I try to learn rules of how basic melody ("Cantus Firmus") should be built. At the moment I read this document. The second rule there is:

The penultimate note should go to the final in a stepwise manner i.e.
from one note above or below the final. If approaching from below the
leading note should be raised (except in the phrygian mode)

What is "leading note" and what does it mean to "raise a note"?

I did check Wikipedia and it says:

a leading-note is a note or pitch which resolves or "leads" to a note
one semitone higher or lower

This statement is also not clear to me. What does it mean "leads to" and "resolves"? Are these two different things or just two different names for the same thing? Does "leads to" mean just "precedes"?

Basically these are synonymous terms: "leads to" and "resolves."

A very important concept in tonal harmony is the strong sense of movement in the half steps of the diatonic scales. In solfege these are the tone pairs TI to DO and FA to MI.

Things can get confusing if we discuss the leading tone and resolution_and_ jump between different musical styles. You mentioned cantus firmus which suggests 16th century counterpoint, modal scales, and the species counterpoint teaching of Fux. In the 18th century homophonic style the leading tone and harmony have a different treatment with parts rooted in the older style. Let's look at the two separately. Just remember: two different styles, two different approaches.

16th century

The quote "...penultimate note should go to the final in a stepwise manner..." is describing the clausula vera, the final cadence in 16th century style. The idea is the final tone - the tonic - should be approached by two voices in contrary motion one voice moving by a whole step and the other moving by a half step. When the final is approached from below by a half step that penultimate tone is the leading tone. The exact handling depends on the mode so let's just run through each mode.

In Ionian and Lydian modes the tones above and below the final are a whole step and a half step. Let's use C as a final. The whole step above is D and the half step below is B. When B and D move to C to end this is the clausula vera. The B a half step below the C is the leading tone.

In Dorian, Aeolian, and Mixolydian modes the tones above and below the final are both whole steps. Let's use D as the final. The two whole steps are the E above and the C below. If we use those diatonic pitches and move C and E to D to end it is not a clausula vera! One voice needs to be altered to make a movement by half step. The convention is to raise the tone below the final by a half step. This will make our C become a C#. This gives us the correct movement for a clausula vera and the C# has become a leading tone (because it is one half step under the final.) Note: The unaltered tone a whole step below the final can be called the subtonic.

In Phrygian mode we have a unique situation. The tones above and below are a half step and a whole step. Instead of the half step being located under the final, it is located above the final. Technically we fulfill the definition of a clausula vera, because when the voices move to the final one moves by whole step and the other by half step. But we don't really have a proper leading tone below the tonic. The tone above is sort of like a leading tone. This half step approach from above give a unique flavor to the Phrygian mode the other modes don't have. To illustrate, let's use E as the final. The half step above is F and the whole step below is D. When D and F move to E we have a clausula vera without altering any tones with accidentals, but technically there is not a leading tone.

18th century

Briefly, let's consider 18th century harmony. During that time period the modes were no longer used. Instead harmony used the major/minor system. In that system we can shift the tonic around temporarily using tonicizations and modulations. Without going into too much detail, any diatonic major or minor chord in a given key can temporarily become the tonic. The root of such chords will become the temporary tonic, and the half step below that tone will be the temporary leading tone. For example, in C major the chords D minor, E minor, F major, G major, and A minor can all become temporary tonics. The tones a half step below each of those roots will be temporary leading tones - C# to D, D# to E, E to F, F# to G, and G# to A.

You can link the 18th century style back to the 16th century style by constructing a clausula vera to lead to any of those tonics. But in modern terminology we don't call it a clausula vera. Instead it is called a secondary or applied dominant and label them with Roman numeral analysis symbols. For example, the temporary leading tone move to D in the key C major would be labelled like: V6/ii to ii.

I packed a lot of theory into a very short description. Take time to digest it and continue to read up on these topics.

• the leading tone is a half step below a final/tonic


• half step movements in the diatonic scale have a strong sense of pull or movement


• resolution and important harmonic movements often involve half step movements

Leading note (or tone) refers to the 7th note in the major scale. It's always one semitone below the root, which gives its name to the key. So, in key C, that note's B. Resolution is 'coming home comfortably'. Try playing some notes in key C, and stop on a B. It feels like you're nearly home, but need one more step. That's usually to C.And that's resolution, where tension gives way to a calmer feeling. Then it all feels at rest. That's why we call the B here the leading note, as it literally leads to the C.

The same idea works when we stop on D, the note above C. That needs to be resolved, which it does in a downward motion, D>C. As noted in your text. It's common in jazz to flatten that D to D&fat;, giving it a smaller route home to C.

It's also the reason why the harmonic and melodic minors use a different 7th note in their scales from the natural minor - they both use a sharpened leading note, so it works just as it does in major keys.

leading tone in melodies:

The leading tone effect is a pychological phenomen that you can hear and observe (detect) in a melody (melodic representation)

many tunes are ending so so la ti do, or do do do ti do and do re ti do. whereby the halfstep ti_do is the function of the 7_1 leading tone to the tonic. As Michael explains this "rule" has been developed in the modes of church chant and later by the Renaissance composers in the 16th century. In addition to Tim I want to emphasize that in that time it was not used to notate the alteration of the 7th step, it was up to the performers whether they would raise it to a leading tone in the dorian, aeolian and mixo lydian modes. I didn't live at that time but I was occupied by this questions the last days When did the aeolian mode change to the harmonic minor?.)

leading tone in harmony: harmonic representation

The function of a leading tone can't be explained without the psychological phenomens and terms of

energy and tension:

In all intervals there is a certain degree of dissonance and consonance. (Ernst Kurt)
e.g.:

a major 7th sounds sharply dissonant and has the tension to resolve into a perfect octave. This energy to resolve in a perfect interval is the tension of the leading tone to the final (tonic).

Another example is the suspended 4th of a major triad 1-3-5 as 4_3 resolving into a consonant third (Fa_Mi) notice: the final "Amen" or the clause fa-mi-re-mi.

The tritone Fa-Ti is also considered as dissonant (so far that it was the devils tone and forbidden - also in your exercises! ;)
in this interval of an augmented 4th is a maximum of tension: Ti leading to Do and Fa leading to Mi.

Initially, the leading-tone effect originates from the last step of the fundamental scale (e.g., B–C in the C major scale), whereby the sense of the critical approach to the goal, of direction, is bound with the seventh scale degree (B), and the sense of dissolution, resolution, is bound with the attainment of the fundamental tone, C, once more. The problem, initially in general terms, focuses on the entrance of an energetic moment that is given in a sounding [moment]. The transference from the sensation of drive to that of nearness is the psychologically basic function that has evolved in dynamic hearing. But with it, the essential is not exhausted; for it is available in two ways: in the drive in the leading tone, but also in its resolution, the leading tone step.

Ernst Kurth

in:

Ernst Kurth at the Boundary of Music Theory and Psychology

by

Daphne Tan

https://books.google.ch/books/about/Ernst_Kurth_at_the_Boundary_of_Music_The.html?id=9y00nQEACAAJ&redir_esc=y

also available as Pdf:

Ernst Kurth at the Boundary of Music Theory and ... - UR Research
https://urresearch.rochester.edu/fileDownloadForInstitutionalItem.action?itemId..