6ths by scale degree vs 7ths [closed]

When you look at 7ths off Ionian you get the same major/minor intervals as 3rds except the special dominant 5th. When you look at the 6ths you get quite a different pattern of major/minor. I can see why of course, but what should i read up on to learn about these differences and how they function in the same way as the dominant 5th for 7ths? I also notice that for 4ths the 4th degree gives us a b5 interval rather than a P4, so I guess the same question applies here. Thank you!

I don't think you need to read anything in particular.

When you examine the series of intervals above the degrees of the scale you are essentially getting the inverted intervals of the modes of the scale.

Let's step through some examples...

MAJOR/Ionian

Sevenths: M7 m7 m7 M7 m7 m7 m7
Sixths:   M6 M6 m6 M6 M6 m6 m6
Thirds:   M3 m3 m3 M3 M3 m3 m3
Root:     C  D  E  F  G  A  B

...invert the interval above to get a new tonic below, a sixth above C is A, so the new tonic is A

Root: A B C D E F G

...invert the interval of the series Sixths: M6 M6 m6 M6 M6 m6 m6

Thirds:   m3 m3 M3 m3 m3 M3 M3
Root:     A  B  C  D  E  F  G

...the series of sixths above C Ionian is effectively A Aeolian.

...if we do the same of the thirds...

Sixths:    m6 M6 M6 m6 m6 M6 M6
Root:      E  F  G  A  B  C  D

...the series of thirds above C Ionian is effectively E Phrygian.

So, each time you increment the interval up - thirds above, fourths above, etc. - the reason that the interval qualities change (the third above the supertonic is minor, but the sixth above the supertonic is major, or the fourth above the dominant is perfect, but the fourth above the subdominant is augmented) is because the part added above the base scale is shifting through the various modes.

A finally caveat: don't misunderstand any of the above to mean something is in a particular mode. Parallel thirds in C isn't literally being in C Ionian and A Aeolian simultaneously. Being in a mode or in a key is not the same as just identifying the modes of a scale.

This is a very open question, and hard to answer.

for 4ths the 4th degree gives us a b5 interval rather than a P4

This is called the "tritone" and it is in modern harmony what defines a dominant chord. If you look at the dominant 5th (say, G7 for C ionian), you see that it's made up of G - B - D - F.

The interval B - F, although technically a 5th, it's a b5, which is the same interval as F - B. Harmonically, this interval is considered to constitute a "dominant" chord and it's the key for dominant substitution (ie: you can substitute G7 for C#7 and you will find that it contains the same tritone: C# - F - G# - B)

When you look at the 6ths you get quite a different pattern of major/minor

I don't know what to respond to this. I find that the 6th interval creates a very rich, diatonic sound (ie: it shows the tonality of the scale a lot), and it's use extensibly in rock and country. I have also heard it called the "Nashville scale".