# Encoding ISO-Latin-1 @@f57v # LAST REVISED: 2025-09-18 IDENTIFICATION * Nickname: "The 4 times 17 sequence" * Page: f57v = HB/n112 (Rene) = p112 (Stolfi) * Folio: f57 * Panels: f57v * Bifolio: bH1 = f57+f66 * Quire: H (Rene) = VIII (Beinecke) ATTRIBUTES * Language: B (Currier) * Hand: 2 (Currier) * Subsets: C (Rene), cos (Stolfi) * Subject: cosmological * FirstWord: @'dairal' DESCRIPTION Page shape and state: Page f57v comprises panel f57v only. On the BL2014 images, the panel is ~2490 pixels wide (across the bottom half) and ~3550 pixels tall. The actual height is assumed to be 235 mm giving a scale of ~0.0662 mm/pixel. The free vert edge of this folio is not straight. The top part of that edge is curved towards the gutter, and unnaturally clean, as if a sliver ~10 mm wide at the top and ~90 mm tall had been neatly cut away from the flap. The flap appears to be ~160 mm wide in the bottom half but then narrows gradually to ~150 mm near the top. Panel-relative coordinates below will assume the ideal panel with uniform width ~160 mm. The BL 2015 image of page f57v may be distorted by the parch not being flat. The panel appears to be tilted in the BL2014 scans, with the top edge rising by ~10mm above the previous panels. However, the scan of f57r shows that the cause is almost certaing the loose binding between this quire and the previous one. Page layout: Page f57v is traditionally assigned to Cosmo section because its main contents is a circular diagram. However there are no depictions of suns, moons, or stars. Diagram: The diagram of f57v is centered at ~(0.5,0.4) WE-NS. It is slightly off-center in the WE sense, so that the outer edge of the diagram is ~5 mm from the W (free) edge of the panel (which is already missing ~1 mm from the cut-away) but only ~2 mm from the E (binding) edge. The diagram is defined by four pairs of concentric mechanical circles, C1 to C8 from the outside in, with radii ~78 mm and ~70 mm, ~64 mm and ~57 mm, ~51 mm and ~44 mm, and ~39 mm and ~33 mm, respectively. On the BL2014 image the larger circles are about 2% taller than wider; even accounting for that, circles C1 and C2 deviate by up to ~0.5 mm from the ideal ellipse in the NW and NE sectors. These distortions are smaller for the smaller circles: C8 is only 0.5% taller than wider, and had negligible deviations from the ellipse. There is a faint dot (CTR) at the precise center of circles C1-C8, that lies where the compass pin-prick should be. (It is not the more conspicuous dot that is penned near it; see below.) Its coordinates in the BL2014 image are 1733,1462 (in pixels, from the top left corner). Inside circle C8 is a simple squarish cartoon-style cloud (SQC), with a single continuous traced outline. It is inscribed in an imaginary quadrilateral, tilted ~30° CCW, that measures ~12 mm on the NW and SE sides, ~11 mm on the SW side, and ~13 mm on the NE side. The outline of SQC consists of eight circular lobes: four at the corners, ~5 mm wide, spanning a bit more than 180°, and four along the sides, ~4 mm long, spanning ~90°. Inside the SQC cloud there is a small circle C9, hand-drawn with pen, with diameter ~3 mm. The center of this circle is ~1.1 mm away from the center CTR of the other eight, in the 01:00 direction; and thus it barely encloses CTR. There is a penned dot (CPD) inside the circle C9. It is ~0.3 mm away from the center of C9, hence ~1.4 mm away from CTR, also in the 01:00 direction. In the space between the SQC cloud and circle C8 there are four naked human "angels", of indeterminate sex, visible from the chest up, oriented with the heads towards the center. Two are seen mostly from the front, two mostly from the back; two have both arms raised, two have only one. Three have long dropping hair (LH) and one has short messy hair (SH). Here are the combinations (with directions relative to the angel: N: SH, back, two arms straight in "V", at 01:30 and 10:30. W: LH, front, left arm straight at 01:30. S: LH, back, two arms straight in "V", at 01:30 and 10:30. E: LH, front, right arm out at 09:30 then bent 90° up, holding a ball. The f57v angels extend inwards from C8 by various amounts, between ~15 mm and ~20 mm The stretched arms are between ~15 mm and ~20 mm long. The bent arm of the E angel measures ~10 mm to the elbow and then ~12 mm to the hand. Text layout: Within bands defined by circles C1-C8 of f57v, there are four rings of text: * Ring R1 (outermost), line , between circles C1 and C2. * Ring R2, line , between circles C3 and C4. * Ring R3, line , between circles C5 