I understand why notes within key signatures are denoted as sharps / flats but what drives the conventional naming of enharmomic notes, i.e a diminished seventh in C contains Ab and not G#. Why is it not the latter, given the key signature doesn’t have any sharps or flats?
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2If you talk about dim 7 on VII: What is the diminished 7th of B? Is it Ab, or is it G#? There’s your answer. – Lazy Dec 24 '23 at 01:35
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Diminished seventh from C is Bbb... which is, funny enough, enharmonic with A, but since it's a diminished seventh and not a major sixth, it's Bbb. – Divizna Dec 24 '23 at 05:59
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1@Divizna In 12-TET, the diminished seventh is enharmonic to the major sixth. In 19-TET, however, the diminished seventh is enharmonic with the augmented sixth rather than the major sixth, and by no longer being redundant it has its own distinct function. – 000 Dec 24 '23 at 08:42
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@Lazy - ah, of course! Thank you. – Ryan Dec 24 '23 at 08:45
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'A diminished seventh in C contains Ab and not G#'. C diminished itself actually contains Bbb - enharmonic to A, but will be called Bbb due to it being the 7th note diminished - which would be a Bbb note. If you mean the only diminished chord in key C -Bo - then that indeed will contain Ab, as the changed 7th note is the 7th away from B (the chord root) - G# is only a 6th away, interval-wise. – Tim Dec 24 '23 at 10:28
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It has something to do with there already being a G-natural in the scale, and you don’t repeat notes in a scale. – Blue Skin and Glowing Red Eyes Dec 25 '23 at 11:53
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Tonal theory understands chords as stacks of thirds. This means that any chord with B as its root would also contain some type of D, F, and, for a seventh chord, A. A "seventh" chord, by definition, must contain the interval of a seventh. B-something to A-something is always a seventh; whereas, B-something to G-something is always a sixth.
Thus we have:
- Bmaj7 = B - D# - F# - A#
- B7 = B - D# - F# - A
- Bmin7 = B - D - F# - A
- Bmin7b5 = B - D - F - A
- Bdim7 = B - D - F - Ab
If we extend the theory to include sixth chords, then B6 = B - D# - F# - G#.
These chords are defined unto themselves, irrespective of the larger key context. Bmaj7 is Bmaj7 no matter whether that chord appears in a B major context or an F major context.
For similar reasons, we have:
- Bdim7 = B - D - F - Ab
- Ddim7 = D - F - Ab - Cb
- Fdim7 = F - Ab - Cb - Ebb
- Abdim7 = Ab - Cb - Ebb - Gbb
- G#dim7 = G# - B - D - F
Aaron
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6"Tonal theory understands chords as stacks of thirds" but why ... because that theory (theory = talking about a practice) evolved for the purposes of describing the practices of a culture where harmony is mainly constructed as stacks of thirds. Not because of physics or chemistry or biology. (Which you know perfectly well of course) – piiperi Reinstate Monica Dec 23 '23 at 23:42
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3@piiperiReinstateMonica More precisely, harmony developed from the coincidence of multiple horizontal lines of music, and it was discovered that by interpreting them as stacks of thirds, a consistent theory could be developed. – Aaron Dec 24 '23 at 00:02
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3@piiperiReinstateMonica Rameau introduced the "stacks of thirds" reasoning in 1722. Theory was pretty consistent before then, though; Rameau and the stacks of thirds approach added an organizing principle equating certain progressions. But modern theory takes this much too far. There's no reason to call an augmented sixth an augmented thirteenth, for example. Chords that are actually stacks of thirds don't really get farther than 9th chords -- anything higher than that and you have to start talking about which notes to omit, showing that it's not really a stack of thirds. – phoog Dec 24 '23 at 01:21
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2Similarly, the augmented sixth and Neapolitan sixth chords show why this answer is incorrect: the Neapolitan sixth chord isn't really an inversion of the chord on the lowered second scale degree, and the augmented sixth chord isn't really an inverted "diminished third chord" -- there's no such thing. Both of these are chords that arose from considerations of counterpoint or voice leading ("multiple horizontal lines of music"), yet they make less sense when analyzed as stacks of thirds, not more. – phoog Dec 24 '23 at 01:35
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1@phoog that doesn’t change the fact that the core ideas in tonal theory are based on thirds. – Aaron Dec 24 '23 at 02:05
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@phoog It's also worth pointing out that tonal theory doesn't try to explain augmented sixths as stacks of thirds. It explains them as augmented sixths arising from contrapuntal motion. – Aaron Dec 24 '23 at 04:03
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@Aaron the core ideas in tonal theory are based on the triad and the seventh chord. The fact that these can be described as stacks of thirds leads to the theory of inversion but isn't strictly necessary for it. "Tonal theory doesn't try to explain augmented sixths as stacks of thirds": that is exactly my point; it is precisely for this reason that statements such as "Tonal theory understands chords as stacks of thirds" are incorrect. – phoog Dec 24 '23 at 08:40
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All the answers seem to focus on the definition of seventh chords. However, it merely passes the buck: what drives the choice of the root?
