Here's a set of relationships that makes treble octave tuning simple. 1) Assume a pure twelfth as the standard "width control" interval. 2) Consider the following notes as an example: A3, D4, A4, A5. 3) All have coincident partials at A5. 4) All can be tested at A5 using test note F3. 5) All "beat rates" will be occuring at pitch of A5. 6) To describe the relationships, assume F3-A3 is 7 bps and A3-D4 is 1bps. Then F3-D4 is 8 bps. 7) Since D4-A5 is pure (0 bps), F3-A5 will be 8 bps, the same as F3-D4. (Easy to hear) A3-A5 will be 1 bps at 4/1. 8) Since D4-A4 is a fifth, about a half bps slower than A3-D4, then F3-D4 is 8 bps and F3-A4 is 7.5 bps. This also means A3-A4 is about one half bps at 4/2. 9) Thus we can say that the tempering of the fourth A3-D4 determines the pitch of A5, and since the 3rd/10th/17th test requires that F3-A4 be intermediate of F3-A3 and F3-A5, the fourth also determines the fifth and single octave. 10) Using the one test note, and listening to all 4 notes at A5 is very easy to hear and do. This relationship is generally good from at least the lowest plainwire notes and at least as high as A6. IMHO. Ed Sutton -------------- next part -------------- An HTML attachment was scrubbed... URL: <http://ptg.org/pipermail/pianotech_ptg.org/attachments/20090325/2f4689ec/attachment.html>
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