and C6. * Ring R4 (innermost), line , between circles C7 and C8. Faint radial lines, roughly aligned with each other but not with the diagram's center, run across the bands of these four text rings, from circle to circle, passing through word gaps. The line across R1 is at ~10:10, that across R4 is at ~09:45. Ring R2 has two parallel strokes ~1 mm apart, while those across the other rings are single. All strokes are tilted ~20° CW from the radial direction. The three innermost rings R2, R3, and R4 have extra-wide word gaps surrounding these radial lines. The outermost ring R1 does not have such gap. At ~10:45 there is a sudden reduction in "font size" between the words @'v,sa,l,y' and @'saeas' (or @'soeos'), as the oht changes from ~2.0 mm to ~1.0 mm and the nibwd changes from ~0.6 mm to ~0.35 mm. The o-height then increases gradually as one goes CW from that point, being ~1.3 mm at 06:00 and ~1.7 mm at ~10:00. There is a similar reduction of font size at the start of ring R3, which similarly recovers along the ring. All four text rings of f57v are unusual in that they (1) have many words consisting of a single glyph, including isolated @C and @I that don't ligate to anything; and/or (2) they have several occurrences of the rare glyphs @v, @x, @j, and @g, and/or (3) they use five weirdos (&170, &171, &172, &249, &391) that hardly occur at all in other pages. Rings R1, R3, and R4 of f57v contain a mix of single glyphs and normal-looking words. Ring R2 has only 68 isolated glyphs, consisting of four almost-exact copies of the same 17-glyph sequence except for these "hiccups": * @I in the first period becomes @C in the rest, * @j in the first period becomes @m in the rest, * @f in the first two periods becomes @p in the other two. There are nine "labels" on page f57v: * Label L1, line , outside circle C1 at 10:15. * Label N1, line , between figures, at 01:30. * Label N2, line , between figures, at 04:30. * Label N3, line , between figures, at 07:30. * Label N4, line , between figures, at 10:00. * Label D1, line , radial, towards 11:00. * Label D2, line , radial, towards 02:00. * Label D3, line , radial, towards 05:00. * Label D4, line , radial, towards 08:00. Label L1 is an isolated word (@'dairal'), with baseline parallel to circle C1, ~2 mm away from it, reading in the CW direction. Labels N1 to N4 lie inside circle C8. They are oriented in approximately tangential directions, but with straight baselines, and read in the CW direction. Labels N1 and N2 are placed as if they were continuations of the arms of the N angel: N1 is close to C8 and directed towards the shoulder of the E angel, while N2 is closer to the SQC cloud and slightly overlaps the top of the head of the W angel. Label N3 is parallel to the West arm of the S angel, starting near her left elbow, and displaced inwards from it, almost collinear with the arm of the W angel. Label N4 is placed close to C8, between the elbow of the E angel and the armpit of the S angel. Labels D1 to D4 radiate from the side lobes of the SQC cloud, ~30° CCW of the head of the nearest angel. They have straight radial baselines and read outwards. They divide the middle region into four equal quadrants, and the head of each angel is mostly centered in its quadrant. Near the bottom right corner ((0.8,0.9) WE-NS) there is a non-Voynichese glyph that looks like an "y" with a macron accent. The macron protrudes a little on the right side. The "y" looks like a "v" with a tail attached to the upper end of the right arm; the tail starts vertical then bends to the left and extends beyond the left end of the "v". This glyph is omitted from most transcriptions. Figure drafting: Each circle is smooth and precise to a fraction of a millimeter (apart from the image distortion due to parch warping). Some parts are apparently traced with the same yellowish brown ink used for the text and drawing outlines, with ~0.2 mm wide lines. These strokes are often faltering into dashes and dots, as if the "pen" was half-dry. However, some parts -- such as around 06:00 on C2 and C3 -- are very faint (sometimes invisible) and may be pencil traces. The artistic quality of the drawings is rather poor. Faces, hands, arms, and torsos are ungainly, with wrong proportions. The E angel has six fingers. The hair of the N angel is a jumble of strokes, and his arm has a double outline. The S angel has an enormous nose that seems to start high up in the forehead. Voynichese handwriting: The writing as it stands today is very clumsy, with some glyphs malformed, sometimes