Newcomer's basic questions

Hello list,

I'm a newcomer here, and actually to ji as well, so I hope you'll be
indulgent...
(In Belgium, where I did my musical studies, the subject doesn't seem to
be a hot topic, I'm afraid. They rather have you investigating how many op.
Czerny wrote, to make you a "good pedagogue"...)

Up to now, I've actually spent more time listening to different intervalls /
tunings (with the help of my k2000, and some charts found on the web) than
trying to understand where they came from... Now that my ear convinced me
it's worth the effort, I would like to spend time on theory.

So I picked a lot of what I found on the web about JI...
..and I'm trying to understand (ahem).
When you speak about, for ex., 5-limit JI, do you mean the ratios may
comprise up to the 5th harmonic...?
If so, when I'm faced with a major seventh 15:8, I suppose it was calculated
with, say, a perfect 5th 3:2 * a major 3d 5:4 ? But then again, where does
25/24 come from...

Also, I'm wondering where I could find an overtone's list; those I found
stop at the 11th harmonic.

Are there good books explaining those basic things ?
Shoud I try to find a copy of Partch's 'Genesis of a music' ?

Many thanks,

PhJ

Definitely
either get it from David Doty at JInetwork or the recent repress from Amazon.com

Good Luck
Pat
SEJIS
p.s.
you must read it twice--at least
hah!

Philippe Jonckheere wrote:

> From: "Philippe Jonckheere" <Philippe.Jonckheere@euronet.be>
>
> Hello list,
>
> I'm a newcomer here, and actually to ji as well, so I hope you'll be
> indulgent...
> (In Belgium, where I did my musical studies, the subject doesn't seem to
> be a hot topic, I'm afraid. They rather have you investigating how many op.
> Czerny wrote, to make you a "good pedagogue"...)
>
> Up to now, I've actually spent more time listening to different intervalls /
> tunings (with the help of my k2000, and some charts found on the web) than
> trying to understand where they came from... Now that my ear convinced me
> it's worth the effort, I would like to spend time on theory.
>
> So I picked a lot of what I found on the web about JI...
> ..and I'm trying to understand (ahem).
> When you speak about, for ex., 5-limit JI, do you mean the ratios may
> comprise up to the 5th harmonic...?
> If so, when I'm faced with a major seventh 15:8, I suppose it was calculated
> with, say, a perfect 5th 3:2 * a major 3d 5:4 ? But then again, where does
> 25/24 come from...
>
> Also, I'm wondering where I could find an overtone's list; those I found
> stop at the 11th harmonic.
>
> Are there good books explaining those basic things ?
> Shoud I try to find a copy of Partch's 'Genesis of a music' ?
>
> Many thanks,
>
> PhJ
>
> ------------------------------------------------------------------------
> Ideas on how we can improve ONElist?
> http://www.onelist.com
> Check out the Suggestion Box feature on our new web site
> ------------------------------------------------------------------------
> You do not need web access to participate. You may subscribe through
> email. Send an empty email to one of these addresses:
> tuning-subscribe@onelist.com - subscribe to the tuning list.
> tuning-unsubscribe@onelist.com - unsubscribe from the tuning list.
> tuning-digest@onelist.com - switch your subscription to digest mode.
> tuning-normal@onelist.com - switch your subscription to normal mode.

I tried to email this to Phillipe privately,
but Euronet sent me a message that it will not
relay to/from spammers. Guess that's what Juno is . . .
So I sent it here.
------------------------
Dear Phillipe,

You wrote to the Tuning List:

> When you speak about, for ex., 5-limit JI, do you
> mean the ratios may comprise up to the 5th harmonic...?
> If so, when I'm faced with a major seventh 15:8,
> I suppose it was calculated with, say, a perfect
> 5th 3:2 * a major 3d 5:4 ? But then again, where does
> 25/24 come from...
>
> Also, I'm wondering where I could find an overtone's
> list; those I found stop at the 11th harmonic.
>
> Are there good books explaining those basic things ?
> Shoud I try to find a copy of Partch's 'Genesis of a music' ?

Pat Pagano replied:
> Definitely
> <snip>
> p.s.
> you must read it twice--at least

I definitely recommend Partch's book - it's what
got me started in this whole thing. And I agree
with Pat, but in my case I had to read it about
5 times to finally understand it.

Pat mentions the Just Intonation Network, and David
Doty (who's in charge of it) also wrote a good
introduction called "The Just Intonation Primer".

I've also written a book, called "JustMusic: A New Harmony"
and, although it's not as finished as I want it to be,
I'd be glad to offer you a copy.

If you have access to the web, you can find out a lot
on my website, and there's a hyperlinked microtonal
dictionary - perfect for newcomers. Also many links
to other microtonal sites.

