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Margo Schulter has noticed a correspondence that had lead to an update of file
RAST.PDF
Here is what she has to share:
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Erv Wilson, Rod Poole, and 21:22:27:28
A Moment of Convergence in a Tuning's Evolution
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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).
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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.
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| liner notes to Dec. 96,Rod Poole CD |
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1. Correlating Rod's 13-note tuning to his 17-note system
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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.
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2. A note on 21:22:27:28 and the Byzantine Hard Chromatic
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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.
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3. Conclusion
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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.
This 22 tone scale of Wilson's believed to be from 1967 was found in a series of papers, charts and scales based stellating Hexanies in i have not seen before. One particular method resulted in the example below which seems to form the core of the scale above. Wilson took the 1-3-7-11 hexany and stellated it with 5 and /5 to complete the 8 basic triads found within which results in the 14 tone structure to the left. The result of this type of stellation has unexpected results. for instance 4 other hexanies are formed each which occurs twice. All involve the added 5 plus three factors of the 1,3,7,11 set. Because of the relationship of most of the added pitches to this stellate being 3/2 above and below, to form this 22 tone scale. 4 more hexanies also appear. The result is one of many 22 tone scales that contain a great variety of compact hexany subsets. 
