Yahoo Tuning Groups Ultimate Backup tuning intervalic spectrum and rast maqam and bayat-e-tork mode.

Dear ozan

Happy new year , although I don't know you celebrate spring like iran for nowrooz.

Firstly =====about rast intervalic-structure u employ:

1/1 12/11 32/27 513/400 3/2 128/81 243/128 2/1

I have a spreadsheet of serie N/K (n=1,2,3,.....,2k ******** k upto 1200)

I found a good approximation of your structure in k=110 :

1/1 120/110 130/110 141/110 3/2 174/110 197/110 2/1

Which is equal to :

1/1 12/11 13/11 141/110 3/2 87/55 197/110 2/1

The cent difference of mine with yours is equal to :

0 0 -4.93 -0.88 0 1.72 1.5 0

Secondly=====is pitch cluster you wrote a 3D concept of interval positions in a intervalic-space like ji-scaling?

I wrote that My concept of interval-spectrum is limited by sense of changing different intervalic-taste !!

My 13/11 is very near to your 32/27 in taste because of small difference of 5 cent which is not important in melodic sense .

I told before that I think the limits of spectrum are + or - 10 cents from a k-edo degree.

I tested it with a melody in bayat-e-tork mode with my HAMAVA SCALE MAKER software:

0 200 350 500 700 900 1000 1200 (bayat-e-tork mode in 24-edo)

I scaled it to pythagorean order with changing 350 from300 to 400 cents . I heard bayat-e-tork from 300+30 to 300+65 with maximum effect on 45-50.

So u see that for neutral third in for example pythagorean order I have 350±15As an :

intervalic spectrum.

It was interesting that two different mode have intervalic-spectrums

With overlap.

the overlap is the position of mode-confusion.you don't know where are you.a new and unknown modal taste !!

a spectrum contains intervalic degrees of edo with different cardinalities and different ji-systems and others which are near.

we can have good sounding choices in spectrum of digrees of scale but we are free to use it.in some intervals we are more limited like fifth so our spectrum has limits with smaller distance than for example neutral third.

________________________________

From: Ozan Yarman [mailto:ozanyarman@superonline.com]
Sent: Sunday, January 02, 2005 3:15 AM
To: tuning@yahoogroups.com
Subject: Re: [tuning] eastern interval-spectrum theory (was: dear ozan : thanks a lot for reply !!)

Dear brother Mohajeri,

Just a week ago I had the pleasure of receiving Julien Jelaleddin Weiss in my home. He must be in Tahran as we converse, giving a Qanun recital on his own custom-tailored instrument. I was wily enough to make copies of the theoretical sketches of this Frenchman that makes use of koron symbols next to many others.

I myself am not knowledged in Persian art music, but have the feeling that ornate maqams in both our cultures have a similar theoretical basis. Below are the intervals I employ for the Saba maqam:

1/1 12/11 32/27 513/400 3/2 128/81 243/128 2/1

In all actuality, the correct scale should be something like this:

ASCENDING

1/1 11/10 32/27 32/25 3/2 8/5 243/128 2/1

DESCENDING

2/1 16/9 128/81 3/2 9/7 32/27 12/11 1/1

Notice that different ratios are still expressed with the same notes, hence the concept of `pitch-cluster`. Does this have some bearing to the topic at hand?

Cordially,

Ozan

----- Original Message -----

From: Mohajeri Shahin <mailto:shahinm@kayson-ir.com>

To: tuning@yahoogroups.com

Sent: 30 Aralık 2004 Perşembe 11:34

Subject: RE: [tuning] eastern interval-spectrum theory (was: dear ozan : thanks a lot for reply !!)

Dear monzo

Thanks for your reply .

You are right about nature of persian music ,

I think that the concept of interval-spectrum is very applicable for musical cultures like my country which the base of music is melodic . harmony is not so important as melody.

my imagine of interval-Spectrum is a region of cents with 2 limits which gives the sense of a specified interval. The center of spectrum I think is better to be degrees of 12*k edo (k=2,4,6,8,.....) (as a dsfinition).

As I told u and u wrote,the koron of segah is 356 cents which is with a good approximation the 16th degrees of 54-edo (5416=355.5556 cent) .it is in an spectrum which its center is 350 (which is 7221 , 4814 , 247 ).

......

Dear monzo

As the definition in ur ency.:

An interval intermediate in size between the Major Third <http://tonalsoft.com/enc/major3rd.htm> and the Minor Third <http://tonalsoft.com/enc/minor3rd.htm> .

Neutral Thirds measure about 350 cents <http://tonalsoft.com/enc/cents.htm> (¢) and typical examples are 11/9 (347¢), 27/22 (355¢) and 16/13 (359¢).

I myself think theoretically that the best spectrum for neutral third is 350 ± 10 , (340 ......350 ......360) which is the sum of spectrum of minor third with spectrum of great dieses :

But I must test it musically to see IF THE SPECTRUM HAS THE REAL TASTE !

