Archives for Mosaical Metrology and Mosaistics, AMMM Vol. II, No.
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Archives for Mosaical Metrology and Mosaistics, AMMM Vol. II, No.
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confident that “This value is well within the realm of reality.”9) However, this would only be realistic if one single person such as Moses were expected to carry the tablets in a rucksack or two handbags from the Sinai to the Promised Land. Of course, this violates the biblical rules on transportation in the Ark of the Covenant. § 4. The objections raised in Niv Hamidrashia by my learned friend are entirely beside the point, since the issue is not at all whether Moses was able to carry both tablets, as he does on Rembrandt’s famous painting or Michelangelo’s great sculpture, which my worthy opponent may have had before his mind’s eye.10) While this is a matter of artistic license, the specifications set by the Bible (Exodus 25, 16 and 21) require the Tablets of the Law to –––––––––––––– 9) Sic Kaufman (N. 7) pp. 26 and 34, who interprets the talmudic passage “and (their thickness is) three” (Note  15 infra)as fingerbreadths in order to “preserve the notion of a Tablet”, which “implies that the thickness is much less than the length or breadth” (Idem pp. 28–29), a thickness of three handbreadths being absurd, indeed.10) As a design problem of experimental archaeology, the weight of the tablets had to be such as to be carried in a coffin-like wooden box (Aron) by several men, but not single-handed by one. [7]
[The printed graphics were replaced by their equivalents from this website]  The rectangle ABCD represents the Ark of the
Covenant ofYaHUH (Yahuweh), which is a box made out of acacia wood for transporting the two stone Tablets of the Law from the Sinai to the Promised Land. The Bible gives its precise measurements: “two cubits and a half was the length of it, and a cubit and a half the breadth of it,” (Exodus 37, 1). In it is the circle later named after Thales of Miletus touching the short sides of the box in the middle at points E and F, while cutting its long sides at points K, L, M, and N. The rectangle KLMN represents the
MosaicalTablets of the Law lying side by side, divided in two by line OP. The four right triangles KLM, KLN, KMN, and LMN make use of the later so-called Pythagorean numbers 3, 4, and 5 divided by two (3 : 4 : 5 = 1.5 : 2 : 2.5), each of the Tablets being 1 by 1.5 cubits, or translated into handbreadths: 6 by 6 and 3 (Ammah wa-Chetzi), as the Babylonian Talmud (Nedarim 38a) puts it, if duly
corrected.[Professor Dr. Asher Kaufman’s small tablets are marked blue.] [8]
be laid into the Ark, and we know that Moses put them there (1. Kings 8, 9).11) The Ark was carried by staves (Exodus 25, 14), which may be arranged lengthwise at 1.5 cubits distance or breadthwise 2.5 cubits apart (Exodus 25, 10), the former like a stretcher or hand-barrow for two carriers, and the latter like the axles of a four-wheel chariot or sedan with at least four carriers, so that it seems likely that the tablets had the average weight of an adult human body.12) § 5. A well-fitting glove reveals the shape of the hand for which it was made, and in the same way the measurements of the Tablets of the Law are implicit in those of the Ark of the Covenant, as shown by the diagram on p. 8.13) This being so, –––––––––––––– 11) Cf. 1. Kings 8, 9: “There was nothing in the Ark save the two stone tablets, which Moses put there at Horeb.” 12) See Ed Metzler, Discovering Mosaistics (N. 1) p. 34. If each of the Tablets of the Law weighed 36 kilograms, both of them had 72 kilograms or 144 metric pounds (= 158.73 English pounds avoirdupois), which is a good average human weight to be carried on a stretcher or in a coffin, cf. Note 10 supra. 13) The trouble with
