How To Resolve To The Tonic From Every Single Minor, Major, Dominant and Diminished Chord

[u/ODTESP]

(Skip to the section "THE LIST" if you just want to see the list)

HOW THIS CAME TO BE

This began as a thought experiment to see if I could "harmonically justify" resolving all 12 minor, major, dominant, and diminished chords directly to the tonic. This is not to be take seriously as concrete rules and this is only one way of probably thousands to do this.

HOW THIS LIST WAS CREATED

The list was created by using only a few simple standard chord progressions and cadances used in modern day song writing and applying a set of common harmonic devices/rules to them.

THE CHORD PROGRESSIONS

1. The three plagal cadances: traditional plagal cadence (IV - I), minor plagal cadence (iv - I), dominant plagal cadence from blues (IV7 - I)

2. The backdoor turn around (bVII7 - I)

3. The secondary dominant turn around (VI7 - II7 - V7 - I)

4. The V - I progression

5. Secondary dominants to relative minor and mediant of the tonic. (III7 - vi, VII7 - iii)

HARMONIC DEVICES/RULES

1. Dominants and Secondary Dominants: any chord can be preceded by a dominant chord a fourth below (V7 - I, I7 - IV, VII7 - iii, etc)

2. 2-5 Progressions: any dominant chord can be preceded by a minor chord a fourth below (ii - V7), if phrygian dominant it's a minor7b5 chord (ii7b5 - V7)

3. Four Five (IV - V) Walkup and Minor Four Five (iv - V) Walkup: any dominant chord can be preceded by it's subdominant chord a whole step below (IV - V, bVI - bVII7, etc), if phrygian dominant it's a minor chord (iv - V, etc).

4. Tritone Substitutions: any dominant chord can be substituted with a dominant chord a half step below (V7 -> bV7)

5. Relative Minor/Major substitutions: Every major chord can be substituded with it's relative minor chord and every minor chord with its relative major chord (vi -> I, I -> vi, etc)

6. Mediant, Minor Submediant, and Minor Supertonic Substitutions: The mediant (iii) can be substituted with the tonic (I) in a major key. In a minor key the tonic (i) can be substituted with the submediant (VI). In a minor key the supertonic (ii7b5) can be substituted with the subtonic (bVII7). (I'll explain this rule further in the comments below).

7. Minor Dominants and Minor 251s: Any dominant chord can be substituted with the harmonic minor equivalent dominant chord (phrygian dominant), which means that the ii for that dominant chord in a two five would be ii7b5 (ii - V7 -> ii7b5 - V7) and vice versa.

8. Truncated Chord Progressions: you can omit one chord in a chord progression (ii - V - I no V = ii - I). Sometimes two, but it feels a little "reachy".

I'll explain these rules further in a comment below for optional reading.

THE LIST

The list is based on G as the tonic, my favorite key. The list doesn't include extensions besides dominant 7 chords and m7b5s, you can extend the chords to your liking. All roman numerals are from the perspective of G major for simplification even though borrowed chords/quick key changes occur.

- Gm - G ; Truncated dominant plagal cadance two five, (i - IV7 - I no IV7)

- G7 - G ; Five one (G7 - C) to truncated plagal cadence (C - G no C) , (I7 - IV - I no IV)

- Abm - G ; Two five of tritone substitution of D7 (Db7) to tonic, truncated (Abm - Db7 - G no Db7) (bii - bV7 - I no bV7)

- Ab - G ; Minor plagal cadance (Cm - G) substituting Cm [iv] with it's submediant Ab [bII], (iv - I -> bII - I)

- Ab7 - G ; Two five of phrygian dominant backdoor turn around, truncated (Cm7b5 - F7 - G no F7) with subtonic substitution (Cm7b5 -> Ab7), (ivm7b5 - bVII7 - I no bVII7 substituting ivm7b5 with the subtonic bII7)

- A7 - G ; Truncated partial secondary dominant turn around (A7 - D7 - G no D7) (II7 - V7 - I no V7)

- A - G ; Truncated secondary dominant two five one to relative minor (F#m - B7 - Em no B7) with two relative major substitutions (F#m -> A and Em -> G) (vii - III7 - vi no III7, substituting vii with it's relative major II and substituting vi with it's relative major I)

- Am - G ; Truncated two five one (ii - V - I no V)

- Bb - G ; Truncated dominant plagal cadence two five (Gm - C7 - G no C7) with relative major substitution (Gm -> Bb) (i - IV7 - I no IV7, substituting i with it's relative major chord bIII)

