“Numbers and combinations of numbers are used in the sacred writings to convey instruction under a figurative guise, and ignorance of numbers often shuts out the reader from this instruction.” —St. Augustine,[1]De doctrina christiana, II.xvi.25
If someone has a better link to this translation in English rather than Latin, please provide it.
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“Most men nowadays,” he says, “take part in music for the sake of the pleasure it gives; but originally it was included in education on the ground that our own nature itself… wants to be able not merely to work properly but also to be at leisure in the right way.”
If someone can find a link to a translation of Aristotle’s Politics, Book 8, that is closer to this quotation than what we cite in the footnote in the paragraph above (Aristotle, Politics, Book 8), please let us know so we can add a footnote and link to it.
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“Play has its uses, but they belong rather to the sphere of work,”
Can you help us to verify this quotation? We could not verify this quotation either in the likely spot of Part III of Book 8 of Aristotle’s Politics, nor elsewhere online.
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in Chapter 5 of Book 8 Aristotle emphasized that the sort of music that is only “for our amusement and refreshment, like taking a nap or having a drink,” is not of serious importance, although it may be “pleasant and help us forget our worries, as Euripides says” (Bacchae[2] 381).
Originally this was written as “Chapter 6 of Book 8” before we corrected it to “Chapter 5 of Book 8” based on this source. Let us know if you find evidence to the contrary. The similar translation goes:
“It is not easy to determine the nature of music, or why any one should have a knowledge of it. Shall we say, for the sake of amusement and relaxation, like sleep or drinking, which are not good in themselves, but are pleasant, and at the same time ‘care to cease,’ as Euripides says?”
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Chapter 5 of Book 8 Aristotle emphasized that the sort of music that is only “for our amusement and refreshment, like taking a nap or having a drink,” is not of serious importance, although it may be “pleasant and help us forget our worries, as Euripides says” (Bacchae[3] 381).
Can someone help identify the Euripides quotation with an original source better than ours? We found and cited this one from here but there may be something better/more definitive; the quotations are pretty different.
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“The poets do not depict Zeus as playing the lyre and singing in person,” pointed out Aristotle[4] (1339b).
Can you find a more precise source for this quotation? We did find one that quotes this precisely, but it seemed perhaps less authoritative than this one, even though that says slightly differently: “Zeus does not sing and harp to the poets himself.”
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“In fact we call the performers ‘technicians’ and think that a man should not perform except for his own amusement or when he has had a good deal to drink.”[5]
Originally this was missing the open-quotation mark, which we added. This is similar but not exactly the same as from this source:
“But professional musicians we speak of as vulgar people, and indeed we think it not manly to perform music, except when drunk or for fun.”
“In fact we call the performers ‘mechanics’ and think that a man should not perform except for his own amusement or when he has had a good deal to drink.”
Should we change the citation link and add a footnote for this other source, or do you have one that is closer to the quotations used in all instances to use across this chapter?
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Marshack (1990: p. 20) observed that such clothing “would probably not have been worn in the activity of hunting, butchering or daily domestic activity.” He added that “The assumption that ivory beads, bracelets and head bands evidence the beginnings of an awareness of ‘self’ is Eurocentric.” The “self” is still merged into the kosmos.
For portable art, the practice of covering images such as the Willendorf “Venus” with red ocher may be more than merely decorative. The red color may have symbolized the blood of life. Whatever was being signified, red ocher coloring predates the Cro-Magnons, being found as early as 100,000 BC in Neanderthal burials (Marshack 1990: p. 3).
Art became more cognitive by the late Ice Age. Marshack has shown the extent to which images from the Magdalenian period (15,000–10,000 BC) through the neolithic “were essentially ‘time factored,’ that is they were not simply ‘art,’ but were made at the right time, to be used at the proper moment, in the proper way, and for proper cultural reasons. … In fact symbolic carvings may in some measure have been made so they could be used ritually and ceremonially.” Cave art probably helped heighten and even coordinate seasonal rituals. “The ritual and symbolic use of the caves found in the Franco-Cantabrian area may have been ‘scheduled’ to that calendar frame, along with the manufacture and use of different classes of imagery and the performance of different types of rituals both inside and outside of cave sanctuaries” (Marshack 1990: p. 9).
Can you help us identify what text is meant by “Marshack 1990” so we can amend the footnotes and Bibliography throughout this chapter? At first we thought it was The Roots of Civilization and was an edition in 1990 following the original 1972 edition, but we could not find this in that text and need help amending the citations which originally said “Alexander Marshack, The Roots of Civilization (New York: 1972 and 1990)” with link to this page.
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What kind of creation? This question brings us back to the ultimate purpose of art. What was being expressed was a re-creation not of the artist’s personal experience but something more universal—the kosmos. Antiquity’s major public ceremonies were kosmos-renewing, and it was at these ceremonies that music was most pronounced. The celestial movements of the planets were emulated in song, dance, and instrumental playing (harps or lyres and flutes).
[Omitted text: “Whatever could be measured by number was standardized.”]
[Omitted text: “What once seemed to be realistic representational art now is perceived as reflecting a cosmological iconography.”]
“while most persons devote this art [of music] to social gatherings for the sake of correcting conduct and of general usefulness, the ancients went further and included in their customs and laws the singing of praises to the gods by all who attended feasts, in order that our dignity and sobriety might be retained through their help. For, since the songs are sung in concert, if discourse on the gods has been added it dignifies the mood of every one.”[6]
Originally this was cited as “XIV.627f.”—can someone confirm the precise citation? It seems likely this was a typo for roman numeral 14 instead of roman numeral 16, and the line breakdown is not easily available online in English translations such as this source or the one we cite in the footnote.
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Most artists were public servants (Greek demiourgoi, literally “workers for the demos”), and as such dependent on the civil state, palace, or temple for their livelihood. Some were outright slaves.[7]
Supervising them were various officials such as the choregos (originally in charge of the chorus, later the person who financed it), and the aesymnetes who beat the time for the choral dances. (I will discuss these officials in greater detail below.)
They were Greek demiourgoi, from the many blind men who were trained as musicians to the metic foreign “guest workers.”
The logic here is confusing; the first paragraph describes the demiourgoi; the second paragraph says the demiourgoi were supervised by choregos and aesymnetes; and the third paragraph says the choregos and aesymnetes themselves were the demiourgoi. Can you help?
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Supervising them were various officials such as the choregos (originally in charge of the chorus, later the person who financed it), and the aesymnetes who beat the time for the choral dances.
Can someone verify aesymnetes (originally spelled aissymnetes by the author) are those who beat the drum for choral dances? We could not find it online; Wikipedia says it “was the name of an ancient Greek elected office similar to, and sometimes indistinguishable from, tyrant.”
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Euripedes was sufficiently political to be exiled. [Omitted text: (Aeschylus ?)] I suppose that the modern analogy would be for an American business leader or politician to write a Broadway play.