Kaufman’s tablets (N. 7) p. 34 is thatthey bear no relation to the measurements of the Ark, and make it look like a sham package, since they are way too small coveringonly one square cubit of its bottom, which is 3.75 square cubits. [9]
the Bible could afford to refrain from stating them explicitly, for everybody in his right mind is able to infer that each of the tablets is one by one and a half cubits.14) At some point in history, probably during the Persian period with the introduction of the seven-palm cubit, it was deemed necessary to clarify that the Bible means the six-palm cubit by translating the measurements of the tablets into handbreadths: six by six and three. These three numbers were then mistaken to refer to the three dimensions, reading “and their thickness is three” (Nedarim 38a), which must again be emended by deleting the words “their thickness is”, that were once erroneously inserted.15) –––––––––––––– 14) See Ed Metzler, Discovering Mosaistics (N. 1) p. 32 onmy discovery of these measurements. 15) The Babylonian Talmud (Nedarim 38a) reads: ha-Luchot ’Orkan Shishah we-Rochban Shishah we-(‘Oviyan) Sheloshah, “the Tablets, their length is six, and their breadth is six and (their thick- ness is) three.” Their breadth of 6 +
3 = 9 handbreadths is identicalwith that of the Ark of the Covenant: Ammah wa-Chetzi Rochbo, “a cubit and a half was the breadth of it” (Exodus 25, 10 = 37, 1), while the length of the Tablets is a cubit or 6 handbreadths each, adding up to the length of the Ark (Ammatayim wa-Chetzi, “two cubits and a half ”), of which half a cubit or 3 handbreadths are needed for getting hold of the Tablets, cf. Ed Metzler, Discovering Mosaistics (N. 1) p. 80 Note 34.[10]
Fractions Resulting from the Geometry of the Tablets § 6. The thickness of the tablets is one tenth of a cubit, as I found out when I discovered the three-dimensional structure of the Ten Command- ments.16) Their text was written boustrophedon in 10 lines of 32 letters each, entered into squares like those of a crossword puzzle, which disclosed the proportions of the Tablets of the Law.17) Since they were designed to be carried from the Sinai to the Promised Land of Israel, it was only a matter of common sense to use as much of their surface for writing as possible, both front and reverse as the Bible says (Exodus 32, 15). Of course, the two –––––––––––––– 16) Cf. Ed Metzler, Discovering the Three-Dimensional Structure of the Ten Commandments (Herborn 1986), forming chapter II of my book Discovering Mosaistics (N. 1) pp. 61–92; as well as Asher S. Kaufman (N. 7) p. 25, who writes about it: “His work reveals some brilliant insights, especially his interpre- tation of the verse Exodus 32, 15.” 17) See Ed Metzler, Western Philosophy (N. 5) p. 8 Note 9; and Discovering Mosaistics (N. 1) pp. 71 Note 16, and 77 Note 29 on the arrangement of letters within squares as in ancient Egypt. [11]
sides had to be numbered as face A and face B by using the alphabetical letters Aleph and Bet, and this is how I got the number of 32 letters per line, namely by counting from the initial Aleph of the text to the first occurrence of the letter Bet, which is the first letter of the second line on the reverse of the first Tablet of the Law.18) § 7. The 10 lines (Sephirot or Devarim) run in vertical columns from front to reverse, and from reverse to front, passing over the top of the tablets to their opposite sides on each of the lines in an uninterrupted chain of letters, 15 up and 15 down, one on top, and one to the side connecting the lines and marking the space between them, as can be seen from the diagram on p. 13.19) Each tablet –––––––––––––– 18) Cf. Ed Metzler, Western Philosophy (N. 5) Note 21. In counting, double or triple letters had to be reduced to singles, for the original text was written in an uninterrupted chain of letters without spaces between the words, see Ed Metzler, Discovering Mosaistics (N. 1) pp. 69, 72, and 136.19) The letter connecting lines 5 and 6 is the Kof in Poked Awon Avot “visiting the iniquity of the fathers” (Exodus 20, 5 = Deuteronomy 5, 9), which also connects the two Tablets of the Law, and being repeated at the beginning of the second tablet, it brings the number of letters from 319 to 320, cf. Ed Metzler, Discovering Mosaistics (N. 1) pp. 75 Note 24, and 144 Note 34. [12]
