Likes: Obviously there's plenty of music that uses augmented and diminished triads (or diminished 7th chords), but I was thinking that what if you'd "replace" the major-minor triad polarity with augmented-diminished polarity. Any examples?
Music based on augmented and diminished triads
Obviously there's plenty of music that uses augmented and diminished triads (or diminished 7th chords), but I was thinking that what if you'd "replace" the major-minor triad polarity with augmented-diminished polarity. Any examples?
Compare it this way: the diatonic seven-note scale is the result of stacking fifths, F-C-G-D-A-E-B. This is called "interval projection."Originally Posted by Dim7
Whole tone scales are the result of the projection of the major second: C-D-E-F#-G#-A#. It also has a major third projection (C-E-G#) (augmented chord) and tritones (C-F#, D-G#, etc.)
Diminished scales are the result of the projection of the minor third, with M2 and m2: whole-half scale:C-D-Eb-F-Gb-Ab-A-B or half-whole scale: C-Db-Eb-E-F#-G-A-Bb (both octatonic) with a harmonic component of: C-Eb-Gb-A (diminished seventh chord).
The tritones present in both forms make these inherently weak, tonally, and somewhat unstable, since they lack perfect fifths as a stabilizing factor.
Bartok and Stravinsky both did this; the later French composers Franck and Faure did this as well. Listen to Frack's G minor quartet, and Faure's chamber music. Schoenberg's Chamber Symphony No. 1 uses the who;e-tone scale; Ernest Bloch was fond of the octatonic scales because of their similarity to Jewish scales.
Diminished chords and augmented chords are fundementally different from each other in a way that man/min are not. It isn't really an equivalent duality. There is a great deal of music that moves between different scales to dramatic effect. You might like to look into Debussy or Scriabin.
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The seven-note diatonic scale, and tonality, were ostensibly established on the basis of sonority, and the stacking of fifths. It was a compromise from the ideal of 'just' intervals, and has always had its limitations.
The chromatic scale creeped in only later. The diminished and augmented scales are not based on sonority or stability, but are projections of geometry.
The chromatic, 12-division octave/distance model is well-suited to constructing abstract pitch geometries, while the ratio model offers insight into an interval's sonic quality and stability.
A sense of tonality and tone-centers is strongest when it has fewer notes, as in the 7-note diatonic and 5-note pentatonic scales. They produce a sense of tonality as much for what they leave out. The more notes that are added, the more ambiguous the perception of a tone center becomes.
Augmented and diminished scales invite geometric divisions, based on symmetries of 12. These divisions are "in-octave" and recur in cycles which fit the octave.
The fourth & fifth, which tonality is based on, do not divide the "12" octave evenly; they go outside the octave, to new denominators, before finally reconciling; as in the fifth (7x12=84), and the fourth (5x12=60).
Augmented chords as the foundamental harmonic structure could be found in a couple of Liszt later works. You may find them also in some Russian operas or those works based on a hexachord harmonic stuff in the late 19th. cent. and early 20th. cent. music literature.
This is a very short composition by Rebikov, I used to play whan I was a child:
In a world which is ruled by gangsters and maniacs, art means nothing but just a junk food and there's no hope for human's salvation throughout... (Shāmlou)
Major and minor chords are used especially in early tonality because they are stable (with a fifth) and sonorous.
Augmented and diminished chords, are mainly the result of voice movement, and must be 'resolved' into a more tonal chord. They are not primary functions, but came about secondarily, and are 'vagrant chords' as Schoenberg called them in his Harmonilehre ("Alright, buddy, get moving along. Either resolve or disappear, but don't be hanging around here.")
In a general sense, these chords are not really tonal, because they are transitional, and do not stabilize or reinforce the tonality; if anything, they weaken tonality.
Thus, we see the entrance of "abstract pitch geometries" which have less to do with tonality and sonority (but are still part of it), and more to do with geometric divisions and symmetries in the 12-note chromatic scale.
Eventually, we will begin to see this geometric and symmetric thinking take more and more precedence over the formerly tonal, sonorous world of early tonality.
Thus, the establishment of "modern musical thinking" begins to assert itself, and tonality is left further and further behind, weakened if it still is present, and ideas of symmetry begin to take hold. The stage is then set for Schoenberg's ideas, and the eventual total abandonment of the older tonal way of thinking, based on sonority and tonal stability.
I have to disagree with you here. It depends on the context but both augmented and diminished triads can exist in their own right (not purely as the result of voice leading) and have a dominant function. They can be very tonal!
It might be an exercise to compose something in the Locrian mode as its tonic chord contains a diminished 5th. It's too easy to slip into the Phrygian mode. One composer that made extensive use of it was Peter Mennin.
Last edited by Frasier; May-25-2015 at 11:56. Reason: typo
That's correct, Ché2007. In the '371' the passing 6/4 (Vc) is rare and Bach generally prefers VII6. Its function is clearly dominant and the tonality is not by any stretch of the imagination weakened.
Lukecash12 liked this post
Good point! The 371 are a harmony teachers greatest resource!
King Crimson's The Construction of Light, I believe does this, but it also includes sections in the minor and the major (and other) modes as well — at least the live septet version from 2014 (Orpheum Theater, LA) does. Don't have a score, obviously, and would like to verify these observations …
In the past they have done 10 minute instrumental pieces using whole tone scales with predominantly augmented chords, and others with significant octatonic passages, but I can't think of others where these materials are used in contrasting sections of the same work.
Dim7 liked this post
It sounds like you are referring to dominant flat-9 chords. Diminished seventh chords do not have a dominant function. Prove me wrong.
Spell the chord, explain in detail. I think you are incorrect.
Didn't mean to post in this thread
Last edited by Gaspard de la Nuit; Oct-02-2015 at 19:53.
"Only in being hidden does the Divine reveal itself."
I was referring to diminished triads and augmented triads.
If you don't believe diminished 7ths have a dominant function in tonal music then I don't think me explaining it to you will be of any help...
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