Two 31-equals spaced 15.42 cents apart so as to achieve an NI interval

Inspired by Margo, I came up with a splendid maqam tuning with at least one
nobly intoned ratio.

First, calculate the noble mediant between 27:25 and 14:13.

(27+14)*phi / (25+13)*phi=131.55 cents

In SCALA, type:

equal 31

copy 0 1

move

131.55

merge

1

Voila!

Oz.

Inspired by Margo, I came up with a splendid maqam tuning with at least one
nobly intoned ratio.

First, calculate the noble mediant between 27:25 and 14:13.

(27+14)*phi / (25+13)*phi=131.55 cents

In SCALA, type:

equal 31

copy 0 1

move

131.55

normalize

merge

1

Voila!

Oz.

Hi Oz,

Lest I be accused of spawning a whole new brand of musical numerology,
I should empasise that not all noble mediants result in nobly intoned
intervals, just as not all whole number ratios result in justly
intoned intervals.

I personally don't find that noble mediant to sound like a point of
maximum complexity balanced between two justly intoned intervals, even
though, in it's simplest form it is also the noble mediant of 1/1 and
13/12.

-- Dave Keenan

--- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@...> wrote:
>
> Inspired by Margo, I came up with a splendid maqam tuning with at
least one
> nobly intoned ratio.
>
> First, calculate the noble mediant between 27:25 and 14:13.
>
> (27+14)*phi / (25+13)*phi=131.55 cents
>
> In SCALA, type:
>
> equal 31
>
> copy 0 1
>
> move
>
> 131.55
>
> normalize
>
> merge
>
> 1
>
> Voila!
>
> Oz.
>

--- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@...> wrote:
>
> Inspired by Margo, I came up with a splendid maqam tuning with at
least one
> nobly intoned ratio.
>
> First, calculate the noble mediant between 27:25 and 14:13.
>
> (27+14)*phi / (25+13)*phi=131.55 cents

Oops! I just noticed this formula is wrong.

It should have been

14+(27*phi)
----------- = 132.04 cents
13+(25*phi)

(not that it would make any audible difference)

In lowest terms this is

1+(13*phi)
---------- = 132.04 cents
1+(12*phi)

Note that it is only the larger-numbered ratio whose numerator and
denominator are multiplied by phi.

But still I do not find it to be nobly intoned, nor anything else
below about 200 cents, except possibly around 70 to 90 cents, which is
not predicted by the noble mediant rule-of-thumb, but is predicted by
Paul Erlich's Harmonic Entropy.

-- Dave Keenan

>
> In SCALA, type:
>
> equal 31
>
> copy 0 1
>
> move
>
> 131.55
>
> normalize
>
> merge
>
> 1
>
> Voila!
>
> Oz.
>

Thanks for the correction, and for the comments Dave.

Oz.

----- Original Message -----
From: "Dave Keenan" <d.keenan@bigpond.net.au>
To: <tuning@yahoogroups.com>
Sent: 16 Kas�m 2007 Cuma 1:55
Subject: [tuning] Re: Two 31-equals spaced 15.42 cents apart so as to
achieve an NI interval

> --- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@...> wrote:
> >
> > Inspired by Margo, I came up with a splendid maqam tuning with at
> least one
> > nobly intoned ratio.
> >
> > First, calculate the noble mediant between 27:25 and 14:13.
> >
> > (27+14)*phi / (25+13)*phi=131.55 cents
>
> Oops! I just noticed this formula is wrong.
>
> It should have been
>
> 14+(27*phi)
> ----------- = 132.04 cents
> 13+(25*phi)
>
> (not that it would make any audible difference)
>
> In lowest terms this is
>
> 1+(13*phi)
> ---------- = 132.04 cents
> 1+(12*phi)
>
> Note that it is only the larger-numbered ratio whose numerator and
> denominator are multiplied by phi.
>
> But still I do not find it to be nobly intoned, nor anything else
> below about 200 cents, except possibly around 70 to 90 cents, which is
> not predicted by the noble mediant rule-of-thumb, but is predicted by
> Paul Erlich's Harmonic Entropy.
>
> -- Dave Keenan
>
>
> >
> > In SCALA, type:
> >
> > equal 31
> >
> > copy 0 1
> >
> > move
> >
> > 131.55
> >
> > normalize
> >
> > merge
> >
> > 1
> >
> > Voila!
> >
> > Oz.
> >
>
>