Tuning (4/5)

How To Tune a Piano:

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

Part IV of V

Did you hear about Francis Augustus, the Potter with a bad temperament?
Even when he made a kil'n, he fired all his employees.


The Potter F-A Temperament:
This temperament spans a M10th, and four pivotal thirds are used to create a foundation.  The three notes above the high-F are tuned in sixths rather than octaves in order to "carry the feeling of the temperament."  Also, because the tuner can use the M6-M3 test to check sixths, one hand is free to remain on the tuning lever.  (With octaves, the M3-M10 test is preferred and requires both hands.)
Again, notes to tune will be orange, and tuning direction will be green.  Checks will be bulleted.

• Lift the dampers and use the temperament strip to mute the outside strings from the C below middle C to the A above middle C.
• Tune A440 to F2 with a tuning fork as in exercise 5.
• Tune low-A to A440
• low-F/low-A 3rd ≤ low-F/A440 10th.
• Tune low-F flat to low-A at about 6.9 bps.
• Tune high-F to low-F.
• C#3/low-F 3rd ≤ C#3/high-F 10th.  I'll call this the M3-M10 test.
• Tune C# (above middle C) sharp to low-A at about 8.7 bps.  We now have four pivotal thirds.
• low-F/low-A 3rd at about 7 bps < low-A/C# 3rd at about 9 bps < C#/high-F 3rd at about 11 bps < high-F/A440 3rd at about 14 bps.
• Tune D sharp to low-F at about 8 bps.
• low-F/low-A 3rd at about 7 bps < low-F/D 6th at about 8 bps < low-A/C# 3rd at about 9 bps.
• low-A/D 4th and D/high-A 5th should sound good.
• Tune A# flat to D at about 9.2 bps.
• low-A/C# 3rd < A#/D 3rd.
• low-F/C# 4th and low-F/C 5th should sound good.
• Tune low-F# flat to low-A# at about 7.3 bps.
• low-F#/low-A# 3rd < low-F/low-A 3rd.
• Tune D# sharp to low-F# at about 8.4 bps.
• low-F/D 6th < low-F#/D# 6th.
• low-A#/D# 4th should sound good.
• Tune B flat to D# at about 9.8 bps.
• low-A/C# 3rd < low-A#/D 3rd < B/D# 3rd.
• Tune low-G flat to B at about 7.7 bps.
• low-F/low-A 3rd < low-F#/low-A# 3rd < low-G/B 3rd.
• low-F/D 6th = low-G/B 3rd.  This is called the M6-M3 test.
• Tune E sharp to low-G at about 8.9 bps.
• low-F/D 6th < low-F#/D# 6th < low-G/E 6th.
• B/E 4th and E/high-A 4th should sound good.
• Tune middle C flat to E at about 10.4 bps.
• low-F/C 5th and C/high-F 4th should sound good.
• low-A/C# 3rd < low-A#/D 3rd < B/D# 3rd < C/E 3rd.
• Tune low-G# flat to middle C at about 8.2 bps.
• low-G#/C# 4th should sound good.
• Test adjacent M3rds, M6ths, P4ths, and P5ths.
• Check all M6-M3 tests.
• Tune high-F# sharp to low-A.
• Check 3rds, 4ths, 5ths, M6-M3, and M3-M10.
• Tune high-G sharp to low-A#.
• Check 3rds, 4ths, 5ths, M6-M3, and M3-M10.
• Tune high-G# sharp to B.
• Check 3rds, 4ths, 5ths, M6-M3, and M3-M10.

