Making a P12ths Tuning. (Long)

[Richard Brekne]

Hi folks. 

Since I got like tons of off list email about how to do
this, I thought I would try and write it out. 

A few points to think about while you sort out the
directions may help. First most essential element is that
every instance of a 12th is tuned perfect using the 3rd
partial of the lower note against the fundamental of the
upper. Secondly when using Tunelab for this remember always
that one notes 3rd partial is anothers 1st, and anothers
4th, and still anothers 5th.. and so on. So when you look at
Tunelabs phase display you can actually see some pretty
relevant information for several notes at any given time.
The particular way in which I set up this tuning exploits
that in a nice way because of the identical frequencies
involved for any given 12th. I can see the correct frequency
for two notes at once... Sound familiar ear tuners ??


SO... this is what you do.

Phase 1 (takes about 3 minutes when you have the routine
down)

-- First set up a tuning file with the numerical editor so
that notes G1 to F6 all use the 3rd partial for their tuning
partial.

-- Then set the phase display to D3 and move the offset so
that the frequency in Hz reads 440 and transfer this offset
to the basic offset in the << Set >> drop down menu, and
then press Insert so that D3's present offset value (which
now should be 0) is entered as a reference point into the
tuning editor. Press Enter and then ESC to return to the
phase display.

-- Then tune A4 directly while the phase display is still
reading D3. This sets A4's fundamental to 440.

-- Then tune A3 by ear so that it fits nicely in-between D3
and A4 (about 3.5 bps narrow of perfect to D3) Alternatively
you can use tunelab to help you with this by temporarily
changing D3's offset by -1.38 cents, and tuning A3 to that.
That tunes A3's 2nd partial since you are set on D3's 3rd.

-- Then move the display to read A3 and change the offset to
stop the phase display from moving.

-- Then enter this value for A3 using first the Ctrl-E key
(this Clears the offset as well... very important !) and
then use the Insert key to add this as a reference to the
numerical editor. 

-- Then move the phase display up to A4 and repeat as for
A3.

-- With the numerical editor open highlight D3, A3, and A4
in the Reference Points box and press << Set >>. Answer yes
to the question about 3 point interpolation.

-- Then Press Enter, and then ESC to enter the value and
return to the main display.


Now just tune from D3 up to A4. When you are done with this
octave and fifth range, set the phase display to read for
D#3 and tune A#4 directly from this. Proceed chromatically
thus until you reach E6. This insures that you are tuning
fundementals for A#4 - E6 pure to the 3rd partials of D#3 -
A4..... perfect 12ths.

Phase 2 (takes again about 2-3 minutes)

-- First, select A5 on the phase display and stop the
display by changing the offset. Press Ctrl-E, then Insert,
then Enter, and finally ESC to return to the phase display.

-- Then do the same for E6. 

NOTE (reading the 3rd partials up this high can be
tricky...just keep repeat playing the notes instead of
letting them sustain... offsets for A5 should be somewhere
around 17 - 20 cents,,, and for E6 32 - 36 cents)


-- Then using the numerical editor again select A4, A5, and
E6 and press the << Set >> button, again answer yes to the
question about interpolation.

Now just tune F6 up to B7. You can check A#4 to E6 along the
way to see how well their calulated 3rd partials line up
with the fundementals taken from the 12ths below. C8 you
should be able to figure out on your own.

Phase 3

-- First set the phase display to read G2.

-- Then while playing D4 stop the phase display by changing
the offset. Press Ctrl-E, Insert, Enter, and then Esc to
return to the phase display, and tune G2 at this time.

-- Then set the phase display to read G1.

-- Then play D3 to and stop the display and continue as for
G1.

-- Then with the numerical editor highlight D3, G2, and G1
in the reference points box and press << Set >>.

Now just tune from C#3 down to G1. As soon as you reach F#2
you can tune the octaves below at the same time. This gives
you 6:3 octaves for those lowest notes.

Thats it !

Alternatives for the stretching the bass downwards are
possible by tuning G1 either by ear and then entering its
value into the editor before << Set >>-ing the tuning for
the bass, or by experimenting with the different 12th
types... ie 9:3 and 6:2. The 9:3 is easy to get... just set
the phase display to read D3 and tune G1 directly to it.
That will be quite low for most pianos. The 6:2 is done by
temporarilly setting D3's tuning partial to 2, stoping the
display while playing D3, and then tuning G1 to that. In
each case when you have decided on G1, set the phase display
on G1, stop the phase display by adjusting the offset, enter
the value into the numerical editor as before and calculate
the bass using the << Set >>

Good luck.


The Perfect 12ths tuning, and this approach to accomplishing
it is and will remain free public domain... ie patent,
royalty and all of that kind of other nonsense free.
Constructive comments and suggestions to these directions
are welcome ! These directions will also be on my website in
the very near future.

Cheers

RicB

mailto:rbrekne@broadpark.no