In, for example, the C major key, the available tensions for the C major seventh chord are 9, 13, because:

Harmony 3 - Berklee, Barrie Nettles, p17:

For diatonic chord progressions, available tensions and other non-chord tones will be diatonic.


Harmony 3 - Berklee, Barrie Nettles, p15:

Available tensions are non-chord tones which are a whole-step above a chord tone (a major ninth reduced by an octave).

Which means there are other available tensions, just non-diatonic. i.e., for a C major seventh: 9, #11, 13. But the #11 is flat out denied "available tension" status by some sources:

Secondary dominants - aucklandguitarschool.co.nz:

“Available tensions” are non-chord tones that are diatonic and a major 9th above a chord tone.

Anyhow, if I would assume that available tensions do include the non-diatonics, what would I call them as a whole to minimize ambiguity? All available tensions? Chromatic tensions? NCTs that are a major 9th above a chord tone?

And so, just to clarify, would one use a non-diatonic available tension in a non-diatonic chord progression?

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    I wouldn't even call some of those extensions 'tensions'. – Tim Feb 15 '20 at 8:12

Definitions are not always that strictly adhered to, and different authors/sources may use slightly different definitions.

It's pretty common usage to define "available tension" just for a certain chord type, without considering a related scale. E.g., a Cmaj7 chord could be used as a I chord in major (where the #11 wouldn't available diatonically), but it could also be used as a IV chord in the key of G major, where the #11 is available. So you could say that in principle, the #11 is an available tension for a major seventh chord. If you want to use it depends on the context. Note that even if the major seventh chord is a I chord, you could add the #11, which would give the chord a lydian flavor.

And concerning the definition mentioning "a major 9th above a chord tone", it's not correct, at least not for dominant seventh chords. E.g., the tension b9 is very common for a dominant seventh chord resolving to a chord a perfect fifth below.

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