of the Decalogue  [13]
has 10 vertical and 15 horizontal lines, yielding 150 squares of 0.1 cubit, which is also its thickness because of the letter-unit on its top, so that it consists of 150 cubic letter-units by reason of its geometrical properties.20) These determine both the number of 320 letters on the inscription of the Tablets of the Law and their weight of 36 kg each, which is the heaviest weight-unit of the Bible known as the ancient Israelite talent (Kikar), and divided into 3000 Shekels or 6000 drachmae, multiples of the 150 letter-units.21) § 8. In Hebrew the letter-units were called Midot Ketivah or Ketivot, and their number of 32 survives in the Baraita of 32 Rules (Midot) as well as the 32 mysterious paths (Netivot) of –––––––––––––– 20) Understanding the geometry of the tablets and the ark as well as its metrological and musical applications is what is meant by perceiving the harmony of the spheres ascribed to Pythagoras and Moses (above Notes 3 and 4), which like the Greek synienai used by Porphyrius (Vit. Pyth. 30) here stands for intellectual rather than sensual perception, insight rather than hearing, shared at least by Moses, the author of the 10 spheres (Sephirot) of the Decalogue, with Pythagoras, cf. Ed Metzler, Western Philosophy (N. 5) Note 7; and Discovering Mosaistics (N. 1) p. 135.21) On the number of 3000 Shekels per talent, see Exodus 38, 25–26; and Ed Metzler, Discovering Mosaistics (N. 1) p. 40. [14]
wisdom in the Sepher Yetzirah.22) This basic book of Kabbalah, which hitherto was looked upon merely as a work of Jewish mysticism, represents a mystification of the graphical details of the Mosaical Tablets of the Law, as I discovered when comparing my results with its detailed description of the Ten Sephirot.23) Like Sepher “book” and Sopher “scribe”, the term Sephirah has a clear graphical connotation in Hebrew. It is a synonym of Davar “word”, which originally meant “drift”, and stood for the 10 boustrophedon lines of the Decalogue that were written like furrows ploughed by an animal being driven back and forth across the field. Similarly, the 32 Netivot proved to be the 32 letter-units of every line.24) –––––––––––––– 22) Cf. Ed Metzler, Discovering Mosaistics (N. 1) pp. 131–2, and 137–8. See also the Akdamut Millin by Rabbi Meir ben Itzhak of Worms, Germany, an acrostic poem forming a double alphabet, followed by the author’s name, and ending with the 32-letter wish, Yigdal be-Torah ube-Ma‘assim Tovim, Amen, we-Chazak we-Ematz, which precedes the Reading of the Torah on Shavu‘ot, including the text of the Decalogue (below Note 36). 23) Their identity with the Decalogue was not recognized by Gershom Scholem, cf. Ed Metzler, Discovering Mosaistics p. 150. 24) By mistaking the initial Kaf for Nun, cf. Ed Metzler, Discovering Mosaistics (N. 1) pp. 132 Note 9, and 137 Note 22.[15]
in the Omer and Tzintzenet Laid Before YaHUH § 9. Another way of dividing the Tablets of the Law is by drawing 6 vertical and 10 horizontal lines not for writing purposes, but for reasons of weights and measures, yielding 60 nearly square rectangles of one handbreadth or 1/6 cubit by one tenth of the length of the tablets or 0.15 cubits = 3/20 · 1/6 = 1/40 square cubits. Since the thickness of the tablets is 1/10 cubit, one sixtieth part or Manah “portion” of them is 1/400 cubic cubits or 222 cm3, if the Mosaical cubit measures 44.6 cm.25) Its weight is 6000 drachmae (Hebrew –––––––––––––– 25) On the cubit of 44.6 cm, see Ephraim Stern, Weights and Measures, in Encyclopaedia Judaica, vol. 