Originally here the author had written “(Aeschylus ?)”; we removed it. Can you provide information about any similar political post held by Aeschylus? There was a note by the author to fill this in originally.
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The general idea was reported by Athenaeus[8] (XIV.627)
Should this be XVI instead of XIV since Chapter 16 was mentioned a few paragraphs earlier? And can you help us confirm it’s 627 and not 6–27? (We don’t have a source with line numbers.)
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The general idea was reported by Athenaeus[9] (XIV.627): “Many of the barbarians also conduct diplomatic negotiations to the accompaniment of flutes and cithara to soften the hearts of their opponents.”
Can someone find a source link that is closer to the text of this quotation? The one we cite in a footnote and link in the text is a bit different: “And, moreover, many of the barbarians make all their public proclamations to the accompaniment of flutes and harps, softening the souls of their enemies by these means.”
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Some philologists (e.g., Shipley[10] 1984: pp. 16ff.) went so far as to derive Latin “ordos”
Can you help us find where “ordos” is in the cited text? We don’t see “ordos” on page 16 or the pages after (at least it doesn’t come up in search) in the source; only “arthro.” Or, is it a different source that should be cited than the one in the footnote?
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In an age when most art was ceremonial, this meant that the subjects beginning with rulers as the primordial artistic subjects were standardized. Looking at Mesopotamian royal statues, one finds a sameness over the centuries. They seem realistic at first glance, but on closer examination this impression turns out to be only illusory.
Citation needed.
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The most famous set of statues are those of the ruler Gudea of Lagash c. 2100 BC. Every naturally rendered detail has a symbolic meaning, which is spelled out in the texts engraved on these statues.
Investigators have long analyzed the symbolism of public architecture—the Mesopotamian ziggurats, their orientation, number of stages (seven), and colors (corresponding to those of the planets).
then one may call the musical scale “frozen astronomy.” The seven strings of Apollo’s lyre symbolized the five planets, sun, and moon. There are some remarkable parallels, including the seven notes of the normal scale (denoted by the first seven letters of our alphabet, A through G).
Citation may be needed.
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Athenaeus (XIV.618) noted that many professions had their own work-songs: a mill-song (himaios), for grinding flour, an ioulos for the wool-spinners, and so forth.
If you tell us a link to add over “Athenaeus (XIV.618),” then we can add a footnote citation once you have checked this point is made at this point in a text.
Schneider added that even marriages were accompanied by group-songs during the wedding night, as were the funerals with their choral prayer-songs.
Can you help us find the source and page number(s) in the text, so we can add the full citation in a footnote with page number? It’s probably in Marius Schneider, “Primitive Music,” pp. 1–82, in Egon Wellesz (ed.), Ancient and Oriental Music, (London: 1957), probably around either pp. 38f. or p. 4.
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The seven notes of the scale equated to the seven movable bodies in the heavens. The numerological symbolism of the time described the number eight as the “rebirth” number, probably because it started a new octave or, in Semitic cultures, a new seven-day week.
Citation(s) needed.
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The seven notes of the scale equated to the seven movable bodies in the heavens. The numerological symbolism of the time described the number eight as the “rebirth” number, probably because it started a new octave or, in Semitic cultures, a new seven-day week.
Also of a periodic nature in both music and calendar-keeping was the number 12. It signified the octave’s 12 tones, and also the 12 months of the year. And, as noted in Alphanumeric Notation and the Calendrical-Musical Kosmos, music and astronomy may have shared similar symbols for their notation.
Plutarch stated in Moralia: “The Chaldeans say that Spring stands to Autumn in the relation of a Fourth, to Winter in the relation of a Fifth, and to Summer in the relation of an Octave.” And Curt Sachs also pointed out that “the ancient Chinese also viewed the Spring as distant from the Autumn by a Fourth and from the Winter by Fifth.”[11] But they viewed the spring as distant from the summer by a second, not by an octave as the Babylonians did.
Originally this section was written as notes instead of as full sentences before we made the fragments complete sentences. It may still need some fleshing out and explication though, if you’re able to help.
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Plutarch stated in Moralia: “The Chaldeans say that Spring stands to Autumn in the relation of a Fourth, to Winter in the relation of a Fifth, and to Summer in the relation of an Octave.”
Please provide a source link and citation we can use in a footnote. We could not find it.
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Plutarch stated in Moralia: “The Chaldeans say that Spring stands to Autumn in the relation of a Fourth, to Winter in the relation of a Fifth, and to Summer in the relation of an Octave.” [Omitted text: [Reproduce his diagram.]] And Curt Sachs also pointed out that “the ancient Chinese also viewed the Spring as distant from the Autumn by a Fourth and from the Winter by Fifth.”[12] But they viewed the spring as distant from the summer by a second, not by an octave as the Babylonians did.
The author wanted to reproduce Plutarch’s diagram (originally he had a note at this location in the chapter text: “[Reproduce his diagram.]”). Can you please identify and provide a link, especially if one is in the public domain? Or link to one?
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And Curt Sachs also pointed out that “the ancient Chinese also viewed the Spring as distant from the Autumn by a Fourth and from the Winter by Fifth.”[13]
We could not find this quotation in the source material. Can anyone else verify and add a page number to the footnote if so? Page 109 at the bottom of this source comes close, but not quite this language.
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There were five tetrachords, and five “extra” calendrical days in the year (bridging the gap between the 360-day public-sector administrative calendar and the actual 365-day solar year). [Omitted text: [DEFINE TETRACHORD]]
Here the author included a note: “[DEFINE TETRACHORD]”—can you help us by adding a transition and a definition of a tetrachord here?
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Wind instruments seem to have begun with the horns and bones of animals. (We still call the brass instruments “horns,” and Latin “corni” provides the root for the modern “cornet.”)
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Others were slaves, and then there were the Greek flute-girls. (For an idea of the disparaging of practical music see Boethius, who wrote at the beginning of the sixth century AD, Principles of Music.) (See Curt Sachs,[14]The Rise of Music in the Ancient World: East and West [1943].)
Please confirm if Boethius is excerpted here and/or if this concept about sex and stringed instruments is in here; if so, what page(s) is/are it/they on?
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Sound was made on the stringed instruments by rubbing, that is, friction. The primordial creative friction was of course that of sex.
Also sexual were the number-relations of the musical string-lengths. (These lengths were the inverse of the frequencies of the musical tones as we would measure in vibrations per second.)
Can you help us find the source of this concept? And add citations?
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Each octave renewed itself from A to A’, making the number eight (for A’) the signifier of rebirth.
Example 2 (Chapter 5 body):
CC’cc’
Example 3 (Chapter 5 general queries):
C, C’ c, c’, c”
Should the musical notation about octave be a curved apostrophe and/or quotation mark like this, or should it be a straight apostrophe/quotation mark? Or should it be noted entirely differently? (This occurs throughout this chapter.)