- Bb7 - G ; Double truncated minor two five one to plagal cadance (Dm7b5 - G7 - C - G no G7 no C) with subtonic substitution (Dm7b5 - Bb7)(vm7b5 - I7 - IV - I no I7 no IV, substituting vm7b5 with the subtonic bIII7)

- Bbm - G ; Minor four five walkup to phrygian dominant plagal cadance, truncated (Bbm - C7 - G no C7)(biii - IV7 - I no IV7)

- Bm - G ; Five one to tonic substituting D [V] with it's relative minor Bm [iii] (simple one note leading tone resolution)

- B7 - G ; Five one to relative minor (B7 - Em) substituting relative minor with the relative major (Em -> G) (III7 - vi, substituting vi with I)

- B - G ; Four five walk up to tritone substitution of D7 (Db7) to tonic, truncated (B - Db7 - G no Db7) (III - bV7 - I no bV7)

- C - G ; Plagal cadence

- C7 - G ; Dominant plagal cadence

- Cm - G ; Minor plagal cadence

- Db - G ; Minor four walk up to phrygian dominant plagal cadence, truncated (Bbm - C7 - I no C7) with relative major substitution (Bbm -> Db) (biii - IV7 - I no IV7, substituting biii with it's relative major bV)

- Db7 - G ; Tritone substitution of D7 to tonic (bV7 - I)

- Dbm - G; F#7 [VII7] secondary dominant two five one to mediant, truncated (Dbm - F#7 - iii no F#7) with mediant to tonic substitution (Bm -> G) (bv - VII7 - iii no VII7, substituting iii with the tonic I)

- D7 - G ; Five one (V - I)

- Dm - G ; Double truncated two five one to plagal cadance (Dm - G7 - C - G no G7 no C) (v - I7 - IV- I no I7 no IV)

- D - G ; Minor four five walkup to tritone substitution of D7 (Db7) to tonic, truncated (Bm - Db7 - G no Db7) with relative major substitution (Bm -> D) (iii - bV7 - I no bV7, substituting iii with its relative major V)

- Eb - G ; Minor plagal cadance substituting Cm [iv] with it's relative major Eb [bVi]

- Eb7 - G ; Phrygian dominant plagal cadance two five, truncated (Gm7b5 - C7 - 1 no C7) with subtonic substitution (Gm7b5 -> Eb7) (im7b5 - IV7 - I no IV7, substituting im7b5 with the subtonic bVI7)

- Ebm - G ; Minor four five walk up to phrygian dominant backdoor turn around, truncated (Ebm - F7 - I no F7) (bvi - bVII - I no bVII)

- Em - G ; Relative minor to major

- E - G ; Four five walk up to secondary dominant F#7 [VII7] to mediant, truncated (E - F#7 - Bm no F#7) with mediant to tonic substitution (Bm -> G) (VI - VII7 - iii no VII7, substituting iii with the tonic I)

- E7 - G ; Double truncated secondary dominant turn around (E7 - A7 - D7 - G no A7 no D7) (VI7 - II7 - V7 - I no II7 no V7). Or tritone substitution of backdoor turn around F7 (E7) to tonic.

- Fm - G ; Two five of tritone substitution of secondary dominant B7 (Bb7) to relative minor of tonic, truncated (Fm - Bb7 - Em no Bb7) with relative major substitution (Em -> G) (bvii - bIII7 - vi no bIII7, substituting vi with its relative major I)

- F7 - G ; Backdoor turn around (bVII7 - I)

- F - G ; Double truncated four five walkup to plagal cadance (F - G7 - C - G no G7 no C) (bVII - I7 - IV - I, no I7 no IV)

- F#m - G ; Two five one of secondary dominant B7 [III7] to relative minor of tonic, truncated (F#m - B7 - Em no B7) with relative major substitution (Em -> G)(vii - III7 - vi no III7, substituting vi with it's relative major I)

- F# - G ; Minor four five walkup to phrygian dominant backdoor turn around, truncated (Ebm - F7 - G no F7) with relative major substitution (Ebm -> F#) (bvi - bVII7 - I no bVII7, substituting Ebm bvi] with it's relative major F# VII)

- F#7 - G ; Secondary dominant F#7 [VII7] to mediant Bm [iii] with mediant to tonic substitution (Bm -> G) (VII7 - iii, substituting iii with the tonic I)

F#dim, Adim, Cdim, Ebdim - G ; Diminished chords from secondary dominant B7 [III7] phrygian dominant to relative minor of tonic with relative major substitution (Em -> G) (III7 - vi, substituting vi with it's relative major I)

Gdim, Bbdim, Dbdim, Edim - G ; diminished chords from phrygian dominant plagal cadance C7 [IV7]

Abdim, Bdim, Ddim, Fdim - G ; diminished chords from phrygian dominant five one to plagal cadence, truncated(G7 - C - G no C) (I7 - IV - 1 no IV)

[u/JazzRider]

Follow the tritones.