16 (1974) at 379. Contra, Asher S. Kaufman (N. 7) pp. 27 and 34, who uses a Mosaical cubit of 42.8 cm, which he distinguishes from “the normal standard of 44.65 cm, already in use at the time of King Solomon”, cf. Idem, Determining the Length of the Medium Cubit, in Palestine Explora- tion Quarterly, vol. 116 (1984) pp. 120–32. However, the Mosaical cubit is identified by the systematic context of Mosaical metrology, since a cubic cubit of 44.63 cm equals 40 Omers of 2.22 liters each, see Ed Metzler, Discovering Mosaistics (N. 1) p. 24 Note 21, p. 80 Note 33, and pp. 194–95 Notes 15 and 18. [16]
Beka‘ “half-Shekels”) divided by sixty, equalling 100 drachmae or 600 grams, if the archaeological value of one ancient Israelite Beka is 6.0 grams.26) Hence the density of the Manah weight-stone, and of the Mosaical Tablets of the Law is calculated by dividing its weight of 600 grams by its volume of 222 cm3, which is 2.7 and corresponds to the specific gravity of granite.27) § 10. The volume of one Manah weight-stone being 222 cm3 proved to be exactly one tenth of the empirical value, by now generally accepted in archaeology for the ancient Israelite Omer, which is about 2.2 liters and one tenth of an Ephah or Royal Bat of approximately 22 liters.28) Thus, the Manah in the Omer had a metrological meaning, –––––––––––––– 26) According to Ephraim Stern (N. 25) at 387, the seven weight-stones found in Israel with Beka or B written on them have an average weight of 6.03 grams. 27) Cf. Ed Metzler, Discovering Mosaistics (N. 1) pp. 25 Note 22, 34 Note 4, 76 Note 27, and 84 Note41, confirmed byKaufman (N. 7) pp. 31–34. Although granite is a very hard stone, we know from the pyramidion of Amenemhet III and the obelisk of Sesostris I that it could be inscribed in Middle Kingdom Egypt, regardless of how it was done. 28) See Ephraim Stern (N. 25) at 380; and Exodus 16, 36: “Now an Omer is the tenth part of an Ephah.” [17]
the Omer full of Manah laid before YaHUH [The printed graphics were replaced by their equivalents from this website]  The legendary “broken tablets” of Moses were mathematical fractions of the Mosaical Tablets of the Law, which according to talmudic tradition bore no inscription, and filled the empty space of half a cubit or three handbreadths in the Ark of the Covenant, one handbreadth between the tablets, and one between them and the wood on either side, being sideways wrapped in cushioning fleece (Tzintzenet, diminutive of Tzinah, from Tzon “sheep”), as indicated on the above diagram by the six vertical blue lines. And Moses (Exodus 16, 33) said about the Ark (El ha-Aron, correct for El Aharon): Take a little fleece (Tzintzenet), and put therein an Omer full of Man, i. e. 10 Manah weight-stones, and lay it before YaHUH, i. e. the first tablet beginning with “I am YaHUH” (Exodus 20, 2). The Omer is a vertical slice of one sixth of a tablet or one handbreadth, which is horizontally cut up into ten portions (Hebrew Manah) of 0.15 cubits, and 0.1 cubit thick as determined by the one letter-unit on top of the tablets, divided for writing into 150 cubic letter-units of 0.1 cubit (pp. 8 and 13). Since the Manah is one handbreadth wide and wrapped in fleece, the other spaces are filled with stones of 0.1 cubit, leaving 6 · 1/45 cubit for the fleece. [18]
rather than a biological one, constituting the daily ration of grain for one person distributed from Omer pots by judges over tens in conformance with the decimal system of judicial structure and the biblical measures of volume.29) The Omer full of Manah laid before YaHUH (Exodus 16, 33) was neither “before the Ark”, as Rashi thought, nor a “golden pot” within it, as Rabban Gamaliel the elder taught Saint Paul, but a row of ten Manah weight-stones adding up to one Omer, and laid in front of the opening words “I am YaHUH” of the first Tablet of the Law.30) § 11. When carrying the Ark of the Covenant, the broken tablets filled its empty space of half a cubit (Luchot we-Shivrey Luchot Munachim ba-Aron), as the diagram on p. 18 demonstrates, –––––––––––––– 29) Even today a quorum of 10 Jews is called a Minyan after the 10 portions (Manah) in the Omer, see Ed Metzler, Discovering Mosaistics (N. 1) pp. 44–5, 118 Note 46, and 178 Note 38. Contra, the entomologist Frederick Simon Bodenheimer, who believed that it was the excretion of scale-insects on tamarisks. 