When laying out the notes in the two-dimensional Wicki-Hayden layout, which is the most symmetrical layout I know of, it is visually clear that D is the "most central" note.
Why, then, doesn't D play a central role in music theory? Or does it? And similarly for the related Dorian scale.
D's central position in Wicky-Hayden layout is an artifact of the fact that Dorian mode is a symmetric scale (its descending interval pattern and ascending interval pattern are the same) in some tunings, including the twelve tone equal temperament (and it's the only such diatonic mode).
Even though I'm sure this mathematical property of Dorian mode has been exploited by some musicians, I'm not sure whether it has any real psycho-acoustic importance. Not all mathematical properties have psychological consequences.
In this case, Western musical tradition does not seem to care about this symmetry as much as it cares about the fact that I-IV-V triads create a major (Ionian) scale (another mathematical property).
Besides, this symmetry does not exist in just intonation (with its greater and lesser whole tones, between C-D and D-E respectively). It's a by-product of certain tunings.
One could equally say that G#/Ab is also 'central'.I guess that looking at a keyboard,each is valid. But a violin, a guitar, a sax., a trumpet?
In written music, one could argue that D is in fact not central, as C takes that position, being in the exact middle of the treble and bass clefs.Symmetry is co-incidental, and not that important, otherwise all girls would be called Hannah and boys Bob!
Good question. I've wondered about this before too. For example, in my answer to this question I used D as my central note in the table, because its half way between the sharp keys and the flat keys. Similarly, the Dorian scale is symmetric so that it is its own inversion -- sort of a musical palindrome (WHWWWHW). Also Sir Issac Newton recognized this symmetry: when comparing the color wheel to a musical scale, he started with red at D.
As for why this symmetry isn't more generally significant, I'm not sure there's really a good answer, unless it has to do with music in general eschewing symmetry. These asymmetries give the scale directionality and purpose. For example the half-step between the leading tone and the tonic gives rise to the whole idea of tonality, and dominants resolving to tonic.
D is the most important note. Take a look at the Graduale Romanum (or any repository of Gregorian chant) and see how D dominates as the final. Look at the music from the middle ages, or of Machault, of Dunstable and Dufay - same story. But these last two started a trend to base harmony on triads, and they are either major or minor - and so they modes we know today as "major" and "minor" inexorably became central, and by about 1600 all other modes were considered "out" - at least as far as classical music is concerned; in folk music(s) D is still pretty important.
Here's my two cents (the way I've justified this to myself at least)
Let's look at the A minor pentatonic scale, which is symmetric: A C D E G. (intervals 3,2,2,3 semitones.) Now another way building it up from fifths: C G D A E. Indeed either way it looks like D is the central note.
Now let's look at this scale harmonically. We have four fifths, two minor thirds, and one major third, C-E.
With this major third, we can construct a total of two triads: C major C E G and its relative minor, A minor A C E. These are the only fully consonant triads available in this scale.
So the most fundamentally harmonic thing about this set of notes is the pair C-E. Now we normally name an interval by the lower note, as it is the more fundamental. Hence the note that most stands out in this group of notes is the C. So we can reorder to get C D E G A, known as C pentatonic major, or (uniquely out of the five possibilities) simply C pentatonic.
The same applies for the diatonic scale of Am/Cmaj (or simply C). We ad one extra fifth at the beginning and the end and get the following portion of the cycle of fifths: (F) C G D A E (B). Now we have three major thirds, which enables us to build three relative major/relative minor chord pairs: Fmaj/Dm, Cmaj/Am and Gmaj/Em. But again, the most central of these is the major third C-E.
D does play a central role in music theory, in the sense that it's the center of the Circle of Fifths which is intimately linked to key signatures.
... F♭ C♭ G♭ D♭ A♭ E♭ B♭ F C G D A E B F♯ C♯ G♯ D♯ A♯ E♯ B♯ ...
This is why the Wicki-Hayden keyboard (which features a chain of P5's along its /-diagonal) has D in the middle.
However, as you point out in your question, the central note D gets little emphasis in music theory. Rather, it's the seven notes in the center, forming the diatonic scale of “natural” notes, that are collectively emphasized.
