Tuesday, March 11, 2014

Wilson / Poole / 21: 22: 27: 28 - A Moment of Convergence in a Tuning's Evolution

Page 1 of Modeled on Baglama Scale

Margo Schulter has noticed a correspondence that had lead to an update of file RAST.PDF
Here is what she has to share:

  Erv Wilson, Rod Poole, and 21:22:27:28
        A Moment of Convergence in a Tuning's Evolution

Erv Wilson's RAST.PDF (p. 17 in the version of 11 March 2014) may have a connection to the evolution of Rod Poole's 17-note JI guitar tuning. The direct and obvious "moment of convergence" on this page of Erv's is the appearance of the conjunct soft diatonic mode 21:22:27:28, or in other words 1/1-22/21-9/7-4/3-88/63-12/7-16/9-2/1. This same mode is featured by Rod in a typeset page from a CD insert (December 1996), made available in JPEG format by Ron Sword and reproduced as p. 18 of RAST.PDF, focusing on this 21:22:27:28 tetrachord and its conjunct octave mode as the nucleus of "The Death Adder/December 1996" (see Examples One and Two).
Page 2 of Modeled on Baglama Scale

Of course, this connection leaves open the question of "Who influenced whom?" -- a question which may be moot when two artists such as Erv and Rod enjoy a close association over a period of years, and also share a strong sense of trusting and following their own ideas and intuitions. By 10 May 1995, for example, Rod had proposed a 29-note guitar tuning which Erv mapped to generalized keyboard, including all the notes in Rod's later 17-note set, plus others, some found in Kraig Grady's Centaur (21/20, 5/4, 7/5. 5/3, 15/8).
An intriguing possible further connection is suggested by the sketch at the bottom of Erv's p. 16, where the diagram of the conjunct 21:22:27:28 mode at the top of the page is connected to a diagram of a 17-note instrument, where it is proposed that this mode should start on the 7/4 step of the 17-note tuning, or step 14. The initial steps of this 17-note tuning from the "open string" are shown as 1/1, 33/32, 13/12, 9/8, and 7/6, which matches Rod's 17-note system.
liner notes to Dec. 96,Rod Poole  CD

1. Correlating Rod's 13-note tuning to his 17-note system

In Rod's system, this 21:22:27:28 mode indeed appears in its precise conjunct form at one location: the 7/4 step. The following diagram shows the mode of interest at the top, and the steps of the 17-note tuning at the bottom:

Since many of Erv's Rast-Bayyati pages are dated 1992 or 1993, his interest in Mansur Zalzal, his 27/22 wusta (or wosta) middle finger fret, and tunings featuring Zalzalian or middle intervals (sometimes know as "neutral" intervals) may have been a theme that he and Rod focused on in the early years of their association. By 1995, this interest had led to Rod's 29-tone guitar concept -- and, by 1996, had for him focused on the 21:22:27:28 mode as the nucleus of at least one type of guitar tuning featuring septimal and Zalzalian steps.
Rod's "13-note expanded scale" of December 1996 growing out of this mode is interesting to compare to the standard 17-note set. Unlike the 17-note set, it includes some pairs of steps at a comma apart, as does the 29-note concept of 1995. If we again apply Erv's sketch at the bottom of his page on the 21:22:27:28 mode and begin it on the 7/4 step of the eventual 17-note tuning, some of the additional steps do match. Here I compare the lower 4/3 tetrachord of the mode, and then the upper tetrachord and 9:8 tone completing the octave, with extra tones of the 13-note set in 1996 show above the modal steps:

Three of the extra tones, at 3/2, 11/7, and 27/14, together with the 
2/1 octave make possible the option of a disjunct 21:22:27:28 
tetrachord at 3/2-11/7-27/14-2/1, in addition to the conjunct 
tetrachords of the basic 7-note mode.

