a fundamental to call my own...

Catching up on all those old Tuning Digests I missed
last summer while I was in Arizona, I ran across:

[Drew Skyfyre, Mills TD 1523.3, 1998 September 6]
> BTW, I adopted Joe Monzo's system of tuning the fundamental,
> and refer to it as the Monzo Fundamental, so if there isn't
> another name for it, and it's o.k. with you, Joseph...

Yes!

I'm honored and delighted to have *something* musical
named after me!

(especially after finding out that all the stuff I thought
I 'invented' that was so 'new' - prime-factor notation, lattice
diagrams, etc. - has quite a history from Fokker to Wilson etc.)

That is, 'if there isn't another name for it'...

BTW, if anyone's curious about what that system is, it's simple:
call 1 Hz your basic inaudible low 'C', which gives a 'middle-C'
of 256 [= 2^8] Hz.

To compare the 'A's with A-440:
In 12-eq, this gives an 'A' above 'middle-C' of ~430.539 Hz.
The 5-limit JI 'A' a 5:3 above this 'middle-C' is 426.666... Hz,
and the Pythagorean 'A' a 27:16 above 'middle-C' is 432 Hz.

These 'A's are in the general area of the pitch-reference
that was prevalent in the late 1700s - mid 1800s in France and
England, and late 1800s in Italy. The following chronological
list is adapted from Ellis's table in Appendix 20, section H,
'The History of Musical Pitch in Europe', in Helmholtz,
_On the Sensations of Tone_:

1625 Lavenham (nr. Ipswich)
1670 Newcastle-on-Tyne
1696 London
1701 Fulham Parish
1788 Windsor
1811 Paris
1823 Paris
1826 Paris
1843 Wimbledon
1846 England
1854 Lille, France
1877 (Tonic sol-fa)
1878 Norwich
1884 Italy - official army band

This range lies right at the boundary between the categories
Ellis called 'Mean Pitch of Europe for Two Centuries' and
'The Compromise Pitch' (which was followed by 'Modern Orchestral
Pitch').

If you call 'middle-C' your n^0 or 1:1, then the bottom end
of the audible range would give a 16 Hz 'C' with the ratio
2^-4 or 1:16, and the note an 'octave' above '5-line high C',
which is pretty much the useful limit for instruments and notation
on the high end (exceptions noted) has the ratio 2^4 or 16:1.

This gives a very neat symmetrical layout to the whole 'usable'
range of pitches.

An explanation with a musical example can be found in my original
paper about my theory:
http://www.ixpres.com/interval/monzo/article/article.htm

For those reading this paper, note that what I had called
'matrix addition' is more properly referred to as 'vector addition'.
Eventually I'll get around to correcting it.

And please, everyone, call me monz or joe.
'Joseph' is only for copyrights.

-monz

Joseph L. Monzo monz@juno.com
http://www.ixpres.com/interval/monzo/homepage.html
|"...I had broken thru the lattice barrier..."|
| - Erv Wilson |
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