midiviz

04 — Double bass: geometry, fingering systems, posture, test cases

Input for extending strings/fingering.js (state per note: string + frame base b, the semitones of finger 1 above the open string, + finger, with a per-finger offset table) to the double bass, and for animating a bassist’s left hand, bow and posture.

0. Ten-line summary

  1. Tuned in fourths, E1 A1 D2 G2 = MIDI 28 33 38 43, written an octave up [WDB][V]. A 3/4 bass has a ≈1050 mm string, 3.2× the violin’s [GOL][V].
  2. The low-position frame spans a whole tone: fingers 1-2-4 at 0, +1, +2, with 3 and 4 moving as one digit (Simandl 1881) [WSI][PAT][V]. That whole tone (102 mm in I) is wider than the cello’s minor-third frame (98 mm) [calc].
  3. Three notes per string per position, so shifts are routine (one every few notes, semitone shifts on one finger included). Shift costs must be far lower than the violin’s [PAT][V].
  4. Simandl’s positions ½ I II II½ III III½ IV V V½ VI VI½ VII are a semitone apart, b = 1…12: seven full + five half positions up to the octave [PAT][TBP][JM][V].
  5. Near the neck heel finger 3 replaces 4 (frame 1-2-3 at 0, +1, +2). Sources put the switch where the top note is +8 to +12 above the open string [PAT][TB1][FRE][V].
  6. From the octave (b = 12) the thumb stops notes. Petracchi’s three thumb frames T-1-2-3 span a minor third, major third or perfect fourth; 4 is rarely used; low thumb reaches down to +7 [DBH-P][NTB][PAT][V].
  7. Style alternatives: Italian 1-3-4 (Bottesini, Billè) [PAT][TB2][V]; open hand 1-2-3-4 over a minor third (Franke, Karr, Morton’s “extension fingering”) [PAT][TB3][V]; Rabbath’s six harmonic-node positions with the pivot (thumb fixed, reach a minor/major third) [PAT][DBH-R][V].
  8. Open strings are used more than on the violin (beginners, fast and jazz playing), but Morton says avoid them in lyrical playing and never two in a row [PAT][UNB][V].
  9. Morton’s shift rules: ≥ 2 notes per position; shift on a semitone, ideally same finger; shortest travel; shift early; in running notes shift on the weak note [PAT][V].
  10. Posture: thumb behind the neck about opposite finger 2, rounded fingers, elbow floating; bass turned ~45° and leaning on the player; nut at eye/eyebrow height; French bow held like a cello bow, German bow palm-up like a viol bow [JM][IUP][WDB][V].

1. Instrument

1.1 Tunings [WDB][JM][V]

| Setup | Strings | MIDI | Notes | |—|—|—|—| | Orchestral | E1 A1 D2 G2 | 28 33 38 43 | “the only modern bowed string instrument that is tuned in fourths” | | 5-string, low B | B0 E1 A1 D2 G2 | 23 + above | “several major European orchestras” | | 5-string, low C / high C | C1 + E…G / E…G + C3 | 24 / 48 | high C for solo tessitura | | C extension | E string down to C1 | 24 (gates at 25–28) | “Most professional orchestral players use four-string double basses with a C extension”; wooden or metal “fingers” at C♯ D E♭ E, or fingered by reaching over the scroll | | Solo tuning | F♯1 B1 E2 A2 | 30 35 40 45 | a tone up, lighter strings; solos published for both tunings | | Fifths (Red Mitchell, Quarrington) | C1 G1 D2 A2 | 24 31 38 45 | rare |

Solo-tuning parts are usually notated as if in orchestral tuning [?]: expose tuning, don’t detect.

1.2 Notation

Notated “an octave higher than it sounds”, also in tenor and treble clef; Italian solo music is often at sounding pitch [WDB][V]. GM files store sounding pitch (open E = 28). Offer a “written pitch” switch instead of guessing.

