Jazz standards are often shared as "charts" or "lead sheets", which are simplified sheet music that show a piece's melody, annotated with chord symbols. This information is enough for jazz bands to coordinate and play complex music together, or enough for a competent jazz pianist to perform an ornate solo piece for piano.
I'm going to talk about some methods that a jazz pianist/composer might use, starting from a lead sheet, to fully realize a piece of music.
:: Harmony, Voicing, Chord Movement
1. Closed voicings, Root position triads and tetrads: The most basic thing you could do with the chords written is to play them in root position below the melody, voiced exactly as they are notated, i.e. tertian voicings, with occasional alternations for suspended chords, sixth chords, missing upper chord tones, et cetera. For the most part, you'd play ^1, ^3, ^5, ^7 in that order, and you just hold the chord until the next one comes along. Super boring.
2. Closed inversions: Instead of playing the root note constantly in the bass, look at the melody when a chord appears. If, when the chord comes into play, the melody has a chord tone of that chord, then play whatever inversion of the chord puts the melody note at the top. If the melody doesn't have a chord tone when the chord comes in, find the next note of the melody that is a chord tone, and play the lower notes like the inversion that fits it, and then just move the upper note with the melody. You can also chose inversions on the criterion of minimizing how much your hands move over the keyboard, for smoother voice leading at the expense of not nestling up so tightly to the melody. Maybe the melody needs some space sometimes.
3a. Shell voicings: The next trick you might try is to play the chord more spread out over two hands, perhaps playing (^1 and ^3) or (^1 and ^7) (or (^1 and ^10) if you can reach it) in the left hand (a "shell") and other chord tones in the right hand. On .m6 and .maj6 chords, you can use ^6 instead of ^7 in the shell. Dropping ^5 from the chords entirely, when the chord contains a perfect fifth, is another good way to create a more open, spread out voicing in jazz. And if you have a bass player, then it's common for a pianist to not play the root note. You can also play a shell in the left hand and a triad/tetrad inversion in the right hand to match the melody.
3b. Drop 2 voicings: If you start with a closed triad/tetrad or one of its inversions and you drop the second note from the top - drop it down an octave - that's a drop 2 voicing. They're a very nice way to give you a more open sound without too much thinking. The dropped note will be your bass note, instead of a shell. This is an alternative to shell voicings, not really a step more or less advanced. They're both good techniques. You can use one or the other in different sections. Once you're familiar with them, you might try combining them to see if you can get smoother voice leading from the combined space of open chord voicings, shell and drop two.
To get comfortable with drop-2 voicings, first try e.g. all the C.maj or C.maj7 inversions with dropped notes. Just get comfortable moving between them. Then try F.maj or F.maj7. Now move between C.maj7 dropped inversions and F.maj7 dropped inversions. Now introduce G.7 dropped inversions or D.m7 dropped inversions. Get comfortable moving between each pair of chords types. It's really pretty powerful.
4a. Barry Harris chord movement: Especially when a melody moves by 1st and 2nd intervals, there's an easily applied technique for chord movement in the right hand that is taught by Barry Harris. Every note of such a melodic phrase has a chord under it. Suppose the chord indicated over the phrase is C.maj6. The scale which matches this is the major6-diminished scale, [C, D, E, F, G, Ab, A, B]. If you play alternating notes of this scale, you either get inversions of C.maj6 (i.e. [C, E, G, A]) or inversions of B.dim7 (i.e. [B, D, F, Ab]). When you have a melody that moves by step, you can apply one of these chords below each melody note, usually alternating between a C.maj6 inversion and a B.dim7 inversion. In the Barry Harris system, other chord types are associated with other scales. We'll just look at major6-diminished and minor6-dininished scales. In either one, you're just swapping between inversions of two chords and using that to make chord runs in lockstep with the melody.
So the C major6-diminished scale works with C.maj6. The chord A.m7 is an inversion of C.maj6, so the C major6-diminished scale scale also works with it. More generally, any time you have a .m7 chord, you can use the major6-diminished scale that's rooted a minor third above the tonic of the .m7 chord. Also, clearly the C major6-diminished scale works with the B.dim7 chord. For any .dim7 chord, you can use the major6-diminished scale that is rooted a minor second above the tonic of the .dim7 chord. In 12-TET, things are even easier: B.dim7 is enharmonic with D.dim7, F.dim7, and Ab.dim7, so you can play the C major6-diminished scale with lots of things.