30) Cf. Paul’s Epistle to the Hebrews 9, 4: the Ark, “wherein was the golden pot that had manna, and Aaron’s rod that budded, and the tables of the covenant.” The rod may be a Torah “pointer” (Moreh “teacher” or “road sign”), whence “herm”, below Note 45. [19]
in order to prevent the Tablets of the Law from sliding sideways and damaging each other.31) The broken tablets had to be wrapped in fleece for cushioning them off against the Tablets of the Law so that the Manah stones could only be used once in front of YaHUH, while the spaces between and behind the tablets were filled with twice fifteen of the smaller cubic letter-units, making up 1/5 of one tablet and weighing 600 Shekels or 7.2 kg called a Tzinah “golden fleece” (1. Kings 10, 16), in contrast to Tzintzenet “little fleece” (Exodus 16, 33), being but 1/6 tablet of 500 Shekels or 6 kg.32) After the geometry of the Tablets of the Law had fallen into oblivion, they were believed to have been broken in anger.33) –––––––––––––– 31) See Ed Metzler, Discovering Mosaistics (N. 1) pp. 42–43 and 58. The length of the Ark (above p. 18)
adds up to 2.5 cubitsfrom right to left: 1/45 + 1/6 + 1/45 + 6/6 + 1/45 + 1/10 + 1/45 + 10/10 + 1/45 + 1/10 + 1/45 = 225/90 = 2.5 cubits. 32) Cf. Ed Metzler, Discovering Mosaistics (N. 1) pp. 43 Note 30, 51 Note 48, and 195 Note 16. The Golden Fleece of Greek mythology (below Note 46) preserves the original idea that Tzinah and Tzintzenet derive from Tzon “sheep”. 33) See Exodus 32, 19. The Talmud reports that the Broken Tablets bore no inscription, and lay in the Ark of the Covenant, cf. Ed Metzler, Discovering Mosaistics (N. 1) pp. 42–43 Notes 27–28. [20]
Greek for Hebrew Merkavah of Jewish Mysticism § 12. The deification of the Mosaical Tablets of the Law resulted from their being deposited in the Holy of Holies of the First Temple, built by King Solomon in Jerusalem almost 500 years after Moses had made them in the Sinai, thus idolizing the very same stone that prohibits idol worship, and naming Israel’s god YaHUH (Yahuweh) after its first two words.34) Consequently, the wooden box (ha-Aron), in which they were carried, became the divine chariot (Hebrew Merkavah) of Jewish mysticism, whence the Pythagorean harmony of the spheres (from Greek harma “chariot”).35) The –––––––––––––– 34) Cf. Ed Metzler, Western Philosophy (N. 5) Notes 5 and 29; Discovering Mosaistics (N. 1) pp. 86 Note 46, and 142 Note 31; as well as p. 18 supra. 35) Anthropomorphism changed the box in which the stone tablets lay into the dwelling (Mishkan), in which YaHUH resided, the throne, on which he sat, or the chariot (Merkavah) that he rode (above Note 12), likewise personified as Harmonia and Hermes, see Ed Metzler, Discovering Mosaistics (N. 1) p. 146 text accompanying Note 40; and Western Philosophy (N. 5) Note 32; cf. Note 45 infra. [21]
biblical basis of Merkavah mysticism is the first chapter of the prophet Ezekiel, which has always been understood as a description of the graphical details of the Tablets of the Law, and this is why it has been selected as the Haftarah for Shavu‘ot “Pentecost”, which is a holiday commemorating the legislation of the Decalogue.36) § 13. After discovering the Jewish blueprints of Pythagorean philosophy in geometry, religion, and vegetarian diet reminiscent of Daniel 1, 8–16 I investigated whether or not the musical theory of Pythagoras likewise had Mosaical roots, and so I found the congruence of our