I am learning chords on the baritone ukulele and which is essentially the 4 top strings of the guitar. If I finger the notes E (2nd fret D string), G# (1st fret G string), C# (2nd fret B string) and open E string I get a C# minor chord in 1st inversion but this is also an A major 7 chord without the root note. So how can I know what chord this is? If it depends on the context then can someone please explain how? For example, if I have a chord progression with an A major 7th chord, will playing this C# minor in 1st inversion always work as a substitution?
It depends on the orchestral arrangement how well a root-less chord works. Taking a page from accordions, they have bass buttons and chord buttons (I'll spell the latter as lowercase here; there are different conventions). Since the chords are assembled from just 12 notes (usually sounding in more than one octave), there is no choice in inversions. In the extreme case, an accordion starting its chord octave at E (common for some larger instruments) has em represented as E-G-B while b7 (seventh chords are usually lacking the fifth) has A-B-D#, a voice-leading nightmare.
However, the typical accordion accompaniment pattern alternates bass notes and chords in rhythmic patterns like E-em-B-em B-b7-D♯-b7 and even while the (lower) bass notes do not sound simultaneously with the chords in this kind of pattern, the different inversion does not really cause problems.
In a similar vein, guitar chords and picking patterns (and I would presume similarly for the ukulele) tend to make sure that the root note is in the bass, and other chord notes are picked as convenient without bothering a lot about inversions.
Coming back to your original question: there exist accordions with 3 chord rows, and accordions with 4 chord rows. Where 4 chord rows are available, they denote major, minor, seventh (with missing fifth) and diminished (again with missing fifth) chords, let's call them c: C-E-G, cm: C-E♭-G, c7: C-E-B♭ and cdim: C-E♭-B𝄫. It turns out that the accordions having only 3 chord rows (common in France and Russia) actually employ what the 4-row scheme calls gdim in the position of c7: G-B♭-E. Used as c7, in contrast to the 4-row version this has the fifth but instead omits the root.
In connection with the typical alternating bass accompaniment, the functional difference is of so little relevance that many accordion players playing 3-row chord systems (partly in parallel with 4-row chord systems) are not even aware of the difference.
So after all that long windup: if there is a bass note either in the orchestra, or you play in a manner interspersing the root note with the chord, it is unlikely that a root-less chord would cause harmonic confusion. It takes comparatively little effort for having the suggestion of a root (partly even the basic harmonic progression might suffice) attach itself to an execution not actually playing it.
Look at what chords come before of after should help identify a root omitted major seventh versus minor triad.
Let's assume the key of
If we alternate chords
Am (or root omitted
Fmaj7) then go to
G7, the identity of
Fmaj7 is kind of hazy. Play it a few times with complete chords
Fmaj7 with root and then a few times with the root omitted chord. It does become unclear. It's a bit of the relative minor sound, but also a bit of a pre-dominant to
G7 sound. The
Am can sort of start sounding like an incomplete
Fmaj7, but it isn't entirely convincing.
Now try a new context. Play
C C E7 Am | G7... That
Am should sound un-ambiguously as a minor triad. No confusing it as a
Fmaj7 in this case. So, relating a chord to its dominant can be one way to clarify the identity.
Sorry, your example chords are for what seems to be
E major. My examples transposed...
E C#m (Amaj7) | B7...
E E G#7 C#m | B7...
A lot depends on what you are really trying to do, and your question combines both distinguishing chord qualities and making substitutions.
To distinguish a major seventh chord, you really want the root and major seventh. That particular sonority is critical to a major seventh chord. With a dominant chord you can omit the root and still retain the sense of dominant harmony, because the 3rd and 7th of the dominant are the really important tones in that chord. But root omission doesn't work for a major seventh chord. If the important point is to get the sound of a major seventh chord, include the root and major seventh.
If the matter is substitution, then distinguishing the chord types is not that important. In fact, it the similarity of chords that allows them to be substituted. If the real concern is getting a playable chord, then don't worry about the change in chord quality with the substitution. If the substitution is to get harmonic variety, then course some distinguishing of chord qualities is the actual goal.
C#m/E] So how can I know what chord this is?
That more of an analysis question. Yet another consideration. In your example you compare a first inversion
C#m/E with a second inversion
Amaj7/E. Even if we set aside the concern about the root omission second inversion chords get special attention. Without going into details, second inversion chords have special use cases like passing chord or cadences. In harmony analysis there is a tendency to go with whatever description is simplest and clearest. Given a choice between a complete first inversion triad or an incomplete second inversion seventh chord you would probably go with complete first inversion triad. This is just a generalization. You would need specific chords and voicings to finally decide what chords to name.