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McClain[15] (1976: pp. 19f.) pointed out that the 2:1 interval can only generate octaves: CC’cc’ and so forth. But it cannot “fill out” these octaves with tones. For that, “male” intervals are necessary, beginning with 3. This is basic Cosmology 101.
Can someone familiar with this musical concept or who can research it check this point and add exposition if necessary (associating numbers with being “male” for example)?
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The ratio 3:2 creates the most basic musical interval next to the octave: the fifth. This is the second overtone (Table 5.1).
The most basic musical ratio is that of the first overtone: the octave (from C to c; see Table 5.1).
We need someone with musical expertise to help us arrange Table 5.1 and insert it in Chapter 5. See this General Queries for Chapter 5 link to view the table notes. (If the table has been inserted into the chapter body already, please notify us here so we can remove this query and insert an internal link to the table over the words “Table 5.1” instead.)
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The ratio 3:2 creates the most basic musical interval next to the octave: the fifth. This is the second overtone (Table 5.1). In our example it represents the G over the first C.
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Can someone who knows Greek check this for us: We weren’t sure what the single quotation punctuation mark should be—a curved normal raised comma as in a contraction, or “harmonia,” or just a typo that should be removed? For now we went with a curved normal raised comma-style apostrophe.
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When the Greeks used the term “harmony” (’armonia), they did not refer to the harmonizing arrangements of modern songs and orchestras, but to the acoustics of tuning the scale. As a matter of fact, Greek music ignored “harmony” in the modern sense. It was melodic and multivoiced but not aiming at the triad chords that have marked post–Renaissance European music down to the present day.
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In the beginning was chaos: undifferentiated sound. Musical order emerged as the pitch continuum was divided into discrete tones. Sound came into being.
Originally the author had a note here to insert an illustration: “[Illustration: scale.]” Can you help us figure out what might have been meant here, and find us a public domain or Creative Commons image to insert?
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Let us set C at “30” (or 360, so that we may use convenient calendrical notation—which is very likely what the ancients did, at least according to Ernest McClain[16] and others. If we take this tone, and halve the length of the string, we get the octave. (Pitch is inversely proportional to string length.) Mathematically, if middle C is 360, then the higher C’ is 720. And high c is twice again as high, 1,440.
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To reduce all this to basic principles of length (and hence pitch), only a single string could be used—one which did not vary in thickness or tautness. It was divided by a movable bridge, which was moved back and forth along a canon—a ruled scale extending the length of the string.
Check spelling of “canon”: Wikipedia’s Monochord page uses the Greek transliteration: kanōn. We could not find “canon” used this way in a brief search.
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We can go on doubling the original tonic indefinitely, by successively dividing the string length in half. But that will produce only “empty” octaves (C, C’, c, c’, c”, etc., in a ratio of l:2:4:8:16:32:64:128:256 and so forth.
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Hint 1: “By the same token, numbers beyond 1 and 2 have been imbued with maleness and femaleness by classifying them as odd or even. The Pythagoreans held that ‘odd numbers are male, even numbers are female’ (Aristotle, Metaphysics 986a, quoted in Seidenberg[17] 1962b: p. 2).”
Hint 2: “Robert Stieglitz[18] (1982: p. 257) called this line of reasoning mathopoeic: ‘the poet might say that the “One” gave birth to a “Female” (= 2) and a “Male” (= 3), who in turn mated and thus begot successive generations of “sons” and “daughters” (2p3q5r), formed in the “image” of their prototypes.’”
Hint 3: “Plutarch (Isis and Osiris, Chapter 56) asserted that the ancient Egyptians knew the 3 x 4 x 5 right triangle and the male and female deities associated with it. The upright perpendicular measuring 3 represented Osiris, while the base measuring 4 (an even number, and horizontal, as it is presumed they thought a woman should be) signified Isis. Their offspring was Horus, the hypotenuse 5, a male odd number. Pythagoreans thus built on an old tradition in asserting that “Five is the marriage number.” Plutarch called this triangle the Nuptial Figure.”
Hint 4: “Inasmuch as 4 could be expressed as 22, the number 60 could be rendered as 22 x 3 x 5. In any case, 60 could be generated by multiplying twos and threes and their combinations (‘offspring’).”
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To fill out the scale we need a series of fifths. This is in nature the second overtone one hears over low C: the G. And musicians soon found that this note could be produced by the ratio 3:2.
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The first fifth—from C to G—is thus 3:2. But to go up another fifth, we must multiply the first 3:2 by another 3:2. In other words we must square it. This produces 9:4—the note D. It relates to C’ as 9:8, and this fraction thus represents the whole tone—C to D.
We thus see that to add one fifth to another, we must multiply their ratios. And this is what is meant by “geometric” growth.
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A whole tone scale can be made by proceeding by whole tones. On the piano, we would get the series C, D, E, F♯, G♯, A♯ (=B♭), then back to C. But we would not get the other six tones. To do this, we must continue tuning by fifths.
For ease of visualizing this on the black keys of a piano, let us begin by a fifth below middle C: F. This gives us what musicians call the “circle of fifths,” consisting of F, C, G, D, A, E, B, F♯, C♯, G♯, D♯, A♯—and then, a fifth above A♯, E♯. (Alternatively, if we begin with C, we will end up with B♯.)
However, as every pianist knows, there really is no E♯ (or B♯). That is F. We would seem to have arrived back at our starting point.
But in fact, we have not done so, for a very good reason. To return to a higher octave of our starting F (or C), we would need some doubling, that is, power of 2 in the denominator of whatever fractional system we are using. Its powers are 9, 27, 81, 243, and so forth, with the power always ending in an odd number—a 9, a 7, a 3, or a 1. Thus, as we reach the circle’s return at the seventh octave, we get a slight dissonance, an out-of-tuneness. Since antiquity, musicians have called this a “comma” (Greek “komma”). This represents the ratio of tuning by odd-numbered intervals relative to even ones.
Ancient harmonic theorists represented this by the following “fork”: 1, 3, 9 on the left, and 2, 4, 8, 16, etc., on the right.
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[Omitted text: Yet in the numerator we have powers of the “male” 3. And this is a “dominant” gene, so to speak.]Its powers are 9, 27, 81, 243, and so forth, with the power always ending in an odd number—a 9, a 7, a 3, or a 1.
Does the current second sentence above work on its own when the antecedent of “Its” was cut (related to male/female numbers)? Originally before this sentence was the sentence that we cut:
Yet in the numerator we have powers of the “male” 3. And this is a “dominant” gene, so to speak.
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A whole tone scale can be made by proceeding by whole tones. On the piano, we would get the series C, D, E, F♯, G♯, A♯ (=B♭), then back to C. But we would not get the other six tones. To do this, we must continue tuning by fifths.
