Topic: Traditional Tunbur Tunings and Spirals of Fifths
2 scales
| File | Description | Notes | Period (¢) | Limit |
|---|---|---|---|---|
| farabi22ud | Al-Farabi 22 note ud scale | 22 | 1200.0 | 17 |
| farabi9 | Al-Farabi 9 note ud scale | 9 | 1200.0 | 11 |
Thread (6 messages)
From: Cris Forster (2005-06-17) Subject: Traditional Tunbur Tunings and Spirals of Fifths Dear Mr. Lumma, Let's start from the beginning, as obnoxious and stupefying as it is. And in the future, if there is a future, please try to remember that I am a trained historian who reads original sources, and who has a passion for footnotes. Without historical context and meaning, all numbers are meaningless. Here is Mr. Yarman's diatribe before he disappeared to wherever: >Hah! Hark at the one who presumes he has monopoly over >interpreting Maqam Music theory. Hark at those who assume >that JI intervals used by Maqam Music can be correctly >represented both in pitch and notation by a pure cycle of fifths. >Even a simple scrutiny of the link to a taksim recording on the >bottom of that >same page would confirm the usage of intervals >around 12/11 and 13/12. Of course some people do not concern >themselves at all whether the frets give these interval or not. Here is my COMPLETE non-edited response: >From my manuscript Musical Mathematics: A Practice in the >Mathematics of Tuning Instruments and Analyzing Scales > >****************************** > >"A numerical analysis reveals that Al-Farabi's length ratios >include six prime factors: 2, 3, 7, 11, 17, 149, and Ibn Sina's, >only four prime factors: 2, 3, 7, 13." > >****************************** > >Obviously, the moveable frets on uds and tunburs do not exclude >any prime factors. > >For that reason, equally obvious is the fact that within a given >civilization, theorists and theories may differ and coexist, but not >at the expense of myopic and historical denial. I chose to respond with a prime factor analysis because Mr. Yarman thinks that because he heard "intervals around 12/11 and 13/12," he therefore has license to dismiss "pure cycle of fifths" as a basic tuning theory of the modern Turkish tunbur. To read my text on the modern Turkish Tunbur, please visit: http://www.Chrysalis-Foundation.org/Modern_Turkish_Tunbur_&_53_TET.pdf Now, had you read this PDF (Tuning Message #59094), you would have immediately noticed my references to: Signell, K.L. (1986). Makam: Modal Practice in Turkish Art Music. Da Capo Press, New York, New York. an extremely informative published Ph.D. dissertation. Also, had you read this PDF, you would also have immediately noticed my historical allusions to Al-Farabi's tunbur tuning in the first paragraph, and to Al-Farabi's and Safi Al-Din's tunings in Figure 81. In Figure 81, it should be clear to you that nothing about my studies, writings, and comprehensions is haphazard. Figure 81 clearly illustrates a tuning principle first described by Al- Farabi more than a thousand years ago: two spirals of fifths, one ascending 12 fifths, the other descending 12 fifths. Of course, if you want "natural laws" based on Mr. Yarman questionably perceived "intervals around 12/11 and 13/12," you'll have to ask him. I take no responsibility for the ludicrous assumption that on the tunbur there exists a historic systematic13-limit tuning. However, on the ancient uds and on modern tunburs the frets are moveable, not just with respect to tunings, transpositions, etc., but for MUSICALLY EXPRESSIVE PURPOSES. You're numbers ain't gonna help you here! To begin reading about the tunings of the ancient Arabian masters from original sources, please visit: http://www.Chrysalis-Foundation.org/Manuscript.htm Yes, I am upset that an argument of Destructive Criticism -- based on the "perceived" existence of 'a 13-limit fly in the 2/1 ointment' -- should be used by someone who is absolutely ignorant of how tunburs have been traditionally tuned for more than a thousand years. Of course, unless you read Arabic or French, you will need my Musical Mathematics to cross-examine my historical analysis of systematic tunbur tunings. Should I hand you this tool for potentially Destructive Criticism? Cris Forster, Music Director www.Chrysalis-Foundation.org >The assumption behind at least one brand of music theory, Mr. >Forster, is that those who move frets do not do so haphazardly, >but unknowingly follow (to some degree of approximation) >natural laws. An effort to discover such laws does not necessarily >seek to upset people such as yourself, though if you like being >upset it's fine I suppose. >-Carl
