# How far can the term "tonality" be stretched? Until it breaks!



## millionrainbows (Jun 23, 2012)

In a "scale" (not a mode or tetrachord), the pull towards a tonic is inherently determined by vertical harmonic factors, not horizontal "emphasis" by repetition or accent. That comes later.

All intonations are "modeled" roughly after these "pure" ratios (see chart below), since "exact pure fifths" cannot be fit into an octave, and have been reduced by 2 cents each in ET. Major thirds (4:5) are even harder to accomodate. This chart is the "harmonic" model. No existing tuning can ever get all the intervals to be pure.

Most dissonant intervals to most consonant intervals, within one octave:

1. minor seventh (C-Bb) 9:16
2. major seventh (C-B) 8:15
3. major second (C-D) 8:9
4. minor sixth (C-Ab) 5:8
5. minor third (C-Eb) 5:6
6. major third (C-E) 4:5
7. major sixth (C-A) 3:5
8. perfect fourth (C-F) 3:4
9. perfect fifth (C-G) 2:3
10. octave (C-C') 1:2
11. unison (C-C) 1:1



> But what about the Tristan chord?It has undefined tonality but is not atonal.


You have chosen a "glitch" in tonality, which does not clarify, but only obscures. Wagner's chord is ambiguous, but it is in reference to a tonal context, so this is "tonal chromaticism" at its most extreme. I agree that "it has undefined tonality but is not atonal," but you are jumping the gun by using the term 'atonal.'

That term only becomes relevant when 12-tone music removes the vertical hierarchy of harmony, replacing it with ordered rows. Yes, there are different degrees of tonal strength; all Western tonal music is based on this ebb and flow.



> I would agree that music that has a tonic is tonal but I would disagree with a statement that tonal music must have a tonic at all times.


In order to be tonal (and not "atonal"), music must have *reference *to a tonic. This can be very strong, or become very ambiguous. In Wagner's case, this is ambiguous function, but is still clearly in the tonal realm, because of context. You can't just "zero in" on the tristan chord and say that because its function is ambiguous, that the whole opera is "not tonal because it doesn't have a clear tonic in one area."

Even in later "true chromaticism," as used by Bartók or Frank Martin, constantly-shifting tone centers are still _"referring"_ to a tonic. Additionally, this type of "true chromaticism" is still _harmonic_ in nature, so this factor_ "refers"_ it to tonality. Therefore, "true chromaticism" is _"tonal,"_ even if there is no constant tonic, because all of its structures are _harmonic_ in nature,_ i.e., they "refer" harmonically to a tonic_ or localized chord root.

The only way tonality can be completely "dispensed with" is by dispensing with the vertical hierarchy.

When, as in 12-tone and serialism, _the pitch material becomes non-harmonic, by replacing the tonal/harmonic hierarchy_ (see chart above) with an ordered row hierarchy, the music can be said to be _non-harmonic_ in structure, or _"atonal."_

Read my blog "Understandng Bartók" first.


----------