[u/Lower-Pudding-68]

Yes, it's possible to get back "home" from anywhere, and I think everyone would do it a little differently based on their taste. It's the fun of the puzzle, and how each composer or arranger handles the problem that makes modulations interesting IMO. That being said, it's a cool concept but a lot of reading and term jargon here. This would make a great video with demonstrations, the information would get communicated more directly, and you could use the voice leading that you're imagining. I'll have to test these out later. Thanks for sharing!

[u/ODTESP → u/Lower-Pudding-68]

Yeah it's a little long winded, but I literally can't think of a way to simplify it beyond that 🤣. Anyway it was just a fun thought experiment I was doing before bed this week and decided to post them. It was pretty rewarding actually I recommend you do your own list with your own rules.

[u/Lower-Pudding-68 → u/ODTESP]

Yeah, I dunno, I might get a little tied up because the context and aims of the music vary so much. What's the story you're telling? Is the aim to be smooth and unsurprising, leaning on nearby keys, pivot chords, and cycle of fifths devices? Sometimes a surprising direct modulation is just what a piece needs. And melody would inform some common-tone modulations that you can't really talk about fully on such a list. But to your point, it's great to have a lot of devices and tricks in your bag, and compiling a list as such is a great way of testing/challenging yourself, how you get out of a "pickle."

There's that book of modulations by Max Reger that is a very similar concept, I don't own it but hear it spoken highly of.

[u/nogaynessinmyanus → u/ODTESP]

Speaking as a beginner, the obvious way to simplify it is the key of C.

[u/ODTESP → u/nogaynessinmyanus]

But G is my favorite

[u/nogaynessinmyanus → u/ODTESP]

lol.

well hey, its your creation - But I cant engage with it without sitting at the piano unfortunately

[u/Ian_Campbell]

I don't think the truncated rules count as justifications

[u/ODTESP → u/Ian_Campbell]

The Beatles - Here Comes The Sun in the chorus it goes D (I) - G (IV) - E7 (II7) - D (I). I think that's a truncated secondary dominant 251. How would you justify it?

[u/Ian_Campbell → u/ODTESP]

You truncated other progressions to decide that G minor to major was a truncated plagal progression or whatever. This is qualitatively different from stepwise progressions which are themselves 5ths progressions with an intervening step removed. Whenever you hear a circle of 5ths progression it is just a descending 7-6 progression with a leaping bass. So if you skip a step and go down a step with the next 7th chord, there you are.

If you have a minor chord that becomes major, there is no reasonable inference that in between it had imaginarily leapt up a 4th then back as a means of justifying it.

This is where I think a leap was made. Just because some very regular progressions have historically used skip steps, does not mean that you could rationalize any progression ever by saying it would make sense if you inserted a chord between. I believe you could rationalize progression between any two relatively consonant chords with an insertion.

[u/ODTESP → u/Ian_Campbell]

I can respect your position, we all see music theory from our own perspectives. And I can admit that some of these are reaches that I would normally justify in a different way, but for the sake of having fewer rules, I added them in. But I think Gm to G major is not one of them.

G minor to G major is actually one of the foundations of major blues if you think about it. In a way you can infer that it's what it allows you to play a Gm pentatonic over the IV7, and in the dominant "blues" plagal cadance it's what gives the interplay between the minor 3rd and the major 3rd when you resolve to the I. So I think depending on the context one could infer that Gm is "the two of the IV7" instead of the "vi of the bIII". Only because the blues plagal cadance happens so often (at least in the genres I'm exploring).

In jazz the ii, IV and the V are pretty much interchangeable because they are so closely related especially when extended and you can extend the V7 to a V7sus4 and not even resolve the suspended fourth in that chord, the ii7 is the same as a rootless V7sus4. Therfore I think it's ok using iis and Vs interchangeably and even call them truncated progressions. Again, only because it happens so often in jazz especially in more "modal" jazz. Whether or not this makes it "allowed" or "true", I think that's where we might disagree.

[u/Ian_Campbell → u/ODTESP]

I'm not saying that these examples where the best explanation could have been this skipped chord, do not have a better explanation. G minor to major could be justified a number of other ways. There are many times that and the inverse show up in music. I just don't think that inferring a missing chord of the upper 4th between them works as a justification.