So with just one scale, we can play chord movement over melodies when there is an annotated chord of any with a .maj6, .m7, or .dim7 quality. Pretty handy.
Next let's look the minor6-diminished scale. In this one you interlace C.m6 with B.dim7, giving you a scale of [C, D, Eb, F, G, Ab, A, B]. Notice that this has a B instead of a Bb, so it's like a harmonic minor scale with an added note, rather than a natural minor scale with an added note. To get away from the key of C for a moment: if you see, oh, a G.m6 in a score, you can play the G minor6-diminished scale over it, and if your melody moves by small steps, 1st and 2nd intervals, then you can compose chord motions in your right hand that alternate between inversion of G.m6 and F#.dim7. And it will sound pretty good without much thinking.
One of the inversions of C.m6 is A.m7b5, so any time you see a chord with a .m7b5 quality, you can play the m6-dim scale tht's rooted a minor third above that. For example, the key of C major has B.m7b5 as a diatonic tetrad, and a minor third over B natural is D natural, so you can play the D minor6-diminished scale when you see B.m7b5. Nestle the chords up to the melody and you'll have something quite pretty. Clearly the m6-dim scale also works over dim7 chords.
What if you see a .maj7 chord? In the Barry Harris system, you generally treat annotated .maj7 chords as .maj9 chords. And, e.g. F.maj9 is just A.m7 over F, so you can play the C maj6-dim scale.
What if you see a dominant seventh chord, like G.7? In the Barry Harris system, you generally treat an annotated .7 chord like a .9 chord or a .7b9 chord. Let's look at some examples.
The chord G.9 is B.m7b5/G, and we've already seen that B.m7b5 goes with the D m6-dim scale, so you can play the D m6-dim scale over G.7.
The chord G.7b9 is B.dim7/G, so you can play either C minor6-diminished or C major6-diminished, because both of those scales work well with B.dim7.
How about Db.7, which is the tritone substitution of G.7? Well, in the Barry Harris system, we could treat this as Db.9, which is F.m7b5/D. So we could play Ab major6-diminished.
Alternatively we could treat Db.7 as Db.7b9, which is the same as F.dim7/D, and that would lead us to play Gb maj6-dim or Gb m6-dim. I think.
So now we've covered .6 and .m6 and .m7 and .maj7 and .7 and .dim7 and .m7b5. And those are pretty much all of the functions of chords in jazz. Every chord you see in jazz will either function like one of those, or perhaps be a non functional passing chord. I think. I'm not so sure about augmented chords. Sometimes they're passing chords in line cliches. Sometimes they're altered dominant chords. Probably other things.
One more trick that fits neatly into the Barry Harris method of chord movement is to move a few notes through the relevant diminished scale in lockstep with the melody, but not the whole chord in your right hand. So you might have two notes fixed, and move two notes through the scale. This can create very cool harmonies with very little thought as to what you're really doing.
We could talk a little more about Barry Harris methods and concepts, like how every dim7 chord is related to four dominant chords, but I think that's probably enough for now.
4b. Chord movement by partial inversion: Complex chords with upper extensions can often be played as one triad/tetrad over another triad/tetrad. I might call these polychord voicings.
The benefit of thinking of upper extension chords in terms of two triads or tetrads is that triads and tetrads are invertible, whereas chords spanning more than an octave (9th chords, 11th chord, 13th chords) are not. So while your left hand is fixed playing one thing (or perhaps busy playing a bassline), the other hand can move through inversions of its notes (and passing chords between the inversion). The Barry Harris chordal movement system is a simplified form of this that doesn't require much thought, but you can find inversions within more types of chords than Harris specified and you can use more kinds of passing chords than dim7.
Before talking about partial inversions over polytonic chords, let's just have a primer on upper chord extensions.
Here are some brief tips for getting into extensions.
* The .m7 and .m6 both play well with [9, 11, 13]. See a minor chord quality, play natural extensions.
* The .maj7 and .maj6 both well with [9, #11, 13]. See a major chord quality, play #11.
* The .dim7 and .m7b5 both play well with [9, 11, b13]. See a diminished chord, play a b13.
