problem with

Thanks Paul for your provocative questions. Some of these things I'm
putting all together for the first time.

paul@stretch-music.com wrote:

I'm having trouble understanding what you mean by usable notes in 72.

I guess the idea of a "pitch continuum" best describes it.

Dave Canright sent a reply to my original email which reads:

BTW, I was thinking more about 72ET as representing the harmonic series.

>From a practical standpoint, you could consider 72ET to be a pitch
continuum, where ANY interval is approximated well (with a maximum error
of 8 1/3 cents), and this viewpoint is particularly appropriate to
strings and such instruments, where the variable tuning is all by ear
anyway. For fixed pitch instruments, it may be more reasonable to think
of the 72 tones as only representing intervals that are "nearby" (the
max error leads to ambiguity); in that view, the harmonic series is
represented very well up to harmonic 12 (worst error 3.9c), but with 13
the error jumps to 7.2c, so from there on, the approximations are not
clear representations of the harmonic relations... IMHO anyway. So one
may need to be content with "only" pure octaves, fifths, thirds,
sevenths, ninths, and elevenths! Not bad!

-Dave

It's interesting in light of Dave's suggestion that Joe Manieri's book
is called "Preliminary Studies In The Virtual Pitch Continuum."

To get back to your next question

Again, I'm not quite seeing what you're trying to do hear, but I
really doubt that appealing to the 43rd overtone is really going to be
useful.

My line of thinking has been, "what are all these ratios?" mentioned on
the tuning list, in terms of actual pitches? You'll have to forgive me
but my math education ended in the 12th grade.

Seeing the overtone series divided into its overlapping pitch
duplications (at the octave) helps simplify a lot of the mystery. When
Lou talks about 81/80 as a threshold, I honestly can't say that I know
what this means pitchwise. Likewise with your thread regarding 75/64

Therefore I have constructed the overtone series, isolating octaves to
seperate staves and thereby put some sound to the to the numbers.
That's all.

I took the liberty of thinking maybe I could use the 72 to approximate
these pitches, and although they reach the maximum error of 8 cents, it
is tempting to give it a hearing. It's actually a blast.

This exercise has, for me, led to a surprising vindication of 12-tET
with its beautiful chromatic run 32, 34, 36, 38 and 48, 51, 54, and 57
[in 72, that is, and with one 7� out note.]

There is a also a chromatic run on the -50� keyboard at 31, 33, 35, 37.
The -33� keyboard has 47, 50, 53, 56, 59, and 63. And the -67� keyboard
has 46, 49, 52, 55, and 58 [all in 72 with some 8� errors.]

With these isolated errors carefully noted, the composer has the option
to use them with this caveat, in compositional situations where the
error can be masked, say piano (tuning) "stretching" or articulations
like staccato or pizzicato.

When you ask me what I am hearing, I want to say another second to
replace 9/8 but in reality there are many seconds as in Kiganda music
which has fascinated me for years with its variable seconds ranging
between 190 and 279 cents all on the same instrument. Kubik goes to
great lengths to explain, musically and linguistically, how these
intervals are considered the same.

Gerhard Kubik in an article "Embaire Xylophone Music of Samusiri
Babalanda" in Composing the Music of Africa, edited by Malcolm Floyd,
Ashgae, Brookfield USA, 1999 (very expensive) www.ashgate.com has an
18-slat pentatonic xylophone tuning starting from low to high as:

273; 279; 196; 245; 207;
230; 242; 241; 240; 269;
190; 220; 256; 200; 240;
249; 225.

The music is isorhythmic with two interlocking pentatonic melodies.
Each melody has an octave ambitus and each is played in octaves very,
very rapidly.

So I don't know if this answers your question but this is my line of
thinking. As to the 8+� error, I think you're right that it's
stretching things. In some ways, I guess, I'm hoping that maybe the 72
temperament might lessen the pain [of the 13th] and for now at least,
keep the expense down of firing up yet another bank of synthesizers.

Yours,
RT

P.S. I came across an interesting website while researching 72 on the
web

http://www.xs4all.nl/~huygensf/groepen.html

and from this site I got hold of Julia Werntz at the Boston Microtonal
Society at 27 Valentine St., Cambridge, MA 02139. Through her I'm
finally getting hold of Joe Manieri's book for which he is charging
$20. She mentioned that it is undergoing a revision. She also just did
her doctorate on equal temperments and is sending me her dissertation,
so that should be an interesting read.

--- In tuning@y..., Rick Tagawa <ricktagawa@e...> wrote:

>
> My line of thinking has been, "what are all these ratios?"
mentioned on
> the tuning list, in terms of actual pitches? You'll have to
forgive me
> but my math education ended in the 12th grade.
>
> Seeing the overtone series divided into its overlapping pitch
> duplications (at the octave) helps simplify a lot of the mystery.
When
> Lou talks about 81/80 as a threshold, I honestly can't say that I
know
> what this means pitchwise. Likewise with your thread regarding
75/64

Well, I'd really like to simplify the mystery for you completely, so
let's talk, but for now . . . What about the ratios listed in my
table at the bottom of your webpage? Those are all "consonant" -- at
least, they are as consonant as the first few x-o and x-u intervals
that you've been looking at, and include those, but include many more
as well -- are those a mystery to you too?

>
> P.S. I came across an interesting website while researching 72 on
the
> web
>
> http://www.xs4all.nl/~huygensf/groepen.html
>
> and from this site I got hold of Julia Werntz at the Boston
Microtonal
> Society at 27 Valentine St., Cambridge, MA 02139. Through her I'm
> finally getting hold of Joe Manieri's book for which he is charging
> $20. She mentioned that it is undergoing a revision. She also
just did
> her doctorate on equal temperments and is sending me her
dissertation,
> so that should be an interesting read.

I've been to 27 Valentine St. I've met Julia Werntz and Joe Maneri
I'm familiar with Joe Maneri's (note the spelling -- why does
everyone always misspell his name?) philosophy as exemplified in this
book -- there is not one mention of the harmonic series or frequency
ratios in it. Hopefully, you'll find it valuable anyway.

--- In tuning@y..., paul@s... wrote:
> I'm familiar with Joe Maneri's (note the spelling -- why does
> everyone always misspell his name?)

Just one very small possibility: a very well-known marimba/vibes
player (both interesting jazz and SpyroGyra): Mike Manieri.