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Does the name of the inversions (first, second, etc.) refer to a specific interval (3rd, 5th, etc.) or just the next chord tone?

For example, a Cmaj7 chord in first inversion starts with the 3rd, and the second inversion starts with the 5th. But here's the point: what is the second inversion of a Cmaj7(no5) chord (Cmaj7 shell voicing), since this chord does not have a 5th degree?

Also, what about extensions? Let's take a chord with these intervals: R, 3, #4, 7 (a chord with a Lydian sound where I do not play the 5th to make the fingering easier). We can think of this chord as a maj7(#11)(no5), but also as a maj7add#4(no5). What would be its inversions? Does the chord with the #4 on the bass count as a second inversion? Or should we treat it as a #11 (the highest note) and therefore call it a third inversion?

What about a 7(b9) chord? What is its first inversion? Is it the chord starting on its 3rd or starting on its b2 (since the b2 is the second note that comes after the root), or do we treat it as a b9)?

My question is: how does the inversion naming convention work when we have "missing" intervals, added notes, extensions, or alterations?

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  • "I do not play the 5th to make the fingering easier" I'm not sure what instrument we're talking about about playing a #4 and playing a b5 would be the exact same fingering, wouldn't it? Commented Jul 1 at 5:50
  • I do not play it but I can. What I mean is that this chord started as a R, 3, 5, 7, #11, I just left the 5th to fret it with ease. But theoretically the natural 5th is in the chord. That is why I think it is weird to name that chord with a b5
    – VorganHaze
    Commented Jul 1 at 5:53
  • If you leave out the 5th, it's no longer a Lydian chord, it's a b5 chord. Also Lydian chords usually have the #4 instead of the 3, so keeping the 3 and having a #4/b5 will make it sound "less Lydian". The biggest thing will be the tritone and how it resolves (or doesn't). Beyond that, the simplest name is best, and inversion naming doesn't help or make sense with such a chord. Tritones are symmetric, so we don't really hear one note as on top and the other on bottom. Inverting a tritone is only meaningful to pedantic theorists. Commented Jul 1 at 5:57
  • I said Lydian becase it came from that mode (that was the scale uses to solo over that chord. I did not intent to say this was a lydian chord, just its context.
    – VorganHaze
    Commented Jul 1 at 5:58
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    I guess I'm not sure why you're thinking about where the chord "came from". If you're playing an equal tempered instrument and you play C E F# most ears are going to hear an inverted half diminished F#7 chord (no 3) or a C major chord with a b5. How a chord sounds is what matters, not where it "comes from". You can come up with all kinds of complicated names for the same chord, but the mosts helpful name will generally be the one that reflects how our ears will hear it, not where it "came from". Commented Jul 1 at 6:04

4 Answers 4

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Inversions are named for their lowest-sounding notes - in other words, the answer to your first question is "a specific interval". Also, inversion naming is part of common practice music theory and can fall apart outside of that context.

Cmaj7 (no 5) cannot appear in second inversion because the lowest sounding note of a second inversion C major chord is a G. If the chord is in second inversion then the 5 is present and if the 5 is not present then G cannot be the lowest sounding note of the chord. If B is the lowest sounding note then we still say third inversion even if the G is not present.

R, 3, #4, 7 is a situation where we have left common practice and therefore things can get dicey. Inversion naming was not created or refined for such chords. However, I'd prefer to name this a major 7 (b5) since that's much clearer than something containing a #4 and no 5. In that case the inversion naming gets easier. Cmaj7 (b5) has a lowest note of E in first inversion, Gb in second, B in third.

What about a 7(b9) chord? What is its first inversion? Is it the chord starting on its 3rd or starting on its b2 (since the b2 is the second note that comes after the root)

No. A 9th is not a 2nd. C7(b9) has E lowest in first inversion, G lowest in second inversion, Bb lowest in third inversion, Db lowest in fourth inversion. But really when you get as jazzy as a b9 I strongly suggest switching to slash notation and calling it C7(b9)/Db.