I find that it is much easier to understand just-intonation
ratios thru their prime-factorization. The exponents
of the prime factors are positive for the numerators
(of the ratio expressed as a fraction) and negative
for the denominators. I came up with this myself
about 7 years ago, but getting on the List exposed
me to many others who've done it before.

The prime-factor "2" is generally ignored, because
it only represents octaves. This is the main reason
I began using prime-factorization - calculating
fractional ratios gets complicated very quickly if
you want to use a scale or system that is not very
small and close to the 1:1. Ignoring (i.e., factoring out)
all those powers of 2 simplifies the math immensely.

For example, the ratios you mentioned in your post
would be expressed as: (view in a fixed-width font)

15:8 [2^-3 *] 3^1 * 5^1
3:2 [2^-1 *] 3^1
5:4 [2^-2 *] 5^1
25:24 [2^-3 *] 3^-1 * 5^2

Simple matrix-addition can be used now to calculate
intervals, using only the exponents (the placement
of the exponents indicates the assumed prime-base).
Your example above would be:

"perfect 5th" 3:2 | 1 0 |
"major 3rd" 5:4 + | 0 1 |
--------------
"major 7th" 15:8 | 1 1 |

So it's trivial to start with 25:24 and subtract any
other interval from it, to see what combinations of
any two will result in it.

Here's just one example:

| -1 2 | = 25:24
- | 0 1 | = 5:4
--------------
| -1 1 | = 5:3

So 25:24 is, among other things, a "major 3rd" 5:4
above a "major 6th" 5:3.

You could calculate many other combinations.

Using prime-factorization also gives the model
for using lattice diagrams to represent ratios.
I find this extremely useful as an aid in understanding
the mathematical interrelatioships among the notes.

You'll see lattices used on the List too, so you
might as well understand how they work. I also
have a paper I wrote about that on my site,
although my lattices are a bit different from
the ones others post to the List.

Mine are a variation on rectangular lattices,
the others here use triangular. There's a
good explanation of triangular lattices on
Graham Breed's site (and much more info too):

http://www.cix.co.uk/~gbreed/lattice.htm

My book is *filled* with lattice diagrams.
It started out as an explanation of my theories,
but turned into a very detailed exploration of
historical and contemporary tunings, all represented
on the same kind of lattice. It was a way for me
to see the relationships between all different kinds
of proposed JI tunings.

Now I'm working on how to incorporate ETs into the
lattice. Next comes meantones and well-temperaments.
I think you'll enjoy visiting my site.

- Monzo

|\=/|.-"""-. Joseph L. Monzo...................monz@juno.com
/6 6\ \ http://www.ixpres.com/interval/monzo/homepage.html
=\_Y_/= (_ ;\ c/o Sonic Arts, PO Box 620027, San Diego, CA, USA
_U//_/-/__/// | "...I broke thru the lattice barrier..." |
/monz\ ((jgs; | - Erv Wilson |

___________________________________________________________________
You don't need to buy Internet access to use free Internet e-mail.
Get completely free e-mail from Juno at http://www.juno.com/getjuno.html
or call Juno at (800) 654-JUNO [654-5866]

>From: "Philippe Jonckheere" <Philippe.Jonckheere@euronet.be>
>
> Are there good books explaining those basic things ?
> Shoud I try to find a copy of Partch's 'Genesis of a music' ?
>
A couple of people have already mentioned the Just Intonation Network. You
can get more information at http://www.dnai.com/~jinetwk/ or
JINetwk@dnai.com. There you can order David Doty's excellent Just
Intonation Primer, and, while the Partch is an excellent and necessary part
of any bibliography on the subject, David's introduction is short, to the
point, and much more "user-friendly" for a beginner wanting to learn about
JI. It is also free (except for shipping) to anyone who joins the Just
Intonation Network. The above web site also includes the JI Network
"store," really a catalog of JI-related books, recordings, and other
material that you can order. The books include not only Partch's Genesis,
but also important works by Barbour, Harrison, Chalmers, and others, and
back issues of Xenharmonikon and 1/1.

^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
^ Bill Alves email: alves@hmc.edu ^
^ Harvey Mudd College URL: http://www2.hmc.edu/~alves/ ^
^ 301 E. Twelfth St. (909)607-4170 (office) ^
^ Claremont CA 91711 USA (909)607-7600 (fax) ^
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

Hello Joseph,

>I tried to email this to Phillipe privately,
>but Euronet sent me a message that it will not
>relay to/from spammers. Guess that's what Juno is . . .

I'm sorry for this, I've e-mailed my drastic isp to let your address trough.
(both ways, that's why I'm replying here)

>I definitely recommend Partch's book - it's what
>got me started in this whole thing. And I agree
>with Pat, but in my case I had to read it about
>5 times to finally understand it.

Well, I've ordered it today at amazon, and I wonder how many times I'll have
to read it to grasp something :-)

I'm on my way to your site and to the JI network, I'll be back here after
some homework...

Many thanks for your time !

PhJ