becoming hard to identify. See below. However, most if not all of these malformations may be the result of bad restoring. See below. The o-height varies between ~1.9 mm for some glyphs in R2 and R3 to ~0.9 mm in R1 after 10:45. Inside C8, it is about ~1.3 mm for the radial labels (N2) and ~1.5 mm for the other ones (N1). Quillos and weird glyphs: There are five weirdos that occur on this page specifically: &170 ("claw") = a polyline with three segments starting at x-height, then going E, SE, E ending at baseline; with a dot above the last seg. This symbol occurs 4 times in text ring R2 (the 4x17 sequence) and once in ring R4, at 00:00. On the first occurrence, the dot seems to be connected to the top corner of the polyline by a very faint stroke. &171 ("fancy puff") = an UNSLASHED one-leg gallows with three loops of specific shapes. This symbol occurs four times in text ring R2 (the 4x17 sequence) and once in ring R4, at 03:00. Starting at the top of the leg, goes W (not E), curves up (CW) by 180° with radius ~0.5 oht, continues E past the leg by ~1 oht, curves up again (CCW) by 270° with same radius, goes S by ~2 oht crossing itself, turns CW by 270° with somewhat smaller radius, goes E for ~2 oht crossing itself, turns sharply to S with a corner, goes S by ~1.5 oht, then curves CCW by 270° with radius ~0.5 oht, goes W by ~1 oht crossing itself, and stops some distance E of the leg. The occurrence in ring R4 is a bit different: it has an extra 270° CCW loop instead of the sharp corner, and instead of the third loop it has a sharp corner to E and an elliptical loop that returns to the corner and ends there. &172 ("updown lambda) = an @r with straight truncated plume starting at mid-height of the @i stem. This symbol four times in text ring R2 (the 4x17 sequence) and once in ring R3, at 08:00. Two symbols similar to this one also occurs on f66r, in the column of single glyphs at left of the text. They have been transcribed as &172 and &195, but may be both different or both the same as the one on this page. &249 ("angular @C") = a polyline starts at baseline, then NW to mid-height, then NE to x-height, then E as a @C-lig. An angular version of @C. It occurs once in ring R4 at 00:05. &391 ("lov") = like Roman "L" with "9" in the NE quadrant, sprouting from anywhere on the bottom stroke, with the horz troke connected to a @v-like chevron. It occurs four times in ring R2 (the 4x17 sequence). Malformed glyphs: Many places: the @a glyphs are excessively open at the bottom. Many places: the @r glyphs have extra-curly plume. It may be yet another weirdo specific to this page. Several places: the @x has an extra-long "neck". * R1, 10:45: the word may be @'saeas' or @'soeos' or any in between * R1, 00:15: the @g may be @m. * R1, 05:00: the isolated @a has an angular left stroke. * R1, 05:45: the @a in @'opaiin' is open at bot and top, like @'ei'. * R2, 10:45: the @j is probably @d. * R2, 01:15: the @I is probably a @C. * R2, 04:15: the &172 has a bent arm, probably should be straight. * R3, 06:00: the @o seems to have an @y-like tail, but it may be a later accident. * R3, 09:00: the @a in @'otal' is open at bot and top, like @'ei'. * R4, 11:30: the @a in @'aiin' has an angular left stroke. * R4, 03:00: the last loop of the &171 fancy gallows is malformed. * R4, 06:10: the @o in @'teodar' is open at bot and top, like @'ei'. * N1, 02:30: the first @a in @'otodaram' is open at bot and top, like @'ei'. The 15 most common words in the page Including 13.00 r 8.00 v 5.00 &170 11.75 l 7.00 x 5.00 &172 10.00 y 6.50 k 4.50 s 10.00 o 5.00 m 4.00 &391 8.50 d 5.00 t 4.00 &171 LATER INTERVENTIONS Stains and wear: Ink density varies a lot in this page. On each "angel" and in the text one can see some barely visible strokes with fuzzy borders, alternating with brown-black, sharp-edged strokes. There are a few light brown smudges, resembling finger marks, near the S and N edges of the panel. On the BL2014 image there is a dark brown stripe with a sharp slightly wavy border along the top edge of the panel. It is ~4 mm wide at the NW corner and tapers down to zero at the NE corner. It does not seem to be a real stain, and is not present on f57r. It is probably just proper shadow, due to the light coming at an angle from S and to that that strip of parch being folded away from the camera. Holes and scrapes: There are no wormholes or visible wormscrapes on f57v. Backtracing and restoring: In spite of the varying ink density, there is no visible evidence of double-tracing or missed joins on the framing