1.3 Sizes [GOL][V]

| inches (cm) | 4/4 | 3/4 | 1/2 | 1/4 | |—|—|—|—|—| | Full height, body bottom → scroll | 74.8 (190) | 71.6 (182) | 65.7 | 61.4 | | Body, bottom → shoulder | 45.7 | 43.7 (111) | 40.2 | 37.4 | | Scale, nut → bridge | 43.3 (110) | 41.3 (104.9); Kay 41.5 | 38 (96.5) | 35.4 (89.9) | | Upper / lower bout | 21.3 / 26.8 | 20.3 / 25.6 | 18.7 / 23.6 | 17.3 / 21.9 | | Scroll → shoulder | 29.1 | 27.9 | 25.5 | 24.0 | | Neck width at nut | 1.8 | 1.7 | 1.6 | 1.5 |

“An ‘average’ 3/4 size bass has a scale length … 41-42 inches with an afterlength … around seven inches”; there are no standards [GOL][V]. A maker builds 7/8 basses at 41½–42 in [TB4][V, snippet]. A 1/2 bass is “only about 15% smaller” than a 4/4 [WDB][V]. Bow 60–75 cm [WDB][V]. Default L = 1050 mm.

1.4 Body (3D) [WDB][V]

Violin form or viol (gamba) form, rarer busetto and pear shapes; carved round back or flat back angled at the top. Sloped shoulders meet the neck in a curve, so the player can lean the bass and reach the high register. Proportionally deeper body; curved bridge; fingerboard flattened under the E string (Romberg bevel); metal worm-gear machines; thick endpin; tailpiece on a cable.

1.5 Frame widths [calc]

d(n) = L·(1 − 2^(−n/12)), L = 1050 mm:

b 1 (½) 2 (I) 5 (III) 7 (IV) 9 (V½) 12 17 24
d(b) mm 59 115 263 349 426 525 657 788
semitone 56 52 44 39 35 29 22 15
whole tone (Simandl 1→4) 108 102 86 77 68 57 43 29
minor third (open hand 1→4) 158 149 125 112 99 84 63 42
perfect fourth (T→3 diatonic) 249 235 197 176 157 132 99 66

Violin P4 frame at a = 2: 73 mm; cello minor third at a = 2: 98 mm. The open-hand minor third only shrinks to the low Simandl width near b = 9–10, which fits Morton’s advice to use extension fingering “particularly in upper neck positions” [PAT][V]. The 1st-position whole tone is 87 / 94 / 102 / 107 mm on 1/4, 1/2, 3/4, 4/4 basses.

1.6 Landmarks

1.7 Range

1.8 Harmonics [calc]

Nodes: 1/2 at +12 (sounds +12); 1/3 at +7.02, +19.02 (sounds +19); 1/4 at +4.98, +24 (+24); 1/5 at +3.86, +8.84, +15.86, +27.86 (+27.86). They are Rabbath’s anchors (§2.7); orchestras tune by harmonics [WDB][V]; scales often end on the octave G harmonic (§4.3) [FRE][V].

2. Fingering systems

2.1 Simandl (German / Viennese) [WSI][PAT][JM][V]

2.2 Position names → b

A full position has finger 4 on a natural of C major on the G string, a half position on an accidental [TBP][V]; “G-string = I (A), II (B♭), III (C), IV (D), V (E♭); ½ (A♭), II ½ (B), III ½ (C♯), V ½ (E)” [JM][V]. Simandl’s original: “eight positions … half … to the seventh … plus four intermediate positions … twelve”; Sankey renumbers each semitone “half position to the eleventh” [PAT][V], i.e. Sankey = b − 1 [calc], matching a forum “8 position” for 4 on F♯ [TB1][V, forum].

b Simandl Rabbath Finger 1 on E A D G (MIDI) G string 1, 2, 4
1 ½ – 29 34 39 44 A♭ A B♭
2 I 1st 30 35 40 45 A B♭ B (45 46 47)
3 II 1st + pivot 31 36 41 46 B♭ B C
4 II½ 1st + pivot 32 37 42 47 B C C♯
5 III 2nd 33 38 43 48 C C♯ D (48 49 50)
6 III½ 2nd + pivot 34 39 44 49 C♯ D D♯
7 IV (heel) 3rd 35 40 45 50 D E♭ E
8 V 3rd 36 41 46 51 E♭ E F
9 V½ 3rd 37 42 47 52 E F F♯
10 VI 3rd 38 43 48 53 F G♭ G (1-2-3, §2.3)
11 VI½ 3rd 39 44 49 54 F♯ G G♯ (1-2-3)
12 VII / thumb 4th 40 45 50 55 G A♭ A (1-2-3), or T on the octave

b = 1, 2 on every string and b = 5 on G are on Silliman’s chart [SIL][V]; G-string names from [JM][TBP][TB1][V]; other cells [calc]. Billè names half positions by spelling (A♯ “first advanced”, B♭ “second backward”) [PAT][V]: keep b internal, names for display.

