Tuning shorthand

[David Renaud]

No luck in archives......so...

Coleman Beat Indicator

Take a long ruler(or strip of cardboard) and lay it down on the keyboard.
Write numbers 1-2-3-4-5-6-7-8  on the strip in positions over
C-C-G-C-E-G-Bb-C corresponding with the partials of C
Do it with a second strip, identical.

Place the 1 over C and the 1 of the second strip over the C an octave higher.
Notice that the numbers 2:1, 4:2, 8:4 line up. These are some levels where
the structure of the two sounds have common frequencies speaking. A 4:2
octave is one where the 4th partial of the bottom note and the second partial of
the top note are in perfect unison and are beatless. Other coincidental partial
levels will not be pure and can still phase, but the 4:2 level is pure. This is
less stretch than a 6:3 but more than a 2:1, so the 2:1 sounds are left wide and
the
6:3 sounds narrow when 4:2 is pure.

Some exercises:

Place 1 on C, and 1of the other strip on G.
notice that both the 3:2 and 6:4 line up. This is why we have more then one
beat rate singing in a fifth. Tuning 3:2 what we want to do, sometime a
noisy 6:4 can get in the way.

We can test C4-G4 as a 3:2 with Eb3 below the C4.
Put one strip on C4, and the other on Eb3, observe.
Then put one on G4 and one on Eb3, observe.
We can observe in both cases the lowest common partial
is the G5. This is the 3:2 level of the C4-G4.
This works as a test because we are testing a common
component of each tone(C4 and G4) against a common reference
point(Eb3). When the beat rates are the same that component of the
tone is in the same place.

The Pace program is excellent for outlining these tests.

I hope this helps a little.


DaveAAAP@AOL.COM wrote:

>  Can someone help me out in understanding tuning shorthand?  When I start
> studying different temperament and tuning techniques, I get bogged down
> trying to figure out what they are trying to say.  I'm sure it's simple and
> logical, but I've never seen a dictionary of terms and I don't want to miss
> anything.
>   Why is tuning an A3 to an A4 a 4:2 octave and tuning A2 from A3 a 6:3
> octave?  How do you figure these ratios?
>   Is the big "M" different from the little "m" (I'm assuming Major and minor)
> and does "P" mean perfect or pure?
>
> Dave Streit
> Beaverton, OR