[Dixielandjazz] Sarah Vaughan

[philwilking]

That is an example of the difference between "Tempered" tuning and "Just" 
tuning.

It happens because our nervous system does not really want to hear 
absolutely even percentage differences of frequency going from one tone to 
another, but a simple mechanical device can't be made to "tweak" tuning "on 
the fly" without becoming hopelessly complicated.

So a G Sharp is really a very sharp G, but not quite up to halfway in 
frequency between G and A, and an A Flat is really a very flat A, but not 
quite down to halfway in frequency between A and G. So really, every time 
you modulate between keys, you should stop and retune all keyboard and 
fretted instruments. Good luck with that. In reality, adjacent keys in the 
cycle of fifths are only a teeny bit different in frequencies, so you can 
usually get away with sliding around between, for example, F, C, and G. But 
the farther afield you go from your base tuning (C in this case), the more 
out of pitch you sound.

This is why some keyboard instruments such as harpsichords had multiple 
manuals. Each manual could have its own strings tuned to a given key.

Even before J. S. Bach (died in 1750), efforts were underway to get around 
this problem. Eventually it was figured out that if you make all the sharps 
a tiny bit sharper and all the flats a tiny bit flatter, you can use one key 
or fret for both the G Sharp and the A Flat and so on. And most of the 
audience can't tell the difference. However, a good musician can hear it. 
The error gets worse the farther from the center of the keyboard you go.

You can demonstrate it for yourself using a freshly tuned high quality piano 
or (better) a high quality electric keyboard which is set to "Equal Tempered 
Tuning."
Strike any key which sounds in the middle of your voice range. Strike it 
several times to set the pitch in your mind. Now, starting on that pitch, 
sing the child's "I know more than you do" chant: "Nyah, nyah, nyah, nyah, 
ny-ah, ny--ah." Try to find the last "Ny--ah" on the keyboard. The 
difference in pitch between your voice "Ny--ah" and the closest tone on the 
keyboard is the difference between "Just" and "Equal Tempered" tuning. Your 
nervous system, left to itself, will use its own frequency choices, not 
something designed for a machine.

Phil Wilking - K5MZF
www.nolabanjo.com

"Only two things are infinite:
the Universe and Human Stupidity.
And I am not sure about the Former."
Albert Einstein

-----Original Message----- 
From: Robert Ringwald
Sent: Monday, November 18, 2019 13:29
To: philwilking
Cc: Dixieland Jazz Mailing List
Subject: Re: [Dixielandjazz] Sarah Vaughan

Ken,

I've heard that there is a difference between an A flat and G sharp. Having
never studied music theory, can you tell me what the difference is. I wonder
if I could hear it.