2.3 The 4 → 3 switch

| Source | Rule (above the open string) | |—|—| | Forum summary of Simandl [TB1][V, forum] | 1-2-4 “up to the 4th finger on the F♯” (+11, b = 9); 1-2-3 “until the 3rd finger on the A” (+14), “until 1st on the octave G”; then T-1-2-3 | | Morton, Concepts and Ideas [PAT][V] | 3 not 4 “from E♭4 till F♯4” (written: +8…+11); avoid 4 above E♭4 written | | Morton, Primer [PAT][V] | 3 instead of 4 “from a major six above the open string” (+9) | | Nanny 1920 [PAT][V] | 1-2-4 to “6th position (9th degree)”, 1-2-3 from the 10th degree; whole tones 1-4 in positions 1–5, 1-3 from 6 (degree ≈ b [?]) | | Freides [FRE][V, forum] | 2-4 “thumb behind neck” to F♯ (+11); 2-3 “thumb at side of neck” for A♭, A (+13, +14) |

Consensus [calc]: 4 normal while its note is ≤ +9, contested at +10/+11, 3 from +12. One may “transition to 123 a few positions early, especially if your 4th finger is a bit short” [TB1] → the hand-size option.

2.4 Italian 1-3-4 (Bottesini, Billè) [PAT][TB2][V]

Asioli (1823) → Bottesini’s Metodo (1869) → Billè’s Nuovo metodo (1922), still standard in Italy. “In the first position on the d-string they will use finger 1 for e, finger 3 for F and finger 4 for F♯” [TB2]. Billè: change position whenever an ascending scale reaches C, E or G on a string; “the last half tone has always to be played by the 3rd and 4th fingers”, a mid-scale half tone by 1-3 [PAT]. Critics: 3 is the weakest finger [TB2]. Frame 1: 0, 3: +1, 4: +2.

2.5 French school: Nanny [PAT][V]

Eight positions of two degrees (14, one past Simandl/Billè, to B on the G string); 1-2-4 low (his F- and G-major one-octave scales match Simandl), 1-2-3 high, thumb from the 7th position.

2.6 Open hand 1-2-3-4 (minor third) [PAT][TB3][V]

Franke (1820), Dragonetti, Gale’s “open hand”, “the Karr technique”, Morton’s “extension”, Wolf’s “four-finger system”, Pedersen. Morton: Simandl (“regular”) for lyrical playing, especially low; extension for fast playing, especially high [PAT]. Gale’s “Triangulation” interleaves closed hand, open hand and thumb [TB3]. Players use “a pivoting or rolling movement … since statically maintaining such a wide stretch may overstress the hand” [TB3]. Sankey’s Simandl edition has an appendix on extensions, finger 3 and low thumb [TB1][V, forum]. Edgar Meyer’s and Streicher’s systems were not verified [?]; Streicher’s method is listed among those “evolving from the Simandl technique” [PAT][V].

2.7 Thumb position [WDB][DBH-T][DBH-P][NTB][PAT][V]

Frame Steps T→1, 1→2, 2→3 Offsets T 1 2 3 Span T on G3 (55)
Chromatic ½ ½ ½ 0 1 2 3 m3 55 56 57 58
Semi-chromatic 1 ½ ½ 0 2 3 4 M3 55 57 58 59
Diatonic 1 1 ½ 0 2 4 5 P4 55 57 59 60

2.8 Rabbath: positions, pivot, crab [PAT][DBH-R][DBH-S][JM][V]

| Position | G-string anchor | b | Node | |—|—|—|—| | 1 | finger 1 on A | 2 | – | | 2 | finger 1 on C | 5 | 1/4 | | 3 | finger 1 on D, thumb at the neck base, pivots to the octave | 7 | 1/3 | | 4 | thumb on G | 12 | 1/2 | | 5 | D | 19 | 2/3 | | 6 | G (“harmonic position”) | 24 | 3/4 |

2.9 Bows [WDB][IUP][V]

3. Shifting and string crossing

3.1 Morton’s rules (Concepts and Ideas, 1991, via [PAT][V])

  1. ≥ 2 notes per position (rests and open strings count; may be dropped in lyrical thumb position [MOR][V, snippet]).
  2. Shift on a strong beat; in runs of equal notes on the weak note; with uneven notes in the shorter.
  3. Shift by a semitone on one string, 4. with the same finger.
  4. No same finger twice when crossing strings in legato.
  5. Avoid open strings, especially lyrically; 7. never two open strings in a row (both ring).
  6. Shortest hand travel. 9. In lyrical playing III–IV on lower strings beats ½/I with open strings.
  7. Shift as soon as the passage allows. 11, 17. 3 instead of 4 from written E♭4. 12–16. thumb rules (§2.7).