* Finally the .7 plays well with basically anything from here [b9, 9, #9, 11, #11, b13, 13], but you don't learn them by picking randomly from that set. The quick rule of thumb I follow gives you templates in 3 families:
1) You can play all natural extensions, or.
2) You can play b9 or b13 or both, or
3) You can play #9 or #11 or both.
People will play more kinds of dominant chords than just those - for example, an V.7alt chord in a 2-5-1 might have any extensions in addition to b5 or #5 (though you won't get [b5 with #11] since these are enharmonic in 12-TET, nor [#5 with b13]). Anything is pretty much fair game. But those three templates are the first categories to learn.
Again, for all these chords, (minor, major, diminished, dominant), you don't have to play every extension, but try selecting upper extensions from this pool. Try these sounds to start, anyway. They're worth getting to know.
Where do these sounds rules for upper extensions come from? You just find tables of "available" extensions online, usually in tandem with a discussion of "avoid notes". They're not all identical, but they're all close. I don't know who came up with them. The earliest reference I've found is in an issue of Musician magaize in the late seventies. I wouldn't be shocked if it was some professor as Berklee College of Music.
This particular set of available extensions came from Walk That Bass on youtube. But there's nothing magic or theoretical about them. You just have to start somewhere and these are some nice sounding chords.
A little reflection will show there are common and good sounding chords that aren't captured by the rules of this table. For example, if we looked at diatonic .maj7 extensions in a major scale, we have [9, 11, 13] on scale degree I and [9, #11, 13] on scale degree IV. If we looked at diatonic .m7 extensions in a major scale, we have [9, 11, 13] on II, and [b9, 11, b13] on III, and [9, 11, b13] on VI. But it's good to get away from diatonic chords and learn specific sounds. Jazz is more than just "skip a note, play a note" for a given scale.
Okay, back to polychords.
Here are some chord voicings that can be broken up in triads or tetrads in each hand. Bill Evans loved chords like these:
A.maj/B.m7b5 is B.m11b5.
C.maj/D.m is D.m11.
A.maj/G.7 is G.13#11.
Bb.maj/G.maj is enharmonic to G.7#9 in 12-TET.
Eb.maj/G.7 is enharmonic to G.7#9b13 in 12-TET.
Db.maj/G.maj is enharmonic to G.7b9#11 in 12-TET
I think I specifically found those on a site talking about how to sound like Bill Evans.
Let's cover some polytonic voicings of the available extensions from Walk That Bass. We'll look at 13 chords that occupy every extension.
C.m13 = C.m7 + (D.m or D.m7) _ Diatonic on II.
C.maj13#11 = C.maj7 + (D.maj or D.7) _ Diatonic on IV.
C.m13b5 = C.m7b5 + (D.m or D.m7)
All of them can be expressed with a right hand chord rooted on D natural! Pretty cool. And even better, you can play minor over minor and you can play major over major. Super easy to remember. Let's also look at polytonic voicings of diatonic 13th chord qualities not already discussed:
C.maj13 = C.maj7 + (D.m or D.m7) _ Diatonic on I
C.m11b9b13 = C.m7 + (Db.maj or Db.maj7) _ Diatonic on III.
C.13 = C.7 + (D.m or D.m7) _ Diatonic on V.
C.m11b13 = C.m7 + (D.dim or D.m7b5) _ Diatonic on VI.
C.m11b5b9b13 = C.m7b5 + (Db.maj or Db.maj7) _ Diatonic on VII.
These aren't as easy to remember. Some have Db as a tonic, and they all have mixed sonorities in the two hands. I think they're still valuable chords to learn. One should be able to play the II chord's extended sonority on top of scale degree VI and vice versa.
So there's a simple library of ways to extend your chords with polytonic voicings. The full 13 chord gives you a scale that you could makes runs over. Or you could harmonize a melody using inversions of the left hand chord and the right hand chord. Hopefully all of your melody notes for the measure are in that 13 chord? I guess you can just throw a .dim7 on any melody notes that aren't in either scale. Aother option would be to use only inversions of the right hand chord and .dim7 chords to harmonize the melody.