For ease of visualizing this on the black keys of a piano, let us begin by a fifth below middle C: F. This gives us what musicians call the “circle of fifths,” consisting of F, C, G, D, A, E, B, F♯, C♯, G♯, D♯, A♯—and then, a fifth above A♯, E♯. (Alternatively, if we begin with C, we will end up with B♯.)
However, as every pianist knows, there really is no E♯ (or B♯). That is F. We would seem to have arrived back at our starting point.
But in fact, we have not done so, for a very good reason. To return to a higher octave of our starting F (or C), we would need some doubling, that is, power of 2 in the denominator of whatever fractional system we are using. Its powers are 9, 27, 81, 243, and so forth, with the power always ending in an odd number—a 9, a 7, a 3, or a 1. Thus, as we reach the circle’s return at the seventh octave, we get a slight dissonance, an out-of-tuneness. Since antiquity, musicians have called this a “comma” (Greek “komma”). This represents the ratio of tuning by odd-numbered intervals relative to even ones.
Ancient harmonic theorists represented this by the following “fork”: 1, 3, 9 on the left, and 2, 4, 8, 16, etc., on the right.
Can a music expert check that this makes sense?
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Ancient harmonic theorists represented this by the following “fork”: 1, 3, 9 on the left, and 2, 4, 8, 16, etc., on the right.
[Omitted text: [Reproduce Illustration 5.]]
Suppose we try to tune the scale by thirds, e.g., C, E, G♯, C. We are back at the tonic. Yet here again we encounter the same problem: The third is 5/4. And (5/4)2 is 25/16. We thus are dealing once again with powers of 5 (odd number) divided by sequences of even-numbered powers of 2. We soon encounter another type of comma.
Originally here the author had a note to insert an image here, but we’re not sure which image. Can you help us figure out which might have been meant? Perhaps Plutarch’s diagram mentioned in this query, or a scale illustration mentioned in this query, both of which we ask about a little earlier in this chapter body? His original note was: “[Reproduce Illustration 5.]” and we don’t know if there was a numeral after the period after 5 or not, but we don’t know what Illustration 5.1 would have been based on our two aforementioned queries.
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Suppose we try to tune the scale by thirds, e.g., C, E, G♯, C. We are back at the tonic. Yet here again we encounter the same problem: The third is 5/4. And (5/4)2 is 25/16. We thus are dealing once again with powers of 5 (odd number) divided by sequences of even-numbered powers of 2.
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We soon encounter another type of comma [Omitted text: [: what the ancients called the __.]].
Originally, instead of a period after the word “comma” the author had added a colon and a note with a missing term at the end; can you help us figure out what it was so we can add it back?
Original Text: “comma: what the ancients called the __.”
Was it Greek komma from earlier, maybe, or a symbol (more likely)?
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Setting the intervals by fifths (3:2 ratios) produced one mathematical-tonal series, doing so by thirds (5:4 or 6:5 for the major and minor third respectively) another.
Calendar-makers solved this problem by setting a year-end “time out of time.” After all, they hardly could take an average of 360 days and lengthen each day. The sun rose and set 365 1/4 times each calendrical year as measured by the sun, and there was nothing to do but add some extra days.
But musicians found a different solution available—indeed, dictated. They hardly could add an “extra note” to the gamut of octaves. (If they had, there would be two separate keys for G♯ and A♭ in one of the higher octaves.) Musical tuners did what calendar-makers could not do: Having drawn an analogy comparing musical tones and octaves to the days and months of the year, they then adjusted each tone slightly, so as to temper each tone by just enough so that there would be no “large” disparities developing among the “later generations” of tones such as G♯/A♭. At least, this was the “equal temperament” system developed thousands of years before Bach took the great step toward re-establishing the tendency with his Well-Tempered Clavier in 1722.
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By the time of classical antiquity we find the Platonic followers of Pythagoras using the mathematics of musical temperament to rationalize economic and social inequities.
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Not only classical Greece but also in India the Rg Veda dealt with the cosmology of musical temperament. But unlike the western European tradition, it proscribed arguments over tuning the scale. (And partly as a result, henceforth, Hindu music went its own way, as did its astronomy, calendar-making, and financial and economic development.)
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a. The sequence of overtones: 2:1, 3:2, 4:3, 5:4… versus circle of fifths.
The tones can be generated mainly from the first six numbers: 6:5:4:3:2:1.
The following text originally was in this location in the chapter body right before Table 5.1. Can you help us expand what was meant here in a way that flows with the chapter body? The text that was here was:
a. The sequence of overtones: 2:1, 3:2, 4:3, 5:4… versus circle of fifths.
The tones can be generated mainly from the first six numbers: 6:5:4:3:2:1.
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But just as calendars became solarized, so did the mathematics of tuning the scale. And just as the solar calendar rounded off the dimensions of the year, so did musical temperament.
Generation of Notes by Threes Versus by Twos and Fours
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Thus (per McClain[19] 1978: p. 33): A tyrant suffers “exactly 729 times” as much as a philosopher, “king of himself” (Republic[20]572b).
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discussed his Chart 23: “The gap which remains between a♭ and g♯ at the bottom of the circle is now narrowed to a diaschisma worth about 20 cents or 3/10 x 20 = 6 degrees, wondrously close to the 5 1/4-day shortage between the ancient calendar base of 360 days and the true solar year… The ratio results from the reciprocal meanings of 45:32…”
The material of the work of the title The Myth of Invariance by Ernest G. McClain appears to have been removed from the Internet Archive sometime between 2025 and 2026. Please help us find a different publicly accessible source link to the cited work, if one is available.
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Please note that another title by the same author still has a functioning link and needs no correction: Ernest G. McClain, The Pythagorean Plato: Prelude to the Song Itself (Maine: 1978). Citations to The Pythagorean Plato (in-text, footnotes, and in the Bibliography) still function.
The Hindu drum of Shiva which fills the world with life (and sound) may be understood as the intersection of powers of two with powers of 3, or sequences of octaves and fifths.
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A “comma” is “a small disagreement between two different definitions of a tone”; e.g., the Pythagorean, diaschisma, diesis (McClain[22] 1976: glossary).
↑The blind musician is a familiar character from the Bronze Age through classical antiquity. It was because they were blind that they were turned over to the temples or other public institutions, which trained them in music, gardening, or other craft for which eyesight was not essential. See Samuel Noah Kramer and John Maier’s Myths of Enki, The Crafty God, for Sumerian practice. This spread to classical Greece.
↑A. Seidenberg, “The Ritual Origin of Counting,” Archive for History of Exact Sciences, Vol. 2 (1962b), pp. 1–40.
↑Robert R. Stieglitz, “Numerical Structuralism and Cosmogony in the Ancient Near East,” Journal of Social and Biological Structures, Vol. 5 (1982), pp. 255–266.
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What McClain[1] (1976: p. 119) called the “Jubilee” comma, 50:49, requires a mathematical base 1,260:630 to incorporate both this ratio and the “lunar” diesis of 125:128.
