General Queries: 5. Music, Temperament, and Social Concord
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General Queries:
5. Music, Temperament, and Social Concord
General Query: 5. Music, Temperament, and Social Concord
Table Query
We need someone with musical expertise to help arrange Table 5.1 (see below) and solve its queries so we can insert Table 5.1 back into Chapter 5 above the section Generation of Notes by Threes Versus by Twos and Fours (where this query marker has been placed). The line breaks and spacing appear to have been distorted. We also are not sure if Table 5.1 is supposed to be all one table with notes as merged columns inside the main table, or if it should be three separate tables (Table 5.1, Table 5.2, Table 5.3) with normal paragraphs interjecting, as the three stacks of preformatted gray-background text make it appear below. If you are familiar with wikitext, that format is ideal; if not and you can share it as a spreadsheet attachment or Google Sheets link, that would be very helpful.Suggest an edit or addition for this table-related query. Join the research!
- Hudson’s Notes for Creating Table 5.1 (It Needs Rearranging)
octave 1 2 2:1 octave
fifth
fourth 3:2 fifth 2 3 4 4:3 fourth major minor third third
G♯/A♭ 5:4 major third
6:5 minor third 4 5 6 7 8 whole tone
9:8 whole tone 8 9 10 11 12 13 14 15 16[1]
David Wulstan (p. 227)Verify CitationCan you help us identify the title of this text and create a full citation so we can add a footnote and bibliographical note? relates the frequency ratio to the length:
uniTable Query“uni” should be combined with “son” to make the word “unison,” correct? Where should this word be placed within Table 5.1? whole major fourth fifth octave sonTable Query“uni” should be combined with “son” to make the word “unison,” correct? Where should this word be placed within Table 5.1? tone third 0 I II III IV V VI VII
Frequency ratio: 1 9/8 5/4 4/3 3/2 5/3 15/8 2/1
Length ratio: 1 8/9 4/5 4/5 2/3 3/5 8/15 1/2
Using the Sumerian sexagesimal system, and assigning to the “children of Anu” specific tones according to their ratios, we get the following series (see McClain[2]: p. 197):Verify CitationCan you help us verify the citation? The cited text and page number don’t seem related to the content.Dead Source LinkThe source link no longer works; Ernest G. McClain’s The Myth of Invariance appears to have been removed from the Internet Archive. Please help us find a different publicly accessible source link.
30 60 60 30 C e♭ e f f♯ G A b♭ b c c♯ d
“Waxing” 360 384 400 432 450 480 540 576 600 648 675 720
“Waning” 720 675 648 600 576 540 480 450 432 400 384 360
McClain[3] (1978: p. 25) represented the 360 days of the year corresponding to the vibrations (or arithmetic settings) based on tones, in accordance with factorial 6! = 720. The above chartTable QueryTo what does the “above chart” refer—the entirety of Table 5.1, or just the third section directly above this paragraph? divides the octave into 360 parts—numbers which reflect the basic interval-proportions.
Ptolemy assigned 36,000 years to the precession of the equinoxes (McClain[4] 1978: p. 26). Modern astronomers know that this is much too large a number (which is 26,000 years). But the number 36,000 evidently was “round” to the ancients.
McClain[5] (1976: glossary) defined “calendrical scales” as those “which can be defined by integers 2p3q5r < 720, ‘the ‘days and nights’ of a schematic year.”
- ↑ Note: The pitch of a string depended on its thickness, and also the tension. Hence, the monochord was the key. One chord avoided the problems of varying thickness, tension, or other qualities outside of length.
- ↑ Ernest G. McClain, The Myth of Invariance: The Origin of the Gods, Mathematics and Music from the Rg Veda to Plato (Maine: 1976), p. 197.Verify CitationCan you help us verify the citation? The cited text and page number don’t seem related to the content.Dead Source LinkThe source link no longer works; Ernest G. McClain’s The Myth of Invariance appears to have been removed from the Internet Archive. Please help us find a different publicly accessible source link.
