purlJam

<planning>
1. **Design Strategy**:
   - User wants a tank top with NO ribbing, worked IN THE ROUND (seamless)
   - Beginner difficulty level — must simplify construction, avoid complex techniques
   - Worsted weight yarn — using standard gauge: 18 sts = 4" (4.5 sts/inch)
   - No ribbing means we need clean edge finishing alternatives: I-cord bind off, picot, or simple bind off with rolled edge (stockinette naturally rolls, which could be used intentionally as a design feature)
   - For a beginner, a rolled stockinette edge is the simplest "no ribbing" option — worked in the round, stockinette will naturally roll at the hem, which is stylish and requires zero extra technique
   - Worked in the round = seamless body until underarm, then split for front and back worked flat (or use steek — too advanced for beginner)
   - Best beginner-friendly approach for in-the-round tank: Work body in the round to underarm, then work back and front flat separately (this is standard seamless bottom-up construction and is beginner accessible)
   - Neckline: For beginner, a simple scoop or crew neck is easiest. I'll go with a classic scoop neck — flattering, easy to execute, wider neckline means less complex neck shaping
   - Armhole finishing: No ribbing = I-cord bind off or simple bind off with rolled edge. For beginner simplicity, a simple bind off with natural roll works. But I-cord bind off is neater. Let me go with a simple stockinette rolled edge for armholes and neck (consistent with the no-ribbing aesthetic and beginner level)
   - Sizes: Will include XS, S, M, L, XL for full range
   - Standard fit: 2" positive ease
   - Construction: Bottom-up, in the round to underarm, then separate front and back worked flat

2. **Construction Plan**:
   - Cast on for full body circumference (front + back sts) onto circular needle
   - Work in the round in stockinette to underarm
   - Divide for front and back at underarm
   - Work back flat: shape armholes, work to shoulder, bind off
   - Work front flat: shape armholes, shape scoop neck, work to shoulder, bind off
   - Three-needle bind off or standard bind off + seam for shoulders
   - For beginner: standard bind off and seam shoulders (simpler to understand)
   - Finish armhole edges and neckline: simple bind off or rolled edge (no ribbing required)
   - Actually for armholes worked in the round — we pick up stitches and work a few rounds, then bind off. Without ribbing, just knit a few rounds and bind off = rolled edge finish
   - For neckline: pick up, knit a few rounds, bind off = rolled edge

3. **Quality Assurance**:
   - Need to confirm stitch counts work for all sizes
   - Armhole shaping must be symmetrical — when working flat, shaping happens at beginning and end of RS rows
   - Scoop neck: need to calculate center stitches to bind off and neck decrease rows
   - Shoulder stitches must match front and back
   - No ribbing means hem will roll naturally — mention this as a design feature in pattern notes
   - Need to ensure the in-the-round body transitions cleanly to flat armhole shaping
   - Underarm cast-on (a small number of sts cast on at underarm for seamless construction) — actually for a tank top worked bottom-up to underarm, we simply place stitches on hold at the underarm division and work each piece flat. No underarm cast-on needed for a sleeveless garment.
   - Pain point: beginner working flat after working in the round — need clear instruction about this transition
   - Pain point: scoop neck shaping — need to be very clear and step by step

4. **Final Calculations**:

   GAUGE: 18 sts = 4" in stockinette; 4.5 sts per inch
   Row gauge: approximately 24 rows = 4"; 6 rows per inch

   SIZES: XS, S, M, L, XL
   Target finished bust (with ~2" ease):
   - XS: 32" finished (30" body + 2" ease) → actually finished bust = body measurement + ease
   - Let me define finished garment bust measurements:
     * XS: 32" → half circumference = 16"
     * S: 36" → half = 18"
     * M: 40" → half = 20"
     * L: 44" → half = 22"
     * XL: 48" → half = 24"

   STITCH COUNTS (full circumference, for working in the round):
   - XS: 32" × 4.5 sts/inch = 144 sts total (72 front, 72 back)
   - S: 36" × 4.5 = 162 sts total (81 front, 81 back)
   - M: 40" × 4.5 = 180 sts total (90 front, 90 back)
   - L: 44" × 4.5 = 198 sts total (99 front, 99 back)
   - XL: 48" × 4.5 = 216 sts total (108 front, 108 back)

   For even stitch counts that work nicely with shaping, let me round to even numbers:
   - XS: 144 sts (72/72) ✓ even
   - S: 162 sts (81/81) — odd per piece, which works fine for centered neck shaping
   - M: 180 sts (90/90) ✓ even
   - L: 198 sts (99/99) — odd per piece, fine for neck
   - XL: 216 sts (108/108) ✓ even

