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– Unisons
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– Octaves
– ETD’s
– Repairs
– Etc., your choice.

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Piano Tuning Theory – Preorder and Save!

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piano-tuning-theory

90% of this book is standard theory that all technicians learn when they begin their studies, but some of the theory has been developed by data that the author has collected.

(The following example may be of interest to tuners who enjoy using beat speeds to check octave sizes. The author is aware that many technicians do not favour octave checks and prefer to tune octaves directly. This discussion, therefore, may not be of interest to them.)

Example: Tuning pure 4:2 or wide 4:2/narrow 6:3 octaves.

This has been a question that has been debated and there are advocates for both.

The author performed a study that may help one determine when to tune a pure 4:2 and when to tune a wide 4:2/narrow 6:3.

The study used the concept of Octave Spread.

Octave Spread has been defined by the author, as how “out of tune” the 6:3 partials are, when an octave is tuned as a pure 4:2. On some pianos, the 6:3 partials are very close. On other pianos, they are very far apart.

The author has defined the following categories:

Small Octave Spread: 0.0 – 0.5 cents

Medium Octave Spread: 0.5 – 1.0 cents

Large Octave Spread: 1.0+ cents

(The cents value indicates how far apart the 6:3 partials are in an octave when it is tuned as a pure 4:2.)

When using the standard octave checks, there is a window where unequal beat speeds will “sound” equal to the tuner. This is defined by the author as The Human Limitation in Beat Speed Difference Recognition.

From tests with subjects, this limitation has been found to be about 3%. It does not depend on tuning experience.

This 3% window is very close to the 0.0 – 0.5 cent bin for the Small Octave Spread.

So, even if an octave is a wide 4:2/narrow 6:3, but also has a Small Octave Spread, it will “sound” like a pure 4:2/pure 6:3, when using the standard octave tests.

When tuning wide 4:2/narrow 6:3 (when the spread is wide enough to be heard using the standard octave tests) there is a limit when subjects indicate that the octave does not sound “clean”. This limit is equal to a spread of about 1.0 cents.

If an octave has a spread of approximately more than 1.0 cents, it sounds better as a pure 4:2, which has a very narrow and wildly beating 6:3, according to subjects’ responses.

The attached flow chart may be used to aurally assess the spread (which is an indication of the inharmonicity of the piano) and possibly determine the best octave size.

(The author uses “Octave Spread” and “Octave Scale” interchangeably.)

*In some cases, the octave will not tune as a pure 4:2/pure 6:3, will not sound good as a wide 4:2/narrow 6:3, and will not sound good as a pure 4:2. Sometimes, tuning it as a pure 2:1 will work. Sometimes, it may sound good as a narrow 4:2/wide 6:3, if it can be tuned as such. Rarely, the octave may have to be tuned directly, without check notes.

octave-spread

Tenor Damping

The longer the strings are, the longer the dampers have to be to effectively dampen. 

The lowest tenor string is one of the longest strings in an upright. But the damper cannot be higher; it will hit the hammer. It cannot be lower, it will rub on the top bass string. (See in the photo above. Notice the chopped bottom of the damper block.)

Notice how Yamaha tries to deal with this problem by, 1, having the hammers edge higher so they can keep the damper longer and, 2, adding an over damper on the bottom tenor note. 

Yamaha MP100 Friction Test

Flex down, remove hammer, whack, measure: -5.5 cents

Flex up, remove hammer, whack, measure: 8.5 cents

Difference: 14 cents. Typical. Much easier to tune. There is a sufficient pitch window. 

More Friction Tests in the Low Friction Steigerman

Bass section looked like it had low bearing as well. Friction test: 3 cents. 


Treble section showed some more angle. Friction test: 13 cents. Easier to tune. 

Low Friction Pianos

Here’s a Steigerman with a low bearing on the agraffes. Tuning it, I had the feeling the pitch was sliding quite easily. Even with long non-speaking length, I was getting pitch changes when I removed the hammer force after a slow pull.

