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I've been learning some harmonic function from around the web, but teachers are a bit sparce in the online world. I have some of the details but crucial details are missing.

Chord Families For Major Scale

Tonic: I, iii, Vi
Tonic Prolongation: iii, Vi
Predominant: ii, IV
Dominant: V, Vii°

What are the families for the minor scale?

Also, aside from that issue, I can't find information suggesting where the degrees of major and minor quadad scales prefer to lead in a progression. Does anyone have links or information?

For major and minor scales I have full details, like:

Major

I: leads to any
ii: leads to I, V, or vii°

I really recommend Seth Monahan’s channel about harmony.
Search it on YouTube.

I have full notes on harmonic function. Let me simplify the question. Is harmonic function the same for minor and major quadads and altered chords as it is for the basic major and minor triads?

In the major scale the primary chords - I, IV and V are major chords. ii, iv and iv are minor.

The iii is not commonly used. The vii is a diminished and it's not used in its root often as it's an odd sound.

The vii is often used in its seventh. This is called a diminished seventh. The diminished seventh has three invertions. I think the vii7d may be used instead of a V rather than any vii chord.

The tonic chord is the root position so I. The vi is not a tonic. You can have an interrupted cadence l. E.g ii-V-vi. It however is a surprise.

This compares to a perfect cadence which is a V-I. eg. ii-V-I. You need to remember that it is often more complex as you often have the chords with sevenths and often in their inversion.

In the minor scale there are several forms - natural, melodic or harmonic. I won't confuse you with this one!

It makes a huge difference the period of music as there are a few patterns but frequently broken and even major and minor distinction goes with some pieces in modes and some without clear keys. To start with i found it helpful to try and identify keys and cadences.

Should say in major scale - ii, iii and vi are minor triads

What is your definition of quadad? What language did you learn this terminology in?

What are Major and Minor quadad scales? (Your OP)

What are quadad (and altered) chords? (Your follow up post)
Are you using it to mean seventh chords here? That wouldn't carry to scales.
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Chord progressions move through voice leading. It doesn't matter if it's a major or minor key. All chords move from any to any but some movements are more acceptable to the ear. Thus we build a theory of music, i.e. what has worked in the past. It doesn't mean you can't go from a IV to a iii.

Try playing C - Am - F - Em, one bar of each, and try to find a path back to C. It's not easy but you can use a half bar of Em with a half bar of G and make it work with the bass travelling from E to D to C. It's just not easy.

Look at The Beatles' turnaround in She Loves You, I-vi-iii-V. Try singing it using the more common I-vi-IV-V and see how bland it sounds. She Loves You remains their biggest selling single in the UK. Who else was using iii at the time?

Their follow up was I Want To Hold Your Hand with the same chords twisted into I-V-vi-III7. How do you get back to the tonic G from B7? See how they managed it. That song remains their biggest selling single in the US.
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Your chord families use unfamiliar terminology to me.

The tonic is I. Any other chord from the key not containing a 4 or 5 (scale degree) is a tonic family chord. Moving by a fifth (up for a dominant, down for the subdominant) creates travel. Moving anywhere else just maintains the tonic feel. I've never actually heard the term Tonic Prolongation.

The dominant group is V and vii. As vii is diminished it is usually used as the V7 (adding a bass note a major third down), as an inversion, avoiding the leading tone in the bass, or rootless, avoiding the leading tone altogether.

The subdominant group, rather than predominant, is IV and its relative minor, ii. Predominant, for me, is a chord used in a progression as a path to the dominant.

Movement in the Minor key tends to avoid moving to VII as it leads more readily to III. The v is frequently changed to V, hence the Minor Harmonic scale, to make the pull to tonic greater. On the other hand it tends to be easier to move around and add colour as the move away from tonic is more subtle and the pull back to it is milder.

It is basically seventh. I have seen on the net some people use that term very occasionally. I have never seen it in any classical analysis nor any jazz harmony context.

Tonic prolongation is a term that is now used rather frequently. It includes different techniques that tend to maintain the tonic harmony. For example keep the tonic as a bass pedal, use tonic triad argeggios or as key notes in the melody, some other harmonies can also quickly pass by before returning to I, III being an option. But for example playing I and then a short passing by the dominant going back to I would be considered as remaining in tonic vicinity.

>What are the families for the minor scale?

FAIK generally the same as for minor, also for 7th chords

Quadad is terminology I've seen in a couple of books referring to any four note chord, so all sevenths. It's my fault for using that term losely. zrtf90, I learned a lot out of that, thank you. It turns out my notes were fine, I just needed to understand them more. When you alter chords 9ths, 11ths, 13ths, is it the same roman numerals for progression as the sevenths?

Tonic prolongation is a term that is now used rather frequently. It includes different techniques that tend to maintain the tonic harmony. For example keep the tonic as a bass pedal, use tonic triad argeggios or as key notes in the melody, some other harmonies can also quickly pass by before returning to I, III being an option. But for example playing I and then a short passing by the dominant going back to I would be considered as remaining in tonic vicinity.

I expected the quad for tri in triad but hadn't seen the word before, and Googling didn't help, but couldn't see how that worked for "major and minor quadad scales" so I thought I ought to check.

When you alter chords 9ths, 11ths, 13ths, is it the same roman numerals for progression as the sevenths? I call these chords extensions. Altered chords, for me, are generally altered chromatically with non-diatonic notes but yes, the RNs are still used for the base chord.

I 've never been comfortable using altered or extended chords with RNs but that's just me. I prefer using actual chord names when the numbers start getting added. If you know the numbers and what they imply you probably understand the function in the key of the actual chord name.

In classical analysis they're usually dominant extensions as a way of increasing the tension but in more modern composition occur more frequently in non-dominant chords. In those situations I just find RNs don't convey as much as actual chord names.

Sidokar, thanks. And, er, thanks!