From: Carl Lumma (2005-06-17) Subject: Re: Traditional Tunbur Tunings and Spirals of Fifths Chris, > Here is Mr. Yarman's diatribe before he disappeared to wherever: > > >Hah! Hark at the one who presumes he has monopoly over > >interpreting Maqam Music theory. Hark at those who assume > >that JI intervals used by Maqam Music can be correctly > >represented both in pitch and notation by a pure cycle of > >fifths. Even a simple scrutiny of the link to a taksim > >recording on the bottom of that same page would confirm > >the usage of intervals around 12/11 and 13/12. Of course > >some people do not concern themselves at all whether the > >frets give these interval or not. > > Here is my COMPLETE non-edited response: > > >From my manuscript Musical Mathematics: A Practice in the > >Mathematics of Tuning Instruments and Analyzing Scales > > > >****************************** > > > >"A numerical analysis reveals that Al-Farabi's length ratios > >include six prime factors: 2, 3, 7, 11, 17, 149, and Ibn > >Sina's, only four prime factors: 2, 3, 7, 13." > > > >****************************** > > > >Obviously, the moveable frets on uds and tunburs do not exclude > >any prime factors. > > > >For that reason, equally obvious is the fact that within a given > >civilization, theorists and theories may differ and coexist, but > >not at the expense of myopic and historical denial. > > I chose to respond with a prime factor analysis because Mr. > Yarman thinks that because he heard "intervals around 12/11 and > 13/12," he therefore has license to dismiss "pure cycle of > fifths" as a basic tuning theory of the modern Turkish tunbur. One way to read my reply... """ The assumption behind at least one brand of music theory, Mr. Forster, is that those who move frets do not do so haphazardly, but unknowingly follow (to some degree of approximation) natural laws.""" ...is that it is possible that moveable frets exclude prime factors (though I'm not claming they do). I wasn't making a reference to Ozan's comments at all, nor do I know what you meant by "myopic and historical denial". > To read my text on the modern Turkish Tunbur, please visit: > > http://www.Chrysalis- > Foundation.org/Modern_Turkish_Tunbur_&_53_TET.pdf > > Now, had you read this PDF (Tuning Message #59094), you > would have immediately noticed my references to: > > Signell, K.L. (1986). Makam: Modal Practice in Turkish Art Music. > Da Capo Press, New York, New York. > > an extremely informative published Ph.D. dissertation. > > Also, had you read this PDF, you would also have immediately > noticed my historical allusions to Al-Farabi's tunbur tuning in > the first paragraph, and to Al-Farabi's and Safi Al-Din's > tunings in Figure 81. I don't believe I denied such references or allusions. > In Figure 81, it should be clear to you that nothing about my > studies, writings, and comprehensions is haphazard. I did not call your studies haphazard. I said some believe that the placement of moveable frets is not haphazard. > However, on the ancient uds and on modern tunburs the frets are > moveable, not just with respect to tunings, transpositions, etc., > but for MUSICALLY EXPRESSIVE PURPOSES. You're numbers > ain't gonna help you here! Why is musical expression beyond numbers? > To begin reading about the tunings of the ancient Arabian > masters from original sources, please visit: > > http://www.Chrysalis-Foundation.org/Manuscript.htm Ok, I'll check it out. -Carl
From: Kraig Grady (2005-06-18) Subject: Traditional Tunbur Tunings and Spirals of Fifths How do the systematist fit into this question since they used 11 and 13 limit intervals? i thought i had this paper up, but it seems not to be. > From: Cris Forster <[email protected]> >Subject: Traditional Tunbur Tunings and Spirals of Fifths > > > > >Of course, if you want "natural laws" based on Mr. Yarman >questionably perceived "intervals around 12/11 and 13/12," you'll >have to ask him. I take no responsibility for the ludicrous >assumption that on the tunbur there exists a historic systematic13-limit >tuning. > > > > > > -- Kraig Grady North American Embassy of Anaphoria Island <http://anaphoria.com/> The Wandering Medicine Show KXLU <http://www.kxlu.com/main.html> 88.9 FM Wed 8-9 pm Los Angeles
From: c_ml_forster (2005-06-18) Subject: Re: Traditional Tunbur Tunings and Spirals of Fifths Hi Kraig, Your question goes to the heart and plumbs the depth of the phenomenal achievements of the theorists of the Arabian Renaissance. Before I attempt to answer your question, I would like to apologize to you and other members of the Tuning Group for my less than rational responses to Destructive Criticisms. I take full responsibility for my cantankerous choice of words, and will attempt to change my ways. First, I would like to state that I do not use terms like "systematist," "microtonalist," or "temperamentist," because more is lost than gained by such categorizations. Second, due to serious email font issues, and the lack of a Yahoo graphics page (where Tuning Group Members can upload figures, tables, equations, etc.), I cannot respond to your question without posting yet another page from my Musical Mathematics at www.Chrysalis-Foundation.org. Third, in general, but not without significant exceptions, one must carefully distinguish between the mathematics of tuning uds and the mathematics of tuning tunburs. In my manuscript Musical Mathematics, I devote 248 pages to Chapter 11, Part IV, entitled -- A Collection of World Tunings: Arabian, Persian, and Turkish Music. Since I cannot attempt to answer your question by posting all the required pages from this work, I have chosen the following page that may help -- http://www.Chrysalis-Foundation.org/Al-Farabi's_Distinctions.pdf ****************************** This page CANNOT be accessed by clicking on a button at the www.Chrysalis-Foundation.org website. ****************************** Due to extremely long ratios generated by long spirals of fifths, I invented a new notation that SYMBOLICALLY works very much like the sharps and flats of Western music, and the korons and soris of modern Persian music. A schisma comma is the difference between the comma of Pythagoras (531441/524288) and the comma of Didymus (81/80), and, therefore, equals ratio: 32805/32768 = 1.95 ¢. For more information on the schisma comma, please visit -- http://www.Chrysalis-Foundation.org/Al-Din_&_Ramis.htm Starting on C, if we descend 8 fifths we get Fb, or ratio 8192/6561 = 384 ¢. Now, if we reduce 5-limit E, ratio 5/4 = 386 ¢, by the schisma comma, we also get 8192/6561 = 384 ¢. Since the human ear cannot distinguish between two pitches that are less than 2 ¢ apart, 5/4 and 8192/6561 are for all practical musical purposes identical. In the above-mentioned PDF file, I use a "down arrow" with an "S" on top to indicate a 5-limit ratio reduced by a schisma comma, which, equivalently, represents the exact ratio in the descending spiral of fifths. In the above-mentioned PDF file, I also use the koron sign, which I describe on the following page -- http://www.Chrysalis-Foundation.org/Al-Farabi's_'Uds.htm Here you can examine the ud tuning tradition, which, unlike the tunbur tuning tradition, is NOT based on spirals of fifths. To access the Turkish tunbur page, please visit -- http://www.Chrysalis- Foundation.org/Modern_Turkish_Tunbur_&_53_TET.pdf Hope this helps a little. Sincerely, Cris Forster, Music Director www.Chrysalis-Foundation.org >How do the systematist fit into this question since they used 11 >and 13 limit intervals? >i thought i had this paper up, but it seems not to be. --- In [email protected], Kraig Grady <kraiggrady@a...> wrote: > How do the systematist fit into this question since they used 11 and 13 > limit intervals? > i thought i had this paper up, but it seems not to be. > > > From: Cris Forster <76153.763@c...> > >Subject: Traditional Tunbur Tunings and Spirals of Fifths > > > > > > > > > >Of course, if you want "natural laws" based on Mr. Yarman > >questionably perceived "intervals around 12/11 and 13/12," you'll > >have to ask him. I take no responsibility for the ludicrous > >assumption that on the tunbur there exists a historic systematic13-limit > >tuning. > > > > > > > > > > > > > > -- > Kraig Grady > North American Embassy of Anaphoria Island <http://anaphoria.com/> > The Wandering Medicine Show > KXLU <http://www.kxlu.com/main.html> 88.9 FM Wed 8-9 pm Los Angeles
From: Gene Ward Smith (2005-06-18) Subject: Re: Traditional Tunbur Tunings and Spirals of Fifths --- In [email protected], "c_ml_forster" <76153.763@c...> wrote: > http://www.Chrysalis-Foundation.org/Al-Farabi's_Distinctions.pdf > > ****************************** > > This page CANNOT be accessed by clicking on a button at the > www.Chrysalis-Foundation.org website. It doesn't seem it can be accessed using this url either. > Starting on C, if we descend 8 fifths we get Fb, or ratio > 8192/6561 = 384 ¢. Now, if we reduce 5-limit E, ratio 5/4 = 386 ¢, > by the schisma comma, we also get 8192/6561 = 384 ¢. Since > the human ear cannot distinguish between two pitches that are > less than 2 ¢ apart, 5/4 and 8192/6561 are for all practical musical > purposes identical. If they are identical, why do you want to distinguish them? Could you not simply use the 53-et that some Turkish theorists use? > In the above-mentioned PDF file, I use a "down arrow" with an "S" > on top to indicate a 5-limit ratio reduced by a schisma comma, > which, equivalently, represents the exact ratio in the descending > spiral of fifths. You might find Keenan and Secor's sagittal notation interesting. I think anyway there is no point in introducing yet another special symbol for the schisma. > In the above-mentioned PDF file, I also use the koron sign, which I > describe on the following page -- > > http://www.Chrysalis-Foundation.org/Al-Farabi's_'Uds.htm There are a lot of Al-Farabi scales in the Scala archives, but I didn't find the 9 and 22 note scales on this page there. I give them below, and suggest they be added. One thing to note about these scales is that 159-et does an excellent job of representing them. ! farabi9.scl Al-Farabi 9 note ud scale 9 ! 9/8 27/22 81/64 4/3 3/2 18/11 27/16 16/9 2 ! farabi22ud.scl Al-Farabi 22 note ud scale 22 ! 256/243 18/17 12/11 9/8 32/27 27/22 8192/6561 81/64 4/3 1024/729 24/17 16/11 3/2 128/81 18/11 32768/19683 27/16 16/9 4096/2187 32/17 64/33 2 In 159 equal, these scales are 0, 27, 47, 54, 66, 93, 113, 120, 132 and 0, 12, 13, 20, 27, 39, 47, 51, 54, 66, 78, 79, 86, 93, 105, 113, 117, 120, 132, 144, 145, 152 In terms of the 2deg159 MOS, they are -66, -56, -33, -23, 0, 27, 33, 60, 66 and -73, -66, -60, -56, -54, -40, -33, -27, -23, -21, -7, 0, 6, 10, 27, 33, 39, 43, 60, 66, 72, 76 In other words, 159-et represents them very well, but the 79 note 2deg159 MOS is useless. Other temperaments do better--for instance "guiron", the 118&159 temperament, which is 31deg159.
