Re: introduction and a question about Viennese temperaments early 18

the thing is no one tunes to 3:2 frequencies which would give you that small difference in beat. if you apply that to say 660 and 440, the difference is much greater. That is the real reality. Watch out for difference tones especially if there is a bass not there to further beat against it.

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/^_,',',',_ //^/Kraig Grady_^_,',',',_
Mesotonal Music from:
_'''''''_ ^North/Western Hemisphere:
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_'''''''_^South/Eastern Hemisphere:
Austronesian Outpost of Anaphoria <http://anaphoriasouth.blogspot.com/>

',',',',',',',',',',',',',',',',',',',',',',',',',',',',',

a momentary antenna as i turn to water
this evaporates - an island once again

On the contrary, Kraig, the historical reality was quite different. Nobody in the 16th-, 17th- or 18th-century tempered that high. Surviving tuning instructions specify which notes are to be used, and they inevitably center the region used for laying the bearings on the octave of notes between tenor c and middle c. A number go considerably lower. Usually one begins by taking middle c or tenor f from an oboe or a bassoon, and then tuning DOWN an octave.

There are perfectly good reasons for why they worked this way. Primarily, the strings in this region bear the highest tension of the instrument, and with a wooden framework, you want to start there. If you temper in a higher octave and then move down into the tenor and bass by octaves, the changes in tension you make there will have a greater affect upon the entire framework, throwing your bearing region out-of-tune. On a modern piano with an iron frame, this behavior essentially disappears, so modern tuners are unaware of it. When they have to tune a historical insrument, often in their ignorance, they just do what they always do, i.e. start higher and then move down, which may well be one of the reasons why they often speak disparagingly about the “instability” of a wooden frame; they just don’t know how to handle the beast. Secondly, the strings in the tenor and high bass have the best combination of length (including the very long after-lengths) with load (MPa), or in other words, they are highly extended. This gives you the most advantageous relationship between tuning pin rotation and pitch change, allowing you to work with much greater precision than in any higher octave. This advantage remains true on the modern piano, by the way, which is why I’ve always found it strange that modern tuners begin in the upper octave.

In the 35 years I have been tuning harpsichords and fortepianos, I have never heard difference tones. The only time I have heard them during the tuning of an acoustic instrument is when tuning mutation ranks on an organ. There they are often even more helpful than any beating between harmonics.

---In TUNING@yahoogroups.com, <kraiggrady@...> wrote :

the thing is no one tunes to 3:2 frequencies which would give you that small difference in beat. if you apply that to say 660 and 440, the difference is much greater. That is the real reality. Watch out for difference tones especially if there is a bass not there to further beat against it.

--
signature file

,',',', Kraig Grady ,',',',
Mesotonal Music from:
''''''' North/Western Hemisphere:
North American Embassy of Anaphoria Island
''''''' South/Eastern Hemisphere:
Austronesian Outpost of Anaphoria
',',',',',',',',',',',',',',',',',',',',',',',',',',',',',
a momentary antenna as i turn to water
this evaporates - an island once again