Note that McClain switched the order of numbers in this ratio and wrote: 49:50 (with the smaller number first).
Can you help us figure out if we should reverse the order written in Chapter 5 too?
Maybe Hudson had a reason to swap them, or maybe it was unintentional and should be reversed for consistency?
What McClain[2] (1976: p. 119) called the “Jubilee” comma, 50:49, requires a mathematical base 1,260:630 to incorporate both this ratio and the “lunar” diesis of 125:128.
Note that McClain switched the order of numbers in this ratio and wrote: 630:1,260 (with the smaller number first).
Can you help us figure out if we should reverse the order written in Chapter 5 too?
Maybe Hudson had a reason to swap them, or maybe it was unintentional and should be reversed for consistency?
I point the interested reader to the works of McClain.[3] He may have gone too far in trying to find in the archaic Vedic, Mesopotamian, and Greek mathematics of musical temperament a conscious analog to the 25,920-year precession of the equinoxes. But his basic premise of parallels being drawn between adjusting the calendar and tuning the musical scale were certainly correct and “in the spirit” of ancient higher wisdom.
“The interval CE in Pythagorean tuning gives a C that is too low, an E that is too high: hence Clotho’s and Atropos’s adjustments. Lachesis’s task is to make A♭ and G♯ coincide, adjusting one with each hand. ‘Plato saw the necessity of temperament for systems meant to function in harmony, be they musical scales, planetary orbits, or communities of just men’” (Godwin 1983: pp. 298f., quoting McClain[4] 1977: p. 55).
We could find McClain (the quotation within the quotation) and cite it, but we could not find “Godwin 1983.” Can you help us find the text and a full citation that we can add as a footnote and bibliographical note? It might be related to Cosmic Music, edited by Joscelyn Godwin; however, the edition we found is dated 1989 (not 1983 as written here) and doesn’t have enough total pages to merit the citation here of pp. 298f., so it seems unlikely to be the one.
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He went so far as to try and make sense out of the numerology found in the Bible’s closing Book of Revelation (historically a pitfall which one enters only at the risk of losing one’s sanity).
McClain[5] (1976: p. 163): “Ernst Levy pointed out that the ratio 4:3 produces tones linked by perfect fourths and fifths, that ‘mating’ with 5 produces pure musical thirds, and that the ‘unmusical children’ Socrates predicted from his formula must therefore be those plagued by the notorious commas which make ‘Just tuning’ impractical and motivate the eventual adoption of some form of ‘temperament.’”
McClain[6] (1978: p. 19) stated that Plato theorized “that even the best aristocracy will degenerate in time through a timocracy [rule by the rich], oligarchy [rule of the few], and democracy [rule of the many].” Similarly, “Any tuning which uses the ‘perfect’ ratios of integers—and Socrates’ system uses 1:2:3:4:5:6[—]will degenerate unless the number of tones is rigidly limited. A series of perfect fifths 2:3, for instance, slightly larger than 7/12 of the octave, could agree with the octave series only if some higher power of 2 agreed with some higher power of 3, an obvious impossibility since the first series is even and the second is odd.”
Originally this quotation ended in “if some” and had no close-quotation mark. We found the original quotation and added it: “higher power of 2 agreed with some higher power of 3, an obvious impossibility since the first series is even and the second is odd.” Does it work, or would you cut it sooner?
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Athenaeus[7] (XII.3–41) reported that “To such a point had they carried their luxurious refinement that they had even trained their horses to dance at their feasts to the accompaniment of pipes. Now the people of Croton knew this when they made war on the Sybarites, as Aristotle records in his account of their Constitution.”
Example 2:
Croton went to war with Sybaris. On this topic, Athenaeus[8] (XII.3–41) repeated an anecdote that shows the power of music, so much praised by the Pythagoreans.
A question for someone with access to a version of Athenaeus’s The Deipnosophists that has line numbers denoted: Should this be lines 3–41, or is it line 341? The version we have doesn’t seem to be broken down by line (at this link: Book XII, Chapter 1).
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Athenaeus[9] (XII.3–41) reported that “To such a point had they carried their luxurious refinement that they had even trained their horses to dance at their feasts to the accompaniment of pipes. Now the people of Croton knew this when they made war on the Sybarites, as Aristotle records in his account of their Constitution.”
If you know of a source with a closer translation to the quoted text, please let us know. This is pretty close to the cited text version (Athenaeus, The Deipnosophists: Or Banquet of the Learned of Athenaeus, C.D. Yonge [tr.], Vol. 3 [London: 1854], via Tufts University’s Perseus Digital Library Project, Book XII, Chapter 1), but not exact.
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Athenaeus[10] (XII.3–41) reported that “To such a point had they carried their luxurious refinement that they had even trained their horses to dance at their feasts to the accompaniment of pipes. Now the people of Croton knew this when they made war on the Sybarites, as Aristotle records in his account of their Constitution.” Apparently some Sybarite had insulted (probably made unwelcome advances on) one of the flute-players, who resolved to avenge the insult by playing the tune to the Crotonites. At a signal in the battle all the Crotonite pipers played the melody to which the horses were accustomed, whereupon they rose on their hind legs, throwing off their riders, and so caused an easy victory for Croton.
There was a close-quotation mark but no open-quotation mark here; can you help us find a translation that might have been close to this text so we know if it was a quotation, which part was quoted and which was added?
Originally it was written (the missing open-quotation mark is as originally written):
At a signal in the battle all the Crotonite pipers played the melody to which the horses were accustomed, whereupon they rose on their hind legs, throwing off their riders [, and so caused an easy victory for Croton.]”
We removed the close-quotation mark and the brackets until we know the quotation. It seems approximate to this source or p. 834 of this one, but not exact.
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Athenaeus[11] (XII.3–41) reported that “To such a point had they carried their luxurious refinement that they had even trained their horses to dance at their feasts to the accompaniment of pipes. Now the people of Croton knew this when they made war on the Sybarites, as Aristotle records in his account of their Constitution.” Apparently some Sybarite had insulted (probably made unwelcome advances on) one of the flute-players, who resolved to avenge the insult by playing the tune to the Crotonites. At a signal in the battle all the Crotonite pipers played the melody to which the horses were accustomed, whereupon they rose on their hind legs, throwing off their riders, and so caused an easy victory for Croton.
This last is the editor’s summary from Julius Africanus, Cesti 293. Athenaeus says simply, the Crotonites “struck up the dance tune for the horses; for they had with them pipers in military uniform.”[12]
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He knew that “All the Cardians had schooled their horses to dance at their drinking parties to the accompaniment of the pipes. Rising on their hind legs and, as it were, gesticulating with their front feet, they would dance, being thoroughly accustomed to the pipe melodies. Knowing this fact, Naris purchased a flute-girl from Cardia, and on her arrival in Bisaltia she taught many pipers; accordingly he set out with them to attack Cardia. And when the battle was on, he gave orders to play all the pipe melodies which the Cardian horses knew. And when the horses heard the piping, they stood on their hind legs and began to dance; but since the whole strength of the Cardians lay in their cavalry, they were beaten in this way.”[14]
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But in time music and dance became more Dionysian in character, “for the dancers carry Bacchic wands in place of spears,” and hurled stalks of fennel at each other.
