A different temperament / tuning approach

[Mike and Jane Spalding]

Ric,

I just finished entering your offsets into Excel, and graphed the results.  Very interesting to compare the shape of the two curves.  RCT is a gentle continuous curve.  TuneLab is two straight lines, making an abrupt change of direction at E6.  Seems to say that your tuning made an abrupt change of direction an octave-fifth below, say at A4.  ??

I'll e-mail the excel file off-list to anyone that wants it.

Mike Spalding, RPT

----- Original Message ----- 
From: Richard Brekne <richard.brekne@grieg.uib.no>
To: PTG <pianotech@ptg.org>
Sent: Friday, June 07, 2002 4:19 PM
Subject: Re: A different temperament / tuning approach


> 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
> 
>