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I've been looking at chord progressions on HookTheory. But I'm a bit confused by the relative notation. For example here: https://www.hooktheory.com/trends#node=1.57&key=rel

It is possible to switch between a certain key and relative notation in the dropdown box.

Here the V⁷ corresponds to a seventh chord, while ii⁷ corresponds to a minor seventh, IV⁷ to a major seventh. And then I♭⁷ corresponds to a seventh chord. Is it dependent on the scale degree what kind of seventh it is? Or is the V chord a special case, so that when a 7 is given in superscript then it is a seventh chord, and not a major seventh?

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For any given scale we can decide a set a chords that best go with it—that is the chord tones are picked directly from the scale—by harmonizing it in thirds starting from each scale degree.

So take C Major

note C D E F G A B degree 1 2 3 4 5 6 7

So the first chord starts with C then jumps a 3rd to get E then another get G. Notice that we didn't jump a major 3rd to G# we stayed within scale and used G (E to G is a minor third). Finally jump another 3rd to get B making our final chord: C, E, G, B (CMaj7).

Essentially all we're doing is taking every other note (diatonic thirds) from the scale we wrote out. That will give us a set of chords whose relative qualities will stay the same no matter what note you start from (the key you're in):

IMaj7 - CMaj7 - C E G B iim7 - Dm7 - D F A C iiim7 - Em7 - E G B D IVMaj7 - FMaj7 - F A C E V7 - G7 - G B D F vim7 - Am7 - A C E G viim7b5 - Bm7b5 - B D F A

So if you changed to a D major scale, the iim7 and V7 would now be Em7 (EGBD) and A7 (AC#EG) but ii is still a m7 and the V still a (dominant) 7. So, yes, it depends on the scale degree.

As for some of the confusion over 7ths, yes when it just "7" that's a regular 7th chord or a "dominant" 7th chord that has major 3rd but lowered 7th (C7=C,E,G,Bb). A Major 7th has the major 7th (CMaj7=C,E,G,B) and will be designated as either Maj7 or use a little triangle instead of the "Maj".

You also briefly mentioned a Ib7. While that's not the notation that I'd use, the "b" is probably a courtesy to let you know that the 7th is lowered in this particular I chord which would make it a dominant 7 or a I7. It's worth noting that just because we made a set of chords that are made up entirely of scale tones that doesn't make we can't sometimes use notes from outside of the scale. For instance in a lot of blues and pop you'll see I-IV-V progressions where they are all dominant 7ths.

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The superscripts in Roman numeral analysis come from figured bass notation. This was a notation used in the Baroque period that allowed the continuo player (e.g. harpsichordist, organist, lutenist, ...) to improvise over the written bass note by using the given notes above the bass. Continuo parts were not written out, because they didn't always know what instrument would be playing them, and they wanted to allow maximum flexibility.

For example, a figured bass 53 means a root position triad, whereas 63 means a first inversion triad, and 753 means a 7th chord. But the 5 and the 3 became so common that they were omitted; thus root position now no longer has any numerals, whereas first inversion has only 6. Finally, 7th chords are now denoted 7.

All figures (not just 7ths) were understood to be in the current key, i.e. without introducing new accidentals. For example, in the key of C major, a ii6 is a ii chord in first inversion, i.e. (bottom to top) F, A, D, or F, D, A (figured bass does not distinguish between these).

By going through the different possible 7th chords (among which, in major, ii7, IV7, V7, and vii ø7 are the most common), you can easily see which 7th chord has which chord quality: ii7 is a minor seventh chord, IV7 is a major seventh chord, V7 is a dominant seventh, and vii ø7 is a half-diminished seventh.

You can alter the quality of the seventh chord by adding accidentals to the figured bass, e.g. ♭7 instead of 7. But in certain cases, it is more natural to write the harmony as an applied harmony instead; for example I ♭7 is really V7/IV, and II 7 ♯3 is really V7/V.

In minor, the situation is exactly the same, except with some conventions around the leading tone. Technically one should write V 7 ♯3 to indicate the dominant seventh chord, but the ♯3 became understood, so the notation simplified to V7. The situation is similar for chords based on ♯vii° (leading tone diminished chords): the ♯ in front gets dropped because it is understood. But beware that other chords (like III) can still have the lowered 7th scale degree in it.

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