You would think the German, French, and Italian 6th chords are so named by the historical context in which they first appeared.
(See also Neapolitan sixth chord, and the "Tristan Chord".)
However, the more I research this, it appears the names German, French, and Italian are likely arbitrary.
Here are two citations that support this: 1) "...
theorists disagree on their precise origins and have struggled for centuries to define their roots, and fit them into conventional harmonic theory...
" source: http://en.wikipedia.org/wiki/Augmented_sixth_chord 2)
"Why the national names?
No particular reason, it seems.
But they had to be called something.
Frank, Suzie, and Jack would have done as well."
source:
http://www.ars-nova.com/Theory%20Q&A/Q38.html
My recollections from undergraduate music theory (many decades ago) are that these were introduced in operas from each nation, but this appears wonky now.
However the "Neapolitan" 6th does have a specific origin:
"The chord is called "Neapolitan" because it is associated with the Neapolitan School, which included Alessandro Scarlatti, Pergolesi, Paisiello, Cimarosa, and other important 18th-century composers of Italian opera" source: http://en.wikipedia.org/wiki/Neapolitan_chord
I found a summary of a book that details "...
Augmented Sixth from Monteverdi to Mahler"
(Mark Ellis, Kirklees College and Huddersfield University, UK): http://www.ashgate.com/isbn/9780754663850
music.stackexchange.com/users/2076/filzilla
The names Italian, French and German have a sure and certain origin.
They were coined by John Wall Callcott in his "A musical grammar", oublished in 1806.
Or, better, he quotes the first (italian) from tradition, and coins himself the other two.
Very simple!!
music.stackexchange.com/users/65945/Federico Augusto Agostinelli
Note that the French sixth contains notes belonging to a whole-tone scale.
Despite the strong temptation to draw a parallel to the French impressionist school, famous for their use of this scale (e.g. Debussy's Voiles ), I concur with the previous poster that this is most likely a coincidence.
music.stackexchange.com/users/12098/ninemileskid
in German they are named by the intervals.
ü6,ü56,ü34
(whereby ü = übermässig , that means augmented 6th Italian: ü6 = aug 6th German: ü56 = aug 5th6th French:
ü34 = aug 3rd4th
music.stackexchange.com/users/56219/Albrecht Hügli
The term augmented sixth is ambigious to me.
Sometimes it refers to the 6th being augmented, and sometimes the 5th being augmented with a major 6th.
There are three types of Augmented 6th chord the German, the Italian, and the French.
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Dom asked Jun 18 '14 at 19:49 What about the conventional augmented sixth chords, which have a major 6th and an augmented 5th?
e.g. C-E-G#-A withfunctions R-3-5#-6 as can be played in C Lydian Augmented .
Do you mean to ask why they are called Augmented 6th chords or why they are called German/Italian/French?
–
Basstickler Jun 18 '14 at 20:59
It is interesting, though, that they call these chords augmented sixth.
Other augmented chords do not refer to the extension note being augmented: e.g. Caug7 which has an augmented 5th and a minor 7th.
is there an alternative name for each that better captures how they are constructed?
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Dom asked Jun 18 '14 at 19:49 If we apply contemporary chord names based on enharmonics of the major scale: german: dom7 italian: dom7(no5) french: dom7(b5)
music.stackexchange.com/users/None/
There are three types of Augmented 6th chord the German, the Italian, and the French. Most chords are named for the intervals they contain or their function, but these seem like just arbitrary names for chords. Why are the augmented chords named for their respective countries and is there an alternative name for each that better captures how they are constructed?
Naming convention for augmented 6th chords
music.stackexchange.com
<chords><chord-theory><history>
music.stackexchange.com/questions/20334
music.stackexchange.com/users/7222/Dom
The names for the French, Italian and German chords were coined by John Wall Callcott in his "A musical grammar", published in 1806.  "The chord is called "Neapolitan" because it is associated with the  Neapolitan School, which included Alessandro Scarlatti, Pergolesi,  Paisiello, Cimarosa, and other important 18th-century composers of  Italian opera"   source:  http://en.wikipedia.org/wiki/Neapolitan_chord  There is no agreement as to how augmented chords received these names, with some people claiming that they can from operas in their respective nation, and others saying that they were invented by John Wall Callcott in 1806.
There is no agreement as to how augmented chords received these names, with some people claiming that they can from operas in their respective nation, and others saying that they were invented by John Wall Callcott in 1806.