I said before that you're not limited to .dim and .dim7 passing chords when you advance past Barry Harris. They're still great, but what else can you use? Well, there are lots of weird chords that are suggested by functional chord grammars that categorize most chord types as {Predominant, Dominant, or Tonic} and then tell you how to link them up. We'll look at those in the next section. There are a few chords that I treat as mostly non-functional, that aren't included in these grammars. One such chord is of course the .dim7 chord. You can almost always precede a chord X.y with a .dim7 chord whose tonic is a half step below X. Besides the .dim7 chord quality, my chord grammars don't cover suspended third chords, such as .sus2 and .sus4, and those definitely are usable in some genres as passing chords. I don't use them much in jazz and I'm not going to write about them here. I think, more often in jazz if you see a .sus2 chord, it's just an inversion of a 9 chord with no third present. The difference is whether the there's melodic motion between the 3rd and the 2nd, and I think usually there isn't. I could be wrong, but I'm skipping suspended third chords in this text.
My functional grammars also don't cover augmented chords. Let me show you my best notions for using augmented chords in passing. Here, in brackets, are some transitions between diatonic triad chords, followed by augmented chords that work well in passing between the triads. In these examples, the augmented chord will usually have the same tonic as the first chord, or sometimes the tonic of the second chord.
:: Augmented passing chords.
Tonic with Tonic.
* [I.maj → VI.m]: I.aug # 1-6
* [VI.m → I.maj]: I.aug # 6-1
* [III.m → VI.m] : III.aug # 3-6
Predominant with Predominant.
* [IV.maj → II.m]: IV.aug # 4-2
* [II.m → IV.maj]: IV.aug # 2-4
Tonic with Predominant.
* [I.maj → II.m]: I.aug # 1-2
* [I.maj → IV.maj]: I.aug # 1-4
* [III.m → IV.maj]: III.aug # 3-4
* [VI.m → II.m]: VI.aug # 6-2
Dominant with Tonic.
* [V.maj → III.m]: V.aug # 5-3
* [III.m → V.maj]: V.aug # 3-5
* [V.maj → I.maj]: V.aug # 5-1
~ [VII.dim → VI.m]: VII.aug # 7-6
~ [VII.dim → I.maj]: VII.aug # 7-1
Predominant with Dominant.
~ [II.m → V.maj]: II.aug # 2-5
The best sounding ones are marked with asterisks. The last three progressions sound less polished and are instead marked with tildes. If you want to make more interesting chord progressions, try putting some augmented chords into these places. See how you like it. Try adding 7ths as well.
5. Functional extension of chord progressions: Chord progressions have structure, and you can use the rules of chord progression structure to add in more chords between notated chords. In this way, you could have a chord on every beat or every eighth note or a chord at any other temporal granularity you want. Alternatively you could have a chord for every melody note, and thus play with the same rhythm as the melody, or play chord onsets over a subset of the melody onsets.
Here's the basic idea of functional chord progressions in a major key. Some chords are predominant, some are dominant, and some are tonic. Chord progressions go
[PreD → D → T]
or
[T → PreD → D → T]
You can also skip the predominant. You can also sometimes skip the dominant (a "plagal cadence"). The rules aren't that rigid. They don't rule out most progressions, but they have enough structure to help you think of progressions.
Let's look at which diatonic chords have which functions.
The chords II.m and IV.maj are predominant.
The chord V.maj and VII.dim are dominant.
The chords I.maj and VI.m are tonic.
So you might have a 2-5-1 progression or a 4-5-6 progression or a 4-7-1 progression, and those are all [preD → D → T]. You can also play more than one chord in each category before progressing to the next category. It's called prolongation. This isn't done to excess, but it's legal.
What about III chords? They're a little ambiguous. Some people will tell you that they're tonic primarily and predominant secondarily. They definitely can go before pre-dominants, which is compatible with a tonic function, [T → preD → D → T]. And they go pretty well before VII.m, which is compatible with being tonic if you consider that you can play more than one chord in each category before progressing to the next category [T] => [T →T]. And if you're just alternating [T → D → T], well, that explains why people might think it has a predominant function. Let's just call III weakly tonic. Here's a chord progression in which you might use III.m7: 1-3-6-2-5-1. Tep steps of tonic prolongation. Another popular progression with III.m7 is 1-2-3-2-1, and I guess I'm recommending that we analyze that as two plagal cadences, like [T → preD → T → preD → T].
