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A G major chord in root position is named 5/3 because of the intervals above the bass, but if I move the 3rd and 5th around up higher through the octaves, those intervals change but the chord is still called a 5/3 chord. If I play a G chord in open position, why doesn't naming include the intervals contained in the chord?

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    A guess: the notation began as a shorthand for continuo players to let them know which intervals above the bass to play, but left the actual voicing to the performer. It was not intended to be exact in the way you're suggesting. One can easily imagine that convention carried over into the use of the same notation as an analytical tool. Put another way, 5/3 is only intended to express the chord inversion, not the specific voicing.
    – Aaron
    Commented Mar 13, 2021 at 14:18
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    This is not unique to root position triads. Any chord can be voiced in a variety of ways. Think of them like modern chord symbols. A G7 doesn’t have to be G B D F from bottom to top.
    – John Belzaguy
    Commented Mar 13, 2021 at 17:34
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    @Aaron indeed if they wanted it to be exact they'd just have written it out on a second staff.
    – phoog
    Commented Mar 13, 2021 at 22:35

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When the figured bass notation was widely used, voicings were put to the player. The bass was usually written and the figures indicated the roots above the bass; then in more modern times, the figures were added to Roman Numerals (and sometimes note letters or even root numbers) but these are interpreted as intervals above the root rather than the bass. The voicing is still left up to the performer.

When writing in Baroque figured bass notation, I'd denote a C chord in root position as a C bass note and the figures 53 (written vertically). A C chord in first inversion would consist of a bass note E and the figures 63. (In either case, the 3 could be omitted and actually, both the 5 3 omitted for a root position chord; it saves time, ink, and sand).

When I write out something more modern (mostly Latin or big band styles or country), I write the root letter and the figured bass numbers over the root. So a C chord in root petition is C or C53 and a C in first inversion is C63. The voicing is still u[ to the performer.

Either way is fine and can be deciphered by context.

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  • With reference to the second paragraph: the third and fifth are implied, so the actual baroque figured bass notation for a root-position C major chord is a C with no figures, and for a first inversion chord an E with only a 6. You say they "could" be omitted but they were in fact omitted so consistently that if one were to see a figured bass that did not omit them one might wonder what was wrong with it.
    – phoog
    Commented Mar 13, 2021 at 22:36
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Different voicings DO still include the 5 and 3, just displaced by one or more octaves.

You're falling into the trap of expecting too much from chord names. They're pretty good at describing the harmonic function of a chord, but they aren't full notation. That's why we also HAVE full notation!

You never actually see '5/3' in a chord name. Root position is assumed, unless told otherwise.

(@Bennyboy1973 makes a good point. You'd see it after a cadential 6/4.)

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  • I believe you're likely to see it in a cadence: G6/4-G5/3-C
    – Bennyboy1973
    Commented Mar 16, 2021 at 8:47
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This is rooted in figured bass, which was really something like modern chord naming. You could spread a Major 9th chord over the entire keyboard, but that doesn't change the notes that make up the chord.

A C in the bass with a 53 written over it means that the other notes you need are those a 3rd and a 5th above C.

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Figures like 5/3 are abstractions. The don't really tell you exactly what intervals are above the bass. In effect the figure tells you the chord tone identity (like root, third, fifth, etc.) of the bass.

The figures give you the intervals above the bass for a hypothetical close position voiced chord. So, for example, in the key of C major, with an E in the bass, and the figure of 6/3, we would have a hypothetical chord of E in the bass with a diatonic third above the bass (a G) and diatonic sixth above the bass (a C.)

The actual voicing of chord tones G and C, the number of them and their octaves, as well as the possible duplication of the E in the upper voices above the bass is not specified by figured bass!

why doesn't naming include the intervals contained in the chord?

If the figure gave the exact number of voices and intervals it would essentially be another form of notation, a sort of tablature instead of staff notation. Instead the figures are just a short hand notation.

The original purpose of figured bass was to help keyboard players improvise harmonic filler in the upper voices with the right hand. From the composer's point of view they didn't care about the exact voicings they just needed the right chord qualities for the filler. The main focus of the composition was the bass and the melody. Figured bass was just for the filler.

That business about improvised accompaniment is mainly from the Baroque era. If you aren't familiar with it, look at Baroque solo sonatas like Corelli's violin sonatas. The compositions are just treble with ornaments and bass with figures. Players were expected to improvise and the keyboard player improvised complete harmonies with their right hand from the figures.

In modern times when figures are used with Roman numeral harmonic analysis - like for example I6 V4/3 I - it reflects the fact that such analysis is mostly concerned with chord roots, chord inversions, and the bass line. The melodic aspect of the upper voices doesn't have an impact on the harmonic analysis.

If you want the specific parts to play above a bass, you either need staff notation or some kind of tablature rather than short hand figures.

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Because the numbers actually don't tell you where every note is in the chord, it simply says which note is on the bass voice. It's a piece of important information for harmonical analysis, but you don't need the actual arrangement of the chord for that analysis, you only need the bass.

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    So it DOES represent the inversion, but not the position or voicing. Inversion is about the bass note.
    – Laurence
    Commented Mar 13, 2021 at 15:49
  • Yep, exactly. Historically it was used to tell the performer which chord is intended over the note of the basso continuo written in the score.
    – Krili
    Commented Mar 13, 2021 at 17:54
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    Welcome to MSP. You were probably downvoted because your answer is inaccurate. The numbers do represent the inversion but not the position of the notes. You can edit your answer if you wish.
    – John Belzaguy
    Commented Mar 13, 2021 at 18:17
  • Yes, that's a common reason for downvoting! Strangely, not the only one. Downvote wrong answers, upvote ones you consider particularly good. Best to leave the rest alone.
    – Laurence
    Commented Mar 14, 2021 at 0:00
  • Sorry, I noticed later that I wrote something different from what I was thinking. Thanks!
    – Krili
    Commented Mar 20, 2021 at 12:55

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