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2.0 SYMIs the SQ data part of a larger picture? Would data from the HSYM support or contradict our SQ impressions? Would our methods used provide similar, or disparate, results? The SYM color coded map (sorted by SYM #, B at the top; # 104 at the bottom) of the HSYMs in the “complete” H.C. Robbins Landon edition,15 is read as was the SQ Color Map (see section 1.0), where equal horizontal space equals equal measures across all movements; different colored swaths represent different movement sections; etc. A myriad of details differ between the two, but the maps are not dissimilar. *
SYM (1) {SQ (1)} sorts on the standard numbers assigned to the HSYMs. It is the companion table to SQ (1), and is read in the same fashion. Certain obvious SYM groups (lines 4 - 6 = Le Matin, Midi, Soir; lines 69 - 71, purported to have been composed as a group; lines 75 - 80 (“Paris”); & 86 - 97 (“London”)) are delineated. SYM (1) {SQ (1)} shows a muddle of numbers similar to SQ (1), once again without much appearance of pattern. Compared with SQ, SYM (1) {SQ (1)} may have fewer empty cells in the “A”→“D” cols., but the “E1, E2, F1, F2 & dC+” cols. are additional to the SQ cols.16 As with SQ, repeated patterns do not occur within a group of SYM. An obvious, rather curious, difference between SYM & SQ, pertains to where minuet movements appear, i.e. are they second, third or fourth movements? We provide the detail below (numbers within cells are frequencies of occurrence), but the movement wobble of SQ is hardly to be found in SYM. Only starting with SQ op. 50 do SQ third movements approach SYM frequencies.17 Frequency of movement placement
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SYM (2) {SQ (2)} is the mono sort SYM equivalent of SQ (2). We find 4 repeated patterns (highlighted by red verticals) i.e. the bar-count succession “A1→B3” : 8/8/16/16/8/8/16/16/8/16, used twice (see line #s 4 & 5); 8/8/24/24/8/8/12/12/8/24 used twice (see line #s 16 - 17), but with the addendum of an E1 & E2 on line 17; 8/8/34/34/8/8/16/16/8/34 used thrice (line #s 32 - 34) 12/12/22/22/8/8/16/16/12/22 twice (line #s 59 & 60) For SYM, 93 out of 97 samples (96%) utilize different “A1→B3” arrangements.
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We omit a SYM equivalent of SQ (3) as the SYM data for "S" may be found in SYM (3) {SQ (4)}; but as with SQ, the great majority of SYM samples are "10-S". The SYM collection does contain 2 samples of 14 sections, whereas SQ has none. The precise details are:
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SYM (3) {SQ (4)} is the equivalent of SQ (4) i.e. a sort of the number of different "ML"s used. Both SYM & SQ use 2, 3, 4, 5 & 6 "DL"s. For SYM & SQ, "4-DL" is the most prevalent, followed by "3-DL", then "2-DL". The total of all other "DL" is de minimus. Comparison of number of "DL" samples used
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SYM (4) {SQ (5)} uses 29 lines, vs the 36 lines of SQ (5); i.e. there are fewer SYM "ML"s, for a greater number of samples. Twenty-four SYM "ML"s appear in SQ (the five SYM "ML"s not used in SQ are 19, 40, 48, 50, 52). There are fewer pink highlights, as SYM (4) {SQ (5)}, utilizes only six odd numbers (vs. thirteen odd numbers for SQ). SQ & SYM "ML" ranges are crudely comparable i.e.: Comparison of "ML" ranges used
The number of "ML"s used per "A", "B", "C" & "D" are rather consistent across tables i.e.: Comparison of number of different "ML"s used
In regards "ML" frequency of use: Comparison of % frequency for four "MLs"
In terms of ubiquity, "ML" = 8 appears in 57/80 (71.3%) SQ vs 68/97 (70.1%) SYM; "ML" = 12 appears in 43.8% SQ vs 38.1% SYM, etc. Comparison of ubiquity (as a fraction) for four "ML"s
To be sure, there are interesting differences, i.e. in terms of the “% of total sections lengths”, SQ has only two lengths used more than 10% of the time, vs SYM’s three; certain "ML"s are more prominent in SQ as opposed to SYM; some percentages seem arbitrarily inconsistent, others surprisingly similar; but when comparing SYM (4) {SQ (5)} and SQ (5), “little” truly astonishes.
