Major versus Minor

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Major versus Minor

Postby strachs » Thu Jun 04, 2009 2:32 pm

What is your take on the major/minor phenomenon?

Do you think that Lydian scales a minor third apart have some kind of correspondence, or what do you think is responsible for the whole minor concept?

(Major triads have their precedence in the overtone series, while the minor does not).
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Postby strachs » Wed Jun 10, 2009 5:01 pm

By the lack of response to this question, I take it either I'm being a bit vague as to what I'm getting at, or it's just too big a topic to tackle.

Anyone familiar with the concept knows the basic construct of a major triad - the first, third, and fifth tones of the harmonic series (or overtone series) - a product of nature's laws. The major scale (and the Lydian scale for that matter), a man-made construction designed to provide the basis of melodies and harmonies, is based on three major triads a fifth apart. One point to acknowledge here, is that a major triad is more or less provided by nature, whereas scales are much more remotely related to the Overtone Series (OS), and are more of a man-made construct.

At some point in history, a triad came into use that only partly conformed to this natural construct - the minor triad. It contains the third partial (the scalar "fifth"), but replaces the fifth harmonic (the scalar "third") with a lower pitch - the so-called "minor" third, which conforms more closely to a much higher, and therefore less fundamental, harmonic (the 19th partial most likely).

Although accepted in common practice, theorists have grappled with this construct for centuries, trying to understand why it stands as a different, though paralell structure to the major triad.

Also, as we know, there came to be discovered/invented the whole RELATIVE minor idea: that the scale that supports a major triad contains the same notes as a similarly constructed scale for use with a minor triad whose middle tone is the same pitch as the former major triad's tonic.

There is a difference of three notes between a scale used with a major triad and the scale used with a minor triad built on that same tonic (C major versus C minor: zero flats versus three flats).

In concept terms, we would refer to this as two Lydian scales a minor third apart (C Lydian and Eb Lydian).

So my question was meant to be along the lines of: Does the relative minor's existence as a MODE of a major-type scale (Lydian, say) really demonstrate a relatedness between the two triads, or is this just an artificial byproduct of the man-made scalar patterns that we use to work with the otherwise naturally-constructed triads?

I don't even claim that this question has any practical value to the improvisor or composer. I just wanna know, you know?
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Postby dds1234 » Sat Jun 13, 2009 11:46 pm

I obsessed over this a while back... to the harshest of extremes.

I am thinking symmetrical intervals (Or small possibility inversion intervals) have some form of reign over us... They are all the fundamental intervals in tonal magnetism. Look at the tritone, the minor third, the major third, and the foundation, the perfect fifth. I think it is all natural myself... Let me think about it for a bit.


-Daniel

=^_^=
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Postby strachs » Tue Jul 14, 2009 1:00 pm

Daniel: I have heard of this symmetrical interval theory, involving a descending harmonic series, or "undertone series". I'm not sure whether I believe in it's existence or not. Hindemith certainly discounted it's existence. I have found that almost all instances where it is referred to are also accompanied by heavy references to mysticism and philosophy (like this guy: http://www.khaldea.com/rudhyar/mt/mt_c7.shtml , or this guy: http://books.google.ca/books?id=fvLAARM ... t&resnum=6), which I don't consider valuable resources for this kind of thing.

Much of the material you encounter that discuss the nature of major versus minor discuss the triad only, not the scale. The theories are extremely interesting , but do not go so far as to compare the minor SCALE to the major SCALE.

If defining a minor triad is problematic, defining a minor scale is perhaps even more so.

The major scale (and indeed the Lydian scale) is usually described as the tones of three major triads (naturally occuring) spaced a perfect fifth apart. You could say that the major scale represents three instances of the OS spaced a fifth apart.

So what is a minor scale? Is it three minor triads a perfect fifth apart? If so, what is a minor triad?

In the OS, the major triad is formed by sounding partials 4, 5, and 6 together. What is a minor triad? Well, a major triad has a perfect fifth and a major third. The space between them (the ratio 6:5) is a smaller interval, and usually considered to be the interval that would create a minor triad if combined with a perfect fifth (others propose that 16:19 is the best ratio to use, but that's a different matter).

