[CAUT] professor tuning variables

[Fred Sturm]

On Feb 23, 2009, at 6:11 PM, Ron Nossaman wrote:

> If not for ETDs, it wouldn't be an option today. How about a show of  
> hands for those offering a plethora of alternative temperaments  
> tuned aurally.
> Ron N

	Well, I'll raise my hand as someone who knows how to tune a number of  
non-ETs aurally - though I am more likely to use the ETD for speed and  
convenience. I second Ed Sutton's comment about Jorgensen as not the  
best source. Not quarreling with accuracy, but I think he makes things  
much harder than they are. He worked in the Braid White tradition, all  
sorts of scientific accuracy through utterly precise beat rates,  
throwing in countless checks for supposed precision. The appendix in  
Braid White about mean tone is a true case in point. Talk about making  
the simple incomprehensible! I could never hear at the threshold of  
0.1 beats per second, myself. Well, unisons maybe.
	1/4 comma meantone is easy to remember and easy to do. Balance a  
series of four 5ths to make a beatless M3. Continue with the same size  
5ths until you get to G# (one direction) and E-flat (other direction).  
Each time you tune a 5th, you check to be sure that the resultant M3  
is beatless. End up with 8 beatless M3s and 11 equal 5ths; 4  
diminished 4ths (horribly wide M3s) and one horribly wide wolf 5th.  
Piece of cake.
	The German tradition of WTs are similarly easy: beatless 5ths in the  
flat direction from C or F, and some temperered ones in the sharp  
direction. Different recipes have different numbers and sizes and  
placements of tempered ones, but they aren't rocket science to learn.  
Vallotti and Young are the simplest pattern: 6 pure 5ths in the flat  
direction, 6 tempered in the sharp - tempered equally, at twice the  
tempering of ET. The result is three very wide M3s, three that are  
half as wide as ET, and three pairs of in between sizes.
	All of which is not to say that there aren't some UETs that are next  
to impossible to set except with ETD - but that is mostly a 20th/21st  
century phenomenon, not historical. (There are some theoretical  
historical ones that are next to impossible aurally as well).
	I agree with Zeno Wood about A Guide to Musical Temperament as a good  
introduction (BTW, I reviewed it in PTJ a year or two ago). Another  
good source is Claudio di Veroli's Unequal Temperament. He published a  
book by that title in 1978. Now, 30 years later, he has produced an  
updated and expanded version as an e-book, meaning searchable PDF. He  
has lots of sound samples as illustrations on his website, linked from  
the book. I have a few quarrels with some of his slants and biases,  
but on the whole it is a very solid, comprehensive book on the topic.  
And cheap - about $25 I think.
	
Regards,
Fred Sturm
University of New Mexico
fssturm at unm.edu