HARMONIZING SCALES &
ROMAN NUMERAL ANALYSIS
Last week, we covered the huge concept of Figured Bass. As we round the corner to the final weeks of Music Theory I, we are giving analysis one new update to bring it into the 21st century - this concept we will begin to work on here is the way musicians look at and analyze tonal harmony of Western Classical Music in 2020 (congrats, you made it!). This method was created in the early 19th century (so it’s about 200 years old) and has a few limitations, especially when considering really modern, chromatic music that draws from many different scales or tonalities. However, to date, this is the most encompassing way to analyze music that uses chords (most Western Classical Music) because it not only shows chord type and inversion, but each chord’s relationship to the tonic.
To understand how to make it work, you need to understand how to harmonize scale degrees, which we touched on briefly last week …
HARMONIZING SCALES
To HARMONIZE something is to “add harmony to” meaning that a single note or group of notes (in a melody) are suddenly anchored to a specific tonality by attaching at least one additional vertical note (in the case of TWO-PART HARMONY) or attaching an entire chord (in the case of CHORDAL HARMONY). The most basic and complete way to harmonize is to turn each note of a scale into a triad (three-note chord) with the scale degree as the root.
HARMONIZED MAJOR SCALE
Recall from last week how we added two notes above each scale degree to create triads. We selected the notes based on what is available in the key (in C Major, we’re dealing with all naturals). When you build a chord that exists naturally in the key (meaning there are no accidentals in the chord), you call these chords DIATONIC, meaning “from the scale”. When you use accidentals to build your chords, these chords and harmonies are referred to as CHROMATIC (we won’t get into chromatic harmony until Music Theory II).
In the example above, the seven distinct positions of triads create a triad quality pattern of:
HARMONIZED MAJOR SCALE DEGREES
MAJOR - MINOR - MINOR - MAJOR - MAJOR - MINOR - DIMINISHED (- MAJOR)
This pattern is universal for all major scales. If you build a triad off the root of a major scale, no matter what the first scale degree is, it will be a major triad. If you build a triad off the sixth scale degree, no matter what major key you are in, it will be a minor triad. This pattern is constant, just like the sequence of half and whole steps in a major scale.
HARMONIZED (HARMONIC) MINOR SCALE
The pattern for minor scales, however, will be different because minor scale degree patterns differ from major. For the purpose of harmonization, we will focus on the harmonic minor scale (and not worry about the natural or melodic minor scale). Take a look at how chords occur in C Harmonic Minor compared to C Major.
HARMONIZED HARMONIC MINOR SCALE DEGREES
MINOR - DIMINISHED - AUGMENTED - MINOR - MAJOR - MAJOR - DIMINISHED (- MINOR)
While we can read these chords and analyze them with a basic chord symbol (showing the root, the quality, the type, and even if it’s in inversion), there is still some important information we are lacking when it comes to understanding harmony and that is the relationship of the chord to the tonic. In order to show all the information above plus this important relationship, we will begin to use Roman Numerals.
ROMAN NUMERALS
ROMAN NUMERALS are a numerical system developed in Ancient Rome where numbers are represented by a combination of letters such as “I”, “V”, “X”, and “M”. Because chords in music only inhabit seven positions (for the seven scale degrees), we will only use Roman numerals I, II, III, IV, V, VI, and VII.
Here is how they work …
UPPER CASE ROMAN NUMERALS: represent major triads starting on that scale degree of the scale. So V would be the major triad starting on the fifth scale degree. In a major key, we will encounter major triads on the I (1), IV (4), and V (5).
UPPER CASE⁺: on rare occasions, you will encounter an augmented triad in harmony (it occurs naturally on the third scale degree of harmonic minor - see above). When you do, you will write the chord as an upper case Roman numeral with a superscript “+” to signify that the chord is not just major, but augmented. So in the case of the third triad of harmonic minor, you would write: III⁺.
LOWER CASE ROMAN NUMERALS: represent minor triads starting on that scale degree of the scale. Lower case Roman numerals are the exact combination of letters to represent each position, they are just lower case. In major, we encounter minor chords at ii (2), iii (3), and vi (6). In harmonic minor, we encounter them at i (1) and iv (4).