What is ur idea ?

......

Dear ozan ! where are u yourself?what do you think about this?

________________________________

From: monz [mailto:monz@tonalsoft.com]
Sent: Wednesday, December 29, 2004 1:09 AM
To: tuning@yahoogroups.com
Subject: [tuning] eastern interval-spectrum theory (was: dear ozan : thanks a lot for reply !!)

hi Mohajeri,

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

>
> <snip>
>
> It is told that the structure of persian music is pythagorean
> but if it is so?
>
> It is only one choice. Dear monzo has made a page about one
> the tetrachords in segah played by maestro ebadi ....
> It is in 17-edo.

Mohajeri is referring to this webpage:

http://tonalsoft.com/enc/index2.htm?iranian-segah-mode.htm

> We know that 17 is related to 34,51,..... and 51 is near
> to 53.so we may assum that there is a spectrum of edo's
> with 53 in center:
>
> ....... , 50 , 51 , 52 , 53 , 54 , 55 , 56.......

there is some truth to what you say here, in that,
by the point where there are that many divisions of
the "octave", the differences in step-size are so small
that it is not very noticeable (particularly on traditional
persian instruments, which are not accurately tuned in these
temperaments ... forgive me if i'm wrong about this, in my
ignorance of persian music and theory). i.e, the
step-sizes of the temparaments you list here are:

ET ... step-size in cents

50 ... 24
51 ... 23.52941176
52 ... 23.07692308
53 ... 22.64150943
54 ... 22.22222222
55 ... 21.81818182
56 ... 21.42857143

the difference is much more noticeable for the
lower-cardinality ETs, for example:

ET ... step-size in cents

10 ... 120
11 ... 109.0909091
12 ... 100
13 ... 92.30769231

however, it should also be noted that different ETs
approximate JI in different ways.

note that on my webpage, i point out that both 17-edo
and 24-edo give decent approximations to the cents-values
which you measured from Maestro Ebadi's performance.

this is because both of these temperaments give a
good approximation to both the pythagorean intervals
*and* the (approximate) quarter-tones.

often, 53-edo is also admitted into this company
(that is, tuning families which contain 17- and 24-edo),
because it gives a *superb* approximation to pythagorean
tuning. see, for example, the patterns of error-from-JI
under the family of tunings in which the "skhisma"
vanishes, on the colored applet graphic here:

http://tonalsoft.com/enc/index2.htm?bingo.htm&applet

in the case of Maestro Ebadi's pentachord, 53-edo
*does* give a decent approximation to the _koron_
(which Mohajeri measured at 356 cents) -- which
is 16 degrees of 53-edo, or in precise mathematics,
2^(16/53) = ~362.2641509 cents.

however, 53-edo fails to map the 2nd degree of Maestro
Ebadi's pentachord (which Mohajeri measured at 215 cents),
which falls almost exactly between 9 and 10 degrees of
53-edo.

thus, while 53-edo does usually resemble both 17-edo
and 24-edo in many ways, in this particular case it
fails to give a representation of Maestro Ebadi's
performance which is as good as either of them.

i think that what you (Mohajeri), Ozan, and Can Akkoc
are doing with interval-spectrum theory is very interesting.

-monz

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Dear brother Mohajeri,

13:11 is a meaningful interval next to 32:27, but the same cannot be said for others as far as I can see. In any case, I don't know any musician who can differentiate between 141/110 and 513/400 as these pitches are very proximous. 9/7 is a much better harmonic approximation with only 5 cents difference for the 4. degree of Saba Maqam.

I use the term pitch-cluster to signify a tightly-spread bundle of frequencies within a very short time-frame. All of these can be categorized as the same pitch-class, and the relationship of all ranges between two such consequent clusters can be categorized as the same interval-class. The distribution of frequencies is not as 3D, but as 2D along the pitch-continuum axis. Your concept of interval spectrum seems to be the same, but without articulations, vibrato, portamento, etc...

The fact that some `perde` of Maqams vary to a great extent within seyir (melodic excursions) convince me that pitch-clusters come into play more.

I think you should look at Paul Erlich's article on decatonality for harmonic tolerance: http://lumma.org/tuning/erlich/erlich-tFoT.pdf

I have Dr. Akkoc's article in English in PDF format. It's not very long, I can send it to you if you want.

----- Original Message -----
From: Mohajeri Shahin
To: tuning@yahoogroups.com
Sent: 02 Ocak 2005 Pazar 15:32
Subject: [tuning] intervalic spectrum and rast maqam and bayat-e-tork mode.

Dear ozan

Happy new year , although I don't know you celebrate spring like iran for nowrooz.