Of the six extra notes in the 1996 tuning, Rod's 17-note tuning taken from the 7/4 step incorporates two: 11/7 (at 11/8 from the usual 1/1), and 27/14 (at 27/16). The 3/2 step of 1996 would map to 21/16, a step included in the 29-note design of 1995, but not in the 17-note set, where it would be only a 64:63 comma from the 4/3.
The 11/9 step in 1996 would make possible another very beautiful tetrachord from 1/1 to 4/3 in this 13-note tuning: 1/1-22/21-11/9-4/3 or 22:21-7:6-12:11, an exact mirroring of Qutb al-Din al-Shirazi's Hijaz tetrachord around 1300, 1/1-12/11-14/11-4/3 or 12:11-7:6-22:21. Both these permutations of Hijaz, which John Chalmers's describes as a "neochromatic" form with the large interval as the middle step of the tetrachord, derive from Ptolemy's Intense Chromatic at 22:21-12:11-7:6 or 1/1-22/21-8/7-4/3, with the large interval (7:6) as the upper step. The 22:21-7:6-12:11 form might also be derived from a rotation of a mode built from a chromatic of al-Farabi, 28:24:22:21 or 7:6-12:11-22:21, 1/1-7/6-14/11-4/3 (see al-farabi_g7.scl in the Scala archive).
In the mapping of the 1/1 in this 1996 tuning to 7/4 of the 17-note system, however, an 11/9 step would translate to a 77/72 step, at 116.234 cents, at a 78:77 comma below the 13/12 step appearing both in the 1995 concept and the 17-note tuning. Indeed Ibn Sina's famous `oud tuning features steps at 273/256 (111.389 cents) and 13/12; his 273/256 (39/32 less 8:7), like a hypothetical 77/72, approximates 16/15. However, in Rod's 17-note tuning, the minimum distance between notes is 33:32, which I find is a variety of "minimal semitone." We can, however, find a 22:21-7:6-12:11 tetrachord in this tuning at 21/11-1/1-7/6-14/11.
The 14/11 step of the 1996 tuning would map from the 7/4 step of the 17-note system to 49/44 or 186.334 cents, a bit wide of 10/9, and 99:98 below 9/8 in this scheme.
The 56/33 step of 1996 would likewise translate to 49/33 or 684.379 cents, a bit wide of 40/27, and 99:98 below the 3/2 step.
Rod's 3/2 step of 1996 would translate to 21/16, a step present in the 1995 concept, but in the 17-note system would be a 64:63 comma from 4/3 in a context where steps are at least a 33:32 apart.
Of course, it is important to bear in mind that Rod's 13-note scheme of 1996 has its own musical logic, with the 56/33 step for example very logically placed at a 4:3 fourth above 14/11, although as it happens not included in either the 29-note tuning of 1995 or the 17-note scheme.
Erv's page on the 21:22:27:28 mode and its mapping to the 7/4 step of a 17-note system  raises interesting questions. Is this a record of something Erv conceived or was it one of Rod's concepts? Or, not so surprisingly, could it be the result of much mutual dialogue and discovery.

