source file: mills2.txt Date: Sun, 23 Feb 1997 22:22:19 -0800 Subject: Re: Ghosttone test reply to Matt's questions. From: Matt Nathan Charles Lucy wrote: > > >Even allowing for some [error] in measurement, this is definitely > >nowhere near the the series of fourths and fifths you > >predicted! Will you admit this? > > Patience Matt! This is only the first stage. Yes, but there are already contradictions. shouldn't we iron them out before proceeding? > I see that you expect everything to be laid out on a plate > for you. Of course! I will not automatically jump to your conclusions, just because you do. You're the one who claimed he found a better model for the physics of ghosttones on real strings, and that ghosttones follow a cycle of pi-derived fourths and fifths. I expect you to be able to back this up, or stop making the claims. I have nothing against any tuning system. I do have a problem with unfounded claims being made about a tuning system in order to promote its use. I'm requesting logical exposition of those claims in expectation that failure to produce such exposition will discredit the claims. > Let's add the note names to this simple table of results. > > The values below are from A2 string (110Hz.) > ! > Approx Fret's Heard Heard > Finger Note played Scale Approx. Note heard Scale > Percent at near fret Position Hz Position > 50 A3 220 (Hz) VIII 220 A3 VIII * 1 > 41 F#3 184 VI 550 C#5 III * 4 > 33 E3 164 V 330 E4 V * 2 > 25 D3 147 IV 440 A4 VIII * 2 > 20 C#3 137 III 550 C#5 III * 4 > 17 C3 132 bIII 660 E5 V * 4 The second column, approximate notes played on nearby frets, is irrelevant to the discussion of ghosttones. BTW, 41 percent is probably is mismeasurement of 40, 40 being twice the distance of 20, both positions being nodes which divide the string into 5 parts and produce a pitch near 550 Hz. > So the notes which we produce produce from this are > A, C#, and E. Yes, which are easily explained as falling near the integer multiples of A, in the series 1 2 3 4 5 6. > The Spiral of fourths and fifths runs: > > A E B F# C# in one direction (Vths) > A D G C F Bb in the other. (IVths). You said that the frequencies and volumes of ghosttones followed this dual series. The E's you found (330, 660) were in the wrong octaves to coincide with your ascending fifths series which predicts E to occur in the octave between 110 and 220. You didn't find any ghosttones which produced B or F# in the series of ascending fifths, let alone have them be louder than the C# you found. You found no ghosttones which produced D G C F or Bb. This last fact pretty much destroys the ascending- fourths half of your proposed dual series. Notice that the integer-multiple series (1 2 3 4 5 6) nicely explains your own findings without skipping any expected pitches. It also predicts that you will find an additional ghosttone with an approximate frequency of 770 near the string percentages 14, 29, 43, 57, 71, and 86. Let me know if you find it. > The figures for metronome readings represent the beat > frequencies, as beats per minute (i.e. tempo of the beating). I understand bpm, but what are the beats supposed to be a measurement of in the first place? Matt Nathan Received: from ns.ezh.nl [137.174.112.59] by vbv40.ezh.nl with SMTP-OpenVMS via TCP/IP; Mon, 24 Feb 1997 07:44 +0100 Received: by ns.ezh.nl; (5.65v3.2/1.3/10May95) id AA15697; Mon, 24 Feb 1997 07:44:48 +0100 Received: from ella.mills.edu by ns (smtpxd); id XA15695 Received: from by ella.mills.edu via SMTP (940816.SGI.8.6.9/930416.SGI) id WAA08439; Sun, 23 Feb 1997 22:43:15 -0800 Date: Sun, 23 Feb 1997 22:43:15 -0800 Message-Id: <331137D3.B28@ix.netcom.com> Errors-To: madole@mills.edu Reply-To: tuning@ella.mills.edu Originator: tuning@eartha.mills.edu Sender: tuning@ella.mills.edu