circles. The inked parts, even where they are reduced to scattered dashes and dots, are smooth and precisely aligned with the faint non-inked parts. Their appearance contrasts sharply with that of the circles in the Zodiac section, which are visibly non-circular and were restored by free hand. Some traces in the text and angels are very faint, almost invisible, and may be what remains of the original tracing. Examples are the arm of the E angel between elbow and wrist, and the @C glyph in ring R2 at 07:00 The text and figures of f57v show the usual hints of restoring, starting with the large, abrupt, and scattered variations of trace weight, from semitransparent and almost invisible with fuzzy edges to dark brown opaque with sharp edges. Another strong evidence are the many instances of @r and @s plumes that were traced slowly in the wrong direction (CW instead of CCW). And also some of the glyphs with darker traces are often distorted, sometimes turning into other glyphs. There seems to have been at least thre rounds of restoring, Rt1-Rt3. Round Rt1 is visible in scattered glyps or parts thereof. Its traces are presently faded semi-transparent light brown, with fuzzy rather than sharp edges. The word @'aiin' in R4 at 11:30 may be all Rt1 except the plume of the @n. Round Rt2 restored large parts of the text and some of the figures, in a medium-dark brown opaque ink, with sharp edges. For instance, in the words @'otodal' in ring R4 at 07:00, the @'oto' and the second stroke of the @d are probably Rt2, while the rest is Rt1. Round Rt3 restored a few glyphs or parts of glyphs in a darker ink, and often mangled them. For instance, in ring R2 at ~04:30, the &172 weirdo ("upside-down lambda") would be Rt3, while the @C and @o surrounding it would be Rt2. There is occasional whitegrain on Rt1 and Rt2 traces, but not one Rt3 traces. However these distinctions may be false. Some Rt2 may be Rt1 with a more loaded pen, and likewise some or all Rt3 may be Rt2. This caveat must be taken into account when reading the rest of this section. Restoring in the figures is most evident in the E angel. Specifally: * E angel: Rt3 added a dash under the nose, like a short moustache; as well as a dot on the chin, and the upper (ceter-ward) outline of the upper arm. The eyes, mouth, and some parts of the skull and right shoulder outline are probably Rt1. The "billiard ball" on his hand seems to be Rt1 or Rt2 which was partly restored by the next round, which also added a sixth finger. * S angel, Rt2 restored some parts of the outline, including the left side of the face, and added an enormous nose that seems to be half above the eye level. Ther is double outline (probably original and Rt1) in the nape and armpit. * W angel, Rt3 traced the outlines of the chin and throat, nape, eyebrows and nose, the hairline, and half of the left hand. Rt2 restored the mouth and eyes. * N angel: Rt3 traced the thumb side of the hand, the nape, a ~1 mm dash along the left (W) arm, and what may have been intended to be the face but came out quite mangled. Rt3 also added a couple or random strokes among the hair. Rt2 restored most of the outline. The rest of the left (W) arm outline, the top of the head, and the hair strands seem to be a mix of original and Rt1 traces. The central circle C9 and the almost-central dot CDT are Rt1, while the outline of the cloud SQC is Rt2 or Rt3. One possible classification for the glyphs @r, &170, &171, @y, @I, &172 in R2 starting at ~00:10 would be: * @r: most of stem is Rt1, while the darker dot at the base of the stem and the upper half of plume are Rt2. The latter was traced in the wrong direction (CW rather than CCW) and the extreme curl is Rt1 or Rt2, not original. * &170: the original part is the faint line connecting the first corner to the darker dot (which is invisible in the next two instances of this glyph, and maybe barely visible in the fourth). The rest of the glyph is Rt1. * &171 (the "triple-loop gallows"): the leg is Rt1, and the final part of the flourish starting just before the sharp corner is Rt2. The rest of the glyph is Rt3. * @y: Rt2. * @I: The @i stem and the first 1/3 of the ligature line is Rt1. The rest of the ligature line is Rt2. * &172 ("upside-down lambda): Rt1. If there was any backtracing, it seems impossible to distinguish from the Rt1 restoring. However the double outline on the left (W) arm of the N angel has the same weight, width, and color, so it may be backtracing by the Rt1 Restorer. Coloring: The hair of the four "angels"s is grushed