Yahoo Tuning Groups Ultimate Backup tuning Re: Mohajira

On 28 April 2010 Graham wrote :

> >> At 7 notes, "mohajira" is interesting. It's generated by a neutral
> >> third, being the exact division of whatever fifth you like. > There are
> >> no very small intervals and, in 31-equal, every interval > approximates
> >> something in the 11-limit.
> >
> > (Gene) : Is "mohajira" a good name for the 31&55 temperament also > called
> > semififths I recently mentioned to Jacques Dudon, or just the name
> > for a seven-note scale?
>
> (Graham) : In the 5-limit I've called that "Vicentino" because it > fits is 24 note
> enharmonic. It's also a 31&24 temperament-like thing. Outside that,
> I think it's Jacques' name, so it should be his call.
>
> Here are some details for the 11-limit version, which is currently
> called "semififth":
>
> 1201.165 cents period
> 348.815 cents generator
>
> mapping by period and generator:
> [<1, 1, 0, 6, 2],
> <0, 2, 8, -11, 5]>

Hi Graham, Gene, and all,

"Mohajira" is many things :
- mainly, as Graham said, it is a chain of neutral thirds ;
- that shows many possible cycles and MOS ;
- with most common DE divisions at 3 > 7 > 10 > 17 > 24 > 31 > 55 tones per octave ;
- limited to 7 notes it's a scalar structure of the form [s L s L s L s] ;
- it's a family of scales, with many JI versions ;
- it's also a tetrachord of the form [s L s] (appearing three times in the 7 notes scale) ;
(such a tetrachord was mentionned by Ibn-sina, if I remember well 13/12 39/32 4/3 or symmetrical - it's in John Chalmers's book) ;
- when extended to nine notes and omitting the second and the one before the last (x^ 0 -- 2 3 4 5 6 7 -- 9), it generates a Rast scale ;
- this Rast model contains in itself the mapping of the 3, 5 and 11th harmonics (= x^2, x^8, x^6) ;
- it's an infinity of converging recurrent series of the form x^5 = x^4 + 1/2 such as :
[18 22 26 32 39 48 59 72 88 ... based on the recurrent and natural differential coherence of the neutral third :
x^5 - x^4 = 1/2 (ex. 48 - 39 = 9 = 18/2, 59 - 48 = 11 = 22/2 etc.)
where neutral thirds tend towards 1.2232849566 or 348.91261178844 c. = the classic "fractal Mohajira" ;
- it's a fractal waveform applying this algorithm but not yet resolved geometrically to this day (5th degree equations are sometimes complex) ;
- however it has many waveform substitutes ;
- it's also a galaxy of other fractals ;
- any half of a meantone generator is a Mohajira ;
- any triple of a Miracle generator is a Mohajira ;
- and as a temperament it has also several meta-temperaments equivalents.

Mohajira means "migratory" in arabian and it was named like that because of its circular character and the numerous exotic modes the series contains, whose harmonies, I felt, were travelling between many cultures.
If someone wants to call a linear temperament generated by a neutral third "Mohajira", I have no objection.
I was probably the first one to do it, in the form of harmonic temperaments issued from recurrent sequences, or others, from my earliest photosonic disks.
However I have no claims about extended octave versions.
Is this one a TOP tuning ? (is it yours Graham ?)
My only remark is that primes 13, 17, 19 are missing, while they could be easily approximated at octaves by -1, -10, -6 :
<0, 2, 8, -11, 5, -1, -10, -6] would be a more complete mapping.

If I refer to the values Graham mentions here :
1201.165 cents period
348.815 cents generator
This is clearly a Mohajira tuning to me, and it may be another example, after meantone, of a linear temperament that has valid fractal solutions and vice-versa.
- - - - - - -
Jacques

🔗Jacques Dudon <fotosonix@...>

🔗Ozan Yarman <ozanyarman@...>

🔗Graham Breed <gbreed@...>

On 30 April 2010 02:23, Jacques Dudon <fotosonix@...> wrote:

> - any half of a meantone generator is a Mohajira ;

Even an equal division of a fourth? I'm calling that "semaphore"
which is probably a corruption of "semifourths" meaning the fourth is
equally divided. That's something I can move down to the 5-limit.

http://x31eq.com/cgi-bin/rt.cgi?ets=19+5&limit=7

> Is this one a TOP tuning ? (is it yours Graham ?)