Also: fingers 1-2 (2 preferred) for “money notes” [MOR]; “functional” (hidden) vs “expressive” shifts; shifts have preparation, movement, follow-through, led by the elbow in the neck register and the wrist in thumb position [PAT].

3.2 Other heuristics

4. Test oracles

4.1 Position maps [SIL][V]

| String | ½ (b = 1): 1 2 4 | I (b = 2): 1 2 4 | |—|—|—| | E (28) | 29 30 31 | 30 31 32 | | A (33) | 34 35 36 | 35 36 37 | | D (38) | 39 40 41 | 40 41 42 | | G (43) | 44 45 46 | 45 46 47; III (b = 5): 48 49 50 |

4.2 One-octave scales

| Scale | MIDI | Fingering | Tag | |—|—|—|—| | D major, shifting | 38 40 42 43 45 47 49 50 | D0 D1 D4 G0 G1 G4 @b2, G2 G4 @b5 | [UNB][EE][V] | | D major, beginner | 38 40 42 33 35 37 38 | D0 D1 D4 A0 A1 A4 D0 (top half an octave down) | [UNB][V] | | G major from G1 | 31 33 35 36 38 40 42 43 | E2 A0 A1 A2 D0 D1 D4 G0 @b2 | Simandl/Nanny use I [PAT][V]; digits [calc] | | same, Billè | | E3 A0 A1 A3 D0 D1 D4 G0 | [PAT][V]; [calc] | | F major from F1 | 29 31 33 34 36 38 40 41 | E1 E4 A0 A1 A4 D0 D2 D4 @b1 | half position [PAT][V]; [calc] | | B♭ major from B♭1 | 34 36 38 39 41 43 45 46 | A1 A4 D0 D1 D4 G0 G2 G4 @b1 | [calc] | | C major from C2 | 36 38 40 41 43 45 47 48 | A2 D0 D1 D2 G0 G1 G4 @b2, then C3 as G1@b5, G2@b4 or G4@b3 | [calc], acceptable set | | A major on the G string | 45 … 57 | positions only rise: 1-2-4 to F♯, 1-2-3 above (Sankey I→11th, Billè I→VII) | [PAT][V] |

4.3 Two-octave endings on the G string (Freides) [FRE][V, forum]

| Top | MIDI | Fingers | Frame | |—|—|—|—| | E | 51 52 | 2 4 | b = 7 | | F | 52 53 | 2 4 | b = 8 | | F♯ | 53 54 | 2 4 | b = 9 | | G | 52 54 55 | 1 4, then 3 on the G harmonic | b = 9 + octave node | | A♭ | 55 56 | 2 3 | b = 11 | | A | 56 57 | 2 3 | b = 12 | | B♭ | 55 57 58 | T 1 2 | thumb on G | | B | 56 58 59 | 1 2 3 (T on G, silent) | T 0, +1 +3 +4 | | C | 55 57 59 60 | T 1 2 3 | diatonic | | C♯ | 56 58 60 61 | 1 2, 2 3 (hand slides a tone, thumb to A) | thumb shift | | D | 55 57 59 61 62 | T 1 2, 2 3 | thumb shift |

Another teacher: “the last two notes of a 2-octave G, A♭, and A scales are fingered 2-3, then B♭ is T-1-2, C is T-1-2-3” [TB8][V, snippet]: agrees except G.

4.4 Method books

5. Posture and motion

Left hand, neck. “Thumb in middle of neck”; bass “K” (gap between 1 and 2); “rounded finger”; “straight wrist (elbow floating above heel)” [JM][V]. Simandl: thumb “perpendicular to the neck and more or less opposite the middle finger”, shifting “without rotating or pivoting the thumb” [TB9][V, snippet]; others say opposite fingers 1–2 [XF][V, snippet]; some jazz players wrap the palm round the neck [TB10][V, snippet]. Animate finger 3 pressed down beside 4 in the low positions [WSI]. “The thumb always travels with the hand” [FO][V]. Fingertip span 102 mm in I, 77 mm at the heel [calc].

