Table Query - 5. Music, Temperament, and Social Concord

General Query: 5. Music, Temperament, and Social Concord

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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.

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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

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?OpenSee All Queries 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?OpenSee All Queries 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?OpenSee All Queries  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: p. 197):Verify CitationCan you help us verify the citation? The cited text and page number don’t seem related to the content.OpenSee All QueriesDead 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.OpenSee All Queries

                 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 (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?OpenSee All Queries 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 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 (1976: glossary) defined “calendrical scales” as those “which can be defined by integers 2^p3^q5^r < 720, ‘the ‘days and nights’ of a schematic year.”