Now let's put these categories into practice. Let's say you have an annotated F.maj7 in the key of C, which is to say IV of C. If we want to add in chords before this, we can do a "temporary tonicization", i.e. treat F.maj7 as a tonic chord and use a progression that ends on F.maj7, and then F.maj7 goes on to function in the progression in C.maj. One option is to place a "secondary dominant" before the notated chord, i.e. a dominant of F.maj7. This doesn't just mean the fifth diatonic chord of F major, i.e.
V.7/IV = C.7.
It could be any chord with a dominant function, e.g.
the diatonic seventh of F major, VII.m7b5/IV = E.m7b5
the tritone substitution of the fifth of F major, bII.7/IV = Gb.7
the backdoor dominant of F major, bVII.7/IV = Eb.7
I told you about diatonic chord function before, but now you're seeing some non-diatonic functions. All of these chord can get extensions if you're feeling sassy.
Now that we're playing a chord progresson with a [D → T] function, like [V.7 → I.maj7], we might as well extend it back and play a 4-5-1
[IV.maj7 → V.7 → I.maj7] = [Bb.maj7 → C.7 → F.maj7]
or a 2-5 1
[II.m7 → V.7 → I.maj7] = [G.m7 → C.7 → F.maj7]
or a 6-2-5-1
[VII.m7 → II.m7 → V.7 → I.maj7] = [D.m7 → G.m7 → C.7 → F.maj7]
And all of those "C.7"s can really be any of the secondary dominants we mentioned.
Now let's forget the temporary 5-1 progression targeting F.maj. Another thing we could do is put an A.m before the F.maj, like a fragment of a 6-4-5-1 in C. You know, the Heart And Soul progression. And if we have an A.m, why not target it with a minor 2-5-1?
[B.m7b5 → E.7b9 → A.m7 → F.maj7]
I didn't talk about functional categories in minor keys, but, uh, there's a minor 2-5-1 for you. They usually have altered dominant chords.
Actually, let's go over functional harmony in minor keys. There seem to be two schools of thought. One school says, "Functional harmony in a minor key is the same as in a major key. [F.maj → G.maj → A.m] is [PreD - D- T] regardless of whether your key is A minor or C major. That's a fine perspective. But you might notice above that a B.dim in the key of A minor is acting as a predominant instead of a dominant, as it does in the C major. I've seen at least four people give assignments of diatonic chord functions in minor keys that are consistent with B.dim being predominant. They largely agree. I'll let you look at them.
# PianoWalk.com:
Tonic: I.min, I.m7, I.m-maj7, III.maj7, III.maj7#5, VI.maj7, #VI.m7b5
Predominant: II.m7b5, II.m7, IV.m7, IV.7
Dominant: V.m7, V.7, VII.7, #VII.dim7, #VII.m7b5
# Dan from Music Theory Lessons:
Tonic chords: I.min, III.maj, VI.maj.
Predominant chords: II.dim, IV.min.
Dominant chords: V.min, V.maj, VII.dim or VII.maj.
# MusicTheory.pugetsound.edu:
Tonic: I.min, III.maj, VI.maj
Predominant: IV.min, II.dim
Dominant: VII.dim, V.maj
?: VII.maj // Listed as functional but not categorized.
# Jeff Schrepfer, sourcing functions from many minor scales (the Aeolian mode, the Dorian mode, the harmonic minor, and the melodic minor scales).
Tonic: I.min, I.m6, I.m7, I.m-maj7, bIII.maj, bIII.maj7, bIII.maj7#5, VI.m7b5
Predominant: II.m7b5, II.m7, IV.min, IV.m6, IV.m7, IV.maj, IV.maj6, IV.7, bVI.maj, bVI.maj7
Dominant: V.7, VII.m7b5, VII.dim, VII.dim7
There's a little bit to unpack here, like how Jeff Schrepfer uses bIII.maj as a tonic chord, whereas the other sources use III.maj. I think they all mean C.maj is tonic in the key of A major, but Jeff realizes that C.maj is a minor third above A and uses bIII to indicate a minor third. This is good. Point for Jeff. But if you didn't realize that they were using different notation, you might think there was a disagreement about chord functions here instead of just chord notation.
But if Schrepfer is using e.g. VII to mean a major seventh, you'd expect him to use bVII for chords a minor seventh over the scale tonic, e.g. the diatonic G chords in various minor keys. But he doesn't list any bVII chords.