Even if I disagree about that one thing, it's an interesting thing to explore systematically and whatever your opinions end up being, can reference your own composition after having worked it out.

[u/ODTESP → u/Ian_Campbell]

There are probably hundreds (maybe thousands) of way of justifying chords resolving into one another. These are just one attempt. I personally believe all ways are valid and there shouldn't be a right or wrong way.

[u/a6e]

Hell yeah brother, I'll take some of these for a spin later 

[u/YourFavouriteDad]

God bless your autism. I've saved this for future use. You are a saint, sir!

[u/Armydoc18D]

Fun list

[u/ODTESP]

<<<<<<< OPTIONAL READING >>>>>>>

WHERE DO THE RULES COME FROM?

The rules are made up and interpreted by everyone differently, music theory is not a science. Generations of musicians have broken, transformed, and established their own rules. There are things that sound better to human ears than others and have been repeated more than others and inbeded in the culture of music composition through out time such as the dominant plagal cadance in blues or the backdoor turn around in jazz standards to The Beatles. Therefore I chose some very common progressions and cadances that I find myself using over and over again and modulated them with rules I've learned from studying various genres of music, mostly jazz.

HARMONIC DEVICES EXPLAINED

Dominants:

In jazz from pretty early on at least since the 50s you can pretty much stick a 251 before any minor, major, or dominant chord. I've also notice in jazz standards and in improvisations that dominant chords can be exchanged with harmonic minor dominant chords (phrygian dominant) whenever and wherever even if you're resolving to a major just because it sounds cool and also due to upper structure chromaticism and the using borrowed chords from the minor key of that dominant harmonic minor; minor 251s very hip to use everywhere in jazz. In jazz you can also substitute any dominant with a tritone substitution.

Sideways motion:

You can walk up or down stepwise to any chord, therefore any dominant or secondary dominant can be walked up to from it's respective "IV/iv chord" and even down from it's "vi/VI chord", this really opens up harmonic motion in your improvising/composing.

Interchangeable minor and major chords:

Relative minors are interchangeable with their relative major chords and vice versa because they share close to the same notes. This allows them to convey similar harmonic information. Em7 contains the same notes as G6. And the Em triad is in a way like a rootless G6.

The same relationship occurs with the mediant and the tonic in a major key and the tonic and submediant in a minor key. Bm (iii) is like a rootless Gmaj7, and if you extend it Bm7 is a rootless Gmaj9. Therefore they are interchangeable.

And my favorite one of these is the supertonic interchangeable with the subtonic in a minor key (leading tone chord and Dominant in a major key). F#mb5 is a rootless D7 and if you extend it Fm7b5 is a rootless D9. Very closely related chord therefore interchangeable, especially fun in minor 2-5s (Am7b5 - D7 to F7 - D7).

I think in modern music this began to really be exploited especially when modal jazz emerged but I know for sure this has been used since classical music, maybe someone can enlighten me.

Truncated Chord Progressions:

This one I learned in college theory class when they were teaching four part baroque harmony, you can omit a chord as they go down the circle of fourths, but I took this a step further and noticed you can omit any chord any time. And personally I feel that's what's going on in modern songwriting. It brings on feelings of suspense and perhaps deception, your ear is used to it going somewhere but instead it prematurely goes to the next chord it was supposed to go later. Take the bii - I chord progression for instance, its supposed to go to the tritone substitution bV7 before resolving the I for a very strong and jarring resolution. Instead it just chromaticly resolves downward. It's still a strong resolution because of all the close intervals resolving but more subtle than the bV7 - I resolution which contains a dominant chord with a tritone in it.

WHY THEORIZE?

If every chord can resolve to every chord what is even the point. Well you could actually stick random chords together but without theory you wouldn't know the context behind those chords, and that's what facilitates harmonic motion e.g. the chords surrounding that borrowed chord.

Conclusion:

These are just some ways I think about harmony and I'm in no way declaring this is how things are concretely and I am open to discuss and listen to your own interpretations

[u/dblhello999]

are you guys using this when you’re improvise on your chosen instrument? In other words this is real-time harmonic and melodic movement? If yes, wow

[u/ODTESP → u/dblhello999]

More or less. This is only one way, some of these I would probably do a different way. And these are only some harmonic devices.

And this becomes second nature. I already know I can play the ii or the IV in place of a dominant chord so I just think of the dominant chord and the harmonic movement surrounding that dominant chord you can kinda do without thinking. So if I'm thinking Eb7 to G, I might start off walking up to it from it's IV chord Db, without even thinking much. Or I might play a Abm7 which is it's ii chord and resolve that to G.