- ↑ Ernest G. McClain, The Pythagorean Plato: Prelude to the Song Itself (Maine: 1978), p. 25.
- ↑ Ernest G. McClain, The Pythagorean Plato: Prelude to the Song Itself (Maine: 1978), p. 26.
- ↑ Ernest G. McClain, The Myth of Invariance: The Origin of the Gods, Mathematics and Music from the Rg Veda to Plato (Maine: 1976), glossary.
General Query: 5. Music, Temperament, and Social Concord
Add a Section
The following section called The Role of the Square Root of Two that was meant to go above Summary: ‘Natural’ Tuning Versus Equal Temperament in the Chapter 5 body (where this query marker has been placed). Can you help us solve some of the queries below so we can move it back into the chapter body?Suggest an edit or addition for these queries about the square root of 2. Join the research!
- Hudson’s Notes to Create the Section ‘The Role of the Square Root of Two’
The amount by which each tone must be tempered so that every tonal interval will be precisely equal to every other one is the 12th square root of 2.
Socrates’s numberAdd ContextCan you help us explain/elaborate on: what is Socrates’s number?—and it is about half the precession of the equinoxes—is 12,960,000.Fact CheckCan you help us check the mathematical fact here? This represents 36,002,Fact CheckCan you help us check the mathematical fact of “36,002” here? How does 12,960,000 represent 36,002? (360 days times 60 times 60) and also the product of 4,800 times 2,700, that is, 32 x 23 x 2 x 3.Fact CheckCan you help us to explain/check the math here? 32 x 23 x 2 x 3 is 4,416, which seems unrelated to this paragraph.
McClain[1] (1976: p. 80)Verify CitationCan someone help verify the page number?Dead Source LinkThe source link no longer works; Ernest G. McClain’s The Myth of Invariance appears to have been removed from the Internet Archive. Please help us find a different publicly accessible source link. believed that the six winged horses may refer to 1:2:3:4:5:6, defining everything in allegory: 3p5q < 604 = 12,960,000.Fact CheckCan you help us to check the math here?
- ↑ Ernest G. McClain, The Myth of Invariance: The Origin of the Gods, Mathematics and Music from the Rg Veda to Plato (Maine: 1976), p. 80.Dead Source LinkThe source link no longer works; Ernest G. McClain’s The Myth of Invariance appears to have been removed from the Internet Archive. Please help us find a different publicly accessible source link.
General Query: 5. Music, Temperament, and Social Concord
Add a Section
This subsection below, Social Analogies Based on Musical Temperament, is a stub, so we omitted it from Chapter 5’s body. Can you help us expand it so we can add it back to Chapter 5’s body above the section Ruler/Noise/Harmony (where this query marker has been placed)?Suggest an edit or addition for this query. Join the research!
Social Analogies Based on Musical Temperament
Harmony/cacophony. Concord/dissonance. In society. Babylonian Creation epic Enuma Elish, Tablet I, lines 38–40: (McClain[1] 1976, p. 142Dead Source LinkThe source link no longer works; Ernest G. McClain’s The Myth of Invariance appears to have been removed from the Internet Archive. Please help us find a different publicly accessible source link.; quoting from Alexander Heidel,[2] The Babylonian Genesis [Chicago 1942 (1951): p. 15]):
- “Bel-Enlil is replaced by Marduk = 25 under fascinating acoustical conditions. Apsu, the primeval ‘begettor’ of the gods, is disturbed by the noise of his celestial children… and decrees their death:
- ‘By day I cannot rest, by night I cannot sleep;
- I will destroy (them) and put an end to their way.
- That silence be established, and then let us sleep!’”
- ↑ Ernest G. McClain, The Myth of Invariance: The Origin of the Gods, Mathematics and Music from the Rg Veda to Plato (Maine: 1976), p. 142.Dead Source LinkThe source link no longer works; Ernest G. McClain’s The Myth of Invariance appears to have been removed from the Internet Archive. Please help us find a different publicly accessible source link.
- ↑ Alexander Heidel, The Babylonian Genesis (Chicago: 1942 [1951]), p. 15.
