=== === ============= ==== === === == == == == == ==== == == = == ==== === == == == == == == == = == == == == == == == == == ==== M U S I C T H E O R Y O N L I N E A Publication of the Society for Music Theory Copyright (c) 1994 Society for Music Theory +-------------------------------------------------------------+ | Volume 0, Number 9 July, 1994 ISSN: 1067-3040 | +-------------------------------------------------------------+ All queries to: mto-editor@husc.harvard.edu +=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+ File: mto.94.0.9.klumpenhouwer.fig Some Remarks on the Use of Riemann Transformations Examples Example 1 a) C major-------->E minor-------->G major L R ------------------------> S b) A minor-------->F major-------->D minor L R ------------------------> D Example 2a Example 2b F I/II F I/II D I/III D Bb I/II I/III Bb I/II Example 2c F II D III Bb I Example 3a Example 3b F I/II I/III F I/II Db I/III Db Bb I/II Bb I/II Example 3c F I Db III Bb II Example 4 Valhalla Theme I Q ---->(Bb,+)---------->(F,+) T ---- ^ ^ ---- QW| QW| ---- LW | -Q | (Gb,+)------------>(F,-)---------->(C,-) Example 5 Valhalla Theme II Q ----->(B,-)------------>(E,-) T ----- ^ ^ ---- QW| QW| ---- LW | -Q | (D#,-)------------>(E,+)------------>(A,+) Example 6 Valhalla Theme I (after Lewin's Figure 3b) S ---->Bbmaj----------->Fmaj LP ---- ^ ^ ---- | P | P --- L | S | Gbmaj---------->Bbmin----------->Fmin Example 7 Valhalla Theme II (after Lewin's Figure 4b) D ---->Emin---------->Amin LP ---- ^ ^ ---- | P | P --- L | D | G#min---------->Emaj---------->Amaj +=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+ Copyright Statement [1] Music Theory Online (MTO) as a whole is Copyright (c) 1994, all rights reserved, by the Society for Music Theory, which is the owner of the journal. Copyrights for individual items published in (MTO) are held by their authors. Items appearing in MTO may be saved and stored in electronic or paper form, and may be shared among individuals for purposes of scholarly research or discussion, but may *not* be republished in any form, electronic or print, without prior, written permission from the author(s), and advance notification of the editors of MTO. [2] Any redistributed form of items published in MTO must include the following information in a form appropriate to the medium in which the items are to appear: This item appeared in Music Theory Online in [VOLUME #, ISSUE #] on [DAY/MONTH/YEAR]. It was authored by [FULL NAME, EMAIL ADDRESS], with whose written permission it is reprinted here. [3] Libraries may archive issues of MTO in electronic or paper form for public access so long as each issue is stored in its entirety, and no access fee is charged. Exceptions to these requirements must be approved in writing by the editors of MTO, who will act in accordance with the decisions of the Society for Music Theory. +=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+ END OF MTO ITEM