   Actually let me reconsider. For scoop neck shaping, I want an odd number of stitches per piece so there's a clear center stitch. Let me adjust:
   - XS: 146 sts total (73/73) — 73 per piece (odd ✓)
   - S: 162 sts total (81/81) — 81 per piece (odd ✓)
   - M: 180 sts total (90/90) — even, but I can use center 2 sts approach for neck
   - L: 198 sts total (99/99) — odd ✓
   - XL: 216 sts total (108/108) — even

   Hmm, this is getting complicated. Let me simplify. For beginner patterns, it's actually cleaner to have even stitch counts per piece and bind off a center even number for the neck. Let me use even stitch counts per piece:

   - XS: 144 total (72/72) → 32" circumference ✓
   - S: 160 total (80/80) → 35.5" circumference (close to 36") — actually 160/4.5 = 35.6" ✓
   - M: 180 total (90/90) → 40" ✓
   - L: 196 total (98/98) → 43.6" ≈ 44" ✓
   - XL: 216 total (108/108) → 48" ✓

   Wait, let me reconsider S: 36" × 4.5 = 162, round to 160 (drop 2) = 35.6". Or 164 = 36.4". Let me use 160 for S (35.5" finished = S fits 34" bust with ~1.5" ease, which is fine, or I can say 2" ease for 34" bust).

   Actually let me re-approach this with standard sizing:
   - XS: fits 30-32" bust → finished = 34" (2" ease on 32" = 34") → 34 × 4.5 = 153, round to 152 (76/76)
   
   Hmm, I'm overcomplicating this. Let me use the template's guidance:
   Template says: XS ~70-80 sts, S ~85-95 sts, M ~100-110 sts, L ~115-125 sts, XL ~130-140 sts
   These are PER PIECE (for flat construction). For in-the-round, double them:
   - XS: 76 × 2 = 152 total (76 per piece)
   - S: 90 × 2 = 180 total (90 per piece)  
   - M: 104 × 2 = 208 total (104 per piece)
   - L: 120 × 2 = 240 total (120 per piece)
   - XL: 134 × 2 = 268 total (134 per piece)

   Let me check these measurements:
   - XS: 76 sts × (4/18) = 76/4.5 = 16.9" per piece × 2 = 33.8" ≈ 34" finished bust. For XS (30-32" body), 34" finished = 2-4" ease. ✓
   - S: 90/4.5 = 20" × 2 = 40" finished. For S (34-36" body), 40" finished = 4-6" ease. That's relaxed fit. Too much.

   I think the template sts are for standard fit (2-4" ease). Let me recalculate:
   - XS: 32" + 2" ease = 34" finished → 34 × 4.5 = 153, use 152 (76/76)
   - S: 36" + 2" ease = 38" finished → 38 × 4.5 = 171, use 172 (86/86)
   - M: 40" + 2" ease = 42" finished → 42 × 4.5 = 189, use 188 (94/94)
   - L: 44" + 2" ease = 46" finished → 46 × 4.5 = 207, use 208 (104/104)
   - XL: 48" + 2" ease = 50" finished → 50 × 4.5 = 225, use 224 (112/112)

   Let me verify these: 
   - XS: 76 × 2 = 152 sts → 152/4.5 = 33.8" ≈ 34" ✓
   - S: 86 × 2 = 172 sts → 172/4.5 = 38.2" ≈ 38" ✓
   - M: 94 × 2 = 188 sts → 188/4.5 = 41.8" ≈ 42" ✓
   - L: 104 × 2 = 208 sts → 208/4.5 = 46.2" ≈ 46" ✓
   - XL: 112 × 2 = 224 sts → 224/4.5 = 49.8" ≈ 50" ✓

   Good. All even per piece. Now for neck shaping (scoop), I want to place center sts on a holder. With even stitch counts per piece:
   - Neck width for scoop: approximately 8-10" wide = 8-10 × 4.5 = 36-45 sts
   - Center bind off for scoop:
     * XS: 76 sts piece → center 24 sts (24/4.5 = 5.3") — actually let me aim for about 7" wide neck = 7 × 4.5 = 31.5 ≈ 32 sts center bind off
     * Let me use a scoop neck that's about 7" wide for all sizes (scales slightly):
     
   For a scoop neck: bind off center sts, then decrease at neck edges.
   Let me calculate:
   
   Center bind off (approx 7" for most sizes):
   - XS: 76 sts → center 24 sts (24/4.5 = 5.3" wide) — leaving (76-24)/2 = 26 sts each side for shoulder + neck decreases
   - Actually scoop neck should be wider. Let me think about this differently.
   