in yel. That seems to be the only paint applied to this panel. INTERPRETATIONS Circle drafting The circles must have been traced with a compass using a very fine drafting instrument. The traces of the inked parts are too thin to have geen made with a quill pen. They may have been made with some version of the compass ink point. This device -- like a pair of tweezers with sharp but rounded tips -- was a standard and compass accessory heavily used for technical drafting until laser printers became available. It is simpler to make than a steel pen, thus may have been available in the 1400s and even earlier. Large parts of the circles are very faint, even invisible, and show no trace of ink. It is possible that each circle was drawn once with a pencil point, and then some parts were restored with the ink point, with the compass centered at precisely the same point (CTR). However, the transition between inked and non-inked part is not clear cut, and the inked trace often breaks down to irregular dots and dashes. Thus it seems more likely that each circle was drawn once with the ink point, but the ink flow was irregular and often stopped altogether, leaving only a faint scratch. Glyphs mangled by restoring Text ring R2 would be precisely 4 copies of the same sequence of 17-glyphs. Restoring could explain the "hiccups" in this repetition. The @j and @I in the first period must have been originally a @d and a @C, and the first two @f must have been @p; but the original glyphs, now invisible, were probably mangled by Rt1 if not by the original scribe himself. Circle C9 and the penned dot CDT near the center were apparently intended to be the center of the diagram, but are offset from it. Thus it is likely to be an addition by one of the Restorers, who failed to recognize the true center point CTR. Label attachment to figures It is not entirely clear how the "tangential" labels inside circle C8 (units N1-N4) correspond to the four angels. However, since N1 and N4 are almost perfectly aligned with the outstretched arms of the North angel, even though there was enough space for N4 along circle C8, it seems more likely that those labels relate to the arms of the N and S figure, rather than each label being attached to one angel or to one gap between two angels. The non-Voynichese symbol in the SE corner Years ago it was conjectured that the non-Voynichese glyph in SE corner of f57v could be the Saturn symbol. However, a manuscript from the 1400s has been found that shows the 10 Arabic digits. It has two alternatives for "5", and one of them fairly resembles that corner glyph. On the other hand, there is also another Latin manuscripts where the letter "g" is written precisely like that glyph. Considering its placement, the mark at the bottom right corner could be an aborted quire number. But this folio should the the first of the quire that ends with f66v, so a quire number here would not make sense. Perhaps the Binder started writing the quire number but then decided to flip the bifolio f57+f66 so that this folio became first instead of last. Starting point of text rings The starting point for reading the text rings R1-R4 has traditionally been assumed to be the faint single or double radial line crossing each band in the NW sector. For rings R2-R4, this choice seems pretty safe since each of those rings has an extra-wide word space crossed by the corresponding radial line. There is no similar gap in ring R1 around its radial line, but label L1 outside circle C1, at 10:15, has traditionally been interpreted as a title or "start here" key, confirming that the start of the text is the @v just after the radial line. However, the drastic and sudden reduction in "font" size at about 10:45, by almost 50%, makes it more likely that the start of R1 is actually at that transition. The similar reduction of font size at the start of ring R3 seems to confirm this interpretation. Then label L1 could well be the LAST word of ring R1 -- placed outside the diagram because the Scribe miscalculated and ran out of space at the end of that text ring. That would confirm the suspicion that the radial strokes across the text rings are not original, but additions by a later reader who made the same incorrect assumption about the R1 starting point that we have been making all along. The yellow color The yellow color seems to be the standard translucent yellow (yel). Earlier conjectures that it may have been diluted brown ink, or hard waxy color pencil, or a thick glue-like paint were almost certainly wrong.