440 vs 442 & Stretch Tuning

Most pianos are tuned A440, but the stretch is different from one piano to the next because each Piano dictates its own signature stretch naturally during the tuning process (more on stretch below).

As for A440 vs A442… First, we need to understand the difference between them.

Hertz (sometimes called cycles per second or CPS) is defined: the total number of oscillations in a sound wave in one second. It’s a way to measure and value sound.

The frequency = 1 Hz when: one oscillation occurs in 1 second (so low the human ear cannot hear)
The frequency = 20 Hz when: twenty oscillation occurs in 1 second (about where the human ear can start to hear)
The frequency = 440 Hz when: 440 oscillation occurs in 1 second (A440)
The frequency = 442 Hz when: 442 oscillation occurs in 1 second (A442)
The frequency = 1000 Hz when: one thousand oscillations occurs in 1 second
The frequency = 20,000 Hz when: twenty thousand oscillations occurs in 1 second (around the limit of the human ear)
The frequency = 45,000 Hz = 45kHz (around the limit of a dog’s ear)
 

A-440 in tuning terms means: when you tune A4 it will read/ring at 440 Hz (aka: 440 cycles per second)
When tuning we also use the term: Cent(s)
Here is where things get tricky
There is no easy way to formulate the difference between cents and Hertz because:
Cent is an equal unit used to measure sound, but it comes from a scale based on equal temperament (not pure beats) (more on equal temperament below)
and Hertz is the actual reading (cycles per min) of the sound-waves
BUT Basically…

The difference between A440 and A442 is about 8 cents (7.85…)

AND

There are exactly 100 cents in a Semitone (1/2 step)

SO

8 cents = 2 Hz (the difference between 440 and 442)

Or

1 Hz = 4 cents

↑↑↑ Wait! You just said that “there is no easy way to formulate the difference between cents and Hz!”

Well… there isn’t, it’s impossible. But also… it’s about 4 cents per Hz… give or take, depending on the instrument… temperature… stretch… etc.

In the context of mallet instrument tuning, eight cents (2 Hz) represents a very small value. Often when a bar cracks, significant pitch drops exceeding 30 cents will occur. When doing a repair, we split the bar completely in half and glue it back together (Don’t try this at home). The process for bringing that bar back up to pitch will remove a fair amount of wood from the ends, but even at 40 cents flat often the bar can be brought up without jeopardizing the quality of the sustain. With that said it is much easier to tune an instrument down from 442 to 440. The sanding is done at the middle of the keys. This technique results in the pitch dropping much faster while removing less material (than that to bring the bar up from the ends)

Side note: We do offer tuning service for both: 

• tuning down from A440 to A442 and 
• tuning up from A440 to A442 at our standard tuning price
  

A440 was a United States Standard, but that is changing. The former US standard was A435 (which you might see stamped in some old pianos)

MOSTLY TODAY- mallet instruments are tuned A442, and it is becoming more difficult to get an A440 tuning without using an outside service.

WHY THE HECK TUNE 442!

I’ve heard many things over the years, but these two stand out as real possibilities.
The cut: instruments that are a little sharp will cut through the other instruments.
The heat: Mallet instruments tend to go a little flat when they are under hot stage lights.

Temperature is very important to pitch!

In a warm environment wood and metal keys will drop in pitch and conversely, in a colder conditions keys will ring sharp. All Fall Creek instrument tuning is conducted in a controlled environment maintained at a constant temperature of 70°F. Following tuning, a 24-hour acclimation period is observed to ensure the keys have stabilized before any fine-tuning adjustments are made.  

The Stretch:

Mallet instruments are tuned with equal temperament as well as the piano (and most instruments). Unlike mallet instruments, the Piano (as well as many other string instruments) is an in-harmonic instrument. That means the harmonics (or partials) are out of tune (sharp to their respective fundamentals). But we listen to these partials when we tune so we must compensate for them being (sounding) "flat". This is usually referred to as octave stretching. The only fundamental in perfect tune (in relation to Hz) is A4. Usually the notes below A4 are slightly flat and the notes above A4 are slightly sharp. If they were perfectly tuned, the piano would sound horrible because of the in-harmonic partials. This is why most instruments historically are tuned to the piano (or other string instruments), and not the other way around.

So, we in the percussion industry tune with a stretch, even though technically any mallet instrument could be tuned without a stretch BUT! If we did that, then when the instrument is played along with other instruments…  we find ourselves in a world of pain.

How do we make a stretch that fits everyone’s needs you ask? Simple… you can’t.

In the 1970’s Bill Youhass spent countless hours working with violin players, piano tuners, and percussionist all over the globe developing a template of a stretch that has evolved over the last 50 years. This is our standard stretch that we use on 99% of the time when tuning. From here we can change the Pitch to anything 440, 442, etc. The other 1% of the time, we work to developing custom stretches (as well as pitch) that works best for each organization’s needs and taste.

(some of this is open for debate/ input/ updating etc.)

Rick Byers

Fall Creek Marimbas, Inc.