Can you help us cite this quotation from Athenaeus?
The democrats never responded with a temperament theory of their own. What they did was simply to maintain the tradition of Nemesis, the fair “divider” and avenger of hubris and arrogance of the wealthy.
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The democrats never responded with a temperament theory of their own. What they did was simply to maintain the tradition of Nemesis, the fair “divider” and avenger of hubris and arrogance of the wealthy. [Omitted text:] (I will leave to Chapter 9 an elaboration of how distributive justice was sanctified by religion.)
Theory of temperament = BALANCE.
Subordination of individual egoism—above all that of self-promotion and wealth-seeking—to the common weal.
[/End of omitted text]
Originally here was more text that may be notes:
1. At the end of the paragraph ending with “the wealthy.” was added this parenthetical:
(I will leave to Chapter 9 an elaboration of how distributive justice was sanctified by religion.)
Note that Chapter 9 may have been meant to be Chapter 8 due to renumbered chapters; check when Chapter 8 is fleshed out more.
2. Two further paragraphs of notes after the first paragraph in this section that give hints at how to flesh out this stub section were:
Theory of temperament = BALANCE.
Subordination of individual egoism—above all that of self-promotion and wealth-seeking—to the common weal.
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Commenting on this passage, Miller[15] (1986: p. 73) wrote that “The Mosaic choreia is more than a display of universal rationality. It is essentially a religious movement, a… ‘wholly sacred chorus’ expressing the love felt by man and nature for the transcendent Ruler of the universe.”
Yet at the same time, “Astronomy, music, mathematics, and all the branches of philosophy were not ends in themselves, …but simply preparations for leading the life of virtue and piety which allowed the human spirit to leap into the Kingdom of Heaven.” Philo thus “imagined the Lord as a Socratic teacher.” In his essay “On the Change of Names”[16] (72–73) Philo asked…
Can someone with access to the full text of Miller 1986 check this quotation? We think it might be on page 74 (one page after this link), but we can’t preview it.
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Yet at the same time, “Astronomy, music, mathematics, and all the branches of philosophy were not ends in themselves, …but simply preparations for leading the life of virtue and piety which allowed the human spirit to leap into the Kingdom of Heaven.” Philo thus “imagined the Lord as a Socratic teacher.” In his essay “On the Change of Names”[17] (72–73) Philo asked:
“For what purpose do you investigate the choral dances and revolutions of the stars? Why have you leapt from earth up to the region of the ether? Is your purpose merely to busy yourself idly with what is there? And what great advantage may be gained from all that idle labor? How does it serve to purge pleasure, to overthrow lust, to suppress grief and fear? What surgery has it for passions which rock and confound the soul? For just as trees are useless if they bear no fruit, so also is the study of nature useless if it does not lead to the acquisition of virtue.”[18]
Can someone with access to the original text check the number in parentheses (72–73)? We think it’s 72–73 based on this source link, but originally it was written as 723.
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If man were created after the image of God, it was not as a corporeal image, “since God is not human in appearance and the human body is not godlike. No, the likeness meant by Moses pertains to the mind as ruler of the soul, for the one archetypal Mind of the universe was the model after which the mind in every individual was patterned. … The mind is unseen but sees all things itself, and while it reveals the essences of all other things, it keeps its own essence hidden. … After it has been raised on the wing and has observed the air and all its properties, it is borne still higher to the ether and to the revolutions of the heavens and is whirled round with the choral dances of the planets and the fixed stars in accordance with the laws of perfect music, following the love of wisdom which guides its footsteps.” (Philo,[19] “On the Creation,” 69–71, discussed in Miller[20] 1986: pp. 56f.).
Can someone with access to the full text of James L. Miller’s book confirm the quotation/page numbers? We can’t see these pages (56–57).
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The essence of astronomical movements—the dance of the planets, and hence the highest musical order—was their regularity (once again our “reg” idea), “a predictable cycle of changes, itself unchanging.”[21] Miller[22] (1986: p. 57) added: “the stability and uniformity of the patterns of motions detected in the heavens revealed the existence of an archetypal Mind governing both the psychological and physical dynamics of the temporal cosmos.” It thus reinforced a faith in authority—on earth as well as in the heavens. [Omitted text: (See [tk] on the Persian kings being authoritarian in their art.)]
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(See [tk] on the Persian kings being authoritarian in their art.)
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In Plato’s Laws[23] (II 672e) the idealized Athenian stranger stated that “the art of choral dance as a whole (choreia) is identical with education as a whole (paideia); and the part of it pertaining to the voice consists of rhythms and harmonies.”
If someone can find a translation closer to this than what we’ve cited, please share the full citation with us.
(This is an approximate translation.)
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In Epinomis[24] (982c–e) Plato stated that “as proof that the stars and the whole moving system of the heavens possess intelligence, mankind ought to consider the fact that the stars always do the same things and have done so for an amazingly long time. Because they are carrying out what was planned long ago, they do not alter their plans now this way, now that, sometimes doing one thing and sometimes another, wandering and changing their orbits.” This is why “the nature of the stars is the fairest to behold, for they dance the fairest and most magnificent procession and choral dance of all the choruses in the world…”
If someone can find a translation closer to this than what we’ve cited (such as this one and this one), please share the full citation with us.
(This is an approximate translation.)
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Along these lines, Miller[25] (1986: pp. 41, 5) noted that “Images of harmony… invite us to participate in a reality we normally ignore and draw us back into the primitive immediacy of sensory experience to commune with a divinity that shapes our ends.” But they may be authoritarian (viz. the Pythagoreans): “Images of harmony… tend to silence debates, for they are essentially undebatable.”
Can someone with access to the full Miller text confirm that something relevant to the following quotations is on p. 41? We only saw the exact quotations on p. 5.
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Along these lines, Miller[26] (1986: pp. 41, 5) noted that “Images of harmony… invite us to participate in a reality we normally ignore and draw us back into the primitive immediacy of sensory experience to commune with a divinity that shapes our ends.” But they may be authoritarian (viz. the Pythagoreans): “Images of harmony… tend to silence debates, for they are essentially undebatable.”
Can someone with access to the full text of James L. Miller’s book confirm the quotations?
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Athenaeus (XIV.632)pointed out that Demetrius of Byzantium (On Poetry, IV) noted that the Greeks “used to employ the term choregi, not, as today, of the men who hired the choruses, but of those who led the chorus, as the etymology of the word denotes.”[27]
Can someone help us confirm this attribution if they have a different translation of Athenaeus (it was not evident in Perseus’s version, Book 14, which does not have 632 delineated)? We did find it in Strunk’s Source Readings in Music History on page 55, but are not sure of the line numbers.
