I've just repeated the calculations with Young's temperament (similar to Valotti) and here the best keys are C, D, F, G and B-flat. B-flat is as good as C - but not better.
Kit > I've just tried something similar, using a computer to generate harmonic > series based on different fundamentals covering an octave and comparing > these to the notes on a keyboard tuned to a Werckmeister temperament. > > Rather than comparing all the harmonic series, I've concentrated on the > ones that we use the most frequently - the 2nd, 3rd, 4th, 5th, 6th, 8th, > 9th and 10th. > > I've put up the graph on my flickr page: > > http://www.flickr.com/photos/flowtik/4018720867/ > > There are clear differences between how in-tune the different crooks are - > the worst have a mean discrepancy of around 7 cents from the notes in the > Werckmeister scale, and the best has a mean discrepancy of about 2 cents. > > So which is this marvellous crook with the great intonation? C, D, F or > G?! To my great surprise it turned out to be B-flat - which is strange > because this is the rarest of the crooks we use... Or is it? > > It has puzzled me since I was very small that trumpets and clarinets are > generally pitched in B-flat rather than C like the strings and piano. I > wonder whether the answer could be that this key worked best before the > days when orchestras were all tuned to ET? > > Kit > > >> On Sat, Oct 17, 2009 at 00:54, Kit Wolf <[email protected]> >> wrote: >>> >>> I'm interested to hear you talk about the trumpet here, as the sources >>> I've read on temperaments tend to focus on string and keyboard >>> instruments. It frustrated me that they didn't mention brass and >>> woodwind >>> more often, but I have never been very clear in my own mind what I >>> expected them to say about them. In other words, I couldn't really >>> formulate a question, but I feel sure there must be an interesting >>> answer! >>> >>> Take the situation where a valveless brass instrument that 'naturally' >>> produces notes in the harmonic series plays with an orchestra or >>> keyboard >>> that is tuned to a different (but historically plausible) temperament: >>> if >>> I understand you correctly, 'D' is one of the keys where the >>> discrepancy >>> between the brass instruments and the other instruments is likely to be >>> minimised? Are there any other keys that work particularly well or >>> particularly badly, or are we able to lip everything enough that the >>> natural discrepancy doesn't really matter? Perhaps our ability to >>> hand-stop is the reason horns seem to be crooked in so many more keys >>> than >>> trumpets? >>> >>> These are just examples of the ill-formed questions running through my >>> mind - I'd be interested to hear any comments about playing horns in >>> the >>> days before equal temperament. >>> >> >> >> After writing my comment and reading your reply and questions I >> started calculate and think more on the subject. I know, wrong order >> of doing things ;) >> >> I've looked up the intervals in Werckmeister and Valotti, popular >> temperaments for 18th century baroque, and the distances in cents come >> out like this: >> (I hope the table comes out alright ;) >> >> F: W V D: W V >> just equal >> G 198 196 E 198 196 >> 204 200 >> A 390 392 F# 396 396 >> 386 400 >> Bb 498 498 G 504 506 >> 498 500 >> C 702 698 A 696 698 >> 702 700 >> D 894 894 B 900 894 >> 884 900 >> E 1092 1090 C# 1098 1098 >> 1088 1100 >> >> >> So actually F comes out as slightly closer to the natural harmonic >> series, which maybe explains the "natural" or "peasant" affect >> associated with it. >> >> In retrospect and after calculating I have to rethink my statement and >> would have to conclude that other factors have to do with the (at >> least for me real) relative discomfort of playing in F. It is probably >> a culmination of the differences in the temperament and the tuning >> tendencies/problems of other instruments that make F so much harder to >> play in. The F on a baroque flute for instance is a notoriously bad >> note, and our sounding D (written A, normally played wide open and >> lipped up) will tend to be too flat relative to the D of the strings >> which is based on pure fifths. >> In these temepraments F lies a bit higher on the keyboard than in >> equal temperament and D slightly lower, so that could be a >> contributing factor as well. >> > > > -- > Sometimes my Email program gives the wrong return address. If you have any > trouble replying to me, use '[email protected]' and not 'n802...' > > Sorry for any confusion > > > -- > Sometimes my Email program gives the wrong return address. If you have any > trouble replying to me, use '[email protected]' and not 'n802...' > > Sorry for any confusion > > _______________________________________________ > post: [email protected] > unsubscribe or set options at > https://pegasus.memphis.edu/cgi-bin/mailman/options/horn/c.j.l.wolf%40newcastle.ac.uk > -- Sometimes my Email program gives the wrong return address. If you have any trouble replying to me, use '[email protected]' and not 'n802...' Sorry for any confusion _______________________________________________ post: [email protected] unsubscribe or set options at https://pegasus.memphis.edu/cgi-bin/mailman/options/horn/archive%40jab.org
