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I'm writing a song in F Major key.

I have a chord progression that goes Like

4/4

C7 - C#dim - Dm - Dm

( V7 - V#dim - Vi - Vi )

After this four measures, I wanted to change key to Dm for a moment.

So thinking the last measure's Dm (Vi) as a tonic (i) for the next four measure,

I went

A7 - A#dim - Bm7-5 - Bm7-5

which is the same ( V7 - V#dim - Vi - Vi ) in Dm key.

But I start to think, is ( A7 - A#dim - Bm7-5 - Bm7-5 ) really ( V7 - V#dim - Vi - Vi ) in Dm key ?

or am I still in F Major key and the actual chord progression is

V7/VI - III#dim - iv#m7-5 - iv#m7-5

what are the details that establish a key change ?

  • Is this school homework or something? Why do you care about what the key "really" is? Who's going to act upon your key classification? – piiperi Mar 10 at 11:39
  • @piiperi no I don't have any teachers. because I like to know everything going on in my music – Hyun Yoo Park Mar 10 at 11:41
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    I'm voting to close because, as written, this question is generating some confusion as to what the OP is really asking. – Alex Basson Mar 10 at 12:34
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    @AlexBasson no what I'm asking is very simple. did I really went to Dm key when I went to the A7 part – Hyun Yoo Park Mar 10 at 12:40
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    @HyunYooPark What you're asking is very simple only if you believe there's some objectively true answer possible. But there isn't. Did you intend to modulate to D minor? Or did you just write down chords that sounded good to you and then try to figure out what it meant later? We can't answer that for you. And either way, your listeners are going to hear the music on its own and make of it what they will for themselves, independent of your intent. – Alex Basson Mar 11 at 0:21
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It is subjective. Your feelings define it.

https://en.wikipedia.org/wiki/Key_(music)

... a tonic or tonic chord, which provides a subjective sense of arrival and rest ...

If you feel that the home base moved, then you feel that the key changed. Someone else might feel differently.

If your real question is, how to create those feelings, i.e. how to establish a key, I think there are questions and answers about that already. Use a proper cadence or something. If establishing Dm is what you're trying to do, then why do you move the bass to B instead of D, and via an A#dim instead of C#dim? If you want your audience to think about an elephant, why say "excavator". You might still be able to make it sound clearly like Dm if you write a strong melody line that disregards the obfuscated chords and overlays something that's strongly in Dm.

  • Isn't A#o the same as C#o, maybe with a different bass note, depending how it gets written? Although Go and Eo probably fit the key better anyway. – Tim Mar 10 at 14:02
  • @Tim it's the bass note I meant. A - C# - D bass movement feels more effective for establishing a Dm tonic than A - A# - D. My opinion only though. But the OP wasn't really asking how to establish a key ... he is asking for others to tell him what the key is in a chord progression he wrote. – piiperi Mar 10 at 19:00
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Every modulation is a key change. Usually a modulation will have some close relationship to the previous key, like C>Dm, or C>F, or C>G, involving at least a common note or chord, whereas a key change could be a move a semitone or a tone up.

It's not always necessary to change key signature for a modulation - which may even re-modulate back to the original key - but for a complete key change it's worthwhile changing the key sig.

Quite often a piece will drift in and out of, say, C and Am. Certainly more of a mod. than a key change, but not really worth considering as either, unless one wants to be totally academic. It's just what music sometimes does.

  • I'm not talking about notations. – Hyun Yoo Park Mar 10 at 8:39
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    O.k. it's established you're not talking about notation. What are you talking about? – Tim Mar 10 at 8:48
  • I already wrote it detail as possible in my question. can you tell me what is your not getting ? – Hyun Yoo Park Mar 10 at 8:59
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    @HyunYooPark I think what we're not getting is that you seem to be asking us to explain to you what your musical intent is. You've written down some chord progressions and then asked us "Is my intent to be in D minor or F major?" But of course this isn't a question we can answer—no one can say what your intent is but you. – Alex Basson Mar 10 at 12:31
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    @AlexBasson to be fair, I think you're actually giving a good answer to the question! IOW the answer is: it's a question of intention and perception, not definition. – topo Reinstate Monica Mar 10 at 13:20
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As you change from F (C7 is the dominant) to dm this is a false cadence. To establish this new key Dm I propose a normal cadence in the new key Dm, to make the moduation perfect or unambiguous.

  • going to Dm is not my goal. my attention was doing Parallel structure with ( V7 - V#dim - Vi - Vi ) on dm key – Hyun Yoo Park Mar 10 at 11:30
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Nothing definitively indicates a key change in the kind of situation you are talking about.

Of course it's true that there are many 'textbook' examples of key changes, for example where the change is prepared and fulfilled in a certain way. But in general, there isn't really any one particular thing - or even group of things - that you can point to that 'defines' a key change, and likewise there isn't really anything that defines the 'momentary' key of a piece in the first place.

The nearest thing you will get to a definition of the overall key of the piece will be a combination of key signature, and an instruction as to the key either in the title of the piece, or elsewhere in notation. If there's no such instruction, then at the very least you will have to make your own judgement as to whether the key is major or the relative minor, and while there are many cases where most people would agree, there are some ambiguous cases too.

And of course, you have the same difficulty when discussing key changes, especially (as in your case) between relative minor and major keys. What one person hears as a key change, another might simply hear as a movement to the vi chord.

But I start to think, is ( A7 - A#dim - Bm7-5 - Bm7-5 ) really ( V7 - V#dim - Vi - Vi ) in Dm key ? or am I still in F Major key and the actual chord progression is V7/VI - III#dim - iv#m7-5 - iv#m7-5 ..?

It's up to you, as the person analysing the piece, to decide which perspective is more useful.

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F major and D minor are so closely related as to be almost the same key. I'm inclined to describe what you're doing as simply sequential imitation within a single key.

Does it make any difference, other that in what labels you put on the chords?

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