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The art historian Irene Winter (1989) has elaborated some of the nonnumerical symbolism reflected in Gudea’s 20 surviving statues. There are so many of them, and they resemble each other so closely, as to suggest at first glance that they were true likenesses, perhaps reflecting Gudea’s egoism. However, Winter cited five iconographic qualities indicating that these statues were unlikely to be actual portraits. They embodied stereotypical royal qualities in a seemingly realistic guise, just as their sexagesimal proportions appeared naturalistic at first glance.
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The art historian Irene Winter (1989) has elaborated some of the nonnumerical symbolism reflected in Gudea’s 20 surviving statues. There are so many of them, and they resemble each other so closely, as to suggest at first glance that they were true likenesses, perhaps reflecting Gudea’s egoism. However, Winter cited five iconographic qualities indicating that these statues were unlikely to be actual portraits. They embodied stereotypical royal qualities in a seemingly realistic guise, just as their sexagesimal proportions appeared naturalistic at first glance.
Can you help us find the full citation for Irene Winter (1989)?
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Gudea’s Statue B (iii:1213) stated that his lord Ningirsu gave him heroic strength. Another royal epithet was “outstandingness,” e.g., in a crowd, from whom deities traditionally selected Sumerian rulers. Gudea’s statues depicted him as being larger than life and broad-chested, reflecting the Sumerian word for “ruler,” “lugal,” “big-man.”
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These sections are sometimes stubs, with some parts written out completely and others less so. Can you help us polish them and/or expand the bits that feel like notes rather than prose?
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From “art” and “armos” comes “arete,” “virtue.” The superlative “aristos” (“fittest,” “best”) now connotes the doctrine of survival of the fittest.
I began this chapter with a quotation from Aristotle distinguishing high culture from barbarism. Let us return to his argument, for at this very moment in time an ossification was setting in. Art was becoming bourgeois.
[/End of omitted text]
Aristotle (Politics VIII.3 at 1337b) stated that high culture required leisure time for contemplation, and hence wealth (much as to be a member of the aristocratic cavalry, one needed enough wealth to spend one’s time training with one’s horse). But there also was a danger here: The ruling class might become conservative.
There was omitted text here that was a stub. Would you like to help us expand it so we can add it back to the Chapter 5 body?
Note: The “quotation from Aristotle” was most likely:
“The poets do not depict Zeus as playing the lyre and singing in person,” pointed out Aristotle[28] (1339b). “In fact we call the performers ‘technicians’ and think that a man should not perform except for his own amusement or when he has had a good deal to drink.” Thus, like his contemporaries, Aristotle dismissed musicianship as being a mere craft (“techne”), and as such, unbecoming to men of leisure.
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Aristoxenus (according to Athenaeus[29]XIV.632) decried the decadence of his times (already over two thousand years ago): “Now that our theatres have become utterly barbarized and this prostituted music has moved on into a state of grave corruption,” he accused; few people recalled the old musical arts. Athenaeus added his own view that “It happened that in ancient times the Greeks were music-lovers; but later, with the breakdown of order, when practically all the ancient customs fell into decay, this devotion to principle ceased, and debased fashions in music came to light, wherein every one who practised them substituted effeminacy for gentleness, and license and looseness for moderation. What is more, this fashion will doubtless be carried further if some one does not bring the music of our forebears once more to open practice.”[30]
[Omitted text: [Calliope story.]]
The Key Concept of “Calliope, the ninth muse, integrating the other eight muses by virtue of the aid to memory provided by music” is not discussed in this chapter’s body. Originally there was a note at this place in the chapter body that we omitted to add [Calliope story] here. Can you help us add it to the chapter body discussion and relate it to the chapter thesis? Please include what to add and where in the chapter to add it, and any sources.
Can you help us find and write out the relevant Calliope story here?
According to McClain[31] (1976: p. 112), in the 16th century AD “the new ‘chordal’ harmonies… made the ‘human number 5’ (in the triad ratios of 4:5:6) a factor to be reckoned with.” The result was called “Just tuning.” “[I]ts plague of commas” made music a cacophony, until Bach helped right matters with his Well-Tempered Clavier in 1722. (It would take another century for truly even temperament to establish itself throughout Europe and its overseas culture area.)
Note: The Chinese had used the number five to come up with pentatonic music. Thus, there were many ways of applying any given cosmology to history, calendar-making, etc.
Let us know if you think this was already covered sufficiently in the main body earlier, and/or help us expand these paragraphs with more information.
Below is one note from the author that didn’t fit elsewhere, so we omitted it; can help you help us expand this:
[Omitted text:] 2. The scale really got out of tune. The doctrine of Just Temperament as taught by the Church Fathers through the Middle Ages reduced music to the homophony of the Gregorian chant. It would be more than a millennium before polyphony developed. (Capsule history of tuning through Bach and the moderns.)
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Note: The Chinese had used the number five to come up with pentatonic music. Thus, there were many ways of applying any given cosmology to history, calendar-making, etc.
This paragraph appears to be a stub. Can you help us expand or give context/citations?
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James Miller[32] (1986: p. 17) explained his disappointment at discovering that “Choreia,” via Latin “chorea,” survives in modern English (according to the Oxford English Dictionary) “as a medical term signifying ‘a convulsive disorder… characterized by irregular involuntary contractions of the muscles, especially of the face and arms,’” much as “arthrum”—the root of “joint,” “harmony,” and “art”—survives as “arthritis.” “The tragic fate of my noble Greek word forced me to question my naïve assumption that the mighty themes of order and harmony could be conveyed through the centuries on a verbal vehicle so frail and easily overturned.”
Can you help us figure out where this belongs and add more context around the quotation to support the Key Concepts short point and paragraph here?
…pottery. The latter evolved from bowls (often decorated with cruciform patterns, perhaps to represent the calendrical crossing points at which the bowls were used), to large Greek kraters, bowls to mix wine and water, with ceremonial or other festive subjects showing musicians—some musical instruments.
Can you help us add an example that helps us distinguish Greek kraters from bowls with cruciform patterns? It could be a link to Wikipedia or a reputable open source, particularly for the cruciform patterns.
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Some music-mythology historians have gone so far as to imagine that archaic myths reflect an understanding of the precession of the equinoxes, and also of highly sophisticated tunings by “commas,” or microtonal pitch corrections necessary to put the scale in order.
Do you know of any examples we should add here as a footnote?
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Originally this was written as 'hapiru (straight apostrophe was not intentional). We decided it should be either ‘apiru or hapiru, but not both apostrophe and h per Wikipedia, so we changed it to ‘apiru for now. If you have any insight into the term, let us know, including the orientation of the apostrophe.