diatonic scale with the 10 or 15 horizontals of the Tablets of the Law, as superimposed in the diagram on p. 23.37) First –––––––––––––– 36) The Sefer Yetzirah (chapter 1, no. 8) quotes correctly Ezekiel 1, 14 on the boustrophedon Decalogue, see Ed Metzler, Discovering Mosaistics (N. 1) p. 137 Note 21.37) Our diatonic scale is not a natural necessity, as pointed out by Helmholtz (N. 2) p. 249, but a man-made geometrical con- struction resulting from mathematical convenience and feasibility, mainly from the fact that 7/10 is a good approximation of the square root of 1/2 = 0.5, which divides the octave into two equal intervals, while the further subdivision of each half-octave into three tones or six semitones is simply a matter of mathematical interpolation, cf. Notes 43, 49, and 50 infra. [22]
with the 10 or 15 Horizontals of the Tablets of the Law [The printed graphics were replaced by their equivalents from this website] 
[23]
I noticed that the major Seventh (c : b = 8/15) is defined in fifteenth, the common denominator of the frequency ratios in the upper tetrachord from the Fifth (c : g = 2/3 = 10/15) to the major Sixth (c : a = 3/5 = 9/15), and ending with the Octave (c : c’ = 1/2 = 7.5/15).38) In the lower tetrachord only the major Third (c : e = 4/5 = 12/15) can be turned into fifteenth, the Fourth (c : f = 11/15), the major Second (c : d = 13/15), and the Semi- tone (c : c# = 14/15) being less than a quartertone off the even-tempered standard.39) § 14. Next I observed that the 10 horizontals of the Tablets of the Law are equally relevant to our diatonic scale, supplying better values for the lower tetrachord, which proved to be constructed –––––––––––––– 38) On the definition of the major Seventh (c : b = 8/15) as well as the other frequency ratios see Helmholtz (N. 2) pp. 17, 337, and the Table of Intervals by Ellis pp. 453–56. 39) According to Ellis in Helmholtz (N. 2) p. 526, even if they were a quartertone off, European ears do not appreciate the neutral interval of a quartertone between two semitones of our chromatic scale, and hence persist in mistaking it “sometimes for one and sometimes for the other.” Therefore, the above deviations from the normal frequency ratios are negligible quantities, because the differences c# 15/16 – 14/15 = 1/240, d 8/9 – 13/15 = 1/45, and f 3/4 – 11/15 = 1/60 are very
slight.[24]
in analogy to the upper tetrachord, since what the fifteenths are for the one, the tenths are for the other.40) At the top of the lower tetrachord, there is the Fourth (c : f = 3/4 = 7.5/10) corresponding to the Octave (c : c’ = 1/2 = 7.5/15) on top of the upper tetrachord, followed by the major Third turned into tenths (c : e = 4/5 = 8/10) corresponding to the major Seventh (c : b = 8/15), by the major Second (c : d = 9/10) corresponding to the major Sixth (c : a = 3/5 = 9/15), and finally by the fundamental Prime (c : c = 1/1 = 10/10) corresponding to the Fifth (c : g = 2/3 = 10/15) in the upper half-octave.41) The interval between the two tetrachords is neither tenths nor fifteenths, but f – g = 3/4 – 2/3 = 1/12 = (1/10 + 1/15) : 2, the arithmetic mean of both.42) –––––––––––––– 40) What is so special about tenths and fifteenths that the common denominator of the frequency ratios in the lower tetra- chord is 10, and in the upper one is 15, has mathematical reasons connected with the central importance of the even-tempered Tri- tone f# 7/10, of which Helmholtz-Ellis were not aware, who have but f# 99/140, whereas 7/10 = 98/140 is lacking (below Note 49).41) For the major Second (c : d = 9/10) see Helmholtz-Ellis (N. 2) pp. 17, 332, and 454, from which 8/9 differs by only 1/90. 42) Cf. Note 51 infra.[25]
