Fwd: 7 - Limit Just Intonation

Subject: Fwd: 7 - Limit Just Intonation

This question just appeared on the PIanotech list.

Can anybody help this piano tuner? He needs the offsets from the TET values, not the cents size measured from C..... Get it? .

He is Thomas Cole tcole@cruzio.com

thanks in advance. Paul Bailey

Begin forwarded message:

> Dear historical temperament mavens,
>
> I've been asked to tune a "tack" piano according to Lou Harrison's > instructions (Cinna, 1955). The schema calls for tuning intervals as > ratios and I'd like to know if there is a way to convert these > fractional numbers to offsets. I have only a short window of time on > stage (Sat, 1/20) and it would be very easy to do if I can use RCT.
>
> Tom Cole

He must mean detuning each of the 12 tones on his tuner as much from the
"zero cents default offset" for 12-tET keys as required by the temperament
in question.

Oz.

----- Original Message -----
From: "Paul Bailey" <pbailey@sbcglobal.net>
To: <tuning@yahoogroups.com>
Sent: 18 Ocak 2007 Per�embe 13:59
Subject: [tuning] Fwd: 7 - Limit Just Intonation

> Subject: Fwd: 7 - Limit Just Intonation
>
>
> This question just appeared on the PIanotech list.
>
> Can anybody help this piano tuner? He needs the offsets from the TET
> values, not the cents size measured from C..... Get it? .
>
>
> He is Thomas Cole tcole@cruzio.com
>
>
> thanks in advance. Paul Bailey
>
> Begin forwarded message:
>
> > Dear historical temperament mavens,
> >
> > I've been asked to tune a "tack" piano according to Lou Harrison's
> > instructions (Cinna, 1955). The schema calls for tuning intervals as
> > ratios and I'd like to know if there is a way to convert these
> > fractional numbers to offsets. I have only a short window of time on
> > stage (Sat, 1/20) and it would be very easy to do if I can use RCT.
> >
> > Tom Cole
>
>
>

The base-2 log of a frequency ratio times 1200 is cents.

Most calculators only have base-10 or base-e (ln) logs.
But you can convert log bases using the following formula:

log-base-whatever(your number) / log-base-whatever(base you want)

To find the base-2 log of 8, this would be:

log(8)/log(2)

All of this can be done in google. 7/4, for example, is

http://www.google.com/search?q=log(7%2F4)%2Flog(2)*1200

968.825906 cents.

To find offsets from 12-equal, just subtract from the nearest
multiple of 100 cents.

http://www.google.com/search?q=log(7%2F4)%2Flog(2)*1200-1000

-31.1740935 cents from a minor 7th in this case.

By the way, I'm not familiar with Lou's tuning off the top of
my head, but just intonation can be tuned by ear probably just
as fast as it can with Cybertuner, if you practice it just once
or twice. One of the nice things about just intonation is that
it's great fun to tune!

-Carl

Since he's on a time limitation, explaining the procedure
is not really going to help -- what he needs is the raw data.

I wrote about this tuning here back in 1999, because the
tuning guide published in _Xenharmonikon_ (and presumably
in the score itself?) contains an error. Here are my posts
and the relevant responses:

/tuning/topicId_1533.html#1533
/tuning/topicId_1544.html#1544?var=0&l=1
/tuning/topicId_1544.html#1561
/tuning/topicId_1533.html#1569

So here's the data Tom needs:

(If viewing on the Yahoo web interface, click on the
"Option" link at the top right under the date, and then
click on the "Use Fixed Width Font" link which appears
under that.)

note ratio cents offset from 12-edo
G 1/ 1 0
Ab 16/15 11.73
A 10/ 9 -17.6
Bb 7/ 6 -33.13
B 5/ 4 -13.69
C 4/ 3 -1.96
C# 25/18 -31.28
D 3/ 2 1.96
Eb 8/ 5 13.69
E 5/ 3 -15.64
F 7/ 4 -31.17
F# 15/ 8 -11.73

-monz
http://tonalsoft.com
Tonescape microtonal music software

--- In tuning@yahoogroups.com, Paul Bailey <pbailey@...> wrote:
>
> Subject: Fwd: 7 - Limit Just Intonation
>
>
> This question just appeared on the PIanotech list.
>
> Can anybody help this piano tuner? He needs the offsets
> from the TET values, not the cents size measured from C
> ..... Get it? .
>
>
> He is Thomas Cole tcole@...
>
>
> thanks in advance. Paul Bailey
>
> Begin forwarded message:
>
> > Dear historical temperament mavens,
> >
> > I've been asked to tune a "tack" piano according to
> > Lou Harrison's instructions (Cinna, 1955). The schema
> > calls for tuning intervals as ratios and I'd like to
> > know if there is a way to convert these fractional numbers
> > to offsets. I have only a short window of time on stage
> > (Sat, 1/20) and it would be very easy to do if I can use
> > RCT.
> >
> > Tom Cole

--- In tuning@yahoogroups.com, "monz" <monz@...> wrote:

> So here's the data Tom needs:
>
> (If viewing on the Yahoo web interface, click on the
> "Option" link at the top right under the date, and then
> click on the "Use Fixed Width Font" link which appears
> under that.)

Oops, my bad ... i should have put plus signs on
the offsets which are higher than the 12-edo values:

note ratio cents offset from 12-edo
G 1/ 1 0
Ab 16/15 + 11.73
A 10/ 9 - 17.6
Bb 7/ 6 - 33.13
B 5/ 4 - 13.69
C 4/ 3 - 1.96
C# 25/18 - 31.28
D 3/ 2 + 1.96
Eb 8/ 5 + 13.69
E 5/ 3 - 15.64
F 7/ 4 - 31.17
F# 15/ 8 - 11.73

-monz
http://tonalsoft.com
Tonescape microtonal music software

> Since he's on a time limitation, explaining the procedure
> is not really going to help -- what he needs is the raw data.
//
> > > Dear historical temperament mavens,
> > >
> > > I've been asked to tune a "tack" piano according to
> > > Lou Harrison's instructions (Cinna, 1955). The schema
> > > calls for tuning intervals as ratios and I'd like to
> > > know if there is a way to convert these fractional numbers
> > > to offsets. I have only a short window of time on stage
> > > (Sat, 1/20) and it would be very easy to do if I can use
> > > RCT.

Monz: He has a time limitation for doing the tuning (which is
why he's using RCT), not for figuring out what it should be.
Don't you think knowing how to do this trivial calculation is
useful information?

-Carl

Hi Carl,

--- In tuning@yahoogroups.com, "Carl Lumma" <clumma@...> wrote:

> Monz: He has a time limitation for doing the tuning (which is
> why he's using RCT), not for figuring out what it should be.
> Don't you think knowing how to do this trivial calculation is
> useful information?

Yes, sure. Sorry, i guess my reply seemed a little snooty.

Anyway, now he has the data and the method, so maybe we
should hope to see him hanging around here soon?

;-)

-monz
http://tonalsoft.com
Tonescape microtonal music software