I still sometimes have trouble deciding whether a chord in a song is Imaj7 or iii. The root is usually the clue. But when there are three notes common to both chords, and there is no clue, use those notes, as they constitute either. There's no rule saying a chord has to be in root position, although that version usually sounds most stable.
It will depend somewhat on the voicings of the neighbouring chords, but will generally work fine. It also depends on what other instruments may be playing simultaneously. But, by and large, it's a good ploy to just use and get on enjoying playing whatever song.
The root of a chord is usually never sacrificed, at least not in the big picture of an orchestral arrangement. On the guitar or other stringed instruments we sometimes don't have a choice so we grab what's convenient. With no other context the notes (C#, E, G#) in any order are a C# minor triad. Strictly speaking there is no "chord without a root".
Again, in an orchestra, if a guitarist, or other instrument, is given these notes and the intent is to create an A maj7 then the Bass or other instrument will be playing the A.
One possible clue is the transition from the chord before, another is the Key of the song. If the key is Amaj, as opposed to E maj (C# rel minor), and the chord before it is the V, or V7, or IV, and the melody (singing or other instrument has an A in it) then from a functional point of view the iii serves as a I chord.
In terms of substitutions, yes, the iii is always a possible chord sub for the I, but so is the vi depending on context. In your case you are covering 75% of the chord and not introducing anything new so it is a safe bet to play iii as a sub for I maj7.
In terms of poly chords the major 7th can be constructed by combining a I maj triad and a iii min triad. This overlap is part of the rational behind the substitution.
The only thing you possibly loose is the strength of the resolution to I if that's in the chord progression.
From a theoretical perspective, they are not the same at all, as the root note determines the function of the chord in the key center. I and iii serve very different purposes, so this is not a direct substitution. (Though iii can be considered tonic is some cases, it often serves a pre-dominant or mediant function.) As a counterexample, V7 and vii° (E7 and G#dim, in your case) overlap in the same way as I7 and iii, but they are both dominant and V7 can almost always be replaced with vii° without changing the chord's function relative to the chords surrounding it.
AM7 and C#m will sound quite different and will fundamentally change the structure of the music. If you are ending on the AM7, playing a C#m will essentially change the tonality from A major to C# phrygian.
That said, practically speaking, it's probably fine to substitute. If you are playing with a group, the A root will likely be comped by someone else. Even if you are playing solo, removing a note from the chord is at least guaranteed to not inadvertently cause any harsh collisions, so you're fine as long as you don't mind it sounding a little different. Ultimately, just use your ear; if using C#m instead of AM7 sounds good to you, go for it! Who knows? You might even like it better!
Side note: as mentioned in other answers, the root is the last note you want to drop from a chord, as it changes the chords function (AM7->C#m). The 3rd is second most important as it defines the chord quality (major or minor) and prevents ambiguity (AM7->A...something?). The 7th (if present) comes next, removing it makes it a completely different chord (ie, a basic triad) (AM7->A). And finally, the first note that would usually be omitted, if necessary, is the 5th as it simply supports the root and provides stability, but has little to do with the chord's identity (AM7->AM7(no5)).
Interesting question - because I get in trouble:
what is here first? Theory or practice?
In deed there is no difference as actually there are no chords without root tone.
When a chord is built of thirds and not inverted the lowest note is the root.
To consider viib5 as V7 without root, iii as I7, or g# dim7 as E9 is just a help for learning and understanding the chord construction and its function in a chord progression.
For example, if I have a chord progression with an A major 7th chord, will playing this C# minor in 1st inversion always work as a substitution?
To say c#m is A maj7 without root or I7 is e-minor with an additional third in the bass makes it easier to become insight how these chords are built, how they are related and why they can substituted.
If it depends on the context then can someone please explain how?
I7 as final chord will always be a tonic chord with major 7th and never iii. But it might be easier to imagine for a beginner:
I7? Just play c#-minor and add A in the bass!
(If you’re playing ukulele and there is no low A for the bass tone ... imagine that you are probably singing an A as final tone of the song and this will give the root.)
So the concept “without root” is a theoretical concept for analyzing the function a practical concept for building and playing a chord.
It could also be an E6 chord.
This happens a lot on a 4-string instrument. You'll play notes that FIT a few different chords, without fully defining them. (It also happens on instruments that COULD play more notes, but choose to use a lighter texture.)
You could play this shape when a C#m chord, or an Amaj7, or an E6 was required. If it's the final chord of a song in C# minor, A major or E major it's pretty sure it's the tonic. Otherwise, it's more up for grabs. If it's x in an E, x, A, B7 sequence, C#m would be a good name for it. If it alternates with Gmaj7 in a funky jazz feel, Amaj7 would be a useful way to look at it.