The error in what has been posted up to now is the presumption that an octave has a single beat rate. In fact there are multiple beats, which complicates the issue. I used Tunelab to examine a Mason Hamlin A. I set the tuning curve to 6:3 in the bass and 4:2 in the treble (a common setting), and recorded the frequencies of partials 1,2,3,4,6,8 for notes C3, C4, C5, and C6. Then I used Excel to calculate beat rates for the octaves C3-C4, C4-C5, and C5-C6, and the double octaves C3-C5 and C4-C6. Every octave has beats at the 2:1, 4:2, 6:3 and 8:4 frequencies, and in the deep bass it is also easy to hear the 10:5 and beyond. But these all sound together, so the ear cannot easily parse them. The C3-C4 octave includes the following beat rates: 2:1 -- 0.3 4:2 -- 0.4 6:3 -- 0.1 8:4 -- 1.5 The C3-C5 double octave: 4:1 -- 0.7 8:2 -- 1.2 The C4-C5 octave: 2:1 -- 0.3 4:2 -- 0.3 6:3 -- 0.4 8:4 -- 3.4 The C5-C6 octave: 2:1 -- 0.5 4:2 -- 0.2 6:3 -- 2.2 8:4 --15.6 The C4-C6 double octave: 4:1 -- 0.8 8:2 -- 3.2 Some of the individual partials will sound louder than others -- primarily a voicing issue -- and this will affect which of the beat rates will predominate. But they are all there, each contributing to the sound of the octave or double octave. For example, the 8:4 partial pair in octave C5-C6 is beating at 15.6 beats a second, but it will probably be relatively quiet and may not be noticed at all. However, if the hammers are too hard or other factors accentuate the upper partials, that beat may stand out and annoy the ear. The ear must determine the sweet spot. But it's probably not wise to seek a certain beat rate, because you may not be sure which partial set you are listening to. | || ||| || ||| || ||| || ||| || ||| || ||| || ||| jason kanter -- seattle | || ||| || ||| || ||| || ||| || ||| || ||| || ||| On Thu, Feb 11, 2010 at 8:56 AM, David Ilvedson <ilvey at sbcglobal.net> wrote: > Mark, > > There is nothing to analyse on this tuning, except to say "this is out of > tune". > It sounds like you are concerned your tuning is not stretched enough for > concert work? > Are your tuning aurally? I wouldn't worry about the stretch, but I'd > worry about unisons and stability. > > David Ilvedson, RPT > Pacifica, CA 94044 > > ----- Original message ---------------------------------------- > From: "Mark & Janine Davis" <pianofortetechnology at saol.com> > To: pianotech at ptg.org > Received: 2/10/2010 9:38:22 PM > Subject: Re: [pianotech] Double Octave Stretch > > > >Thank you to all who have responded. > > > > > >Ed, the bottom octaves were beating 1bps and possibly faster and the top > >octaves were close to the beat speed of F3/A4. I never said that both > >octaves were beating 1bps though I understand what you are asking. Your > >question does make me think! All I can say is I checked the tuning fairly > >quickly and what I wrote in my first post was my assessment of the tuning. > >I never analysed the tuning. As I also wrote in the first post the piano > >had been tuned two weeks prior to me inspecting it and stands in a hall > that > >is wide open (doors open all day) and has air con for school assembly and > >performances etc. > > > > > >John, thank you for your time and help. I will try what you have written. > >I do generally tune unisons as you go for grand pianos even the > temperament > >at times too. On uprights I usually use a temperament strip for the > middle > >and for the treble and bass I tune unisons as you go. > > >Thank you, Take care, Mark > -------------- next part -------------- An HTML attachment was scrubbed... URL: <http://ptg.org/pipermail/pianotech.php/attachments/20100211/9f52f63a/attachment-0001.htm>
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