The Tonal System
So far we have spent a little time writing melodies and doing some two-part counterpoint within the modal system, where only the natural notes were used, and the only accidentals occured, if at all, at the point of the cadence when we sometimes raised the final note of the counterpoint to create a half-step leading tone to the tonic. This was the modal system, the basis of which forms the precurser to the system of tonality in use during the common practice period of classical music, roughly the 17th through the early 20th centuries, and which remains in use today in much jazz, rock and commercial music.
Thus to understand the tonal system is to understand how a great amount of music is put together, and forms the basis for any more advanced study in contemporary composition.
Scales based on the Central Polarity
While scales are fundamentally a linear construction, it remains useful to conceive of scales within the larger context of Harmonic Polarity.
Here is our central polarity in major, described on the previous pages, with C in the center (tonic), G the fifth above (the dominant) and F (the subdominant), below:
F — C — G
The Names of the Scale Degrees in major
We can now fill in the spaces between these intervals with scale steps, resulting in a scale that descends downwards to the subdominant and rises upwards to the dominant. This, again, is the central polarity of music:
It is important to think of this as a C major scale, with the C stands at the center of the scale, rather than at its lowest and highest points. This is most helpful in learning the names of the scales degrees, which are based on this perception as C as a central point from which the scale ascends and descends. Frankly, I have never seen this material presented in this way, but it only makes sense, when you look at the names associated with the various scale degress.
The Mediant and Submediant Scale Degrees
So, we have already seen three of the scale names. C is tonic, G above is dominant and F below is subdominant.
Thinking in these terms (G as the Dominant a fifth above, and F is the subdominant a fifth below when in the key of C major), which additional notes are midway between these upward and downward poles?
Looking at the polar scale above, clearly, the E is midway up to the G and the A is midway down to the F. The E and the A are then given the term mediant, because of the are midway between the outward poles of the dominant and subdominant.
- E is the mediant between C and G.
- More generally put, any third degree of a scale is called the mediant.
- A is the submediant between C and F. Just as F is the Subdominant,
a fifth below, A is the submediant, a third below the tonic.
- More generally put, any third degree down from the tonic in a scale is called the submediant.
There remain two notes unaccounted for in the above polar scale, that is, the D and the B. These tones have special functions in music. Therefore they are not considered as pairs in the way that we think of the dominant/subdominant pair and the mediant/submediant pair, but are treated separately in the following manner.
The Supertonic Scale Degree
The tone above the tonic is given the simple and obvious term supertonic. It is one note above the tonic, typically one major whole tone (except in the Phrygian mode). It is also two perfect fifths above the tonic. Thus:
- D is called the supertonic for two reasons
- In the overtonal spine of fifths, it is the next fifth in the sequence from C to G to D, and thus "lives" above the tonic at the distance of two fifths. In terms of harmonic function, this is actually the more important "habitat" for the supertonic note.
- The D, after octave reduction, is also brought down to being a whole tone above the C (or tonic) when featured in a scale. In both Pythagorean and Just intonation, this is our familiar whole tone, with a ratio of 9:8 above the tonic.
The Leading Tone Scale Degree
The B, in its capacity as being only a half step below the C and also the last note of the rising tetrachord from G up to C, is given the special term leading tone. In functional harmony, the seventh step of the scale has a strong tendency to lead back to C or tonic. Thus:
- B is called the leading tone of the C major scale.
- More generally, the seventh step of any major or minor scale is given the term leading tone. It possesses a strong sense of forward motion, "leading" the ear back to tonic.
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Scale tones related to the central triads
If we look at these scale tones and relate them to the central triads:
we can make the following observations:
- The tonic and subdominant triads have at their centers the paired mediant
and submediants, respectively.
- The tonic chord's mediant fixes the tonic chord as the central triad of the key.
- The subdominant chord's sub-mediant relates that chord to the relative minor of the central key.
- The dominant chord possesses the leading tone at its center. This is a vitally important aspect to its character. The leading tone stands at the most dissonant to the tonic, and its presence has the effect of propelling a piece of music towards the tonic key (the "ti-do" effect).
The Names of the Scale Degrees in major
Now that we have seen the logic of these names, based on the polarity of subdominant and dominant, we can also arrange the C scale with the C as the bass, as one would normally play or practice a scale on an instrument. We now understand why the notes have these designations:
Always remember that the "sub" aspect of the subdominant and submediant refers to the downward, inward motion towards the reciprocal realm.
