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I know that a chord is built around a bass note, and depending on the type of chord this bass note will dictate what other notes go into the chord. But do all notes in a chord belong to the same scale?

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According to the chord-scale system, all notes in a chord WILL belong to the same scale. That scale may be pretty exotic (the C Lydian dominant scale is used in one Wikipedia example), and it likely won't be the scale of the piece's home key.

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    In this sense, the statement that all chord tones belong to the same scale is a tautology. There's a chord scale for each and every chord. – Matt L. Feb 4 '19 at 9:44
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A scale is simply an ordered set of notes. It could, if you wanted, be all the notes, semitone by semitone. Called the chromatic scale. So, yes, I suppose, using that scale, any chord, common or very unusual, will have notes that belong to 'the same scale'!

In the general run of things, the majority of chords will contain notes that belong to one scale (or key, which are not the same). Major and minor triads contain the notes from major and minor scales respectively, as do maj. and min. sevenths. Dominant sevenths found in a key (as C7 in key C) contain the notes from F maj. scale.(Not the C maj. as may be expected).

It's when we consider dim and aug, or m7♭5 that extra thought is needed. Let's take Co - C E♭ G♭ B♭♭. Could be considered to contain notes from a diminished scale; not sure if the OP wants to go that far. Or, something such as C7♭9 - using the scale notes from C D♭ E F G A B♭. Look deep enough, and there's a plethora of different scales, and just about enough for any chord to be deemed to use some of those notes. Although thinking along those lines isn't too helpful in understanding that section of music theory for most.

One thing's certain though about chords: this product may contain notes...

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do all notes in a chord belong to the same scale?

Chords that naturally occur within a key and contain only the notes found in the scale (or key) that you're working in are diatonic chords.

http://musictheorysite.com/major-diatonic-chords/

In this link you’ll find the

Diatonic Chord Formula for a Major Key

”For new songwriters this is a must know concept for your chords to sound right.”

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I think there are two concepts you want to consider:

  • local tonality
  • chromaticism versus diatonicism

Even in short pieces of music it is common for the tonal center to change. The music may do something like start in C major, briefly touch on D minor, and then modulate to G major. While we say the music is in C major we get _local tonalities of D minor and G major. The scale then changes with those local tonalities. Considering the local tonality many chord then belong to the scale. For example, using the tonalities above a D dominant seventh chord does not 'belong' to C major, but when it's used locally in a G major passage it does belong to the scale, the scale of that local G major tonality.

The convention for music notation is to use one key signature for a piece of music. In the example above the key signature would be C major - no sharps or flats - and the D dominant seventh chord would require an accidental - an F#. The chord is foreign to the overall key signature, but not foreign to the local tonality.

There are varying uses of chromatic and diatonic, but for this question I consider diatonic to mean the tones of the major scale and its permutations like the 'natural' minor. You could also define this meaning of diatonic as the tones of the key signature.

Returning once again to the example above, the D dominant seventh chord is chromatic in terms of the key signature, but not really chromatic to the local tonality G major.

However, there are times where a chromatic chord occurs without a change in the local tonality. I think the easiest examples to give are from minor key harmony. Let's switch the key for our example and use C minor - three flats in the key signature.

If we play a G dominant seventh chord - the V chord - in C minor we need a B natural which isn't in the key signature. The chord is part of the C minor tonality, but we need an accidental to spell it. The local tonality has not changed, but the chord is chromatic relative to the key signature.

What really is going on with this chord and the scale is the raising of the seventh scale degree. In minor key music the seventh scale degree gets raised and lowered depending on the harmony. Some get bogged down in talking about various minor scale forms: natural, harmonic, and melodic. But, suffice to say natural minor is the basic diatonic form - it's the one used by the key signature - and the raised seventh degree is spelled with an accidental - i.e. chromatically without a change of local tonality.

The second example from minor is not complicated by the 'forms' of the minor scale. It involves a special chord that is usually considered an 'advanced' harmony topic. But, it is used regularly in minor key music so let's not be intimidated. The chord is called an augmented sixth chord.

The description of the chord's basic construction also explains its chromatic identity. Staying in the key of C minor lets start with a iv6 chord which is tones Ab C F. Note that the interval from Ab to F is a major sixth. Alter the F and make it F#. That changes the major sixth to an augmented sixth and the resulting chord Ab C F# is called an augmented sixth chord. Normally this chord will move to the G major chord, the dominant V in C minor.

Notice that the altered note F# is the altered fourth degree of the scale. This is an alteration that has nothing to do with the 'forms' of the minor scale in the previous example. The raised fourth degree simply is not in the minor scale. Clearly the chord does not belong to the minor scale. The chord is chromatic, but not involving a change of local tonality.

That was a lot of technical detail, but to summarize the two basic points: many chords can be understood as diatonic to the local tonality (belonging to the scale), but some chords can be truly chromatic and despite being part of the local tonality use tones that don't belong to the diatonic scale.

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Not always. For instance a diminished 7th chord like G B-flat D-flat E. No normal major or minor scale has those notes in it.

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  • So the diminished and suspended chords are the exceptions? – Francis L. Feb 4 '19 at 4:59
  • But doesn't the F harmonic minor scale have all those notes (G, B flat, D flat, E) in it? – Dekkadeci Feb 4 '19 at 6:44
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    Being picky, the E is really Fb, as the dim7 interval from G is Fb. G>E is M6. – Tim Feb 4 '19 at 8:44
  • The diminished 7th chord is the VII chord of the harmonic minor scale. – Matt L. Feb 4 '19 at 9:39
  • Oops. You're right. Two tri-tones in the harmonic minor scale. – Mark Lutton Feb 5 '19 at 2:02
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There's no way to answer the question without addressing the implied assumptions or misconceptions.

  • Probable misconception about scales: If the OP assumes that all ordered note sets that can be called a "scale" are diatonic, then the assumption is wrong. There are many other kinds of scales, like the whole-tone scale, pentatonic scales, chromatic scales, diminished scales.
  • Probable misconception about chords: If the OP assumes that all the notes of any note-combination that can be called a "chord" can be placed on some diatonic scale, then the assumption is wrong. Counter-examples are: cluster chords, 7♭9 and many other jazz and modern classical chords, anything that has too many consecutive semitone or whole-tone intervals when all the notes are placed within a single octave.
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