If I gave it, and octaves are tempered, it'll be TOP-RMS

> My only remark is that primes 13, 17, 19 are missing, while
> they could be easily approximated at octaves by -1, -10, -6 :
> <0, 2, 8, -11, 5, -1, -10, -6] would be a more complete mapping.

That makes it here as "Semififth 3 dimensions higher".

http://x31eq.com/cgi-bin/rt.cgi?ets=7+31&limit=19

I can change "semififth" to "mohajira" and make those extra dimensions
explicit. But I'll leave the 5-limit contorted class as "Vicentino"
because he did get there first.

Graham

🔗genewardsmith <genewardsmith@...>

🔗Graham Breed <gbreed@...>

🔗jacques.dudon <fotosonix@...>

Ooops, sorry, I thought the meantone generator here as a fifth. But obviously it's the fourth that's considered as generator.
So I should have said "any half of a meantone fifth is a mohajira", but actually I think it's not a totally satisfying statement if I don't precise the range.

--- In tuning@yahoogroups.com, Graham Breed <gbreed@...> wrote:
>
> On 30 April 2010 02:23, Jacques Dudon <fotosonix@...> wrote:
>
> > - any half of a meantone generator is a Mohajira ;
>
> Even an equal division of a fourth? I'm calling that "semaphore"
> which is probably a corruption of "semifourths" meaning the fourth is
> equally divided. That's something I can move down to the 5-limit.
>
> http://x31eq.com/cgi-bin/rt.cgi?ets=19+5&limit=7

Haha, I must have a look to that one also !

> > Is this one aÂ TOP tuning ?Â Â (is it yours Graham ?)
>
> If I gave it, and octaves are tempered, it'll be TOP-RMS
>
> > My only remark is that primes 13, 17, 19 are missing, while
> > they could be easily approximated at octaves by -1, -10, -6 :
> > <0, 2, 8, -11, 5, -1, -10, -6] Â would be a more complete mapping.
>
> That makes it here as "Semififth 3 dimensions higher".
>
> http://x31eq.com/cgi-bin/rt.cgi?ets=7+31&limit=19

Thanks a lot ! very interesting, now we see that it comes even closer to my main fractal of 348.91261179 c., and the octave to 1200 c. !

> I can change "semififth" to "mohajira" and make those extra dimensions
> explicit. But I'll leave the 5-limit contorted class as "Vicentino"
> because he did get there first.
>
> Graham

Perfect !
- - - - - -
Jacques

🔗genewardsmith <genewardsmith@...>

🔗Ozan Yarman <ozanyarman@...>

Jacques, not that this is obvious at first, but Arabic Rast is not the
"norm" in the world that you should select it as the standard over
other intonations of that maqam which you, probably unintentionally,
stacked aside as "ancillary" when pointing out the need to specify its
Turkishness for the distinction. For what it's worth, if there is a
standard sought, it should rather be the Turkic-Iranian version of
Rast for having a performance tradition and repertory that far exceeds
her Arabic counterpart by two centuries.

While not wanting to seem nationalistic in the least - for I am
particularly against non-Islamic notions of describing a society
(morals especially) - I can furthermore state that the inclination to
Arabicize Rast and other maqams over their much more established
Turkic and Iranian intonational renditions is, I fear, rather due to
some "latter-day imperialist mentality" persisting from the days of
the invasion and occupation of the homelands of Arabs, Berbers and
Beduouins by Western powers, sometimes, and perhaps still so, along
with the ignominous collaboration of their indigenous populations.

Please do not take this evaluation as personal, for I do not imply
your person one bit! It might in fact be nothing more than a residual
habit of the Western way of academical thinking.

The difference between the genera, that is, of the Arabic versus the
Turkish Rast, appears to be not a confusion, but a matter of taste
based on culture, memetic and ethnicity. Standardizing a maqam
intonation over another also bears the risk of exalting a genetic pool
over another, which I'm sure you didn't mean!

Cordially,
Oz.

