's likely the best option. Remsense诉 05:47, 4 May 2024 (UTC)

My only concern about that is that key signature is a topic about a notational device, whereas this is really a subset of Key (music), since such keys don't necessary have corresponding signatures (I keep pushing that Bach example). I agree, though, that as a professional musician (with a theory focus) I never encountered this term until Wikipedia. —Wahoofive (talk) 15:50, 4 May 2024 (UTC)

Hmm... I see this as purely a notational device. In 12-TET, notating in G# major vs. Ab doesn't change the pitches, just the notation. - Special-T (talk) 11:54, 5 May 2024 (UTC)

Certainly enharmonic distinctions matter notationlly because they matter conceptually? That F and E-sharp triads are the flat-V and sharp-IV degrees in the key of B can be significant if nothing is written down. Remsense诉 12:02, 5 May 2024 (UTC)

The main thing that distinguishes these keys is simply that they hardly have actual key signatures in practice and for that reason almost never appear as the main key of the piece. It's not that unusual to tonicise G-sharp major without using the key signature, just like it's not that unusual to tonicise C-sharp major without writing a seven-sharp key signature. What's really unusual is to put in a G-sharp major key signature. And if the lack of a normal key signature is what distinguishes them, then I think key signature is a fair place for most of this material. Double sharp (talk) 08:11, 6 May 2024 (UTC)