Yahoo Tuning Groups Ultimate Backup tuning intervals of the first tetrachord of "SEGAH" mode of iranian music

Dear friends

I calculated these intervals of the first tetrachord of "SEGAH" mode
played by maestro ebadi (an Iranian traditional music master)by digital
tuner. What is your opinions?

Fa 0 cent

Sol +15 cent

La b +56 cent ( an interval called LA KORON)

Si b +1.57 cent

Do +9.5 cent

Sori and koron are (1/4 tone - interval) of Iranian music but never
tuned to 50 cent.

Shahin mohajeri

tombak player and researcher , composer

www.geocities.com/acousticsoftombak

my tombak musics : www.rhythmweb.com/gdg

🔗monz <monz@attglobal.net>

hi Mohajeri,

-- In tuning@yahoogroups.com, "Mohajeri Shahin" <shahinm@k...> wrote:
>
>
> Dear friends
>
> I calculated these intervals of the first tetrachord
> of "SEGAH" mode played by maestro ebadi (an Iranian
> traditional music master) by digital tuner. What is
> your opinions?
>
>
>
> Fa ........ 0 cent
>
> Sol ..... +15 cent
>
> La b ... +56 cent ( an interval called LA KORON)
>
> Si b ..... +1.57 cent
>
> Do ....... +9.5 cent
>
>
> Sori and koron are (1/4 tone - interval) of
> Iranian music but never tuned to 50 cent.

hmmm ... fa:do (F:C) is not a tetrachord, it's
a pentachord.

anyway, to be clear, is this exactly what you mean? ...

.............. ------ cents -------

Do .... C ... 700 + 9.5 = ... 709.5
Si b .. Bb .. 500 + 1.57 = .. 501.57
La b .. Ab .. 300 + 56 = .... 356
Sol ... G ... 200 + 15 = .... 215
Fa .... F ..... 0 .... = ...... 0

-monz

🔗Mohajeri Shahin <shahinm@kayson-ir.com>

Hi monzo

Yes، you are right about tetrachord ….i made a mistake …. forgive me!!!!

.. and it is very interesting that due to different Iranian instruments of one kind

We have different intervals with changes in cents( such as TONE )( I think because of timber of instrument …..)

For example the change 0f +15 cent I wrote you for G is the average of different samples.

-----Original Message-----
From: monz [mailto:monz@attglobal.net]
Sent: Thursday, July 29, 2004 12:10 AM
To: tuning@yahoogroups.com
Subject: [tuning] Re: intervals of the first tetrachord of "SEGAH" mode of iranian music

hi Mohajeri,

-- In tuning@yahoogroups.com, "Mohajeri Shahin" <shahinm@k...> wrote:

> Dear friends

> I calculated these intervals of the first tetrachord

> of "SEGAH" mode played by maestro ebadi (an Iranian

> traditional music master) by digital tuner. What is

> your opinions?

> Fa ........ 0 cent

> Sol ..... +15 cent

> La b ... +56 cent ( an interval called LA KORON)

> Si b ..... +1.57 cent

> Do ....... +9.5 cent

> Sori and koron are (1/4 tone - interval) of

> Iranian music but never tuned to 50 cent.

hmmm ... fa:do (F:C) is not a tetrachord, it's

a pentachord.

anyway, to be clear, is this exactly what you mean? ...

.............. ------ cents -------

Do .... C ... 700 + 9.5 = ... 709.5

Si b .. Bb .. 500 + 1.57 = .. 501.57

La b .. Ab .. 300 + 56 = .... 356

Sol ... G ... 200 + 15 = .... 215

Fa .... F ..... 0 .... = ...... 0

-monz

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🔗monz <monz@tonalsoft.com>

--- In tuning@yahoogroups.com, "Mohajeri Shahin" <shahinm@k...> wrote:

> -----Original Message-----
> From: monz [mailto:monz@a...]
> Sent: Thursday, July 29, 2004 12:10 AM
> To: tuning@yahoogroups.com
> Subject: [tuning] Re: intervals of the first tetrachord of "SEGAH"
mode of iranian music
>
>
>
> hi Mohajeri,
>
>
>
>
>
> -- In tuning@yahoogroups.com, "Mohajeri Shahin" <shahinm@k...>
wrote:
>
>
> > Dear friends
> >
>
> > I calculated these intervals of the first tetrachord
> > of "SEGAH" mode played by maestro ebadi (an Iranian
> > traditional music master) by digital tuner. What is
> > your opinions?
> >
> >
> > Fa ........ 0 cent
> > Sol ..... +15 cent
> > La b ... +56 cent ( an interval called LA KORON)
> > Si b ..... +1.57 cent
> > Do ....... +9.5 cent
>
> > Sori and koron are (1/4 tone - interval) of
>
> > Iranian music but never tuned to 50 cent.
>
>
> hmmm ... fa:do (F:C) is not a tetrachord, it's
>
> a pentachord.
>
>
>
> anyway, to be clear, is this exactly what you mean? ...
>
>
>
> .............. ------ cents -------
>
> Do .... C ... 700 + 9.5 = ... 709.5
> Si b .. Bb .. 500 + 1.57 = .. 501.57
> La b .. Ab .. 300 + 56 = .... 356
> Sol ... G ... 200 + 15 = .... 215
> Fa .... F ..... 0 .... = ...... 0
>
>
>
> -monz

the proportion of this pentachord is roughly
30 : 34 : 37 : 40 : 45 . i.e., this is the set
of smallest numbers which give a good approximation
of the integers in the "ideal" JI proportion of
the pentachord.

more exact figures for your cents values are:
30 : 33.96689085 : 36.84909448 : 40.08152779 : 45.19654528 .

to create the lattice, we use the integer
approximations and divide all numbers
by 30 to make that note the 1/1:

30/30 : 34/30 : 37/30 : 40/30 : 45/30 =

1/1 : 17/15 : 37/30 : 4/3 : 3/2

then prime-factor the numbers and write the
exponents of the prime-factors (in order of the
prime-series) as a monzo, thus:

2 3, 5 7 11, 13 17 19, 23 29 31, 37

[-1 1, > (3/2)
[ 2 -1, > (4/3)
[-1 -1, -1 0 0, 0 0 0, 0 0 0, 1 > (37/30)
[ 0 -1, -1 0 0, 0 1 > (17/15)
[ 0 > (1/1)

usually i like to end the monzo at the prime-limit
of that ratio, as i did above.

but in illustrating vector calculations it's more
helpful to make all of them the same length.

since this pentachord makes use of the two higher
primes 17 and 37, but otherwise is 5-limit, there
are a lot of useless zeros in the monzos, so in
this case it's better to use comma-marks after every
number and show only the exponent for primes which
are <>0 , and explicitly tell which primes *are*
being used.

so this pentachord notated that way is:

2,3,5,17,37-monzo

[-1, 1, 0, 0, 0 > (3/2)
[ 2, -1, 0, 0, 0 > (4/3)
[-1, -1, -1, 0, 1 > (37/30)
[ 0, -1, -1, 1, 0 > (17/15)
[ 0, 0, 0, 0, 0 > (1/1)

this matrix of monzos is virtually a lattice already.

i'm making a webpage about this, which has a lattice.

i'll also go into some ET approximations of it
when i have time.

-monz