Here's my best summary of their lists. I think everyone agrees in their own way that
1. A.m7, C.maj7 are tonic.
2. B.m7b5, D.m7 are predominant
3. E.m7 and E.7 are dominant
They might also agree
4. G.7, G#.m7b5 are dominant
But are all silent on one or both of these.
Three of the sources say that F.maj and/or F.maj7 is tonic, but Jeff says that it's dominant.
I think that PianoWalk and Jeff Schrepfer, which seem to be the best of the sources, both say that F#.m7b5 is tonic in differing notation, and the other two sourcs are silent about this chord.
Let's look at one more resource on minor harmony in jazz. The website JazzAdvice.com reccomends gives these 13 chords in a minor key (let's show it in A minor to avoid disagreements about roman numeral notation):
A.m7 → A.m13
B.m7b5 → B.m11b5b9b13
C.maj7 → C.maj13
D.m7 → D.m13
E.7 → E.11b9b13
F.maj7 → F.maj13#11
G.7 → G.13
Most of these are the same as diatonic 13 chords in C major, with two differences. First, A.m13 has a major 13 interval here, whereas it was A.11b13 in the key of C major. And secondly, the V chord in jazz in a minor key is usually played as a dominant from the harmonic minor scale instead of a .m7 chord from the natural minor scale / Aeolian mode. If you keep grabbing alternative notes in the natural minor scale, you get E.11b9b13 as your full 13 chord. So these 13 chords are mostly diatonic in A natural minor, but the I chord and the V chord are diatonic in A dorian and A harmonic minor, respectively.
....
Anyway, you can keep adding chords functionally behind existing ones. It's great. They don't even have to connect to the chords before them, they just have to go somewhere.
Let's go back to major tonality. Want to see something crazy? We looked at this progression when talking about temporary tonicization.
[II.m7 → V.7 → I.maj7] = [G.m7 → C.7 → F.maj7]
Let's target the II.m7 with a minor 2-5-1.
[A.m7b5 → D.7alt → G.m7 → C.7 → F.maj7]
Layers upon layer of tonicization. Here's another cool trick. Here's a 2-5-1 to F.maj.
G.m7 → C.7 → F.maj7
We can replace the dominant V of F.maj, i.e. C.7, with a backdoor dominant from the parallel minor key, i.e. Eb.7 from the key of F minor.
G.m7 → Eb.7 → F.maj7
That will sound fine. Now the trick: instead of thinking of Eb.7 as bVII.7/IV, just think of it as V in Ab major, and precede it by II.m7 of Ab.major, for a backdoor 2-5-1.
Bb.m7 → Eb.7 → F.maj7
It sounds good.
You might want to do some of this ahead of time with pencil and paper to make sure that the chords you add in actually work with your jazz standard's melody. But with a little bit of play, you can create very cool progressions with which to harmonize a piece. And then you voice the chords with shells or drop-2s or invertible tetrads in each hand, and you throw .dim7 chords between whenever you feel like it, or augmented chords and sixth chords, which are also good for passing motions.
6. Non-functional Reharmonization
We just looked at functional chord grammars for choosing harmonizations. You can also ignore all of that and play chord sequences with that aren't generating by considering functional progress. For example, just a pick chord that harmonizes with the current melody note, and with the most melodically prominent note in the measure. Here's one notion of what it means for a chord to harmonize with another.
Every chord plays well with some notes and unwell with the rest. Jazz musicians like to ignore P1 or P5 as being too obvious, so don't try to harmonize a C in the melody with a C chord or an F chord, et cetera. Instead, pick a chord that hits ^3 or ^7 of a chord, or #5 or b5 if it has one of those. Those are strong harmonies. If you're feeling a little sassier, you pick a chord that puts your melody note on an extension, like 9, 11, 13. We've already seen a rule of thumb for which extensions work well with which chord types, but let's review:
* The .m7 and .m6 both play well with [M9, P11, M13]. Minor chord, natural extensions.
* The .maj7 and .maj6 both well with [M9, A11, M13]. Major chord, play #11.
* The .dim7 and .m7b5 both play well with [M9, P11, m13]. Diminished chord, play b13.
* The .7 plays well with anything.
