# Music based on augmented and diminished triads



## Dim7

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?


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## millionrainbows

Dim7 said:


> 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."

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.


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## Che2007

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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## millionrainbows

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*).


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## Il_Penseroso

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:


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## millionrainbows

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.


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## Che2007

millionrainbows said:


> 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.


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!


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## Frasier

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.


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## Guest

Che2007 said:


> 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!


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.


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## Che2007

TalkingHead said:


> 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.


Good point! The 371 are a harmony teachers greatest resource!


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## EdwardBast

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.


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## millionrainbows

Che2007 said:


> 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 sounds like you are referring to dominant flat-9 chords. Diminished seventh chords do not have a dominant function. Prove me wrong.


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## millionrainbows

TalkingHead said:


> 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.


Spell the chord, explain in detail. I think you are incorrect.


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## Gaspard de la Nuit

Didn't mean to post in this thread


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## Che2007

millionrainbows said:


> It sounds like you are referring to dominant flat-9 chords. Diminished seventh chords do not have a dominant function. Prove me wrong.


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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## millionrainbows

These observations are intended to be food for thought, not as 'truisms.' These are general observations, and are not intended to be scrutinized as detailed definitions of anything, or for purposes of argumentation or invalidations.



Diminished seventh are a 'glitch' in the tonal system. Example, Cdim 7: C-Eb-Gb-Bbb) has no stable fifth, so as an isolated harmonic entity (i.e. a chord), it is weak, and does not establish a strong sense of tonality on the 'root' station of C. 

Additionally, the 'root' of a diminished chord is weak (no stable fifth) and the 'root' is in question, as it could be any of the four notes. Additionally, dim 7ths can be considered incomplete flat-nine chords if any of four other notes from the diminished scale are considered as 'roots.' Example, C-Eb-Gb-Bbb can be considered as stationed on any of those four notes (C-Eb-Gb-Bbb), or as flat-ninths if any of these four notes are considered as 'roots': Ab ( Ab7b9: Ab-C-Eb-G-Bbb), B (B7b9: B-Eb-Gb-A-C), D (D7b9: D-F#-A-C-Eb), or F (F7b9: F-A-C-Eb-Gb).

This vagueness or instability can be seen as a flexibility, rather than lacking. For this reason, these chords facilitate key changes. Schoenberg called them 'vagrant chords,' as they are best considered as being temporary and seen as moving between other chords as tyhe result of voice movement, not root movement per se.

The diminished seventh is really more a geometric result of the 12-division of the octave, rather than as a result of diatonic tonality. It is a symmetrical projection of the minor seventh, and is best seen as a 'mechanism' than as a harmonic entity.


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