I performed a friction test. I flexed the pin towards the string, removed force, whacked, and measured. Did the same flexing away from the string.

This test measures the friction at the agraffes, and the residual friction in the pinblock. Usually I get 15 – 20 cents. On this piano, it was 5 cents.

This explains why the pitch so easily followed the pin.

To improved tuning sensation, I might add thicker felt under the strings.

Modified Coil Maker

I just posted a video clip of a modified coil maker that I use to make a bass string hitch pin loop. If you want the whole video to see how I use it to make the coil and hitch pin loop, send me a note.

modified-coil-maker

Pitch Window Method for Stability

Here’s my Pitch Window Method for stability.

Suppose you come to a string and you have to lower the pitch a tiny bit. The first thing I do is assume that the NSL tension is near the bottom of the tension band that produces stability. Now, what I do is a gentle flex of the pin in the direction of the string. This flex has to be very small because we don’t want to damage the pin block.

Now, if the pitch does not go down, that means the NSL tension was not near the bottom of the tension band.

So, that means that the target pitch is not available to us for the pin foot orientation that the pin currently has. 

So, I need to turn the pin foot by the smallest amount possible, and I have to do this without having a change in the pitch.

If I can get the pin foot to move, without having a change in the pitch, that means that the NSL tension now must be lower in the tension band.

Now, I will try the gentle flex in the direction of the string and hope that the pitch will drop by the smallest amount that I’m looking for.

If the pitch does not change, then I must do a very small nudge of the pin foot again and repeat the flex.

Using this method of flex, move the pin foot, flex, move the pin foot, I am able to make a very small change in the pitch and also know where the NSL tension is and therefore leave it slightly high of middle so that I can have good stability.

I hope that helps. If you have any questions, don’t hesitate to ask for clarification.

Note: it is the unbending or unflexing of the pin that puts the tension back into the nonspeaking length. If the nonspeaking length is very long, then the unflexing will not put very much tension back into the nonspeaking length, and the string may be unstable. If the nonspeaking length is very short, then the unflexing actually might put so much tension back into the non-speaking length that the pitch actually rises!

This is called Hooke’s Law.

Sneek Peak at Piano Tuning Theory Book – Chapter 3.6 – Cents

CLICK HERE to read this chapter of my book, Piano Tuning Theory.

In this chapter I develop the common formula for calculating the cents difference between two frequencies.

The book is targeting piano owners and technicians who may not have a strong mathematical background, but are still interested in the theories of piano tuning.

 

You can pre-order the book HERE

Pin Block Repair

I recently inspected a piano with a birdcage action. The customer was very excited to get it working. I told her it would never work great. She understood. 

bird-cage-action

bird-cage-action


I gave her an estimate and she agreed on a schedule. 

Then I opened the top and saw one of the largest pin block frame seperations I’ve ever seen. 

This is the separation after a no glue repair. 

pin-block-crack

pin-block-crack


I gave her the price for that and she said go ahead. 

I’ve seen pin block repairs before that were not glued and decided to try the no-glue repair on this piano. There were eight holes for bolts so that was good. 

pin-block-repair

pin-block-repair


I measured and tried to get bolts that were just long enough. I did not want to start grinding bolts off. 

I decided to have the bolts go out the back but you could do it the other way around. We will add a piece of wood trim to stop the bolt ends from scratching the wall. 

pin-block-repair-bolts

pin-block-repair-bolts


One pin was very close to the bolt. I had to remove the pin, insert the bolt, and re-insert the pin. 

pin-block-repair-bolts

pin-block-repair-bolts


After bolting, we added CA glue because the pins were loose. 

Now we’re tuning it up to see how high she can go. A tone flat and already one bass string broke. The customer was made aware of that possibility. 

The goal is to get it so that each note is working and she can play the piano and it sounds as musical as possible. 

Sometimes we have to remember that we are servicing the customer and not just the piano. ?

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