From: c_ml_forster (2005-06-18) Subject: Re: Traditional Tunbur Tunings and Spirals of Fifths Sorry about that. Anyway, I'm leaving for a long vacation. All my best. Cris Forster --- In [email protected], "Gene Ward Smith" <gwsmith@s...> wrote: > --- In [email protected], "c_ml_forster" <76153.763@c...> wrote: > > > http://www.Chrysalis-Foundation.org/Al-Farabi's_Distinctions.pdf > > > > ****************************** > > > > This page CANNOT be accessed by clicking on a button at the > > www.Chrysalis-Foundation.org website. > > It doesn't seem it can be accessed using this url either. > > > Starting on C, if we descend 8 fifths we get Fb, or ratio > > 8192/6561 = 384 ¢. Now, if we reduce 5-limit E, ratio 5/4 = 386 ¢, > > by the schisma comma, we also get 8192/6561 = 384 ¢. Since > > the human ear cannot distinguish between two pitches that are > > less than 2 ¢ apart, 5/4 and 8192/6561 are for all practical musical > > purposes identical. > > If they are identical, why do you want to distinguish them? Could you > not simply use the 53-et that some Turkish theorists use? > > > In the above-mentioned PDF file, I use a "down arrow" with an "S" > > on top to indicate a 5-limit ratio reduced by a schisma comma, > > which, equivalently, represents the exact ratio in the descending > > spiral of fifths. > > You might find Keenan and Secor's sagittal notation interesting. I > think anyway there is no point in introducing yet another special > symbol for the schisma. > > > In the above-mentioned PDF file, I also use the koron sign, which I > > describe on the following page -- > > > > http://www.Chrysalis-Foundation.org/Al-Farabi's_'Uds.htm > > There are a lot of Al-Farabi scales in the Scala archives, but I > didn't find the 9 and 22 note scales on this page there. I give them > below, and suggest they be added. > > One thing to note about these scales is that 159-et does an excellent > job of representing them. > > ! farabi9.scl > Al-Farabi 9 note ud scale > 9 > ! > 9/8 > 27/22 > 81/64 > 4/3 > 3/2 > 18/11 > 27/16 > 16/9 > 2 > > ! farabi22ud.scl > Al-Farabi 22 note ud scale > 22 > ! > 256/243 > 18/17 > 12/11 > 9/8 > 32/27 > 27/22 > 8192/6561 > 81/64 > 4/3 > 1024/729 > 24/17 > 16/11 > 3/2 > 128/81 > 18/11 > 32768/19683 > 27/16 > 16/9 > 4096/2187 > 32/17 > 64/33 > 2 > > In 159 equal, these scales are > > 0, 27, 47, 54, 66, 93, 113, 120, 132 > > and > > 0, 12, 13, 20, 27, 39, 47, 51, 54, 66, 78, 79, 86, 93, 105, 113, > 117, 120, 132, 144, 145, 152 > > In terms of the 2deg159 MOS, they are > > -66, -56, -33, -23, 0, 27, 33, 60, 66 > > and > > -73, -66, -60, -56, -54, -40, -33, -27, -23, -21, -7, 0, 6, 10, 27, > 33, 39, 43, 60, 66, 72, 76 > > In other words, 159-et represents them very well, but the 79 note > 2deg159 MOS is useless. Other temperaments do better--for instance > "guiron", the 118&159 temperament, which is 31deg159.