Toward *the* optimal scale:

Hi,

Happy Fathers Day to all.

I stupidly suggested files in which various tunings would be compared, with some talk about what to expect next. To avoid blowing the ear or testing tonal memory by inserting such talk, I think that the talk should be eliminated altogether from such files -- to be written elsewhere as a guide to each such file -- if my suggestion should be put into practice. The idea is to have files such as Jerry Eskelin presents, in which the change is made and one can actually hear something change instantaneously.

In any case, Christopher Bailey <cb202@columbia.edu> has kindly provided

>http://meowing.memh.uc.edu/~chris/mahler/grail/
>http://meowing.memh.uc.edu/~chris/mahler/cauldron/

which I have opened in adjacent msie6.0 windows, from which I can compare grail to cauldron. I am assuming that I need to do nothing to my MIDI player to hear particular tunings. Is that correct?

This is a particularly nice way to be able quickly to compare one tuning against another and suggests that these same files in ET, Rainbow, and other tunings might also be made available, in the same order of appearance, on similar pages. With a smattering of text suggesting what listeners should be hearing or at least listening for, I think this would help me more quickly to catch up with you folk.

I also wonder whether the following experiment has been done, or any like it:

Put the subject in a sound booth. Play a fundamental. Have the subject select a most-satisfactory 5th. Record the value chosen, in Hz.

Then have the subject add a most-satisfactory 3rd. Record the value.

Then have the subject adjust the 5th and the 3rd, iteratively, for the most-satisfactory major chord. Record the pitch values.

Finally, have the subject add a most-satisfactory octave above the starting fundamental (or the starting tonic chosen; as one alternatively could first have given a fundamental one octave lower than the first tonic, also to be chosen by the subject.)

Repeat the experiment for enough people to create a statistically significant database, wherein also is recorded the musical background (if any) of each subject.

Create a new, optimized scale based upon the weighted geometric means of the optimal pitch values selected by all subjects, weighting being on a scale of musical experience. Another weighting factor might be based upon each subject's cultural heritage. For instance, a kid who loves rap might hear things much differently from the way a sitar player from India might be expected to do.

Perform other mathematical analysis via such approaches as Fourier analysis, factor analysis, and neural networking, to mine the data for unexpected but useful information.

Alternatively (or next), gather the data from a JAVA-based, interactive sampling of the world Internet population, using the sound cards that people already have installed in their own machines, being sure to gather pertinent software- and hardware-related data for each participant.

Hire me to help. :-)

Thanks,

Steve Langford

--- In tuning@yahoogroups.com, Steve Langford <s@T...> wrote:

> Repeat the experiment for enough people to create a
statistically
> significant database, wherein also is recorded the musical
background (if
> any) of each subject.
>
> Create a new, optimized scale based upon the weighted
geometric
> means of the optimal pitch values selected by all subjects,
weighting being
> on a scale of musical experience.

whoops! you skipped some pretty important steps here, steve! or at
least so it seems to me. suppose the experiments all show the
expected simple just intervals. does this uniquely determine a scale?
not at all!