1/4 comma meantone tuning

[Billbrpt@AOL.COM]

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In a message dated 4/13/01 8:33:16 AM Central Daylight Time, lbeach@sfu.ca 
(Larry) writes:


> How many of you have had the time to waste and put a 1/4 comma meantone 
> tuning on your home piano? ;)  I just tried it on a Yamaha C7 for fun 
> today.  I couldn't get it to work very well unless I allowed the 3rds to 
> beat about 2-3 /sec, and 5ths more narrow than they should.  I figured this 
> must be due to the greater inharmonicity of the modern grand piano compared 
> to relatively no inharmonicity on the organs of Bach's time.  Nevertheless, 
> it sure demonstrated how nice some chords can sound, and how awful a couple 
> of them were.  

There are a  couple of things confusing about your experience but basically, 
I think you must have got it.  The classic 1/4 Syntonic Comma Meantone tone 
is constructed by making a chain of 5ths, each one tempered by 1/4 of the 
value of the Syntonic Comma (21.5).  21.5 ./. 4= 5.38.  Tempering each 5th by 
5.38 will make 8 pure 3rds and leave 4 very wide (wolf) 3rds and the last 5th 
which cannot be tuned will be over 40 cents wide.  This untuned 5th is 
usually left between Ab-Eb but sometimes between Db-Ab.

Now, because the piano has Inharmonicity, this changes all of the above 
slightly just as it skews the values of Equal Temperament (ET) or any other 
temperament.  To come out right, the 5ths will be tempered a little less, 
more like 5.0 or 5.1 which will leave the 3rds tempered but less than 1 cent. 
 They will still sound pure but actually have a very slow beat, not quite 1/4 
of a beat per second.

In such a tuning, the octaves should not have the kind of stretch you would 
usually give ET or a more modern temperament.  The temperament and minimally 
stretched octaves will "kill" all of the usual resonance you expect from the 
piano.  The piano will take on an entirely different quality.  To me, it 
makes it sound "antique".

Personally, I don't really like this sound but if you really want an 
authentic sound for early music which comes from J. S. Bach's time or before, 
it is the temperament to tune.  In a concert setting, you would likely choose 
a piano with low inharmonicity and maybe one which is smaller and less 
preferred.  A second piano used for later compositions tuned in a later Well 
Temperament or Modified Meantone would work for music from later periods.

It's not a bad idea in one's home to have the good piano tuned in ET or a 
late HT and the spinet tuned in 1/4 Comma Meantone.  Children practicing 
early music on the spinet in Meantone learn a different kind of sound and 
harmony.

It's important to remember that the 1/4 Comma Meantone is at the opposite end 
of the spectrum from ET.  While there are even more extreme possibilities 
(the 1/3 Comma Meantone, for example), the 1/4 Comma Meantone represents 
about as radically different kind of sound as you can get from ET.

It is possible to tune a chain of 5ths all the same amount by many other 
fractions of the Comma: 1/5, 1/6, 1/7, all the way to 1/11.  The last is the 
equivalent of ET.  The 1/7 Comma Meantone has become popular in my area.  The 
last untuned 5th rather than being a "wolf" is only slightly dissonant.  It 
ends up making the key of Ab have a very powerful, "electrically charged" 
kind of sound.

Enjoy exploring the sound of the 1/4 Comma while you have it.

Bill Bremmer RPT
Madison, Wisconsin

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