✩ ✩ ✩
www.ozanyarman.com

On May 1, 2010, at 12:10 AM, jacques.dudon wrote:

> Of course I am talking of Arabic Rast, I would have precised
> "Turkish Rast" otherwise. In short (??), do you have any explanation/
> or comments about this old confusion of genera Ozan ?
>
> --- In tuning@yahoogroups.com, Ozan Yarman <ozanyarman@...> wrote:
>>
>> In Turkish Rast, you don't have such a low netural third. Our perde
>> segah is most of the time noticably sharper than the Arabic usage.
>>
>> Oz.
>>
>> âœ© âœ© âœ©
>> www.ozanyarman.com
>>
>> On Apr 30, 2010, at 11:57 AM, Jacques Dudon wrote:
>>
>
>>> Sorry, I meant (x^ 0 -- 2 3 4 5 6 -- 8) for Rast, and x^5 for the
>>> 11th h. of course.
>>> It means also that the scale structures of Rast and Mohajira have a
>>> difference on only one tone :
>>> x^1 of Mohajira is replaced by x^8 in Rast (the first neutral third
>>> is replaced by a major third).
>>> - - - - - - -
>>> Jacques
>
>
>
>
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🔗Jacques Dudon <fotosonix@...>

Thanks Ozan to share your lights on this (I think rather complex)
subject !

Of course you can imagine that I may have heard "different sounds of
bells" from arabic music masters,
and it is always interesting to hear several sounds rather than just
one, a claim true microtonalists should never cease to have.
I know that the formulation of my question was rather clumsy, when in
fact I always have been convinced that there is nowhere something
like this so-called "confusion of genera" except perhaps in some
western musicologists limited understanding - and in the fact that
this same name "Rast" is commonly used to describe very different
modes and in very different cultures and styles of music
(what the maqamat names would be refering to for the Uyghurs would be
another example...).
However one thing still confuses me in your answer, is your mention
of a" Turkish-Iranian version of Rast" - I never heard of "Rast"
concerning Persian music (but I 'm far from knowing everything !).
To come back to Mohajira what is certain anyway, and you will rectify
if I'm wrong, is that intervals such as E half-b / arabic Segah /
Sikah / Wusta Zalal / Mi koron /or "neutral thirds" to use the
western name are present, in various versions and in different modes
and musical styles, in the three cultures.
Note also that I am just as fond of the ("turkish") "perde segah",
who is present in many of my middle-east tunings ! ;)

Cordially,
- - - - - - - -
Jacques

Ozan Yarman wrote :

Please do not take this evaluation as personal, for I do not imply
your person one bit! It might in fact be nothing more than a residual
habit of the Western way of academical thinking.

Cordially,
Oz.

âœ© âœ© âœ©
www.ozanyarman.com

🔗Ozan Yarman <ozanyarman@...>

Dear Jacques,

There appears to be some confusion here. To my knowledge, There is
indeed a Rast-Panchgah mode in Iranian music, which is in fact, just
like the other Dastgahs in usage, formulated rigidly somewhere in the19th Century as a coagulation of both Rast and Panchgah, the latter
differing from the former in principle with only a single alteration
of the fourth degree of the scale (F# instead of F in a C major
setting). We have Rast and Penchgah defined seperately, but the nuance
is a matter of taste in the case of Iran.

You can hear a sample of the Iranian rendition of Rast here:

http://itunes.apple.com/gb/album/national-vocal-radifs-iranian/id331938258

Not surprisingly, the Iranian sphere of cultural influence includes
the Turkics in Iran as well as the mugham traditions in Azarbaijan and
similitudes in Transoxania (Uigurs seem to be Turkic too). While the
perde segah here is noticably lower than our occasional understanding of Turkish segah in Rast, it is still higher than the Arabic
rendition. In effect, the categorization of Iranian and Turkic
intonations under the same heading does great justice in terms of
musicology not only because of the likeness of intonational effect,
but more so because Ottomans and Safavids have a sort of common
Islamic cultural root as the basis of the formation of their
respective court and sufi musics as well as music theory which
persists to this day.

Even with all the diversity in the Middle East regarding the different
execution of maqams whose names remain the same, such does not seem
the case with Rast, the mother of all maqams. Forsooth, Rast is one of
those maqams that remains more or less the same mode throughout,
characterized only with perde inflexions (segah, ajem and evdj
especially) peculiar to the region it has been adapted to. This is much like a Persian word being adapted into Turkish, Arabic, Urdu,
Kurdish, Assyrian, etc... with different pronounciations but same or
similar meanings.

