Just for a bit of clarification:
As both a product of the American Collegiate system and an educator at an
American University who has studied and taught Music Theory, I will share
my
observations:
In general, the current "standard", if we may call it that, among American
Universities that are offering traditional music degrees that require
students to take Theory courses at the undergraduate, graduate, and to
some
degree, post-graduate levels, and that use texts by American publishers
authored by respected educators/theorists in the field or from other
Universities such as those by Gauldin, Kostka/Payne, Piston, etc. is to
use
a "case-sensitive" Roman Numeral analysis system.
Roman Numerals are used for Functional, Tertian-based harmonies.
"Names" are used for Functional, non-Tertian-based harmonies.
Either may be used for non-Functional harmonies, based on the context.
The "case-sensitive" system is as follows:
UC - Major triad.
LC - minor triad.
UC with "+", Augmented triad.
LC with "o", diminished triad.
7th chords are as follows:
UC - Major 7th and Dominant 7th (and by extension, 9ths, etc.)
LC - minor 7th, and half- and fully-diminished 7ths (and 9ths, etc.)
Obviously, any alterations, such as a Dominant 7th chord with a raised
5th,
would produce an Augmented triad ****tion of the harmony, and thus an UC RN
would be used.
The symbols are obvious, except that X7 is a Dominant 7th (or Mm7), and
XM7
is a Major 7th.
In a Major key, the diatonic Roman Numerals are:
I ii iii IV V vi viio
IM7 ii7 iii7 IVM7 V7 vi7 vii%7
In a minor key, they are:
i iio III iv [IV] [v] V VI [VII] viio
i7 ii%7 IIIM7 iv7 [IV7] [v7] V7 VIM7 [VII7] viio7
(#vi%7 also appears, though rarely in triad form)
Note: bracketed numbers represent those chords that can be created with
raised 6 and lowered 7 - lowered 6 and raised 7 are considered to be the
"normal" state for harmonies.
9th chords are generally (comparatively) rare, and 11ths and 13ths
virtually
non-existent, though the system can be logically extended to include them,
and the patterns above remain the same. In the case of altered 9ths, the
alteration is shown on the symbol.
THESE ARE THE DIATONIC CHORDS. There are no others! There is no I7 (like C
E
G Bb as I) in a Major or Minor key in this system. All other chords come
from three places: Another key (Secondary key), another Mode (parallel
mode), or are regularly occurring functional Chromatic, non-Tertian
sonorities. All other harmonies are typically non-functional (and it
should
be noted that numbered chords can also appear in non-functional roles).
Secondary chords use the same numbering system, except the convention is
to
show them a "X/Y" where X is the name of the chord in secondary key, and Y
is the tonic chord of the secondary key. V7/ii for example.
Mode mixture uses the RN of the chord from the parallel mode. For example,
using a minor i chord in a Major key gives you "i", rather than the normal
"I".
Because some chords, when borrowed, appear on what is a lowered or raised
scale degree, b or # is prefixed to the RN to show that the ROOT of the
chord has been altered from its normal state. Thus, in a Major key, mode
mixture (borrowed chords) available are:
i, iio, bIII, iv, v, bVI, bVII
im7, ii%7, bIIIM7, iv7, IV7, v7, bVIM7, bVII7, viio7.
In minor,
I (IV, V, viio, etc. are already in the minor system). ii is possible,
though rare. Any other chords, such as IM7, IVM7, etc. are seen as a
switch
back to the Major mode (again, since so many "borrowed" Major chords are
already in the minor system) and not necessarily borrowing.
The only remaining chords are non-Tertian sonorities. Older theorists
treated these as tertian forms (or likened them to tertian forms) but
newer
conventions are treating these more from their historical origins. As a
result, they give them "names" rather than numbers.
Neapolitan Sixth - N
Augmented Sixth - +6, Italian +6, French +6, and German +6.
Formerly, N has been called "bII", and the +6 family seen as inversions of
II and IV chords.
All chords can appear in secondary contexts. For example, the following
progression, in C, might appear:
C - Ab/C - F#o7/C - G7/B, in which case the RN would be I - N6/V -
viio4/2/V - V6/5 (thus we have a secondary Neapolitan, and a secondary
chord
with mode mixture).
Chords that appear in non-functional contexts are put in parentheses.
There
are a few common "embelli****ng chords" with non-functional uses, and they
are typically named simply as what they would be - (iii6), etc. Some,
where
roots are unim****tant (or even undeterminable), have names instead - (cto7
-
common tone diminished 7).
There are a few other chords that arise out of chromatic motion, or have
other voice-leading origins, that appear in chordal contexts and are felt
to
deserve Roman Numeral status because of their functional im****tance.
V+ (V+7, etc.)
Vsubs6 (V7subs6)
IVadd6 (ivadd6)
These are pretty specific chords and typically only appear on these scale
degrees.
Beyond that, other chords are seen as pu****ng beyond the boundaries of CPP
Tonality. For example, "II" in Major, as a non-functional major chord
built
on scale degree 2 is so rare as to be considered astylisitic. However,
since
the system is clear, it does tell us what it is: A Major Triad (UC RN)
built
on scale degree 2 (II). If we wanted to build a minor triad on raised
scale
degree 4, it would simply be #iv.
The problem comes in when other systems come into play, as we've obviously
discovered. For people who call a major chord built on scale degree 2 "II"
just because the system allows, may not understand (or be telling us in
their analysis) that the chord has a secondary origin. Likewise, calling C
Eb F# A "#ivo7" in C major tells us "what it is", but not what it's
function
is. Normally, it would be a viio7/V, but in this context, it is a
chromatic
embelli****ng chord. Because of it's different function, and it's
"non-chord"
origin we call it a common tone diminished 7 (cto7).
So there's a disconnect in the way many people now use RN to "tell you
what
to play" and the way CPP tonal analysis uses those numbers to describe
functionality. Additionally, because many contem****ary educators are
trying
to reinforce those differences, the system is moving away from "less
informative" symbology to more "descriptive" symbology - or, at least it's
more descriptive in the sense that once you learn what a symbol means, you
understand all of the functional information it conveys.
It seems to me, other styles are trying to move to a "more generic"
system,
to make the RNs useful for both for analysis and playing from.
Unfortunately, this is at odds with the original intent of the system and
obviously, because older systems exist as well, we end up with very
similar
symbols being used in close proximity to each other.
So above is the system most widely used in American Universities and in
most
texts I encounter, except for when people are speaking generically (using
IV
to mean iv, IV, key of IV, etc. which these authors also do), or in older
texts where a "less informative" set of symbology was used (the reader is
expected to "assume" much more).
Best,
Steve
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