That would mean that the lower tone of a minor third interval is itself partial 5 of an OS whose fundamental is not being sounded.

A minor triad, then is either a composite of two OS's a major third apart (combining 6:5 of F and 3:2 of A), or it is a composite of two OS's a perfect fifth apart (combining 6:5 of F with 5:4 of C). Let's call them view 1 and view 2.

Let's say, then, that a minor scale is three minor triads each a fifth apart (Am, Em, Dm, for example). In the case of "view 1" above, such a scale would contain intervals from the OS of F, A, C, E, Bb, and D. In the case of "view 2" above, the scale would contain intervals from the OS of F, C, G, and Bb.

The latter case would seem to imply a more harmonious sharing of resources. In addition, the layout of four vertical structures (instances of the OS) a fifth apart is very much in line with the thinking of the Concept.

In equal temperament, natural intervals are compromised in order to allow playing in different keys on one instrument, and even modulate beteween them. However, the relationships of keys and major/minor triads predates equal temperament and does not depend upon it.

Whether using ET or not, a Lydian scale basically represents three instances of the OS spaced a fifth apart (so does the major scale - it just considers the middle one "home", not the bottom one). Since the minor triad is a composite of two OS instances a fifth apart (at least that's my opinion), a minor scale (or the minor mode, if you will) represents four instances of the OS spaced a fifth apart. The lowest one does not sound it's fundamental, the highest one does not sound it's 6th partial.

F Lydian/ C Major:

F A C Represents OS of F
C E G Represents OS of C
G B D Represents OS of G

F Dorian/ C Minor:

F Ab C Represents OS of Db and Ab
C Eb G Represents OS of Ab and Eb
G Bb D Represents OS of Eb and Bb

Ab Lydian/ Eb Major

Ab C Eb Represents OS of Ab
Eb G Bb Represents OS of Eb
Bb D F Represents OS of Bb

Since the perfect fifth is the strongest vertical interval between two tones IN A SINGLE INSTANCE of the OS, sounding two instances of the OS, spaced a perfect fifth apart is a vertical unity as well. All of the partials of each series are a fifth apart, and so have a natural, harmonic relatedness.

Because of this, the perfect fifth between any two corresponding partials of the two OS instances, can itself be heard as a pure vertical interval, even if the other sounding tone(s) voice partials of the OS instances which are a fifth apart, rather than the OS from which the SOUNDING fifth primarily belongs.

Below is a list of the first six partials of F, Db, and Ab. The F and C are are a fifth apart, and so are primarily associated with the Fundamental F. However, they are also the fifth partial of Ab and Db OS which have (among other intervals) a major third to C and a minor third to F.

1 2 3 4 5 6
F F C F A C
Db Db Ab Db F Ab
Ab Ab Eb Ab C Eb

So, back to the original question (rephrased a bit): what is a minor triad, what is a minor scale, and based on this understanding, is there a relatedness between two Lydian scales a minor third apart?

In my view, a minor triad is a composite of two instances of the OS spaced a fifth apart. A minor scale, then, is a composite of four instances of the OS series spaced a fifth apart, much as the major or lydian scale is a composite of three such instances.

Two OS instances a minor third apart have a common tone (sixth partial of the lower is the fifth partial of the higher). A scale (major or minor), being a construct of OS instances spaced by perfect fifths, manifests fifths between all corresponding partials. Therefore, the fifths between partials 5 and 6 of parallell OS instances can themselves be reckoned as OS series instances whose third and second partials correspond with partial 5 of one OS instance and partial 6 of another.

In a nutshell, the minor triad is not cunstructed in the same fashion as a major triad, as if it were just a different color of the same chord. Like a scale, it is a composite of more than one instance of the OS. Viewing it this way underscores the relatedness of of a minor triad to it's "relative" major triad. It also underscores the relatedness of the relative major and minor scales (or Lydian/Dorian if you prefer).

However, it also shows that minor triads are composites of OS instances. The minor third interval is taken from one OS instance and the major third from another, a perfect fifth above. The fifth partials of these two OS instances form the perfect fifth of the minor triad.





I encourage you to expose any flaws in this theory, since I realize that no one is proposing this theory as such, and I also realize that one can think themself in circles without realizing it.
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