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SYM (5) {SQ (6/7)} presents a combined version of SQ (6) & SQ (7). At the left, one finds a column with alternating lines labeled "A1:B1" (white background) vs. "C1:D1" (black background). The "ML" column provides "Measure Lengths" for "A1" or "C1". The top row provides "ML"s for both "B1" and "D1". A number found at the intersection of a row and column tells how many times a specific pair is utilized. If the number in a col. appears on a white background, the number pertains to an "A1:B1" pair. If the number in a col. appears on a black background, the number pertains to a "C1:D1". For example, at the intersection of line "A1:B1" "ML" = 8 and column "ML" = 12, the number 1 on the white background indicates that the pair (8,12) occurs in one M only; while the number 7 on the black background at the intersection of line "C1:D1" "ML" = 8 and column "ML" = 12, indicates that the pair (8,12) occurs in seven Ts. "E1:F1" pairs are grouped with "C1:D1" pairs in [line "C1:D1" "ML" = 8 and column "ML" = 10] and in [line "C1:D1" "ML" = 8 and column "ML" = 16]. Line sums indicate how many times an "ML" appears as the first term of a ratio, i.e. "ML" = 12 occurs 22 times as the first term of an "A1:B1" pair, and 10 times as the first term of a "C1:D1" pair. Col. sums indicate how many times a length appears as the second term of a ratio i.e. 12 occurs 1 time as the second term of an "A1:B1" pair and 10 times as the second term of a "C1:D1" pair.
Colored cells provide ratio “boundaries” -- i.e. cells located between green and blue cells have ratios between 1:1 and 1:2. Cells located between blue and dark pink cells have ratios between 1:2 and 1:3. As with SQ (6) & SQ (7), there are more discrete “A1:B1” pairs (59) than “C1:D1” pairs (41). Of these, only 18 are common to both “A1:B1” & “C1:D1”. For SYM “A1:B1” pairs, the maximum pair-repeat is 6 (see line “A1:B1” "ML" = 8, col. = 20). The “C1:D1” maximum is 20 times. As with SQ, far more SYM “A:B” pairs fall to the right of the dark pink cells than do the SYM “C:D” pairs. Also, as with SQ, the great majority of cells are empty. *
Similarly to SQ (8), many TMLs on SYM (6) {SQ (8)} are differently partitioned. A number of SYM TMLs are common to both SYM & SQ. The number of SYM TMLs is comparable to that of SQ; but as regards PTs, SYM uses more PTs in M, but fewer in T than is the case for SQ. In regards PTs, there is a single-unit (TML = 46); three three-units, (TMLs = 40, 78 & 88); and two five-units (TMLs = 80 & 94). The remainder are “standard” four-units each, of which five are single-numbered equi-division PTs (i.e. lines 1, 4, 10, 17, & 25). Only three PTs have two equal longer values followed by two equal shorter values (10/10/8/8 (line 2); 12/12/10/10 (line 6), & 16/16/12/12 (line 18)). As with SQ, most four-unit partitions involve “symmetric bifurcation”. *
SYM (7) {SQ (9)} is the companion table to SQ (9). There are more distinct SYM M:T pairs (79) than SYM “A1:B1” pairs (59) or “C1:D1” pairs (41). This follows the SQ pattern, i.e.:
Of the 79 distinct SYM M:T pairs, 18 are repeated, i.e. far more than SQ (where only 8 M:T pairs are used more than once). These 18 SYM repeated M:T pairs are :
In regards what length appears with the most number of other lengths -- for “M” the answers are:
This is far less varied than are the comparable SQ data. There are fewer SYM samples (11 = 11.3%) to the right of the green (1:1) ratio band than there were SQ samples (SQ = 17 samples or 21.3%). In other words, for SYM, there is a greater tendency for T to be shorter than M. However, as with SQ, only one sample falls to the right of the 2:3 ratio band. Six samples fall directly on the 1:1 ratio band -- more than for SQ; but given the larger SYM sample-set, the percentage difference is not large. A crude visual comparison of SYM (7) {SQ (9)} and SQ (9), leaves the impression that SYM (7) {SQ (9)} appears more vertical and horizontal, vs. SQ (9), which seems more “splattered”. In conclusion, our methods used for the SQ data seem applicable to the SYM data, & the SQ & SYM data are broadly similar.
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