Cordially,
Oz.

✩ ✩ ✩
www.ozanyarman.com

On May 2, 2010, at 1:52 PM, Jacques Dudon wrote:

>
>
> Thanks Ozan to share your lights on this (I think rather complex)
> subject !
>
> Of course you can imagine that I may have heard "different sounds of
> bells" from arabic music masters,
> and it is always interesting to hear several sounds rather than just
> one, a claim true microtonalists should never cease to have.
> I know that the formulation of my question was rather clumsy, when
> in fact I always have been convinced that there is nowhere something
> like this so-called "confusion of genera" except perhaps in some
> western musicologists limited understanding - and in the fact that
> this same name "Rast" is commonly used to describe very different
> modes and in very different cultures and styles of music
> (what the maqamat names would be refering to for the Uyghurs would
> be another example...).
> However one thing still confuses me in your answer, is your mention
> of a" Turkish-Iranian version of Rast" - I never heard of "Rast"
> concerning Persian music (but I 'm far from knowing everything !).
> To come back to Mohajira what is certain anyway, and you will
> rectify if I'm wrong, is that intervals such as E half-b / arabic
> Segah / Sikah / Wusta Zalal / Mi koron /or "neutral thirds" to use
> the western name are present, in various versions and in different
> modes and musical styles, in the three cultures.
> Note also that I am just as fond of the ("turkish") "perde segah",
> who is present in many of my middle-east tunings ! ;)
>
> Cordially,
> - - - - - - - -
> Jacques
>
>
>
> Ozan Yarman wrote :
>
> Jacques, not that this is obvious at first, but Arabic Rast is not the
> "norm" in the world that you should select it as the standard over
> other intonations of that maqam which you, probably unintentionally,
> stacked aside as "ancillary" when pointing out the need to specify its
> Turkishness for the distinction. For what it's worth, if there is a
> standard sought, it should rather be the Turkic-Iranian version of
> Rast for having a performance tradition and repertory that far exceeds
> her Arabic counterpart by two centuries.
>
> While not wanting to seem nationalistic in the least - for I am
> particularly against non-Islamic notions of describing a society
> (morals especially) - I can furthermore state that the inclination to
> Arabicize Rast and other maqams over their much more established
> Turkic and Iranian intonational renditions is, I fear, rather due to
> some "latter-day imperialist mentality" persisting from the days of
> the invasion and occupation of the homelands of Arabs, Berbers and
> Beduouins by Western powers, sometimes, and perhaps still so, along
> with the ignominous collaboration of their indigenous populations.
>
> Please do not take this evaluation as personal, for I do not imply
> your person one bit! It might in fact be nothing more than a residual
> habit of the Western way of academical thinking.
>
> The difference between the genera, that is, of the Arabic versus the
> Turkish Rast, appears to be not a confusion, but a matter of taste
> based on culture, memetic and ethnicity. Standardizing a maqam
> intonation over another also bears the risk of exalting a genetic pool
> over another, which I'm sure you didn't mean!
>
> Cordially,
> Oz.
>
> âœ© âœ© âœ©
> www.ozanyarman.com
>
>
>
>

🔗jacques.dudon <fotosonix@...>

Obviously !...
What strikes me is the predominant use of Bb over straight B, and that all the melody is almost in the upper tetrachord (then sounding very much closer to Avaz-e-Afshari to my ears, than for example Dastgah Mâhur) - of course the excerpts start at the beginning of each movement and the first tetrachord might arrive as the answer.

