[Fwd: GhostTones ?]

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Date: 17 Feb 97 00:56:38 EST
From: Charles Lucy <100702.2223@CompuServe.COM>
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Subject: GhostTones ?
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Hi Matt;

I attempted to post the following message in reply to your missive
via cix.co.uk (my regisered address at mills.edu)
When I tried to access bix by tymnet I got "site shut" message.
I am therefore sending it to you with the hope that you will forward it to
tuning list.
(with this note to explain its origins)
TIA
Charles Lucy
Matt wrote:

>You say people wouldn't believe you (you assume) because you
>have a vested interest in having your model be accepted, so
>you are excused from posting your model. It's interesting
>that this logic doesn't also prevent you from posting claims
>that you have a model.

The model and mapping is very straight-forward and is (I hope clearly)
explained at our website (www.wonderlandinorbit.com/projects/lullabies)
in the download and techie areas, plus John Harrison's writings.

I shall restate it, as briefly as possible.

(complete with formulae and numbers)

It seems that by taking steps of fourths and fifths, from a given pitch,
all "harmonics" (ghosttones?) can be mapped in a continuous series.
The interval between the fourth and the fifth is exactly [1200/(2*pi)190.9858 cents] . This interval Harrison called the "larger" interval.
I have used the term "Large"(L).

One octave (Ratio exactly 2) is 5 Large (L) plus 2 small (s) intervals.
Harrison called the "small (s)" interval the "lesser" interval.

Therefore the "small" interval (s) is {1200 - (5*L)}/2 122.5354 cents.


To this basic formula, I have added some musical terms and
further rules.


440Hz is called A4.
Steps of fourths produce flats and multiple flats.
Steps of fifths produce sharps and multiple sharps.

Scales may then be mapped as additions and subtractions of Large (L)
and small (s) intervals.

It seems that notes, which are closer on the spiral of fifths and
fourths are more consonant than those which are a greater number of
steps apart..




>Actually it is theories, not laws, which compete.

To my mind a theory becomes a "Law", when it becomes sufficiently widely
accepted as a "scientific truth" to supersede all previous and
contradictory "Laws". At any one time there are often competing theories.

Eg "Creationism v Darwinism".

True, the theories do compete, and particularly successful theories
eventually compete against the "Laws".

Karl Popper "On the logic of scientific discovery" writes on the
shortcomings of this logic.

I was looking for a better model for tunings and frequency analysis
than Just Intonation provides.



>I keep seeing posts and cross posts which explain that the partials
>of real plucked or hammered strings are not exactly harmonic. I don't
>see anyone arguing what you call "prevailing law". I think this is
>what's called a "strawman"--when you state an opposing argument
>noone actually holds, hoping that by then destroying that
>argument you can indirectly prove your own argument. Unfortunately
>it doesn't prove anything.

Ask the JI advocates where the "harmonics" (ghosttones?) are.

>None of the web sites which links you've posted have any
>description of the mapping of partials. All your web sites
>describe (and not very clearly) is that one can build an
>extensible tuning system on 2 irrational intervals, neither
>of which is pi. I suspect that there are an indefinite number
>of such tuning systems using pairs of irrational intervals,
>all of which would produce beating sonorities.

See above re. pi.

Your suspicions may well be true, yet the obvious irrational and
transcendental numbers are all related (pi, Phi, e, etc.)



>It's one thing to work with materials artistically to get a
>pleasing result, it's another to investigate the physics
>of acoustic bodies, the theoretical structures of tuning
>systems, and the psychoacoustics of human perception.

I suspect that there is more to Harrison's dogmatic insistence on
this particular interval of 2^(1/(2*pi))
(The two pi root of two) as the Large (larger) L interval),
than merely convenient arithmetic.

The more I that learn about the current "science" of acoustics;
the more I believe that it is built on shaky foundations.

If you read best selling biography "Longitude" by Dava Sobel
Walker 1996, you will find that Harrison was a meticulous
scientist and horologist.

>I have no vested interest in any particular model; I'm
>curious about all of them--that's why I read this list.
>If you do indeed have a model, I suggest that this
>particular forum is the _ideal_ place to discuss it--if
>you would only begin to do so.

>Matt Nathan

Good let's do that!

Charles Lucy - Hawaii 15 Feb 97.





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