Just checking: Monzo's alternative notation to Johnston's

Or maybe it wasn't Monzo's, I don't remember but in any case, I want to
make sure I'm getting it straight.

so tell me if I'm wrong:

Any note notated in the familiar fashion (i.e. C, F, C#, E, G#, etc.)
is derived via a 3-limit line from C. So any harmony notated in the
standard fashion is 3-limit.

Then, some other accidental (like +/-) lowers (or raises) any of those
tones so that a 5-limit interval is formed.

Hence, C and E- (or C+ and E) form a 5/4 major third.
A- and C form a 6/5 minor third.

Then some other accidental, like 7 and it's weirdo-upside-down
counterpart, raise or lower a 3-limit interval changing it into a 7-limit
interval.

Hence, C and Bb7 (or CL and Bb) form 7/4s
Or, C and Eb7 forms a 7/6.

And so on, with an "11-izer" accidental, and so on through the primes.

Am I right?

Christopher Bailey

--- In tuning@yahoogroups.com, Christopher Bailey <cb202@c...> wrote:
>
> Or maybe it wasn't Monzo's, I don't remember but in any case, I
want to
> make sure I'm getting it straight.

this?

http://sonic-arts.org/dict/hewm.htm

>
> so tell me if I'm wrong:
>
>
> Any note notated in the familiar fashion (i.e. C, F, C#, E, G#,
etc.)
> is derived via a 3-limit line from C. So any harmony notated in the
> standard fashion is 3-limit.
>
> Then, some other accidental (like +/-) lowers (or raises) any of
those
> tones so that a 5-limit interval is formed.
>
> Hence, C and E- (or C+ and E) form a 5/4 major third.
> A- and C form a 6/5 minor third.
>
>
>
>
> Then some other accidental, like 7 and it's weirdo-upside-down
> counterpart, raise or lower a 3-limit interval changing it into a
7-limit
> interval.
>
> Hence, C and Bb7 (or CL and Bb) form 7/4s
> Or, C and Eb7 forms a 7/6.
>
>
>
>
>
> And so on, with an "11-izer" accidental, and so on through the
primes.
>
>
>
>
> Am I right?

yes. dave keenan and george secor developed a hugely extended version
of this notation system on the tuning-math list . . .

hi Christopher (and paul),

> From: "wallyesterpaulrus" <wallyesterpaulrus@yahoo.com>
> To: <tuning@yahoogroups.com>
> Sent: Sunday, May 11, 2003 6:35 PM
> Subject: [tuning] Re: Just checking: Monzo's alternative notation to
Johnston's
>
>
> --- In tuning@yahoogroups.com, Christopher Bailey <cb202@c...> wrote:
> >
> > Or maybe it wasn't Monzo's, I don't remember but
> > in any case, I want to make sure I'm getting it
> > straight.
>
> this?
>
> http://sonic-arts.org/dict/hewm.htm

paul gave you the reference i would have.

> > so tell me if I'm wrong:
> >
> >
> > Any note notated in the familiar fashion (i.e.
> > C, F, C#, E, G#, etc.) is derived via a 3-limit
> > line from C. So any harmony notated in the standard
> > fashion is 3-limit.
> >
> > Then, some other accidental (like +/-) lowers
> > (or raises) any of those tones so that a 5-limit
> > interval is formed.
> >
> > Hence, C and E- (or C+ and E) form a 5/4
> > major third. A- and C form a 6/5 minor third.

yep.

> > Then some other accidental, like 7 and it's
> > weirdo-upside-down counterpart, raise or lower
> > a 3-limit interval changing it into a 7-limit
> > interval.
> >
> > Hence, C and Bb7 (or CL and Bb) form 7/4s
> > Or, C and Eb7 forms a 7/6.

i prefer to use the greater-than and less-than signs
for 7, thus: C and Bb< (or C> and Bb) form 7/4s,
and C and Eb< (or C> and Eb) form 7/6s.

> > And so on, with an "11-izer" accidental, and so on
> > through the primes.

my HEWM notation is only defined up to the 11-limit.
Daniel Wolf published (in _1/1_) a set of accidental
pairs thru the 23-limit -- it's on my webpage.

> > Am I right?
>
> yes. dave keenan and george secor developed a
> hugely extended version of this notation system
> on the tuning-math list . . .

quite an undertaking ... i haven't studied it closely
enough myself yet.

-monz