On the piano keyboard, this emphasis physically takes the form of the separation between white and black keys. On the Wicki-Hayden keyboard, it takes the form of naturals being placed in the center of the keyboard while the black keys are relegated to the edges.
As for the lack of emphasis on D itself, this largely because modern Western music typically uses only two of the seven modes of the diatonic scale: Ionian (major, C-D-E-F-G-A-B-C) and Aeolian (natural minor, A-B-C-D-E-F-G-A), leaving other modes, including Dorian (D-E-F-G-A-B-C-D) neglected. Why this is the case is the topic for another question.
I think the real answer may be that modes in some ways weren't as fundamental to Western polyphonic music as hexachords were, and those were based around a central "natural" hexachord based on (a somewhat movable) C/ut ("ut" being the original term for "do"). This hexachord ran from C to A, and was symmetrical around E-F (mi-fa). It was accompanied by a "hard" hexachord (ut to la starting on G, which supplied B♮) and a "soft" hexachord (ut to la starting on F, which supplied B♭). The modes were seen as a kind of movement between the hexachords guided by their solfeggio aspects.
This was from Guido d'Arezzo's singing theories, but Guido was the person who started the ball rolling towards modern notation, and early notated polyphonic music was entirely vocal, so his influence on matters like this was incalculable. Information on this can be found here: Hexachords, solmization, and musica ficta.
I'll be frank to admit that I'm still wrapping my head around all this, but it strikes me that a relocatable "mi-fa" may do a better job of explaining modal mutations in even modern music (for example, the use of sharp 6 and sharp 7 in the minor) than a multiplicity of scales does.
The mathematical symmetries in our scales, which have D as the symmetry axis, aren't reflected in music because upward and downward intervals do not have symmetrical acoustic functions.
If you bang a low C on the piano with the pedal down, you will likely hear the first few notes of the harmonic series, especially C's, G's, and E's. This suggests that the notes C, E, and G will sound good together, and that among them, C is naturally the root (most important) note. This process does not work in reverse. No matter how hard you hit a high C key, you will not hear the "undertones" F and A-flat. When the ear hears a minor chord such as C-Eb-G, it is happier to accept it as a deviation from the major, with lowered third and C still functioning as root, than as an inverted formation with G as the root.
So if we think of the diatonic scale as a stack of 5ths, F-C-G-D-A-E-B, then it stands to reason that F and C are much more stable and likely to be used as tonics than E and especially B. And indeed, looking cross-culturally and cross-historically, this is true. The intermediate notes G, D, and A are also viable tonics. Our preference for C reflects more recent trends in Western music, especially the use of the dominant seventh chord G-B-D-F where the resolution of the tritone (B to C, F to E) strongly emphasizes C major.
Any answer that supports the assertion on which this question is based, but which does not explicitly reference a particular instrument or clef is not entirely correct in that regard. There is no really 'central' note in Western music theory (even before atonalism).
The popular clefs and the white keys on a 12-EDO keyboard completely facilitate the major scale starting on C. They completely facilitate the natural minor scale on A. They completely facilitate the Dorian mode on D. Modern music practice likes mid-range major scales on keyboard instruments, so middle C is a popular tone. Why the Ionian mode and the common keyboard are so popular today is another question, and would probably deserve more than a few sentences, but here goes anyway.
One answer is the major triads built on I-IV-V as mentioned in another answer, but that bites its tail a bit: where does the idea of major triads come from, not to mention the diatonic scale? The simplest way to construct the major scale is either through 3-limit (Pythagorean, steps of a perfect fifth up (overtone) or down (undertone)) or 5-limit (perfect fifths and major thirds) means, and to observe the decisions made in the process.
A rough measure of triadic harmonicity is to multiply the harmonics together, so a perfectly major triad ranks very well by this measure 1:3:5 = 15. Also we tend to accept dissonances better in a higher range, so major triads may be said to 'outperform' minor triads by this measure, too, since the minor third is in the higher range.
There are piano methods which point out the symmetry of the keyboard is based around D or G#/Ab rather than the ubiquitous all white keys C major scale.
I think the place I first heard of it is: Mastering Piano Technique: A Guide for Students, Teachers, and Performers, By Seymour Fink