LOWER CASEᵒ: while the diminished triad isn’t as common as the major or minor, it is found on the seventh scale degree of major and second and seventh in harmonic minor. To show a diminished chord, you will begin with a lower case Roman numeral and include a superscript “o” to signify the chord is not just minor, but diminished. We would therefore see viiᵒ in major and minor as well as iiᵒ in minor.
INVERSIONS:
Roman numerals can also be in inversion (as discussed last week). If there is no superscripted number on a Roman numeral chord, you know it’s in root position.
If there is a “6” in the information, such as IV⁶, you know you are working with a major chord on the fourth scale degree in first inversion (with its chordal third in the bass).
If there is a “64” in the information, such as I⁶⁴, you know you are working with a major chord on the first scale degree in second inversion (with its chordal fifth in the bass).
With the above in mind, we can reinterpret the analysis of the harmonized scale degrees in both C Major and C Harmonic Minor into Roman numerals which now, in addition to the type, quality, and inversion, also show the chord’s relationship to Tonic.
ROMAN NUMERALS FOR THE HARMONIZED MAJOR SCALE
ROMAN NUMERALS FOR THE HARMONIZED HARMONIC MINOR SCALE
ROMAN NUMERALS FOR THE HARMONIZED NATURAL MINOR SCALE
*A note on V vs. v …
Upper case and lower case V/v look almost identical and can be easily mixed up. Although you will almost always encounter a major V rather than a minor, v, it’s important that your handwriting is distinctive and obvious enough to distinguish between the two. Oftentimes, musicians will use braces at the top and bottom of all uppercase Roman numerals to create a substantial visual difference from the minor. We find the minor v in the harmonized Natural Minor Scale.
ANALYZING WITH ROMAN NUMERALS
To analyze a piece of four-part harmony (with a soprano, alto, tenor, and bass line) with Roman numerals, you will represent each vertical chord with an upper or lower case Roman numeral including a symbol for augmented or diminished (if necessary) and a symbol for inversion (if necessary). To do this, you will need to know what key signature you are in and analyze each chord in terms of its relationship to the tonic of the key.
Below is a four-part chorale without analysis. Look it over and see what conclusions you can draw. What key is it in - and how do you know? What are the starting and ending chords in terms of their relationship to the tonic (I). Are all the chords in root position or are some in first or second inversion - and how do you know? What would you label the chords with in terms of their relationship to the tonic?
When you’re done drawing your own conclusions, scroll down to see the correct analysis as well as a step-by-step “how-to” video.
Key Signature: _________________
Starting and Ending Chords (are they the same chord?): ____________________
Inversion of chords? Root position, first inversion, or second inversion?
Roman numerals of each chord in relationship to the tonic: ____ ____ ____ | ____ ____ | ____ ____ ____ ____ | ____
When you are done, scroll down for the solution …
ROMAN NUMERAL ANALYSIS SOLUTION …
Key Signature: F Major
Starting and Ending Chords (are they the same chord?): F Major Triad (I) for both
Inversion of chords? Root position, first inversion, or second inversion? All in root position
Roman numerals of each chord in relationship to the tonic: I V I | IV I | V vi IV V | I
REALIZING ROMAN NUMERALS
Now we will learn how, by only reading Roman numerals, we can realize a 4-part harmony where we are in full control about where every note goes! Roman numerals provide more flexibility than Figured Bass because they do not force you to a specific bass line. Instead, you can choose your starting octave as well as what octave each successive bass note appears in (keeping good melodic voice leading in mind, of course).
Here is a blank staff with a Roman numeral progression written below.
First decide what key we are in - you can tell by the key signature and whether the Roman numerals are in major (I) or minor (i).
Next, write out a key for yourself with the scale, triads for each scale degree, and accompanying Roman numerals (see the constant sequences above for major and minor).
Move the triad chord tones written out below each Roman numeral and include its doubled chord tone as well as underline what should be in the bass (based off figured bass symbols for inversions).
Fill in the notes for bass, tenor, alto and soprano for each chord, following the guidelines for good voice leading.
Key Signature: _________________
Scale Degrees: _________________
Harmonized Triads for each Scale Degree: _________________
Given chord spellings including inversion and correct doubling: _________________
*when referring to the “spelling” of a chord - you are being asked to list the notes in the chord.Voice first chord.
Using the starting place of each voice, move through the next 6 chords with good voice-leading.
When you are done, scroll down for one possible solution …