of the Ten Spheres (Sephirot) or Ten Commandments § 15. To Greek or Roman ears Mosheh, the Hebrew form of Moses, transcribed as Mousai or Latin Musae, does not sound like a masculine singular, but like a feminine plural, and hence the personification and deification of the Mosaical arts and sciences adopted by the Graeco-Roman world led to the nine goddesses known as the Muses.43) In keeping with the Torah of Moses, the Muses are concerned with music and literature rather than sculpture and painting prohibited by the Decalogue as objects of idol worship.44) On Greek soil the Ark of the Covenant or divine –––––––––––––– 43) The Mosaical arts of alphabetical music and writing pre- vailed in antiquity, as the Muses did over the Sirens, and as Apollo did over Marsyas, because they were superior to their competitors, and so did modern European music because of the superiority of its man-made scale, cf. Note 54
infra.44) Cf. Exodus 20, 4 = Deuteronomy 5, 8: “Thou shalt not make thee any sculpture (Pessel), or any picture (kol-Temunah)”, because “Thou shalt not bow down thyself unto them, nor serve them!” (Exodus 20, 5 = Deuteronomy 5, 9). [26]
chariot (Harma) was also personified as Harmonia, who became the wife of Kadmos, the brother of Europa and legendary founder of Thebes, the Boeotian city of David, and deified as Hermes, the Latin Mercurius (by syncope from Mercavarius), who like the Harma (Merkavah) whence his name travels between heaven and earth.45) § 16. In Greek mythology Apollo’s lyre was given to him by Hermes, as the Golden Fleece of the Argonauts was also his gift, or translated into plain demythologized language, both came from the Ark, the Golden Fleece being an ingot of gold equivalent in weight to the twice fifteen cubic letter-units between and behind the Tablets of the Law, named after the fleece (Tzinah), in which they were wrapped,46) and the classical 10-string –––––––––––––– 45) The Greek god of travelling salesmen Hermes derives from harma “chariot”, the Ark of the Covenant of YaHUH, and similarly the Roman god of merchants Mercurius “Mercury” from Merc(a)v(a)rius, whence also mercari “to trade” and merx “mer- chandise”; cf. Note 35 supra. The brother of Moses,
Aharon (bymetathesis from ha-Aron “the Ark”) is likewise a personification, see Sendrey (N. 4) p. 61; and above p. 18. As Jews wear hats before the Ark, so does Hermes holding his caduceus or Aaron’s rod. 46) See 1. Kings 10, 16; and above Note 32.[27]
as Blueprints of the Kinnor [The printed graphics were replaced by their equivalents from this website]  If the 10 strings of an ancient Hebrew lyre (Kinnor or Assor) are tuned to produce the musical note c = 15/15, then c’ = 7.5/15; b = 8/15; a = 9/15; g = 10/15; f = 7.5/10; e = 8/10; d = 9/10; c = 1. [28]
Hebrew lyre being designed after the 10 vertical lines on the Tablets of the Law, as illustrated by the diagram on p. 28.47) Since they look like the warp (Hebrew Manor) of a loom, the lyre is called Kinnor in Hebrew (by assimilation from Ki-mnor), while the 10 or 15 horizontals of the tablets are like its weft, and yield the most ancient method of tuning the lyre down to the time of Orpheus (by metathesis from Hebrew Rophe’-us “healer”) into the tetrachords c–f and g–c’.48) § 17. The middle of the Octave (c : c’ = 1/2) dividing it into two equal intervals is the even- tempered Tritone (c : f# = 7/10), which is a good approximation of the square root of 1/2 available already at the time of Moses, for (7/10)2 = 49/100 and 50/100 = 1/2.49) From this fixed point, the –––––––––––––– 47) Cf. Josephus Flavius, Jewish Antiquities, VII 12, 3; and Sendrey (N. 4) pp. 274–75, who mentions (p. 61) that Cinyras, the Greek mythical hero, is a personification of Hebrew Kinnor “lyre”. 48) See Helmholtz (N. 2) p. 255. The Kinnor is also like the furrow (Hebrew ke-Nir) or boustrophedon lines of a ploughed field (Note 24 supra). On Orpheus/Ropheus cf. Italian Orlando/Roland. 49) Cf. Richard Gillings, Mathematics in the Time of the Pharaohs (MIT Press 1972) pp. 214–17; and Sendrey (N. 4) p. 125. Ellis in Helmholtz (N. 2) p. 455 fails to give 7/10
for the Tritone.[29]