Firstly =====about rast intervalic-structure u employ:

1/1 12/11 32/27 513/400 3/2 128/81 243/128 2/1

I have a spreadsheet of serie N/K (n=1,2,3,…..,2k ******** k upto 1200)

I found a good approximation of your structure in k=110 :

1/1 120/110 130/110 141/110 3/2 174/110 197/110 2/1

Which is equal to :

1/1 12/11 13/11 141/110 3/2 87/55 197/110 2/1

The cent difference of mine with yours is equal to :

0 0 -4.93 -0.88 0 1.72 1.5 0

Secondly=====is pitch cluster you wrote a 3D concept of interval positions in a intervalic-space like ji-scaling?

I wrote that My concept of interval-spectrum is limited by sense of changing different intervalic-taste !!

My 13/11 is very near to your 32/27 in taste because of small difference of 5 cent which is not important in melodic sense .

I told before that I think the limits of spectrum are + or – 10 cents from a k-edo degree.

I tested it with a melody in bayat-e-tork mode with my HAMAVA SCALE MAKER software:

0 200 350 500 700 900 1000 1200 (bayat-e-tork mode in 24-edo)

I scaled it to pythagorean order with changing 350 from300 to 400 cents . I heard bayat-e-tork from 300+30 to 300+65 with maximum effect on 45-50.

So u see that for neutral third in for example pythagorean order I have 350±15As an :

intervalic spectrum.

It was interesting that two different mode have intervalic-spectrums

With overlap.

the overlap is the position of mode-confusion.you don't know where are you.a new and unknown modal taste !!

a spectrum contains intervalic degrees of edo with different cardinalities and different ji-systems and others which are near.

------------------------------------------------------------------------------

Dear brother Mohajeri,

I myself am not knowledged in Persian art music, but have the feeling that ornate maqams in both our cultures have a similar theoretical basis. Below are the intervals I employ for the Saba maqam:

1/1 12/11 32/27 513/400 3/2 128/81 243/128 2/1

In all actuality, the correct scale should be something like this:

ASCENDING

1/1 11/10 32/27 32/25 3/2 8/5 243/128 2/1

DESCENDING

2/1 16/9 128/81 3/2 9/7 32/27 12/11 1/1

Notice that different ratios are still expressed with the same notes, hence the concept of `pitch-cluster`. Does this have some bearing to the topic at hand?

Cordially,

Ozan

----- Original Message -----

From: Mohajeri Shahin

To: tuning@yahoogroups.com

Sent: 30 Aralık 2004 Perşembe 11:34

Subject: RE: [tuning] eastern interval-spectrum theory (was: dear ozan : thanks a lot for reply !!)

Dear monzo

Thanks for your reply .

You are right about nature of persian music ,

I think that the concept of interval-spectrum is very applicable for musical cultures like my country which the base of music is melodic . harmony is not so important as melody.

……

Dear monzo

As the definition in ur ency.:

An interval intermediate in size between the Major Third and the Minor Third.

Neutral Thirds measure about 350 cents (¢) and typical examples are 11/9 (347¢), 27/22 (355¢) and 16/13 (359¢).

I myself think theoretically that the best spectrum for neutral third is 350 ± 10 , (340 ……350 ……360) which is the sum of spectrum of minor third with spectrum of great dieses :

But I must test it musically to see IF THE SPECTRUM HAS THE REAL TASTE !

What is ur idea ?

……

Dear ozan ! where are u yourself?what do you think about this?

----------------------------------------------------------------------------

hi Mohajeri,

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

Mohajeri is referring to this webpage:

http://tonalsoft.com/enc/index2.htm?iranian-segah-mode.htm

> We know that 17 is related to 34,51,….. and 51 is near
> to 53.so we may assum that there is a spectrum of edo's
> with 53 in center:
>
> ……. , 50 , 51 , 52 , 53 , 54 , 55 , 56…….

ET ... step-size in cents

50 ... 24
51 ... 23.52941176
52 ... 23.07692308
53 ... 22.64150943
54 ... 22.22222222
55 ... 21.81818182
56 ... 21.42857143

the difference is much more noticeable for the
lower-cardinality ETs, for example:

ET ... step-size in cents

10 ... 120
11 ... 109.0909091
12 ... 100
13 ... 92.30769231

however, it should also be noted that different ETs
approximate JI in different ways.

note that on my webpage, i point out that both 17-edo
and 24-edo give decent approximations to the cents-values
which you measured from Maestro Ebadi's performance.

this is because both of these temperaments give a
good approximation to both the pythagorean intervals
*and* the (approximate) quarter-tones.

http://tonalsoft.com/enc/index2.htm?bingo.htm&applet

however, 53-edo fails to map the 2nd degree of Maestro
Ebadi's pentachord (which Mohajeri measured at 215 cents),
which falls almost exactly between 9 and 10 degrees of
53-edo.

i think that what you (Mohajeri), Ozan, and Can Akkoc
are doing with interval-spectrum theory is very interesting.

-monz

------------------------------------------------------------------------------
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intervalic spectrum and rast maqam and bayat-e-tork mode.

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

🔗Ozan Yarman <ozanyarman@superonline.com>