source file: mills2.txt Date: Wed, 22 Jan 1997 12:54:16 -0800 Subject: FW: Subharmonic chords From: Daniel Wolf <106232.3266@compuserve.com> 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. Received: from ns.ezh.nl [137.174.112.59] by vbv40.ezh.nl with SMTP-OpenVMS via TCP/IP; Wed, 22 Jan 1997 23:12 +0100 Received: by ns.ezh.nl; (5.65v3.2/1.3/10May95) id AA12052; Wed, 22 Jan 1997 23:11:59 +0100 Received: from ella.mills.edu by ns (smtpxd); id XA12077 Received: from by ella.mills.edu via SMTP (940816.SGI.8.6.9/930416.SGI) for id OAA19055; Wed, 22 Jan 1997 14:11:45 -0800 Date: Wed, 22 Jan 1997 14:11:45 -0800 Message-Id: <32E5128D.6892@interlinx.qc.ca> Errors-To: madole@mills.edu Reply-To: tuning@ella.mills.edu Originator: tuning@eartha.mills.edu Sender: tuning@ella.mills.edu