And that is the end of setting the temperament.  We'll conclude Part IV by covering a few basic principles on how to finish the midrange, treble and bass sections.
In the midrange, tune the center strings to the temperament by octaves up to the treble break, where the agraffes stop.  Then tune the center strings down into the low part of the treble bridge.  Check to make sure that ascending adjacent M10ths smoothly increase in beat rates.  After this, unmute one string at a time by releasing the temperament strip from left to right, and tune the unisons.  Always listen to all three strings of each trichord together, and use wedge mutes as needed.
The high treble can be muted with a narrow temperament strip or wedge mutes.  Again, tune the center string of each trichord first.  The high treble is more difficult, because it takes less movement from the lever to change pitch, and the tone dies more quickly.  Test each pitch with adjacent M10ths, double octaves, and M17ths.  Double octaves will sound flat if the high treble is not stretched enough, but if they are tuned too sharp, they will beat.  Also, because the notes surrounding the treble break are often less stable, they should be rechecked after six to eight higher notes have been tuned.
The low bass strings create partials that are close to the fundamentals of higher notes on the keyboard.  (The fundamental creates the unison, the second partial coincides with one octave higher, the third is an octave and a fifth, the fourth is two octaves, the fifth is two octaves and a third, and the sixth is two octaves and a fifth.)  The third and higher partials will create beats, and these intervals should be compromised so that none sounds very bad.  As the pitches get lower, use P5ths, M10ths, and M17ths to test beat progressions.  Once those get "muddy," use M17ths only, and in the lowest octave, use two octaves plus a third and two octaves plus a fifth.  A nice way to check the accuracy of bass notes is to listen to the bass note with its major chord in second inversion played above it.  For example, if C is the bass note, the chord played above it would be GCE.

Only one more part to go!

Folks in Austin II

My parents were here in October to see our first home, again in January around the due date, and back in April to spend time with their grandson.  It's been wonderful.
I picked Bà and Ông up from the airport the evening of Wednesday the 17th.  Their flight was delayed past Drakeson's bedtime, but the next morning he was all theirs.  George and I used a giftcard from my brother-in-law Warren to get professional massages for the first time.  As if the day couldn't get any better, the four of us took the little guy to his first class at the Emler Swim School, and finished the evening with incredible pizza at Pieous.

Swim Class

Kicking

The next day Mom and I did a little shopping for her friends.  Dad stayed home with the baby and spoiled him rotten.  Apparently, Drakeson didn't like "turns," so Dad held him and walked in gentle curved paths all over the house for half an hour.
It was also Drakeson's three-month birthday.  We celebrated by getting our pictures taken in the mall and having a picnic for dinner at Barton Springs.  More mall photos are posted in Drakeson's blog.

Ông & Bà

Precious

Birthday Picnic

On Saturday, Mom and Dad helped George make beer all morning.  Dad and I had a date to see "A Prairie Home Companion" that afternoon, and we were in row F of orchestra seating.  In other words, it was awesome.  After fighting downtown traffic, Dad and I arrived home to a comforting meal of clay pot fish and rice.  Sunday was a little busier.  Mom and Dad came to the church I play for.  Dad brought in a lovely piece of music called "Appalachian Lord's Prayer" written by Rick Sowash for the Harvard University Choir in 2010, and the church choir performed it.  I took Dad to swim a few laps at Stacy Pool, and then all five of us visited Mount Bonnell (lookout) and Camp Mayfield (peacocks).  That evening, my brother-in-law Zach and his girlfriend Rose came over for Mom's shrimp and crabmeat soup.

Peacock

I messed up the waffles on Monday with too much baking soda.  Not only were they awful, but the back of the waffle iron is still a mess.  They were soggy, burnt, and tasted like play-doh.  Mom, Dad, Drakeson, and I walked to the South Austin Recreational Center Playground in the morning.  The afternoon was filled with "Books and Babies" at the library and a short hike on the West Bouldin Greenbelt.  George joined us for a relaxing dinner at the Blue Dahlia Bistro.

Ông & Carrier

Ông on the Slide

Old Hat

Hereditary

Smiling at Ông

And that brings us to today.  In the morning, we went to Barton Springs before warming up with breakfast tacos and a black and white movie called "Woman of the Year."  We lounged at Mozart's Coffee overlooking the water and took one last walk around Town Lake.

A Little Chilly

Good-byes are never fun!!!

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!