FW: TUNING digest 960

----------
From: Paul H. Erlich
To: tuning
Subject: RE: TUNING digest 960
Date: Monday, January 20, 1997 12:00PM

>>'' Even Daniel and Little Wolf
>>preferred 10 12 15 17 to /12 /10 /8 /7, despite the smaller numbers in the

>>latter.*** Only in changing the comparison to 17 20 24 30 vs. /7 /6 /5 /4
>>does the subharmonic version win out. ''

>Check my posting. This is NOT what I said. My overall preference is for /7
>/6 /5 /4, but in the next inversion, I prefer 10 12 15 17 to /6 /5 /4 2/7.

Where is the contradiction? Note that /6 /5 /4 2/7 /12 /10 /8 /7, and that
the inversion of 10 12 15 17 that is comparable to /7 /6 /5 /4 is 17 20 24
30. So didn't I get it right?


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Paul:

(1) You wrote:

''So what were your errors in cents?''

Playing a standing just minor triad from 200 hz in sine waves on the Rayna,
I tuned the following pitches by ear with the tuning knob of an HP
oscillator initially set at 200 hz, each tone coming out of a separate
channel and loudspeaker, the four loudspeakers bunched together and lined
up two metres in front of me. I allowed myself 20 seconds per trial. A
neighbor recorded the frequencies I chose to three decimal places, and I
have calculated my accuracy in cents:

Target pitch relative to lowest tone of triad - Average Cent Deviation
after 10 trials

17/10
+1.6
17/20
+3.3
12/7
-1.8
12/14
+0.1

You can eat another hat if you like, but as far as I am concerned, all this
test measures are the facts that I have overpracticed tuning and singing
harmonic and subharmonic series with factors of 2 in the tonic (harmonic)
or guiding tone (subharmonic) position, and that factors of seven are more
secure than those of seventeen. I have to work on my inversions! In any
case, with a longer trial period the accuracy of all intervals improves
tremendously, the first and fourth chords showing virtually no error..


How did _you_ do? (Send it privately - this is too much schoolyard bragging
for me).

(2) You wrote:

''But do you really hear it (the just minor triad) as originating from the
fifth rather than the conventionally considered "root"?''

''Originating'' is not the best word. For me, in singing or tuning the
tones of a minor triad, the third is always more secure when tuned as a
descending 5/4 rather than as an ascending 6/5. When I want to tune a
pythagorean minor, however, the ascending 32/27 is easier. As far as
''rootedness'' is concerned, I will emind you that I am an absolute Fuxian
and not Rameauvian, in that the sounding bass is more important to me than
a theoretical fundamental bass. (That's one reason why Satie and Stravinsky
were able to so smoothly disassociate the bass line from what went on up
above!).

(3) I responded to my own deficits as a musician by training myself to hear
and tune specific rational intervals. I started back in High School, while
working with Erv Wilson, and have been doing it for 19 years now. Had I
decided, at the same time, to invest as much in 19tet or 31tet, I reckon
that I would probably have reached some comparable ability in those
systems. So, such a test is only a measure of the current state of my
conditioning.


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