Roman numeral analysis

The stage theory, by Jacob Gottfried Weber (1779-1839) and later developed by Simon Sechter (1788-1867) expanded, as well as the end of the 19th century by Hugo Riemann ( 1849-1919 ) established function theory is a means of descriptive analysis of the harmony of a piece of music. Both systems have survived to the present day, with modifications and extensions.

Using the theory of stages can the harmonious plan of a piece illustrate generalized so that comparisons to pieces in other keys are easier because the symbols are to be read in relation to the respective home key. Two pieces are " brought to a ( general ) Denominator ". At the same time, the stage theory reversed harmonic turns ready that can be applied to all keys.

• 2.1 Vierklang, Five sound, etc.
• 2.2 reversals
• 2.3 toner reduction
• 2.4 Fremdton

• 3.1 Example of an analysis

Basics

The basis of the theory of stages is an arbitrary scale that provides the clay material of the basic key of the piece. This can for example be a major or minor scale, but also any other (traditional or newly invented ) scale as pentatonic, church modes, whole tone scales, etc.

Numbering

Initially called the individual notes, seen from the root upwards, steps and numbers them with Roman numerals. The numbering is thus relative to the root, unlike our absolute note names.

The example of a C major scale:

Naming

In addition to these numbers also known from the theory of functions names are used. The first level (root ) is called the tonic, the fourth stage ( fourth) is called subdominant, and the fifth stage ( fifth) is called dominant.

Triads for major scales

About each of these stages can now be a triad construct by two thirds are layered over it. The sounds need to also come from the material of the scale, they are intrinsically ladder.

The example of a C major scale:

Due to the different Terzabstände within the chords built here three different types of triads in major and minor keys with the frame interval remains unchanged.

For example, always describes a II made ​​in any major key a minor triad, namely those triad is formed with diatonic tones over the second stage of the respective scale.

Triads for minor scales

Looking at the chord formation for (natural ) minor ( here C minor ), the following distribution:

(Note: In practice, however, the stage V very often as a major chord - more accurate than major dominant seventh chord - played, but it is not the third part of the natural minor scale. )

Extension of the stages symbols

An extension of the Roman numerals is necessary if

• The triads a fourth, fifth, ... sound is added
• A tone of this triad is replaced by another
• Is other than the fundamental lowest tone ( bass = )
• A tone of the triad is not intrinsically ladder.

In the following, these cases are explained:

Four sound, Five sound, etc.

It is possible to extend the initial triad by coating other thirds. The result is a four-note chords, five sounds, etc. This is indicated with ( Arabic ) numbers that are written on the top right ( as an exponent ) next to the Roman numeral. Its value indicates the interval of the additional tone in relation to the root note of the triad of: a 7 refers to the seventh, a 9, None, etc. Since the intervals already contain one (root ), 3 ( third) and 5 ( Quinte ) in the triad, these sounds are not indicated unless they are intrinsically ladder.

In C major:

Reversals

The classical theory of stages combined in the labeling of chord inversions the grundton - oriented interpretation of the stage with the bass - oriented numbering system of the basso continuo. so is

• A superscript 6 for sixth chord position or first inversion triad or Terzbass
• A superscript 4 and 6 for six-four chord or triad 2nd inversion or Quintbass
• A superscript 5 and 6 for five chord and 1 four-note chord inversion
• A superscript 3 and 4 for Terzquartakkord or 2 Vierklang reversal
• A superscript 2 for Sekundakkord or 3 Vierklang reversal or Septimbass

Since this designation system " around the corner thought " and by combining different perspectives difficulties occur with the concomitant identification of chord inversions and additional tones, use some stages theorists also the numbering system of function theory, the bass sounds characterized by imputed digits. These numbers are like the stages of interpretation grundton - oriented and rename the interval of the bass note in relation to the chord root:

Toner reduction

Also featured sounds that are intended to replace a Dreiklangston. The result is a derivative chords ( the replaced sound is " withheld ", often (not necessarily in jazz music ), this derivative is dissolved but by the three sounded alien is returned to the triad own sound). Where: 4 replaces 3, 6 replaced 5, 9 replaces 8 ( octaved root).

In C major:

Fremdton

Rarely is the fifth of the triad is concerned, almost never the root, but the third all the more. This is because the third ( large or small) should be categorized, the triad in major or minor. If you want to, for example, V. stage a minor scale (originally this triad is a minor triad, see above) provided with the characteristic of this stage leading tone to reinforce the dominant matic effect, the (small ) third must be raised by a semitone. This is done by a 3 with cross ( ♯ ) is placed to the right of the Roman numeral. Since the variation of the third is the most common of this type, is often the only written 3 is omitted and a cross. Does one another tone, this can be described in each case. This can also be performed with added or replaced tones when they should not be head of its own. A lowering of the tone is in analogy with a ♭.

In C minor:

Use

Unlike the function theory, the stage theory does not describe voltage relationships between chords. Since she is but built much elementary, she has great benefits: With their help, some chords, in which the function theory has its limits, of grasping it immediately, because it makes no interpretation of the sound basically, but " only " the tones used describes. See the problems of function harmonious interpretation of the Tristan chord.

The stage theory could this chord clearly describe, but says little about the relationship. This notation is not really clear, but at least possible.

Particularly useful is the use of the stage theory, if you want to identify sequences; the interval relationships of the chords with each other is easier to see and often show musical contexts over long distances, which would not be so obvious in the use of functions.

Because baroque music and jazz to a large extent based on sequences education, the stage theory is probably the most appropriate for the description of these styles. On top of that jazz is virtually no triad is used without the aforementioned extensions, here too the stage theory provides an excellent means. So is anyone who only partially engaged ( practical and / or theoretical) with jazz, the harmonic progression " II -VI " as the expression par excellence is well known.

Example of analysis

A simple example to show the basis of the theory of stages a sequence and at the same time to explain the various uses of scale and function theory, is a section from Mozart's Magic Flute from Quintet No. 5: sound sample in MIDI format ( 2 KB)

Initially the first three cycles, which are characterized as a sequence:

The fourth clock:

The second half:

You can see how both theories complement each other well and have both advantages and disadvantages, which can be easily deal with the other theory.