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  • So, you are saying that a second inversion is always a chord with the 5th on the base, and a first inversion is a chord with the 3rd in the base?
    – VorganHaze
    Commented Jul 1 at 5:46
  • @VorganHaze Yes. Also, if I saw F# C E B in that order I wouldn't even call it a C Maj7 (#4/no 5). I'd call it F#sus4(b5/b7). Commented Jul 1 at 5:48
  • But add11 will imply a natural F, so I am confuse. Also, the chord come from the Lydian scale, so the natural 5th is included in the chord, I just choose not to play it for fingering simplicity (but the chord implicitly still have a 5th, so I think I will use the #4 or #11 because of the function of that interval [also in case of a different tuning system]).
    – VorganHaze
    Commented Jul 1 at 5:51
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    @VorganHaze If you're not playing in ET then I'd add that to the question, although it won't matter in terms of naming inversions. Again, the "first/second/third inversion" naming isn't really useful outside of common practice music, and Lydian chords aren't common practice. They are jazzy even when used outside of jazz. Commented Jul 1 at 6:00
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    @AndyBonner Ok good point, yes. My comments on “as we stray from common practice, ‘nth inversion’ comes unhelpful” still apply. Commented Jul 1 at 14:46
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I think @ToddWilcox has answered your question as well as it can be answered from a technical standpoint. I however suggest you rethink the way you look at and label inversions.

You seem to be approaching this topic from more of a jazz/contemporary viewpoint based on the way you spell chords. The traditional way of identifying and naming inversions develops gray areas with modern chord symbols such as but not limited to (no5), (add2), etc. for that reason it is better to think of inversions in jazz/contemporary music as simply X with Y in the bass. “Y” can also specifically be identified by a chord tone or interval from the root for theoretical or explanatory reasons. This gives complete clarity and eliminates any gray areas or confusion that you might run into. It also gives you the flexibility to use non chord tones in the bass of a chord, which is a very common occurrence and has been for many years.

Another thing to keep in mind is that with the exception of the bass note, chord symbols have no specific hierarchy of note order from low to high. It is less important musically to identify what an inversion is than to just know what the actual bass note of that chord is and how it relates to the root. It is even more so when the root is not a chord tone (Bb/C, Ab/A G/F, etc,)

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There seems to be some confusion between inversions and intervals. They have little to do with each other, in the naming process.

Inversions are simply named with regard to the lowest note played. So a simple C major triad with C at the bottom is root, an E at the bottom, 1st, and a G at the bottom, 2nd. It matters not which order the other two notes are in, whether they're in close or open shape, or how many of each there are in the chord.

So, one needs to look at the lowest note of any note cluster to establish what inversion that chord is, regardless of which order notes are in, or duplicated. If there is an altered note, as in C+, then if G♯ is at the bottom, it's still 2nd inversion. With extensions, such as C7♭9, then if D♭ is at the bottom, it's 4th inversion, if the higher C, which may not even be played, isn't counted. As before, it's the lowest note calling the inversion name.

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  • I know. But I am asking for missing notes, alterations, extension, etc.
    – VorganHaze
    Commented Jul 1 at 15:05
  • @VorganHaze - I hear what you say. There more than likely is no convention for what you ask. Just like a guitarist will play whatever shape/voicing they feel appropriate when faced with a chord symbol, that's the top and tail of it.
    – Tim
    Commented Jul 1 at 16:14
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Particularly in jazz, chord symbols communicate two things that are somewhat independent of each other: 1) The harmony, 2) the voicing.

In a symbol like C7(no 5), the C7 is the harmony, and the (no 5) specifies an aspect of the voicing. That is C7(no 5) is not a harmony. C7 is a harmony (i.e., a chord), and leaving out the fifth is how the harmony should be expressed (voiced).

Similarly C7/Bb is specifying a voicing aspect for a C7 chord. C7/Bb is not a chord in itself. C7 is a chord, putting Bb in the bass is the voicing. It is true that C7/Bb is an inversion, but not every voicing instruction results in an inversion — "no 5", for example. C7(no 5) means "play a C7 harmony, leaving out the fifth, and, as a corollary, don't play C7 in second inversion."

With a chord like C7(b9), the b9 is an integral part of the chord. While it could be played immediately next to the root, conceptually it's the highest note. This means that first inversion is C7(b9)/E and fourth inversion is C7(b9)/Db.

With "add" chords, the "add" is not part of the chord proper — it's more a voicing instruction — so isn't considered when labeling inversions. C7(add #4)/F# is not a chord inversion. It's just a C7 chord with F# in the bass.

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