So if we ignore P1 and P5, then you can use any .maj7 to harmonize a note if it matches the chord's third or seventh (M3, M7 over tonic) or any of its best upper extensions (M9, A11, M13). Here's a table:
.maj7: [M3, M7, M9, A11, M13]
.m7: [m3, m7, M9, P11, M13]
.m7b5: [m3, b5, dd7, M9, P11, m13]
.dim7: [m3, b5, m7, M9, P11, m13]
.7: [M3, m7, m9, M9, A9, P11, A11, m13, M13]
In non-functional reharmonization, you just keeping picking chords that match your melody notes, either harmonizing every melody note or harmonizing key a melody note for the bar, and then do your best to voice them with smooth leading from one to the next. On the one hand, choosing chords randomly feels a little bit lazy. On the other hand, coming up with a chord that matches a given note like this on the fly is not the easiest cognitive task, and it can produce cool results. And if a a technique is difficult to execute but produces good results, there's nothign lazy about that.
7. Work hard to do less. Lots of jazz is beautiful in its minimalism. Some of your skill for compositionl minimalism can be practiced as you learn all these steps. For example, gentle melodic phrases should have space, should breathe like a human vocalist. I've been talking about ways to embellish a piece, but some moments shouldn't be embellished. No composer or performer should be afraid of silence. If you're putting in breaths, don't always have them at the end of a bar. Your chord changes will be more fluent is you conenct them by e.g. anticipating the a chord tone of the next by with a leading tone or an enclosure in this measure.
Using fewer notes at once is another vital skill that you can practice throughout your journey of jazz learning. Try writing a piece that never uses more than three notes at a time while still suggesting functional chord grammars, upper extensions, passing chords. Jazz guitarists are almost forced to do this for ease of playability, and pianists should force themselves to do it too.
For other kinds of minimalism, try reusing rhythms throughout a piece. Try reusing melodies, verbatim or transformed.
Think of a canon, or a round, that plays against itself. A piece like this can be simple to express but hard to come up with. Minimalism in jazz should be like that. So I say again, work hard to do less, to find simple things that you like a lot, things that work surprisingly well. It's much better to pack a punch in a few notes than to cram ten pounds of tricks into a five pound song.
:: Comping, Rhythms, Bass Lines, Counterpoint
Above we saw good methods for taking melodies with notated chords and realizing them as complexly structured musical segments, approaching something like a vocal chorale at the higher levels of complexity. There are other principles of jazz composition worth using as well, like grooves that play a chord with a specified rhythm or suggested stress over an extended period of time, low notes here, high notes there. Bossa Nova and Samba have beautiful chordal rhythms like that. Stride piano is another formulaic method of adding rhythm to your chords, if you like ragtime jazz. I think that a lot of the technique for adding rhythm goes mostly unnamed in jazz: you see a piece that accents 1 and 3+ or something, and it's easy enough to internalize and apply that rhythm to other songs, but it's not complex enough to be worth calling "the groove made famous by Snappy Snow Peas". Simple rhythms like these are especially useful if you're accompanying a solo, and you either need something simple to do in the left hand while you focus on the solo in your right hand (staying out of your own way), or if you're in a band and want to stay out of another soloist's way.
Another thing you can do to enhance a lead sheet is to make up bass line and solo lines and countermelodies. The way to compose melodies and to intertwine them contrapuntally is perhaps the densest, most theoretical, most computationally demanding aspect of music composition, and I will not be talking about it much here, except for solos and bass lines.
I will say that fast soloing and fast composition of basslines are generally a simpler matter than the composition of a beautiful melodies and countermelodies at the heart of a piece. As you become familiar with melodic lines of solos and bass lines in jazz ("licks" or "riffs"), you can start to develop a vocabulary of melodic motives that can be strung together to form melodic phrases and sentences.
Obviously, the core components of melodies, solos, countermelodies, and basslines are moving chromatically, diatonically, or chordally, and moving in any of these ways up or down. But when I talk about melodic vocabulary for solos and bass lines, I mean something more cliched. For example, you might know some riffs for connecting two notes an ascending diminished fifth apart, or a descending major third, or other intervals. By stringing these up, you can make longer melodies and phrases. You might embellish a run up a major7 chord with licks for M3 ascending, m3 ascending, M3 ascending. And these licks don't have to be purely ascending themselves, they could be enclosures that move in both directions, but they will outline an ascending interval. You can also drop notes from the memorized licks to add space and variety and swing.