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It is toward the end of the Bronze Age, c. 1400 BC, that we find ‘apiru leaders descending on Canaan and promising local populations that they would cancel the debts and redistribute the lands—“eat the rich”—if they defected to the side of the ‘apiru mountaineers.
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But as Burkert[33] (1972) pointed out, this latter detail may have been invented to explain away the embarrassing association of later Pythagoreans with tyrants, from Croton to Syracuse and the Athenian oligarchy which ruled brutally. (Most of the Seven Sages were tyrants. Such was the mentality of the archaic Greeks.)
Can you help us find out what page number should be added to the citation?
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(Most of the Seven Sages were tyrants. Such was the mentality of the archaic Greeks.)
Originally this was written “(It was pointed out by [name/citation missing] that most of the Seven Sages were tyrants. Such was the mentality of the archaic Greeks.)” before we removed the first part. Can you help us find the name/citation that was missing? We thought it might be Burkert but can’t find exactly this point about tyrants and the Seven Sages.
And Burkert[34] 1972: p. 113 noted that these two south Italian cities above all others were noted for their worship of Apollo, apparently a transplant from Asia Minor.) Tarentum was the other center of Pythagoreanism, and it was there that the sect survived longest.
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Originally this was written as “BC [(4)] is” and our guess is that the parenthetical was a date, perhaps 400 something BC. If you know what was meant here, let us know.
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Croton went to war with Sybaris. On this topic, Athenaeus[35] (XII.3–41) repeated an anecdote that shows the power of music, so much praised by the Pythagoreans.
If you know of a source with a closer translation to the quoted text, please let us know. This is pretty close to the cited text version (Athenaeus, The Deipnosophists: Or Banquet of the Learned of Athenaeus, C.D. Yonge [tr.], Vol. 3 [London: 1854], via Tufts University’s Perseus Digital Library Project, Book XII, Chapter 1), but not exact.
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Burkert[36] (1972: p. 116) suspected that this was probably the case with Pythagoras in Croton, with the plot being borrowed from contemporary plays on The Suppliants by Aeschylus and Euripides.
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Burkert[37] (1972: p. 115), surveying the sources, stated that “the house of Milo, which was the meeting place of the Pythagoreans in Croton, was burnt down by their opponents, and only a few of those present escaped.”
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And Diogenes Laërtius depicted the anti-Pythagorean revolt “as a blow for freedom from tyranny” (Burkert[38] 1972: pp. 118f.).
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So we have (1) religion as oligarchic, (2) cults as oligarchic, (3) leisure as oligarchic, and (4) sports as oligarchic (the gymnasia), hence “public figures” such as sports heroes (the modern equivalent would be movie actors). Viz. the figure of Alcibiades.
The statement “Viz. the figure of Alcibiades.” is a stub. Can you help expand it?
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For propagandistic history, an oligarch would assign personal motives to their enemies (and imply that the oligarch’s own motives are of course only objective and pure). Thus the opponents of Croton’s Pythagorean oligarchs were accused by Iamblichus of being resentful at having been rejected as students of Pythagoras, corrupted by whatever success they may have won.
[Omitted text: Iamblichus in Guthrie[39] 1987: p. 118: “When they captured Sybaris, and the land was not divided by lot, according to the desire of the multitude, this veiled hatred against the Pythagoreans burst forth, and the populace forsook them.”]
This paragraph was a stub, included as the last paragraph of Chapter 5. Can someone help expand it so we can add it back to the chapter as the final paragraph?
The omitted paragraph was:
Iamblichus in Guthrie[40] 1987: p. 118: “When they captured Sybaris, and the land was not divided by lot, according to the desire of the multitude, this veiled hatred against the Pythagoreans burst forth, and the populace forsook them.”
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Key image: Calliope, the ninth muse, integrating the other eight muses by virtue of the aid to memory provided by music.
This Key Concept of ancient Calliope is not discussed in this chapter’s body. Can you help us add it to the Chapter 5 body discussion and relate it to the chapter thesis? Please include what to add and where in the chapter to add it, and any sources.
For a hint at where in the chapter body it might go, see also this query in the Chapter 5 body: There was originally a note at the end of the chapter in the author’s notes for “END OF CHAPTER 5” to add “[Calliope story]” after the paragraph beginning “Aristoxenus (according to Athenaeus[41]XIV.632) decried the decadence of his times (already over two thousand years ago)…” That was probably a note to add something about Calliope there. Can you help us fulfill that?
Each octave renewed itself from A to A’, making the number eight (for A’) the signifier of rebirth.
Example 2 (Chapter 5 body):
CC’cc’
Example 3 (Chapter 5 general queries):
C, C’ c, c’, c”
Should the musical notation about octave be a curved apostrophe and/or quotation mark like this, or should it be a straight apostrophe/quotation mark? Or should it be noted entirely differently? (This occurs throughout this chapter.)
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Public Renewal Ceremony: …Musical, lyric, and dramatic competitions accompanied early sports contests such as the Olympics and Delphi’s Pythian Games.
There is no mention of early sports contests (Olympics nor Pythian Games) and how they relate to music in this chapter, except in the keywords section. Can you help us add it to the appropriate spot in Chapter 5’s body?
Ultimate dissolution: …The “choregos” shifted from being “master of dance” to its wealthy patron, while “choreia” became a convulsive disease.
This Key Concept is not discussed in this chapter’s body. Can you help us add it?
For a hint at where in the chapter body it might go, see also this query in the Chapter 5 body: There was originally a note at the end of the chapter in the author’s notes for “END OF CHAPTER 5” about this, although these notes need editing and fleshing out. It was probably a note to add something about “choreia” there. Can you help us fulfill that? That note is located in this spot of the Chapter 5 body:
James Miller[42] (1986: p. 17) explained his disappointment at discovering that “Choreia,” via Latin “chorea,” survives in modern English (according to the Oxford English Dictionary) “as a medical term signifying ‘a convulsive disorder… characterized by irregular involuntary contractions of the muscles, especially of the face and arms,’” much as “arthrum”—the root of “joint,” “harmony,” and “art”—survives as “arthritis.” “The tragic fate of my noble Greek word forced me to question my naïve assumption that the mighty themes of order and harmony could be conveyed through the centuries on a verbal vehicle so frail and easily overturned.”
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Theopompus and Posidoniuswrote that Pythagorean oligarchs such as the tyrant Athenion of Athens “at the first opportunity cast aside the mask of philosophy and became a tyrant.”[43]
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↑Plato, Laws, Book II, p. 672e. From Plato in Twelve Volumes, R.G. Bury (tr.), Vols. 10 and 11 (Cambridge, Massachusetts: 1967 and 1968), via Tufts University’s Perseus Digital Library Project.
↑Plato, Epinomis, section 982c–e. From Plato in Twelve Volumes, W.R.M. Lamb (tr.), Vol. 9 (Cambridge, Massachusetts: 1925), via Tufts University’s Perseus Digital Library Project.
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