lower half-octave 10/10 – 7/10 = 3/10 is further subdivided by mathematical interpolation into three tones or six semitones, and so is the upper half-octave 7/10 – 5/10 = 2/10 = 1/5 = 3/15 with an aberration of plus/minus 1 % or less from the even-tempered standard, as elaborated in the charts on p. 31.50) This explains the musical significance of the 10 or 15 horizontals on the Tablets of the Law, which are not an arbitrary whim, but a mathematical necessity. By moving each half-octave a semitone away from the middle, the two tetrachords become disjunct, creating the seventh tone of the heptatonic scale.51) § 18. The hebdomadal periodicity of the Sabbath is a sign of Jewish identity, shared by the heptatonic scale and the seven-day week.52) Yet, –––––––––––––– 50) A quartertone is +
2.9302 % or – 2.8468 %.51) A semitone up f# – g = 7/10 – 2/3 = 1/30 = (1/15) : 2, and a semitone down f – f# = 3/4 – 7/10 = 1/20 = (1/10) : 2 yields the whole tone between the tetrachords f – g = 3/4 – 2/3 = 1/12 = (1/10) : 2 + (1/15) : 2 = (1/10 + 1/15) : 2, see text accompanying Note 42 supra.52) Cf. Exodus 31, 13 and 17: “It is a sign between me and the children of Israel for ever”, just like circumcision performed on the octave of birth (Genesis 17, 11 and 12). [30]
the Twelve-Semitone Scale
the Hexatonic Scale
the Heptatonic Scale
[31]
music was only part of the cultural package deal transmitted from Solomonic Israel to Greece in the golden age of the Israelite (18th) dynasty of Egypt under the House of David-Thutmosis I, and during the centuries that followed, when the Hebrew-Phoenician alphabet gradually superseded Linear B without the intermission of the Greek Dark Ages, as the alleged relapse into illiteracy is called, invented to deny the impact of Israel on Egypt and Greece.53) Like the system of Mosaical metrology, which I discovered ten years ago, the European tonal system springs from the geometry of the Ten Commandments or Sephirot “spheres” on the Tablets of the Law conceived by Moses and perceived by Pythagoras, – being the music of the geometrical mind.54) –––––––––––––– 53) Cf. Ed Metzler, Western Philosophy (N. 5) Notes 4, 24, and 26;
Discovering Mosaistics (N. 1) p. 50 Note47.54) Similarly, our law is called “the law of the geometric mind”, cf. Bernhard Grossfeld, Zahlen und Geometrie als Rechts- symbole, in Festschrift Rüdiger Schott (Berlin 1993) pp. 345–60 Note 4. See also Ed Metzler, Discovering Mosaistics (N. 1) p. 120 Note 52 on the alphabet and the
geometrical mind. The musicalalphabet of our diatonic scale is a geometrical construction, and as such an expression of universal mathematical truth. [32] |
|
– at USA-$ 20.– per issue – Discovering the System of Mosaical Metrology AMMM
VOL. 1, NO. 1 = ISBN 3-924448-03-5 * Discovering the Three-Dimensional Structure of the Ten Commandments AMMM
VOL. 1, NO. 2 = ISBN 3-924448-04-3 * Discovering the Two-Dimensional Structure of the Alphabetical Order AMMM
VOL. 1, NO. 3 = ISBN 3-924448-05-1 * Discovering the Mosaical Roots of Kabbalah AMMM
VOL. 1, NO. 4 = ISBN 3-924448-06-X * Discovering the Israelite Identity of the Pyramid Builders AMMM
VOL. 1, NO. 5 = ISBN 3-924448-07-8 * Conflict of Laws in the Israelite Dynasty of Egypt AMMM
VOL. 2, NO. 1 = ISBN 3-924448-09-4 * The Impact of Israel on Western Philosophy AMMM
VOL. 2, NO. 2 = ISBN 3-924448-10-8 * The Mosaical Roots of European Musical Theory AMMM
VOL. 2, NO. 3 = ISBN 3-924448-11-6 * On Mosaical Matrixes and the Metzler Formula AMMM
VOL. 2, NO. 4 = ISBN 3-924448-12-4 * inscription on the Tablets of the Law, and to prove the priority and centrality of Hebrew script in the world history of writing.” Bibliographical Quarterly of the Jewish Nationaland University Library in Jerusalem, Israel, VOL. 60, NO. 1–2 (1986) pp. 287–88, *3045–47. * ISBN 3-924448-11-6 |
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by Dr.
Ewald (Ed) Metzler-Moziani.
