A different temperament / tuning approach

Richard Brekne richard.brekne@grieg.uib.no
Fri, 07 Jun 2002 23:19:26 +0200


Hi folks...

Just thought I'd post some interesting comparisons between what RCT came up
with on its OT 3 (Clean) calculated curve visa vi the perfect 19ths tuning I've
been fooling around with. Actually RCT's OT3 liked this arrangement quite
nicely. I spent some extra time today on a Hamburg D being really accurate with
Tunelab as described yesterday, and when I was done tuning I turned on RCT,
sampled the 6 A's and ran a quick note for note check. In most cases I got some
degree of blush, and in every case there was little (almost no) movement of the
spinner. I didnt get to sort out all the differences between the RCT cents
offsets table, and the numeric editor in Tunlab... but for your edification
here are the 

Note	TuneLab	RCT

A5	 2.85		2.89
A#5	 3.22		3.30
B5	 3.60		3.75
C6	 3.97		4.19
C#6	 4.34		4.73
D6	 4.71		5.22
D#6	 5.09		5.73
E6	 5.46		6.33
F6	 6.93		6.99
F#6	 8.41		7.74
G6	 9.88		8.47
G#6	11.35		9.41
A6	12.83		10.48
A#6	14.30		11.65
B6	15.77		12.97
C7	17.25		14.24
C#7	18.72		15.87
D7	20.19		17.28
D#7	21.66		18.81
E7	23.14		20.64
F7	24.61		22.65
F#7	26.08		25.01
G7	27.56		27.33
G#7	29.03		30.28
A7	30.50		33.71
A#7	31.98		37.70
B7	33.45		41.69

Interesting that the RCT really stretches the top notes on a so called "Clean"
stretch. This is way beyond the 3rd partial of the octave 5th below, tho this
is only for the last 4 notes. Otherwise the perfect 19ths starts out just a
little lower, then at F#6 goes sharp of RCT's curve  as much as 3 cents at C7,
and there after RCT starts to catch up again.

These are fundemental (first partial) offsets in both cases, but in Tunelab
they are also the exact frequencies of the 3rd partial  for the octave and 5th
below each note. For example the 3rd partial of A5 is exactly 23.14 the
fundemental of E7.  

In other words.. how RCT' curve wanders around the actual 19ths for these notes
by comparing the RCT calculated values to the real frequencies for these as
read in useing Tunelab. RCT's curve starts out by holding the 19th just a tad
wide, then it gets narrow by as much as 3 cents... and in the end gets wide by
around 10 cents. Not exactly an exponential development.

This is a lot of fun and its interesting for me... so I intend to get as
complete and accurate a comparison of these two approaches to tuning as I can.
But one thing is already clear. In terms of general stretch attributes.. the
perfect 19ths is quite viable... and its a very simple thing to accomplish.

RicB




Richard Brekne
RPT NPTF
Griegakadamiet UiB



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