source file: m1371.txt Date: Tue, 31 Mar 1998 13:59:29 -0500 Subject: TUNING digest 1370: Meantone From: Daniel Wolf The various meantone routines compromised fifths in order to better tune thirds. The augmented sixth that comes close to a 7:4 is a residual produ= ct of the tuning routine and its classical functional treatment - with possibly a few late and dramatic exceptions, among them the larger Mozart= Fantasie and certain places in the operas - does not appear to be relate= d to its specific intonation, that is, the augmented sixth is not a unique feature of the keys of D and G or G and C. = Nor would one expect it to be: if the seventh is so well in tune, why wou= ld it be heard as needing to resolve? Of course, this is a rhetorical point = as I think Paul Erlich is in the right direction when he locates resolution = as a property of an ordered collection (he says scale, but this description opens it to other orderings, e.g. by fifths). I doubt, however, that special preference would be given to movement by like intervals, particularly in the _contrary_ motion resolution of an augmented sixth as= this would seem to be extremely difficult for the ear to judge accurately= =2E = = I contend that if a system and the music composed for it, like meantone a= nd its historical repertoire (with the aforementioned exceptions) clearly articulates a five-limit lattice with limited equivalences, the acoustically almost-harmonic seventh will just not get parsed as such, particularly as the would be seventh just does not appear over the fundamentals of the most useful pitches. Of course, new music composers a= re free to try to find ways to introduce such relationships (as I suspect Mozart was doing), but I am unaware of any other than Douglas Leedy who have done so. Leedy's meantone works include strikingly articulated introductions of these intervals, and his _Lou Harrison's Round_ is essentially a transcription to the black keys of the harpsichord of Harrison's slendro _Gending Pak Tjokro_. For those interested, Fallen Leaf Press in Berkeley has published a volum= e of Leedy's pieces for harpsichord in Just Intonation. The harpsichord volume in meantone has not yet been published, but Leedy did contribute a= small article about composing in meantone to the _Perspectives_ forum on microtonality. =