Richard Moody wrote: > > If you tune this same range such that the 6:3 are held beatless, > > or at 0.5bps as they start out in the example above, then you'd > hold > > the 8:4 up a while longer... this would allow for better matching > of > > those triple octaves and would represent quite a stretch. Though > the > > 4:2's and 2:1's would probably beat obnoxiously. > > Maybe try a different machine, I don't know what to say----with > beats like that it seems there is a lot of room for improvement. Ric, this wasnt a machine tuning. It was simply calculated frequencies using the inharmonicity equation with measured (and published) inharmonicity constants for a A3, A4, A5, A6. The numbers are what they are. Unless there is something wrong with the inharmonicity formula, I dont see how they can come out any different. Seems pretty usuall to me tho... Tuning A3 / A4 as pure 2:1 octave types is going to result in some movement up the ladders, especially when you try and match A5's partial ladder to that. The two graphs tho were from a tuning done by Dr. Sanderson for an article he wrote way back when. Grin.. he termed the tuning a "well tuned piano". > > >. We do manage to create a tuning > > that is ET in more ways then not, and the fact that we kill all > key color is good evidence of that. > > Speak for yourself on "we kill all key color". I believe that is > the most specious sentiment in the history of music especially > when applied to temperament. It is a musician's thing, if they want > to > talk to piano tuners about it I am all ears, but ain't holding my > breath. Well, I will be the first to enjoy discussion about key colour in ET. But that being said the kind of key color found in HT is taken out of the equation in a well executed ET. I mean thats kind of the whole point of ET.. isnt it ??? For example... all major 3rds at 13.7 cents apart (I think thats the right number ... Ed ?? ) I certainly like very much of the rest of your discussion on key colour Ric, and I have enjoyed your thoughts on the matter every time they come up. but I think personally we have to admit that there is at least a major type of key colour found in HT's that is not in ET. But perhaps I am wrong in this. In any case It would be interesting to see how well tuners and musicians alike could identify these effects AFTER having a good deal of ear training to reaquaint our ears to these things. I am personally not so swayed by aural comparison tests we hear talk about today as to what conclusions we can draw from them.... that is other then to conclude that the musical ear today is almost frightenly ignorant of our rich and colorfull temperament past. I have conducted a few such experiments myself and I find that those who know what they are listening for (of which there seem to be sparse few of) know right off what they are hearing.... and those that dont remind me much of that first day of tuning school where that "old guy" was trying to get me to hear the beats. Many thanks for your interesting thoughts. Cheers ! -- Richard Brekne RPT, N.P.T.F. UiB, Bergen, Norway mailto:rbrekne@broadpark.no http://home.broadpark.no/~rbrekne/ricmain.html
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