The Names of the Scale Degrees in minor
Every major key has its relative minor, and thus every major scale has a related minor scale. In C major, the relative minor is A minor. When referring to a minor scale, we keep the same designations, shifting the tonic from C to A and keeping all the other scale terms in equal relationship with the minor. Here are the terms in minor, with A in the bass:
The leading tone in minor
This brings us to a final and central topic. Hey, this is really really important, so read carefully! It has to do with the leading tone in minor. You will notice above that the leading tone has been raised in A minor, to create a G#, a half-step away from the tonic. The background for this is as follows:
The major scale became the central scale in tonal music for a variety or reasons, but two primary reasons are:
- It is the only scale (among the six modes) which can form a major triad on the tonic, dominant and subdominant notes.
- It is the only scale that has a half step between the seventh and eighth steps of the scale while also having the subdominant as a perfect fifth below tonic. It is the only scale, we can say, in which the leading tone is a half step away from the tonic while the subdominant is a perfect fifth below the tonic. (Lydian also has a half-step leading tone, but its subdominant is a tritone away from the tonic, not a perfect fifth below/perfect fourth above).
We see that in the natural minor (the aeolian mode), we revert to the "modal" situation which has the seventh step a whole tone away from the tonic. To better define tonality and take advantage of the strength of the major mode, with its half-step leading to tone to tonic, we simply use musica ficta ( as we did when we raised the leading tone in our modal counterpoint practice) and artifically create a leading tone betwen the seventh and eighth degrees of the scale. We raise the leading tone in minor.
Here is an example of notes moving around the minor mode. You'll notice that when there is a passage descending from A past G, or a passage that reaches upwards but does not try to reach the tonic A, the G is a natural note. But when there is a strong motion of the G leading back up to the tonic note, the G is raised a half step to G# in order to create the strong half-step leading tone to the tonic.
Notice how this has been written: The natural minor scale, the Aeolian mode, can move up and down from A to A using the natural notes, but it can also employ an artifically raised leading tone.
- The G natural is used most often when the scale or melody is descending
- The G# is used most often when the scale or melodic is leading back to the tonic. Thus, an artificially raised leading tone is used in minor when the melody is meant to resolve back to the tonic note.
Listen to how this sounds:
The reason for this artificially raised leading tone is to create this strong sense of resolution to the tonic. Here are some examples of folk melodies, paired in major and minor, in which the sense of leading tone in major going to the tonic is strong, and in which the same sense of leading tone in minor is strong by virtue of its raised leading tone.
<some more musical examples will come here>
The Dominant Chord in Minor
We can infer now one final point regarding the scale of minor.
Recall this chart of the tonic, dominant and subdominant triads in major:
Recall also that we can build the same triads in the relative minor key of A minor by creating triads above the three poles of subdominant, tonic and dominant in A;
However, we have noted than when in minor, the tendency is to raise the leading tone. In the natural minor scale, the dominant triad (above) is a minor triad. But when the leading tone is raised, this changes the minor triad to a major triad, which neatly corresponds to the major triad on the dominant in the major key.
Indeed, typically when the melodies presented above are harmonized, that is, when chords are used to accompany them, the raised leading tone in minor is harmonized with a major dominant triad. Thus we have this correspondance:
- The dominant triad in a major key is a major triad, and thus has as its active tone the leading tone of the key.
- The dominant triad in a minor key is naturally a minor triad, as we have seen. This minor triad has as its active tone a tone which is a whole step away from the tonic. This does not create as forward reaching a harmony as does the dominant triad with the true leading tone. We don't have the sound of "ti-do" with the minor dominant triad.
- Thus, in most tonal music, the dominant triad in minor is given a raised leading tone by artificially raising the seventh a half step. This creates the same type of dominant chord in both major and minor.
Here is a passage of a Bach Chorale in A minor. You need only notice that in every case, the G appears as a G#, raising the leading tone and creating sense of resolution to the tonic key. Listen to the recording and experience this change.
<INSERT>
Here is the same recording, played without the raise leading tone (that is, it is completely in A aeolian or A natural minor). While this is not at all unpleasant, can you hear that it has less forward direction and less sense of resolution? This, in essence, is tonality vs. modality.
We will discuss this a little more when we discuss major and minor harmony in greater detail.
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