Thanks for the example !
- - - - - -
Jacques

--- In tuning@yahoogroups.com, Ozan Yarman <ozanyarman@...> wrote:
>
> Dear Jacques,
>
> There appears to be some confusion here. To my knowledge, There is
> indeed a Rast-Panchgah mode in Iranian music, which is in fact, just
> like the other Dastgahs in usage, formulated rigidly somewhere in the
> 19th Century as a coagulation of both Rast and Panchgah, the latter
> differing from the former in principle with only a single alteration
> of the fourth degree of the scale (F# instead of F in a C major
> setting). We have Rast and Penchgah defined seperately, but the nuance
> is a matter of taste in the case of Iran.
>
>
> You can hear a sample of the Iranian rendition of Rast here:
>
> http://itunes.apple.com/gb/album/national-vocal-radifs-iranian/id331938258
>
>
> Not surprisingly, the Iranian sphere of cultural influence includes
> the Turkics in Iran as well as the mugham traditions in Azarbaijan and
> similitudes in Transoxania (Uigurs seem to be Turkic too). While the
> perde segah here is noticably lower than our occasional understanding
> of Turkish segah in Rast, it is still higher than the Arabic
> rendition. In effect, the categorization of Iranian and Turkic
> intonations under the same heading does great justice in terms of
> musicology not only because of the likeness of intonational effect,
> but more so because Ottomans and Safavids have a sort of common
> Islamic cultural root as the basis of the formation of their
> respective court and sufi musics as well as music theory which
> persists to this day.
>
> Even with all the diversity in the Middle East regarding the different
> execution of maqams whose names remain the same, such does not seem
> the case with Rast, the mother of all maqams. Forsooth, Rast is one of
> those maqams that remains more or less the same mode throughout,
> characterized only with perde inflexions (segah, ajem and evdj
> especially) peculiar to the region it has been adapted to. This is
> much like a Persian word being adapted into Turkish, Arabic, Urdu,
> Kurdish, Assyrian, etc... with different pronounciations but same or
> similar meanings.
>
> Cordially,
> Oz.

🔗Torsten Anders <torsten.anders@...>

🔗Margo Schulter <mschulter@...>

> What strikes me is the predominant use of Bb over straight B,
> and that all the melody is almost in the upper tetrachord (then
> sounding very much closer to Avaz-e-Afshari to my ears, than
> for example Dastgah M?hur) - of course the excerpts start at
> the beginning of each movement and the first tetrachord might
> arrive as the answer.

> Jacques

Dear Jacques (and Ozan),

Please let me agree, Jacques, that looking through a couple of
transcribed and printed versions of the radif has made this
affinity between Avaz-e Rast-Panjgah and Avaz-e Afshari very
striking! The very important role in both of gusheh-ha with
A-koron (Ap), a neutral third above the final F in these
transcriptions, often with a closing descent of Ap-F, is a real
link.

As Farhat views it, some of these gusheh-ha with a prominent
tetrachord starting a tone about the final at G-Ap-Bb-C, represent in effect a focus on Shur. Also, as in Afshari,
we have pieces with Ap that may use either D-natural or Dp,
the major or neutral sixth above the final.

What also came to my mind was Delkash, a gusheh in Dastgah
e-Mahur with a lower Mahur pentachord and an upper Shur
tetrachord: C-D-E-F-G-Ap-Bb-C. An interesting touch in this
gusheh and Sekaste, for example, is the introduction of Ep, a
neutral third above the final of Mahur, C. This koron step is
used in pieces which may also have low B-natural as the step
below the final, serving to keep a touch of Mahur in its most
familiar form, as Farhat observes.

The fact that gusheh-ha like Oshshaq can occur in more than
one dastgah makes things intricate, maybe analogously to the
possibility of modulating to a given maqam such as Rast (in
whatever form of intonation one may choose) from various other
maqamat.

Striving to keep to one point at a time, I'll reserve comment on
a fascinating historical question the two of you have raised for
another post, but warmly thank you for teaching me about some
corners of the radif previously quite unconsidered by me, and
giving me an occasion to learn more.

Most appreciatively,

Margo Schulter
mschulter@...

Re: Mohajira

🔗Robert C Valentine <BVAL@IIL.INTEL.COM>

🔗Paul Erlich <paul@stretch-music.com>

🔗Jacques Dudon <fotosonix@...>

🔗Jacques Dudon <fotosonix@...>

🔗Ozan Yarman <ozanyarman@...>

🔗Graham Breed <gbreed@...>

🔗genewardsmith <genewardsmith@...>

🔗Graham Breed <gbreed@...>

🔗jacques.dudon <fotosonix@...>

🔗jacques.dudon <fotosonix@...>

🔗genewardsmith <genewardsmith@...>

🔗Ozan Yarman <ozanyarman@...>

🔗Jacques Dudon <fotosonix@...>

🔗Ozan Yarman <ozanyarman@...>

🔗jacques.dudon <fotosonix@...>

🔗Torsten Anders <torsten.anders@...>

🔗Margo Schulter <mschulter@...>