Tuning (3/5)

How To Tune a Piano:

A Summary of Chapters 6 and 7 from "Piano Servicing, Tuning, and Rebuilding" by Arthur Reblitz

Part III of V

We'll begin Part III with another joke and a few terms that will help us begin tuning.
A young couple found themselves in financial distress and decided that the lady would take up prostitution.  After her first day on the streets, she came back with $100.50.  Her husband said, "That's strange.  Who gave you fifty cents?"  She replied, "Why, all of them, of course."

A cent is one hundreth of any half step, regardless of register.  Cents provide a way to describe how out of tune a pitch is, without any reference to hertz.
There are a few different ways of identifying piano keys.  In the American system, the lowest 4 notes are labeled A0, A#0, B0, and C1.  In the European system, the first full octave is labeled A1, A#1...G#1.  Either way, the the highest (88th) key is labeled C8.  A's, A#'s, and B's have different octave numbers in these systems.
The tools required to tune a piano are a tuning lever to turn the pins, a tuning fork to find A440, and a felt temperament strip and wedge mutes to mute selected strings.  The tip of the tuning lever should fit snugly over the pin and nearly reach the coil of the wire.  The handle of the tuning lever should be parallel to the strings while extending away from them.  Looking downwards at a grand piano, this position is about 5 o'clock.  Because tuning pins are made of steel, which is fairly elastic, the top of the pin can be twisted without rotating the entire pin.  Twisting won't yield as stable a tuning as rotating.
Because tuning pins always flex a little bit, each pin should be tuned sharp and then eased back into its correct position; this procedure is called setting the pins.  Also, because the string crosses several points of friction in a piano, it's important to try to equalize string tension by forcefully striking the key during each movement of the lever.  The procedure of playing loudly while tuning, using increasingly smaller turning movements until the string remains stable, is called setting the strings.

Tuning exercises:
1.  "PURPOSE: To gain a feel for the tuning lever, and to learn to hear beats."
Find the A above middle C.  Lift the dampers with the sustain pedal to protect the damper felt, and then mute the right string.  Put the tuning lever on the left string and slowly lower the pitch, listening to the speed of beats increase until you hear two pitches.  Then reverse directions and tune the string slightly sharp, so that as you release the push, the pin settles in tune.  If the pin is very tight, it might be necessary to move the lever back and forth with increasingly small movements until the pin is in tune when untwisted.  Remember to always detune strings flat, move the tuning lever smoothly, and equalize string tension.  After the left string is in tune with the center string, mute it and practice on the right string.  Leave the center string alone as a reference point.

2.  "PURPOSE: To tune any unison beatless."
Find the A below middle C.  Tune the outer strings to a unison and continue chromatically up to C8.  Higher pitches are more difficult to tune because they require smaller movements, the sound fades more quickly, and higher strings have more false beats.  Once the treble is tuned, begin again with unisons from the G# below middle C and continue downwards.  When you reach the bichords, detune and tune the left string only.  Remember to always leave a reference string untouched, and do not tune the monochords.

3.  "PURPOSE: To learn to tune octaves."
Mute the two outer strings of F above middle C.  Tune the center string beatless to the F an octave down.  Continue tuning octaves chromatically up to C8, and then tune the E above middle C to the octave below it.  Continue downwards to the second lowest A.  High and low octaves are harder to tune than middle octaves.  Lower octaves have simultaneously occurring beats, and if one of these is corrected, the other will beat too quickly.  Try to tune lower octaves so that each of these beats are slow.

4.  "PURPOSE: To learn to judge the speed of beats."
To train yourself to hear beats at 7 beats per second (bps), think in sixteenths at a quarter to 105 on the metronome.  For 8 bps, use 120, and for 9 bps, use 136.

5.  "PURPOSE: To learn to tune A440 to the tuning fork."
Play F2 with the A440 tuning fork and memorize the beat rate.  Mute the outer strings of the A above middle C, and tune the center string against F2 to the same beat rate.  Notice that the F does not need to be in tune.  Clever!

6.  "PURPOSE: To learn to set three important temperament intervals to beat at the correct speeds."
Lift the dampers and use the temperament strip to mute all of the outside strings from the F below middle C to the D above.  The A below middle C will be the reference pitch.  Tune F to A so it is beatless.  Next, widen the 3rd by flattening the F until there are 7 bps.  From this F, tune the D beatless.  Widen the 6th by raising the D until there are 8 bps.  From the D, tune A# beatless, and then widen the 3rd by flattening the A# until there are 9 bps.  Check and compare beat rates.

It is time to try tuning the temperament.  I don't have permission to talk about the Defebaugh F-F temperament, but who's really still reading?  Also, "at least twenty-five schools where piano servicing is taught use this [Reblitz] as a text," so the Defebaugh isn't exactly the world's best kept secret.  Notes to tune will be orange, and tuning direction will be green.
Remember, the tuning direction should always match the theory that P5ths are narrow, and M3rds, P4ths, and M6ths are wide.  Also, bps rates should always increase in ascending adjacent intervals.

• Lift the dampers and use the temperament strip to mute the outside strings from the F below middle C to the A above middle C.
• Tune A440 as in exercise 5.
• Tune the low-A flat to A440 as a "slightly wide 4:2 octave."  In other words, tune the 4th partial of the low-A flat to the 2nd partial of A440.  (Seriously?!?)  You can check by comparing the beats from low-F to both A's; the 3rd should beat 1/2 bps slower than the 10th.
• From low-A, tune low-F, D, and A# as in exercise 6.
• Tune C# sharp to low-A with a slightly slower beat than the A#/D 3rd.
• Tune the low-G# flat to C#, but less than 1 bps.
• Tune C sharp to low-G# with a slightly slower beat than the A/C# 3rd.  Check: the low-F/C 5th should be 1/2 bps narrow.
• Tune low-F# flat to low-A# slightly faster than the low-F/low-A 3rd.  Check: the low-F#/C# 5th should be 1/2 bps narrow, and slightly faster than the low-F/C 5th.
• Tune D# sharp to low-F# slightly faster than the low-F/D 6th.
• Tune B flat to D# slightly faster than the low-A#/D 3rd.  Check: the low-F#/B 4th should be no more than 1 bps wide, and slightly faster than the low-F/A# 4th.
• Tune low-G flat to B so that the beats fit between the low-F#/A# and the low-G#/C 3rds.  Check: the low-G/C 4th should be no more than 1 bps wide, and slightly faster than the low-F#/B 4th.  Also, the low-G/D should be about 1/2 bps narrow and slightly faster than the low-F#/C# 5th.
• Tune E sharp to low-G slightly faster than the low-F#/D# 6th.  Check: the beats of C/E, B/E, and A/E should fit smoothly into their adjacent interval tests.
• Tune high-F sharp to low-G# slightly faster than the low-G/E 6th.  Check: the beats of C#/high-F, C/high-F, and A#/high-F should fit smoothly into their adjacent interval tests.  Also, the F/F octave should sound good.
• Check the entire temperament by listening to all adjacent M3rds, M6ths, P4ths, and P5ths.  For each of these, the bps should increase smoothly as they ascend.
• Another check is called "inside thirds and outside sixths."  For this, start with the low-F/D 6th, and compare the beats to the low-G/B 3rd.  The 6th should beat the same or a little faster than the third.  Repeat this test chromatically three more times to cover the rest of the temperament.

Cliffhanger:  In Part IV, without permission, we will learn something about the Potter F-A Temperament!