Ghosttone test reply to Matt's questions.

>Even allowing for some 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.
I see that you expect everything to be laid out on a plate for you.
Let's add the note names to this simple table of results.

Original was:
> Ghostones
> Finger position
> Percent Approx. Hz of ghosttone
> 50 220
> 41 550
> 33 330
> 25 440
> 20 550
> 17 660

More info. added to above:

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


! NB. The * represents multiplied by frequency
(i.e to give indication of octave)


So the notes which we produce produce from this are
A, C#, and E.

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).


So the ghosttones give us two new pitches in the fifths
direction E Vth and its octaves and
C# III two ocatves higher.

Remember A-C#-E I-III-V (a major chord).
Now all we need to do is ascertain the "exact" value
of either the III or the Vth interval and we have the
tuning defined.

By now resetting the string pitch we can generate all the
other notes that we need, and we find that the fret positions
match the touching positions as closely as we can measure.

Hence as we know that IVth plus Vth equals an octave,
we can generate any number of steps of fourths and fifths.




>Last post you said you could measure the frequencies of
>ghosttones without a tuner, using a metronome and a
>second string. Will you outline the exact procedure for
>doing this so I can proof your method?

I need to get myself or build a metronome to reconstruct
the second part of these experiments, and when done will
complete it.
BTW A stable reference tone is also required (eg. tuning fork)
to complete the experiment.

>> The principle of this is explained in my spreadsheet which I
>> posted last week

>I just reread it. You only posted the spreadsheet data
>with no explanation of the principle of beat frequencies.
>Be sure to include it in the next post. Thanks.


The figures for metronome readings represent the beat frequencies,
as beats per minute (i.e. tempo of the beating).

I may need to reset the reference frequency on the
spreadsheet to get the bpm values for each stage and each
frequency,as I work through each new note that I wish to examine.
(That's the easy part)



lucy Sunday morning - perfect Hawaiian sunshine with breeze.
I'm outta here for a while to search for a metronome.

Does the posting about the Waldorf schools mean that jk,
(my four-year old) is being indoctrinated with JI at the
local Kinderhale? (Is that the school near Stroud in
the Cotswolds?)



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