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Are there any rules of borrowing notes from different scales? If so what are they and what is the scientific explanation of it in terms of sound waves' lengths?

For example I've got a chord progression in a minor scale i IV VI VII. In E minor it would be Em A C D. The chord IV (A major) is wrong, it should be minor (Am). However, many songs use that progression and it sounds ok. How can that be?

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    The second paragraph was already asked and answered by your other question. – Dom Aug 26 '16 at 21:09
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    "Are there any rules of borrowing notes from different scales?" Give them back when you're finished with them. ;^) – Transistor Aug 26 '16 at 21:12
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    The A major chord is not "wrong", it's as much in the key of E minor as is the A minor chord. It's not "borrowed" from anywhere, it is available in E minor. E minor is not equivalent to E aeolian (natural minor). E minor encompasses E aeolian, E melodic minor and E harmonic minor (and E dorian, as some would say), so the notes C, C#, D, and D# are all available without leaving the key of E minor. Please read this question and its answers. – Matt L. Aug 26 '16 at 22:06
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Generally, the neighboring keys in the circle of fifths are good candidates for any chord borrowing. D-major is only one sharp away from e-minor, i.e. the scales are very similar.

Specifically, VII acts as a dominant in a natural minor scale, and IV is a dominant to that, i.e. a double-dominant. This is arguable in your example though since there's a VI between the IV and the VII.

Why going to neighbours in the circle of fifths works so smoothly can be explained easily enough on grounds of physics: a fifth is a frequency ratio of 3:2, which also occurs very early in the overtone series of most instrument sounds. So, adding a fifth on top of any note that's already in the scale will hardly get you out of the scale at all; in your example, the C♯ in the A-major IV chord is actually already present as the third harmonic of the scale note F♯.

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"Should"? Why? Where did you get the idea that a chord sequence should all fit one scale? Mostly it doesn't. Here's a very simple pop-song type sequence. C, C#dim7, Dm7, G7, C, Bb, C. It never strays from the key of C major. But it uses plenty of notes and chords that aren't in the SCALE of C major. And they aren't "borrowed" from anywhere, because it's just fine to use the dim7 on the sharpened tonic and the major chord on the flattened 7th.

We get a lot of people here who confuse a method of improvising with a system of musical theory, and they're all asking variations on the same question - "how can this chord/note be allowed in this key?" They're often guitarists. Someone out there is teaching guitarists a most peculiar musical theory system :-)

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    Ahem... I would argue that the sequence you quoted very much does borrow chords. C♯dim₇ is a secondary dominant leading to the Dm, and B♭ is borrowed from the Mixolydian mode. Yeah, this is “just fine”, but the reason that it also actually sounds good has quite a lot to do with the fact that you're dealing with close harmonic relations there. Your answer reads like anything is allowed, it doesn't matter at all what you do... and while I'd actually agree on the former, that doesn't mean it's not good to still think about rules and precisely when and in which way they should be broken. – leftaroundabout Aug 26 '16 at 21:31
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    Half of C#dim7 consists of notes from C maj. (G and Fb/E) and the Bb is often used in C as well... And mostly chord sequences do fit one scale. There are far more pieces where that's the case. Most = more than 50%? – Tim Aug 27 '16 at 6:33
  • The point is that those chords are chromatic chords IN C MAJOR. No matter that they may be diatonic in some other key/mode. That isn't helpful. What IS helpful is to know their function in C major. Someone is teaching a system that makes almost every piece of real-world music "wrong". They should stop it! – Laurence Payne Aug 27 '16 at 23:22
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    Nobody's teaching a system that “makes music wrong”. They're just teaching a system that, by itself, can't fully describe some music. But that's fine – all models, of anything, only describe a subset of real thing. – leftaroundabout Aug 29 '16 at 22:04
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    Well, blues is definitely an important example which can neither be described on a diatonic nor chromatic basis, as it's fundamentally microtonal. But I don't see how that supports your point. – leftaroundabout Aug 30 '16 at 9:46
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There aren't any rules specifically with scales to this matter.

However, it just takes instinct. The people who improvise like this in such a way that they literally create new scales as they play; have been playing for many years and can hear if it will sound right before they even play it!

Using a V chord in this example but can apply to any chord, It is common that some players will be playing a scale over say.... a V7 chord in some progression and decide to switch from the scale to a V7 arpeggio or V altered arpeggio and add a couple notes into their improvisation. Which combines the scale with the V arpeggio.

There are rules however to adding in notes. To understand them all you have to understand Chord Theory since adding in extra notes into your scale will depend on what type of chord is being played whilst improvising.

Simple example to applying chord theory to improvisation, if the chord in which you are improvising over is a minor (has a flattened third) you're not going to add in a natural third to the scale. Because it would sound horrible!! (unless of course you like the tension)

As for the progression. There aren't any rules to tell you that the AMaj should be a Amin chord. There are recommendations to basic structure, but no rules to say it doesn't sound nice either.

Always remember the most important rule in music:

If it sounds good, it IS good - Duke Ellington

Hope this helps! :)

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