3:1 12th s? Verituner

[RicB]

Hi again all

Yes... perfect 12ths tuning by ear... in case you don't have an ETD.

Essentially the way I do this builds on a test for a 4th.  One takes the 
major third below the 4th and compare beat rates for the two notes that 
comprise the 4th with this major third below. So... if you have a C4-F4 
4th and you want to insure its just a bit wide, then take the major 
third below C4, i.e. A#3 and use that as your control note.  The A#3's 
5th partial and C4's 4th partial compared to A#3's 5th and F4's 3rd.

Now if you throw C5 into this picture you have another note with this 
same A#3 (5th partial) coincident.  i.e. C5's 2nd.  Goes without saying 
then that C6's fundamental is also coincident.

Thereby you have 5 notes with the same coincident partial.  A#3, C4, F4, 
C5, and C6.... i.e 5:4:3:2:1 coincidents sequence.

The 5:3 comprises a major 6th.  It and the double octave major third 
should have identical beat rates  i.e. the 5:3 and 5:1.  This will 
insure a perfect 12th.  The major third (5:4) should beat a bit slower 
then these two, and the octave major third (5:2) just a bit faster but 
still slower then the 5:3, and 5:1.  In addition to insuring a perfect 
12th,  this also insures several key stretch goals for octave types.
The 4:1, 4:2, and 2:1,  are always kept a tad wide. And the relationship 
between the 2:1 and 4:2  is kept really close to constant the whole way 
up. You can play the sequence straight up  5:4, 5:3,  5:2, and 5:1 in 
fairly quick succession and get an aural feel for insuring this picture 
very easily.
I use a Tunelab 97 generated curve to help me look closer at this as I 
tune.  The curve is all based on 3rd partials and goes from A1 to E6.  
D3-A4 is the initial 12th... or temperament 12th if you will. Both notes 
will hold a dial still at 440 Hz.  I set D4 to a nice compromise between 
a 4:2 and 6:3 and then used TL 97 to generate a curve on these three 
anchors. The 12th up to E6 is done similarly.  The bass is done by using 
6:3 octave type for D2, and again for A1 after tuning and zeroing on A2.

Since the curve it has is the result of the inharmonicity of the piano I 
tuned that day... it can only be used as a template for tuning.  But as 
such it works extremely well. It takes almost no time to make whatever 
minor adjustments are needed on the fly to accommodate any given tuning, 
and since I primarily use the aural method above the Pocket PC is just a 
handy dandy reference ready to be used at any point to make sure I'm 
right where I want to be.

Cheers RicB