2. A note on 21:22:27:28 and the Byzantine Hard Chromatic

On the 21:22:27:28 mode itself, Rod describes it as "an enharmonic, tetrachordal scale. The tetrachord (a perfect fourth) is two unevenly-sized, small half-steps, 22:21 and 28:27, separated by a neutral third, 27:22, the Wosta of Zalzal."
Interestingly, this type of tetrachord is what students of classic Greek tuning sometimes describe as a soft chromatic, and modern Byzantine theory calls the Hard Chromatic. In a more moderate form, it appears as the form of Byzantine Hard Chromatic recommended by the Committee on Music in 1881, with a tuning expressed in terms of units of 36-ed2 as 3-10-2 steps or 100-333-67 cents, with a middle interval at 333 cents (a small Zalzalian third at around 63/52 or 40/33) and a third step at 433 cents, very close to Rod's 9/7. Some exponents of Byzantine music report that the large middle interval is in practice often around 11/9 or even a bit wider, so that 21:22:27:28 may reasonably approximate this style of vocal intonation.
While either the classic "soft chromatic" or the modern Byzantine "Hard Chromatic" may aptly describe this mode, Rod's "enharmonic" concept may fit broadly into the Byzantine tradition also. While in classic Greece it tends to imply a yet wider large interval, somewhere at least around 5/4 and ranging up to 81/64 or beyond, for Chrysanthos of Madytos in the earlier 19th century, the mark of the enharmonic was the presence of a small step which could be viewed as in some sense a "quartertone."
For Chrysanthos, 68-ed2 provided a reasonable approximation of the flexible intervals produced by singers -- a conclusion concurred in by the Syrian theorist on Arab music, Mikhail Mashaqa, who reported that the scheme of 24-ed2 he used in his own writing was in fact less accurate than the Greek system of Chrysanthos. Interestingly, Chrysanthos used a smaller middle interval than Rod's 27:22 for his Hard Chromatic, at 7-18-3 steps, or 124-318-53 cents -- but a third note at 441 cents or actually a bit higher than 9/7, and an upper step even smaller than Ron's classic 28:27 of Archytas (63 cents), at 53 cents or a near-just 33:32. In 68-ed2, this 53-cent step (3 scale steps) is literally 1/4 of a regular tone at 212 cents of 12 scale steps -- identical to the tone at 3 steps of 17-ed2.
As shown in Erv's diagrams, the 21:22:27:28 tetrachord would map in a 17-note system to 1-5-1 steps. In this context, musicians and theorists such as George Secor sometimes refer to certain types of motion by a single step as "enharmonic," which along with the dramatic contrast between the adjacent steps at 27:22 (355 cents) and 28:27 (63 cents) might well prompt this expressive term.
Happily, this conjunct 21:22:27:28 mode is indeed available in Rod's 17-note tuning at the 7/4 step indicated in Erv's diagram, and also in offshoots such as Zeta-20 and Zeta-24 at the same location.

3. Conclusion

The documentation in 1995 of Rod's 29-note concept for a guitar tuning, followed by his CD notes describing his 13-note tuning of December 1996 which "began life" as the 21:22:27:28 mode, and then the implementation of his 17-note tuning, suggests that this process of evolution may have been complex and not necessarily linear -- and likewise the artistic collaboration between him and Erv Wilson, with Kraig Grady and his Centaur tuning and extensions also intimately involved in this creative process.
Rod's notes, which focus not only on the selection of certain notes or modes but on the practical task of implementing them on a real-world instrument, suggest that we keep in view all sides of this process.
What Rod's notes and Erv's page together indicate is that the 13-note tuning of December 1996, or more specifically the 7 notes of the conjunct 21:22:27:28 mode plus two of the additional steps (11/7 and 27/14), were mapped to the 7/4 step of the 17-note system partially sketched out by Erv and later implemented by Rod. Thus while the 1995 scheme for 29 notes might be viewed as one source for this system, since it includes all 17 notes, the mapping of the 21:22:27:28 mode that was the nucleus of the 1996 system to the 7/4 step of a 17-note template may represent another step.
The "moment of convergence" between Erv's diagram and the portrait we have in Rod's CD insert of a tuning in progress gives us a richer perspective on a most fruitful and creative collaboration.
I would also like to thank both Ron Sword and Kraig Grady for their generosity and untiring diligence in making these materials accessible to interested musicians and the world at large.

Saturday, March 8, 2014

The Pythagorean Assimilation of Subharmonic Flutes

Wilson's comparison and guide to transcribing
 subharmonic scales to a pythagorean system
    This  stray page found in the records  is being added  to the archives file called Flute Notes.  Wilson is concerned with the way subharmonic scales and their melodies can be assimilated into a pythagorean tuning array. He entertained the idea that subharmonic flute melodies in India could have found their way into string instruments tuned to a pythagorean chain.
    Wilson might be the first to mention the use of tuning the exit hole of a subharmonic flute to either a fourth or fifth of one of the holes, hence these designations in the upper of the two sets of  blocks. This practice he observed in the tunings found within his large collection of South American flutes. The ratios in between the blocks show the difference between the two sets of scales. The chart is one way we might transcribe subharmonic scales and pythagorean scales and melodies into each other. Unsigned or labeled, it was a document the archivist received from him by at least 1978.