Thumb position. Simandl: “placing that part of the thumb between the first joint and the nail horizontally across the string”; 1 slightly curved on the tip, 2 less, 3 straighter [TB11][PAT][V]. Modern teachers raise the elbow (“the hand can come around and over the fingerboard in a much more natural curve”), higher for lower strings, shoulder relaxed [DBH-E][TB11][V]; thumb “at a right angle to the string”, hand about 45° [DBH-T][V]. Going up: lean forward from the hips, raise the elbow, slide the thumb from the back of the neck to its side and onto the string [PAT][V]; “let your bass neck rest on your shoulder” [IUP][V]. Thumb across two strings for a fifth [T][?].

Body. The player “stands, or sits on a high stool, and leans the instrument against their body, turned slightly inward” [WDB][V]; “turn the bass one quarter of a turn … about a 45-degree angle from the body”, tilted back onto the pelvic bone or stomach [IUP][V]. Endpin: nut “between hair line and eyebrow” [JM][V], or eye level to forehead [SBO][V, snippet]; standing players may put 1st/half position at eye level; stool ≈ inseam height [WDB][V]. Short players stop the bass turning with a toe on the ribs [TB12][V, snippet]; Rabbath uses a bent endpin [DBH-S][V].

Bow arm. Bow “straight and even to the floor … straight to the bridge”, wrist in line, arm weight not muscle; “Your bow needs to go faster to play higher notes” [IUP][V]; contact point moves toward the bridge as the left hand rises [TB6][V]. These map onto the #034 bow-speed / contact curves [calc].

6. Algorithms and datasets

7.1 Instrument

contrabass: { name: 'Double bass', open: [28, 33, 38, 43], strings: ['E', 'A', 'D', 'G'],
  L: 1050, maxB: [9, 12, 19, 26], frame: BASS_FRAME, program: 43, heel: 7, thumbFrom: 7,
  tunings: { solo: [30, 35, 40, 45], fiveB: [23, 28, 33, 38, 43], cExt: [24, 33, 38, 43] } }

GM program 43 (0-based) = Contrabass [T]. C-extension notes 24–27 are gate/open notes (finger 0, no frame).

7.2 Frame by zone (offset above finger 1: cost)

The engine’s single per-instrument frame becomes frameAt(b) (or entries with bMin/bMax).

Zone b Offsets (cost)
Neck, closed hand 1–8 1: 0 (0), −1 (0.8 pivot); 2: +1 (0); 4: +2 (0), +3 (1.2 pivot/open hand); 3 alone: +1 (2.5; Italian 0, and then 2: +1 costs 1.5), +2 (1.5 open hand)
Crook of the neck 9–11 1: 0; 2: +1; 3: +2 (1.0 → 0 from b 9 to 11); 4: +2 (0.3 → 2), +3 (1.5)
Upper neck, no thumb 12–13 1: 0; 2: +1, +2 (0.8); 3: +2, +3 (0.6)
Thumb (b = thumb) ≥ 12 T: 0; 1: +1, +2; 2: +2 (0.3), +3, +4 (0.4); 3: +3 (0.4), +4, +5 (0.3); 4: +6 (3)
Low thumb 7–11 thumb table + 1.0 per note (+2.0 on long/lyrical notes)
Harmonics – nodes +5, +7, +12, +19, +24 → sounding +24, +19, +12, +19, +24; cheap when the hand is at b ≥ 9

Thumb as finger 5 with b = thumb base keeps Petracchi’s table readable. Rabbath profile: anchors b ∈ {2, 5, 7, 12, 19, 24}, pivot ±1–2 free of shift cost. Display: bass positionName(b) from §2.2, “thumb” above; Sankey (b − 1) and Rabbath numbers as options.

7.3 Weights vs violin defaults (starting points)

| Weight | Violin | Bass | Why | |—|—|—|—| | shift | 0.94 | 0.4 | a shift every 3–4 notes is normal | | distance unit | mm (L 328) | mm × 328 / L | else every bass shift costs ×3.2 | | shiftSemitone | 0.998 | 0.5 | Morton 3 | | shiftSlide (same finger) | 0.3 | 0.1 | Morton 4 | | secondary shift | – | × 0.6 | Pedersen | | one-note position | – | +0.8 (open strings, rests count) | Morton 1 | | open | −0.075 | −0.3 (beginner −0.6, lyrical +0.3) | §3.2 | | openLong | 1.6 | 1.0 (lyrical 2.5) | Morton 6 | | two opens in a row | – | +0.5 | Morton 7 | | cross | [0, .35, 5, 6] | [0, .25, 3, 6] | crossing replaces shifting in fast playing | | fourth | 0.665 | 0 for b ≤ 8, then §7.2 | 4 is the normal top finger low down | | lowStringHigh | 0.08 | E 0.6, A 0.25, D 0.1 | Simandl’s high-E avoidance | | pos | violin table | 0 for b 1–12; +0.3 / base above 12 (G string 0.1) | G is the solo string | | thumb on a long lyrical note | – | +1.5 | Morton 16, money notes on 1-2 |