Here are some tertian licks I learned from Shan Verma, who also taught me the Barry Harris chord motions:
_ Standard Minor 3rd Up: Initial note, scale note above initial, half step below final, scale note above the final, final.
Example in C major: [E, F, F#, A, G]
Rhythm: [e, e, e, e, q].
_ Standard Minor 3rd Down: Initial note, down a half step, down a half step, half step below final, final.
Example: [G, F#, F, D#, E]
Example: [C, B, Bb, G#, A]
Rhythm [e, e, e, e, q]
_ Chromatic Major 3rd Up: Initial note, up a half step, up a half step, up a half step, final note.
Example: [C, C#, D, D#, E]
Rhythm: [e, e, e, e, q]
_ Chromatic Major 3rd Down: Initial note, down a half step, down a half step, down a half step, final note.
Example: [E, D#, D, C#, C]
Rhythm: [e, e, e, e, q]
_ Triplet Major 3rd Up: Initial note, scale note up, initial note, half step down, initial note, final note.
Example in C major: [C, D, C, B, C, E]
Rhythm: [tr_e, tr_e, tr_e, e, e, q]
_ Triplet Major 3rd Down: Initial, scale note up, initial note, scale note down, half step down, final.
Example in C major: [B, C, B, A, Ab, G]
Example in C major: [A, B, A, G, F#, F]
Rhythm: [tr_e, tr_e, tr_e, e, e, q]
_ Triplet Minor 3rd Up: Initial, scale note up, initial, down a half step, initial, final.
Example in C major: [E, F, E, D#, E, G]
Example in C major: [D, E, D, C#, D, F]
Rhythm: [tr_e, tr_e, tr_e, e, e, q]
_ Triplet Minor 3rd Down: Initial, up the scale, initial, down the scale, half step below final, final.
Example: [G, A, G, F, D#, E]
Rhythm: [tr_e, tr_e, tr_e, e, e, q]
In all of these riffs, when the rhythm ends in a quarter note, that's really an opportunity to plug in the initial note from another riff, with whatever note length that rhythm has at its start.
These riffs aren't entrancingly beautiful or technically impressive, but Shan made them legible to me and they're a fine starting point for building up your melodic vocabulary, alongside scalar motion and arpeggios.
The location of chord pitches in the voiced chordal outline of a piece gives you landmarks to navigate between with riffs like these. Try just moving by chord tones first, and then embellish with riffs.
I don't mean to be critical of soloing as an art form. It can be done with great skill and virtuosity, and it can be as cognitively demanding as you demand of yourself. Good solos and basslines are worth learning and analyzing and imitating. But they are simple enough that I can talk about them here in a few paragraphs instead of writing a book about them, as with general melody and counterpoint.
Licks like these for soloing can be fruitfully applied for basslines as well as solos, but there is also an even simpler way of connecting chord tones in bass lines known as the "walking bass line". It's dirt simple, it's widely used, and it work well against melodies despite not considering any counterpoint.
In the simplest walking bass line in 4/4, with one chord change per measure, you play one chord tone per beat on beats (1, 2, 3), with beat 1 being the root of the chord. Play the 5th on beat 3 more often than chance, and move by major thirds or less as much as possible. On beat four you approach the root of the next chord chromatically, from the top or the bottom. That's it. You can add in eighth-note ghost notes and triplets and things in time, but start with that and it will sound like jazz. If you layer a few of these bass lines in different registers, you will not get good polyphony, but you can do it once in a low register and get away with it.
Other simple bass line composition techniques are, I think - much like chordal comping rhythms - mostly unnamed. You find a rhythm, you play one or two low notes with that rhythm, you apply it in lots of places. It's not complex, but it gets you through a bar of A.m7.
Arpeggios and runs shouldn't be the bulk of your basslines, but you can put them in occasionally for florid moments. The more extensions your chord has, the more your run can be scalar instead of tertian, but things anywhere along that spectrum can be good. If you have a phrase made of lick/riffs that spans an octave, you can run that up two or three octaves for fun as well.
In Afro-Cuban music, there are rigid rhythms that that guide a piece, sometimes a whole genre. I don't know enough about these, but if you look up son clave, montuno, and tumbao, that will be a good starting point to learn more. Within these rhythmically guided genres, there are rhythms and other structural suggestions for bass lines and chords and arpeggios. So there's one more thing that you could try if you want to add rhythm and bounce to a lead sheet.
