Recently I have tossed some thoughts around about the precedent for asserting that the perfect 5:4 and 6:5 mediants exist. I actually expected to be challenged on my comments about unjust mediants from my recent posts on the CAUT list. Theoretically, the only foundation for arguing just 5:4 and 6:5 thirds would be deviation from equal temperament. However, is this, in practice, what mean tone tuning demands of us? Why do some theorists on equal temperament instead, mark such coincidence? Does this merely justify a devotion to the partial scheme in tuning that neglects the role the contiguous third must play in equal temperament? Do we attribute too much to the partial scheme in tuning, or what on a horn without valves, is just a tucket? First of all, we need to observe that more than one reason exists for aural meantone tuning than just tuning to tonic. Signs of difficulty integrating the piano with strings permeate Schubert's famous "The Trout" quartet in A major. http://imslp.info/files/imglnks/usimg/a/a2/IMSLP04119-SchubertPianoQuintetD667.pdf Scanning the work, the piano and the strings almost constantly seem to be moving independently of each other, as if together, these would sound abhorrent. However, when such music forces the pianist into a collaborative situation, even if the composer seems to be taking precautions, could we make an effort to accommodate the artist who performs this music nevertheless in ways that period specific mean tone tuning cannot, but tonic specific mean tone tuning could? To this way of thinking, period tuning is misleading. The aural approach to meantone commits one to a simple, tonic centered approach, one that is collaborative, based on a direct involvement not only of the tuner with the musician, but the programming itself. How can we tune to tonic if the program is not committed to that key-if deviating, to relative minor, dominant, maybe even subdominant-for every piece that is played on the piano we prepare? We do have the option of tuning in different styles simultaneously on many harpsichords. Perhaps period instrument specialists lack willingness to experiment not only with different instruments, but tunings. We have every reason to believe the harpsichord was designed for that. The shift pedal on the piano is terribly misleading about this. We do have the alternative of preparing more than one keyboard also. The tours of Franz Liszt featured many keyboards. Recently, I tuned for a collaborative event featuring this very piece. They used the same instrument for Webern in the same program. What could I do but equal temperament? How often are we in a situation where communication with the musician makes this possible? When is a tonic centered approach most advantageous? I believe in a collaborative with strings, it could be more so than even when a baroque keyboard piece is performed. When a good string quartet plays a triad, or single string player triple-stops with a third, or just plays thirds, the string players do not expand the major mediant or contract the minor mediant, but compromise between the dominant and the tonic of the triad as a group or in the triple-stop, or even plays pure thirds with just the dominant or tonic as a soloist, or during a solo, even as a group when dominant or tonic is absent. Otherwise, the group sounds out of tune. In preparing a keyboard for "The Trout," then, tuning a just 5:4 third in the A:C# would not be correct, even if we tuned to A. Could a pure third then be called just intonation? Theoretically, I could argue the existence of the pure 5:4 third to justify deviating to accommodate the key of A, but when actually tuning to A, even then it would not be just. If I was to have musicians who created the opportunity, I could as a tuner for a performance of "The Trout" tune in the following manner: tonic to tonic octave just A-A tonic to dominant just A-E tonic to subdominant just A-D M & m mediant between tonic (A) and dominant (E) unjust C,C# (mediant) even bps compromise M & m submediant between 2nd tonic, the octave (A) and subdominant (D) unjust F,F# (submediant) even bps compromise dominant to supertonic just E-B subdominant to subtonic just D-G Then the wolf, an unjust compromise between supertonic and subtonic, the B & G, the D#. Then tune the remaining 4ths above and below to the D#, the A# and the G#, pure. That would be the most accurate way to tune to A. Contrary to popular notions, the thirds still would not be pure in a meantone temperament. Did someone already say this on the subject of tuning variables? This is a perspective that some of the most successful musicians actually involved in performing and programming with historical tunings, such as Grammy nominated recording artists David Breitman, http://www.oberlin.edu/con/faculty/breitman_david.html http://bf.press.uiuc.edu/view.php?vol=10&iss=2&f=breitman.pdf and Sanford Sylvan, http://www.pittsburghsymphony.org/pghsymph.nsf/bios/Sanford+Sylvan appear not to have adopted. Ed Foote provided some common misleading information about how to keep a temperament just in one key by indicating that the interval we compromise to keep the most intervals just is the final third in a set of 3 thirds in order from tonic to octave, in the following article, under the rubric "Mean Tone Tuning." http://www.uk-piano.org/edfoote/index.html This is wrong. We still tune the mediant and submediant unjust in tonic specific mean tone tuning as a compromise not with the adjacent third, but with the just fifth around it. The final third in a series of thirds in an octave for mean tone tuning, the submediant, is simply a compromise between the octave, or second tonic, and subdominant. In reality, how often will we get this opportunity, and how many musicians take such risks? http://www.youtube.com/watch?v=k0PBUis8O50 (performance begins at 5 minutes 30 seconds) -----Original Message----- From: caut-bounces at ptg.org [mailto:caut-bounces at ptg.org] On Behalf Of Fred Sturm Sent: Saturday, April 11, 2009 9:17 AM To: caut University Technicians Subject: [CAUT] Schubert temperament redux Over the past couple months, I have done quite a lot of research on tuning history. Among other things I came across a reference to an article by a scholar named Thomas McGeary. Our library doesn't have the Journal of the American Musical Society, where the article appeared, but one of the perks of the caut job is full access to interlibrary loan services. I requested the article a week ago, and yesterday a photocopy appeared in my mailbox. The article is a survey of practical tuning instructions published in German between 1770 and 1840, and was published in 1989. McGeary says he focused entirely on tuning instructions rather than theoretical writings in order to get at what practical musicians were likely to have done. The article makes clear that equal temperament was by far the dominant method of tuning during that period in German-speaking Europe, the only well-known variant being Kirnberger II, a crude and unattractive tuning system that seems to have been discussed more than it was actually used. [Essentially, it has 10 just 5ths and two 5ths that share the comma: VERY narrow. Those two 5ths are GD and DA, hence very prominent in the tuning. There are three just M3s, two intermediate M3s, remainder are "Pythagorean" (wider than ET). Two of the triads containing the just M3s also have the 1/5 comma 5ths, hence the sound is rather bizarre - sounds horribly out of tune to me. K II was the first historical temperament I tried. Haven't touched it since.] Of 22 total sources studied, fully 14 describe only equal temperament, four offer variants of Kirnberger II, and two have both equal and Kirnberger. The remaining two offer tuning methods that were obscure in their time and remain so today (one of them featured just fifths in the natural keys, tempered in the sharps, yielding a "reverse well temperament"). Of the 12 examples published after 1800, 10 describe only equal temperament, one mentions Kirnberger II along with equal temperament, and one offers an obscure, idiosyncratic system, unrelated to any other. McGeary, Thomas. "German-Austrian keyboard temperaments and tuning methods, 1770- 1840: Evidence from Contemporary Sources". Journal of the American Musical Instrument Society 25 (1989), pp. 90 -116. Regards, Fred Sturm University of New Mexico
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