Profiles: simandl, italian (3 at +1 cheap, 2 dear), rabbath (pivot, anchors), openHand (0 +1 +2 +3 cheap for b ≥ 5), beginner (maxB 5, cheap opens, no thumb).

7.4 Test cases (✓ exact oracle, ≈ acceptable-set member)

| ID | Input (MIDI) | Expected | Source | |—|—|—|—| | B1 ✓ | 45 46 47 | G1 G2 G4 @b2 | [SIL] | | B2 ✓ | 34 35 36 (F-major context) | A1 A2 A4 @b1 | [SIL] | | B3 ✓ | 48 49 50 | G1 G2 G4 @b5 | [SIL] | | B4 ✓ | 38 40 42 43 45 47 49 50 | D0 D1 D4 G0 G1 G4 @b2, G2 G4 @b5 | [UNB][EE] | | B5 ✓ | beginner: 38 40 42 33 35 37 38 | D0 D1 D4 A0 A1 A4 D0 @b2 | [UNB] | | B6 ≈ | 31 33 35 36 38 40 42 43 | E2 A0 A1 A2 D0 D1 D4 G0 @b2 | [PAT], [calc] | | B7 ✓ | B6, italian | E3 A0 A1 A3 D0 D1 D4 G0 | [PAT][TB2] | | B8 ≈ | 29 31 33 34 36 38 40 41 | E1 E4 A0 A1 A4 D0 D2 D4 @b1 | [PAT], [calc] | | B9 ≈ | 34 36 38 39 41 43 45 46 | A1 A4 D0 D1 D4 G0 G2 G4 @b1 | [calc] | | B10 ✓ | 51 52 / 52 53 / 53 54 | G2 G4 @b7 / @b8 / @b9 | [FRE] | | B11 ≈ | 52 54 55 | G1 G4 @b9 + octave harmonic (3); or G2 G3 @b11 | [FRE][TB8] | | B12 ✓ | 55 56 | G2 G3 @b11 | [FRE][TB8] | | B13 ✓ | 56 57 | G2 G3 @b12 | [FRE][TB8] | | B14 ✓ | 55 57 58 | GT G1 G2 | [FRE][TB8] | | B15 ✓ | 55 57 59 60 | GT G1 G2 G3 | [FRE][TB8][DBH-P] | | B16 ✓ | 55 57 59 61 62 | GT G1 G2, then G2 G3 with T moved to 57 | [FRE] | | B17 ≈ | 55 56 57 58 | GT G1 G2 G3 (chromatic frame) | [FRE][DBH-P] | | B18 ≈ | 28 29 30 31 32 33 | E0 E1 E2 E4 @b1, E4 @b2, A0 | Morton 3–4 [PAT]; [calc] | | B19 ≈ | 38 38 45 45 47 47 45 43 43 42 42 40 40 38 | D0 D0 G1 G1 G4 G4 G1 G0 G0 D4 D4 D1 D1 D0 | [SUZ] (key [?]) | | B20 ≈ | B19, b fixed at 7 (neck block) | D0 D0 D1 D1 D4 D4 D1 G0 G0 A4 A4 A1 A1 D0 | [SUZ] “4th Pos.”; [calc] | | B21 ≈ | simandl: any note > 55 | not on E (nor A) while D or G can take it | E: [WDB]; A: [calc] | | B22 ≈ | lyrical 40 42 43 42 40 (43 a long note) | D1 D4 @b2, 43 as D4@b3 (semitone shift on 4), back to b2; beginner: G0 | Morton 4, 6 [PAT]; [calc] | | B23 ≈ | 55 57 59 (simandl) vs (rabbath) | thumb on 55 in both; Rabbath labels it position 4 | [PAT][JM] | | B24 ≈ | 31 32 33 32 31, fast vs legato | fast: E2 E4 @b2, A0, E4 E2; legato: 33 as E4@b3 (semitone shift on 4, no open string) | Morton 4, 6 [PAT]; [calc] |

References