Are there two leading tones?

Question

I always took the leading tone to be the 7th degree (the "subtonic") scale degree. According to author David Neumeyer (The Music of Paul Hindemith), there is another? See the following quotes, and please let me know what you make of this: "The strongest intervals from both directions become the principal tonal functions: tonic, dominant, subdominant, and the two leading tones" (Neumeyer 31); "Hindemith restricted the secondary function to the dominant and the lower leading tone" (Neumeyer 55); and "The sharply directed melodic force of the tritone and the two leading tones . . ." (Neumeyer 61).

Thank you.

Answer 1

In addition to the 7th (major) scale degree, the flat second (and sometimes flat sixth) also operates as a leading tone in some music. Like scale degree 7, the flat 2 "leads" to the tonic (the flat 6 "leads" to the dominant).

This is reflected in the analytical chord notation given in Example 3.4.

Notice that the symbol for the first semitone is a downward-pointing arrow (i.e., pointing "down" to the tonic), and the symbol for the eleventh semitone is an upward-pointing arrow (i.e., pointing "up" to the tonic), in both cases reflecting the primary functional purpose of those tones.

When both lower (e.g., 7) and upper (i.e., ♭2) leading tones are used together, they are knows as a double leading tone.

The "Neapolitan" chord contains an example of an upper leading tone. In the key of C, the Neapolitan is a D♭ major chord (in first inversion), in which the A&flat (6 from minor); "leads" to G (the dominant).

X:0
M:none
K:none
L:1/1
[V:V1][_A_d] [GB] |
[V:V2 clef=bass][F,F] [DG,] |

The augmented sixth chord (in the context of a tritone substitution, where it leads directly to the tonic) contains a double leading tone. For example, rather than G7 leading to C, we have D♭7 leading to C. I've intentionally misspelled the D♭7 chord with B rather than C♭ to highlight the double leading tone.

X:0
M:none
K:none
L:1/1
[V:V1][_DF_A=B] [CEGc] |

Wikipedia has a brief discussion of the "upper leading tone". And see also Wikipedia's entry on the Lydian Cadence and its use in early music.

Answer 2

There are two things I know of that could be called two leading tones. I don't think either is what the quote about Hindemith means.

In the major/minor system TI to DO is the half step movement of leading tone to tonic. In phrygian mode you get a second kind of leading tone, a sort of upside down leading tone, the half step from ♭^2 - the lowered second degree - to the tonic.

The other comes from old solfege systems and the "rule of MI" where a tone with a half step above and a whole step below was considered MI. In one of those older systems your could have a scale in solfege like this...

1   2   3   4   5   6   7   1
C   D   E   F   G   A   B   C
UT  RE  MI  FA  SOL RE  MI  FA

...where you can see the third degree and seventh degree are both called MI. In the sense that you have two MI degrees, you could say you have two leading tones.

BTW, I noticed your other recent question about Hindemith's theory writings. If you are new to music theory, you might look for some other sources. Hindemith seems difficult. Talk of two leading tones, enharmonically spelled augmented intervals, etc. are likely to just perplex a beginning student.