A Different Temperament / Tuning Approach

Richard Brekne richard.brekne@grieg.uib.no
Sat, 15 Jun 2002 10:49:38 +0200


Bradley and Mike... I sent this through with a graph attached couple times...
and didnt see it come up... perhaps the graph was a bit to big ?... anyways..
here this is again without the graph.

Cheers..
RicB

Hi folks.

Here is the data and a graph in XL of the piano I tuned today with this. The
range from D3 to A4 are calculated useing Tunelabs 3 point quadratic
interpolation, with  D3(3) at   -1.95,  A3(3) at -1.19, and with  A4(3) at 4.50
cents offset. All other frequencies are taken in reference to these notes. A#4
to E6 fundementals first are tuned these same calculated 3rd partials, and then
each of these is read for its 3rd partials for tuning the fundementals for the
notes higher up. 

Going down the Fundementals of D3 - A4 are read note for note to get
frequencies for the 3rd partials of the first 19 semitones below... and the
process is repeated to the bottom.

The whole process took 2.5 hours.

You can see I had trouble getting good readings for fundementals below the
temperament range... tho most of these are pretty reliable as I spent about
1hour just making as sure of myself as I could in reading these in. Remember in
reading these that the real fundementals of D3 to A4 that resulted from the
calculated curve of 3rd partials for those notes can be seen as the frequencies
for G1 to C#3. 

The treble also wanders a bit once we leave the calculated frequencies, but not
nearly as much. These divergencies are the result no doubt of some combination
of the crudness of the measurement and the pianos inharmonicity. I hope to get
better measuring tools from the UiB physics Dept this fall. But in the meantime
this gives me a basic idea.

I also measured inharmonicity using Tunelab for every note in the piano... but
I am not yet quite sure of what I am looking at. What I really want is the
actuall frequencies of each readable partial 1-12 for each note. RCT does this
but you have to save the whole darn PAZ picture for each note to get them... it
would be easier to simply write off the relavant data by hand. 

The graph shows this data below Piano sounded dynamite by the way. And again..
a quick check with RCT's OT3 liked the tuning quite well... with a few areas of
minor dissagreement.

Cheers..
RicB

A0  3 -14.44
A#0 3 -11.95
B0  3 -12.48
C1  3 -12.11
C#1 3 -12.94
D1  3 -14.03
D#1 3 -13.68
E1  3 -7.24
F1  3 -7.00
F#1 3 -5.11
G1  3 -5.49
G#1 3 -5.23
A1  3 -5.67
A#1 3 -5.98
B1  3 -5.32
C2  3 -5.35
C#2 3 -5.49
D2  3 -6.13
D#2 3 -5.77
E2  3 -6.75
F2  3 -5.93
F#2 3 -5.43
G2  3 -4.43
G#2 3 -3.72
A2  3 -3.91
A#2 3 -3.54
B2  3 -3.04
C3  3 -2.54
C#3 3 -2.04
D3  3 -1.95
D#3 3 -1.96
E3  3 -1.93
F3  3 -1.86
F#3 3 -1.75
G3  3 -1.60
G#3 3 -1.41
A3  3 -1.19
A#3 3 -0.93
B3  3 -0.63
C4  3 -0.29
C#4 3 0.09
D4  3 0.51
D#4 3 0.96
E4  3 1.46
F4  3 1.99
F#4 3 2.56
G4  3 3.17
G#4 3 3.81
A4  3 4.50
A#4 3 5.04
B4  3 5.69
C5  3 6.44
C#5 3 7.29
D5  3 8.25
D#5 3 9.32
E5  3 10.49
F5  3 11.77
F#5 3 13.15
G5  3 14.39
G#5 3 16.23
A5  3 17.29
A#5 3 17.73
B5  3 20.83
C6  3 22.58
C#6 3 23.90
D6  3 27.99
D#6 3 30.32
E6  3 32.75
F6  3 34.20
F#6 3 0.00
G6  3 0.00
G#6 3 0.00
A6  3 0.00
A#6 1 0.00
B6  1 0.00
C7  1 0.00
C#7 1 0.00
D7  1 0.00
D#7 1 0.00
E7  1 0.00
F7  1 0.00
F#7 1 0.00
G7  1 0.00
G#7 1 0.00
A7  1 0.00
A#7 1 0.00
B7  1 0.00
C8  1 0.00


Richard Brekne
RPT NPTF
Griegakadamiet UiB



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