Local context! The "accidental" usually has a function in some other local tonal centre:
In the key of C major
- d-f-g#-b leads to e.g. A-minor (intermediate dominant for vi)
- d-f-a♭-b leads to e.g. G-major (intermediate dominant for V), or e.g. C-major (I)
And so on. There's loads of music where ambiguous function arises (notable post-romantic era) but still a choice is made based on preferance (e.g. key relation with main key, ease of reading or e.g. instrument play, thinking pedal-harp e.g.)
sehe
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I think you meant "d-f-a♭-b leads to e.g. C-major", at least that's what is notated. But, I like your point that secondary dominants are spelled relative to the secondary tonic key. – Michael Curtis Dec 27 '23 at 15:29
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@MichaelCurtis yeah I had different examples playing through my head while writing vs. notating. Fixed a bit by clarifying different resolutions (avoiding re-notating for time) – sehe Dec 27 '23 at 15:35
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Why is it not the latter, given the key signature doesn’t have any sharps or flats?
If you're talking about the diminished seventh built on a root of B, consider that the paradigm of the diminished seventh chord comes not from major tonality but from minor tonality, and C minor does very much contain three flats, including A♭. (The seventh chord on the seventh scale degree in major tonality is the half diminished seventh; for example, in C major it is B D F A.)
The diminished seventh arises from the chromatically altered seventh scale degree in minor (the raised leading tone) and the unaltered sixth degree. This interval is an augmented second or a diminished seventh, depending on the inversion. The diminished seventh chord takes its name from this interval. (As noted by Aaron, the interval between B and G♯ is a major sixth or a minor third.)
The model diminished seventh chord in the "empty" key signature, therefore, is G♯º7, comprising G♯ as the raised leading tone of A minor along with B, D, and F, the second, fourth, and (lower) sixth degrees of that scale. Of course, this is enharmonically equivalent to the Bº7, and that shows why diminished seventh chords are so useful for modulation: they introduce a good deal of ambiguity because of their symmetry and through enharmonic reinterpretation allow you to go to one of three other keys (i.e. Bº7 can be reinterpreted as G♯º7, as Dº7, or as Fº7).
Similarly, you might ask why the C7 chord is spelled that way with a B♭ rather than as an augmented sixth chord with an A♯ when C major has no sharps or flats in its key signature. In fact, this being the "dominant seventh" chord, its prototype is built on the dominant scale degree, and C is the dominant of ... F major, which does have B♭ in its key signature (and also of F minor, which also has B flat in its key signature).
There is an augmented sixth chord, which is often enharmonically equivalent to the dominant seventh chord. The model for this chord is built on the (unaltered) sixth of the minor scale, for example A♭ in C minor. This flat sixth degree is commonly the bass of a first-inversion minor subdominant (in lead sheet terms, Fm/A♭ or Fm7/A♭). This typically leads to the dominant (G7 in this example), but you can add a chromatic passing tone F-F♯-G, giving you the augmented sixth between the A&flat and the F♯. I mention this because lead sheets will typically use the enharmonically equivalent spelling of A♭7 because it's simpler, and that led to the theory of "tritone substitution": A♭7 to G is seen as a substitution for the more standard D7 to G. So this is an example where a change in enharmonic spelling leads to a change of theoretical viewpoint.
phoog
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Until relatively recently, A flat and G sharp were not the same note unless you were a pianist. The wikipedia page on 31 tone Equal Temperament covers historic tunings for the different notes. The G sharp was 15% lower than it is now, but the A flat was 23% higher. This was standard practice for violins and other flexible instruments until the 20th century.
There are a lot of music theory "reasons" for the enharmonic spelling, but the most important one was that they did actually sound different.
les_h
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2Enharmonics are used differently even when sounding the same. A German Sixth resolves differently from a dominant seventh on an equally tempered instrument. One may enter a chord as one and resolve as the other. – ttw Dec 28 '23 at 06:18
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How are you calculating those percentages? Also Pythagorean tuning predates 5-limit just intonation and quarter comma meantone (and harmony for that matter) and G sharp is higher than A flat in Pythagorean tuning, not lower. – phoog Dec 28 '23 at 06:53