Tuning shorthand

[Newton Hunt]

M=major interval
m=minor interval, i.e. m3 is a minor third

A4 is A in the fourth octave
A3 is A in the third octave

A0 is the first note on the piano
C1 is the fourth note
C8 is the last note

Tune A3 to A4 at the 4:2 translate to tune A3 (A220 Hz) to A4 (A440
Hz) so the fourth partial of A3 (which is A5) to the second partial of
A4 (which is the coincidental partial at A5)...

Partials are our name for harmonics since they are not harmonic but
inharmonic (as opposed to enharmonic) (hence inharmonicity) and each
is a part of the whole.

They are the "harmonic series" whereby the string's energy divides
itself into rational fractions of 1, 1/2, 1/3, 1/4, 1/5, etc....

The first partial is defined as the tone produced by the full length
of the string
The second partial is defined as the tone produced by dividing the
string into two equal parts
The third partial is defined as the tone produced by dividing the
string into three equal parts, etc...

These divisions are not equal to a full division of the string length
because the wire has a stiffness factor which prevents it from
vibrating AT the terminals (agraffe and bridge pin) as if it is
hinged.  Instead the vibration begins at some distance from the
terminal points and each successive partial, having far less energy
than the partial below it, defines it's end points further yet from
the terminal points. This characteristic of piano wire and tone is
called inharmonicity and is governed by the tension, pitch, speaking
length and wire diameter.  To produce a good sounding piano with good
tunability inharmonicity must be under control by the scale designer
throughout the piano, especially in the bass.

(Sigh exhalation of high tension release)

There was a system of tuning notation that used key numbers, E44 to
A49 major fifth, but it was more cumbersome than the one we use now
since there was a lot of finger counting that was confusing because no
one I know has six fingers per hand.  (Computer geeks are different,
they count in hexadecimal which requires eight fingers per hand and
octadecimal which requires four fingers per hand.)

Now isn't that more than you wanted to know?

Have a confusing time.

		Newton