   A scoop neck for a tank top:
   - Neck width: approximately 40-45% of piece width
   - XS: 76 × 0.42 = 32 sts center (32/4.5 = 7.1") — 22 sts each side
   - S: 86 × 0.42 = 36 sts center (36/4.5 = 8") — 25 sts each side
   - M: 94 × 0.42 = 40 sts center (40/4.5 = 8.9") — 27 sts each side
   - L: 104 × 0.42 = 44 sts center (44/4.5 = 9.8") — 30 sts each side
   - XL: 112 × 0.42 = 47 sts center → round to 46 (46/4.5 = 10.2") — 33 sts each side

   Wait I need to make sure center bind offs are even numbers (for symmetry with even piece sts):
   - XS: 76 sts → center 30 sts? (76-30)/2 = 23 sts each side... let me reconsider
   
   Let me think about shoulder width too. Shoulder width for each side: approximately 3.5-5" 
   Shoulder sts: 3.5-4" × 4.5 = 15.75-18 sts → use about 16-18 sts per shoulder

   So: piece sts = center neck sts + (2 × shoulder sts) + (2 × neck decrease sts)
   
   Let me work backwards from shoulder width:
   - XS: shoulder = 16 sts (3.6") each side
     - Neck decreases: maybe 6 sts each side (6 decrease rows)
     - Center bind off: 76 - (16×2) - (6×2) = 76 - 32 - 12 = 32 sts (32/4.5 = 7.1") ✓
   - S: shoulder = 18 sts (4") each side
     - Neck decreases: 7 sts each side
     - Center bind off: 86 - 36 - 14 = 36 sts (36/4.5 = 8") ✓
   - M: shoulder = 20 sts (4.4") each side
     - Neck decreases: 7 sts each side
     - Center bind off: 94 - 40 - 14 = 40 sts (40/4.5 = 8.9") ✓
   - L: shoulder = 22 sts (4.9") each side
     - Neck decreases: 8 sts each side
     - Center bind off: 104 - 44 - 16 = 44 sts (44/4.5 = 9.8") ✓
   - XL: shoulder = 24 sts (5.3") each side
     - Neck decreases: 8 sts each side
     - Center bind off: 112 - 48 - 16 = 48 sts (48/4.5 = 10.7") ✓

   All center bind offs are even ✓
   Shoulder sts: 16, 18, 20, 22, 24 — all even ✓

   Now ARMHOLE SHAPING:
   Template says: bind off 3-5 sts each side, then dec 1 st each side every RS row
   
   Armhole depth: For a standard tank/sleeveless: about 7-8" deep
   7" × 6 rows/inch = 42 rows = 21 RS rows
   
   Armhole BO + decreases:
   I want to remove approximately enough stitches so the armhole is properly shaped.
   Total stitches removed per side = BO sts + decrease sts
   The armhole width (at top) should be manageable. 
   
   For a tank, the armhole shouldn't be too deep horizontally. Let's say we BO 4 sts then dec 6 times = 10 sts removed per side.
   - XS: 76 - (4+6)×2 = 76 - 20 = 56 sts remaining for working the front/back ✓
   - S: 86 - 20 = 66 sts ✓
   - M: 94 - 20 = 74 sts ✓
   - L: 104 - 20 = 84 sts ✓
   - XL: 112 - 20 = 92 sts ✓

   Wait, but actually each side of body = front piece sts OR back piece sts. When we BO at underarm, we BO from one side only (the underarm). Let me reclarify:

   When dividing for armholes in a round construction:
   - At underarm point, we BO a few stitches (this creates the underarm gap/shaping)
   - Then work each piece flat and continue armhole shaping

   Standard approach for seamless in the round: 
   - BO 3-5 sts at beginning of next 2 sections (for each side of the piece)
   - Then work flat and dec at each armhole edge

   So for each side of a piece, the armhole shaping is:
   - BO 4 sts at start → creates underarm opening
   - Then dec 1 st at armhole edge every RS row, 6 times
   
   Total armhole stitches removed per side of each piece: 4 (BO) + 6 (dec) = 10 sts per side
   Total per piece: 20 sts removed

   Let me verify with armhole depth:
   Armhole dec rows: 6 RS rows = 12 rows = 2" of dec rows
   Work even after: 7" total - 2" = 5" even
   
   Actually: the armhole depth is measured from the underarm to shoulder. So:
   - Initial BO: takes ~1 row (not much depth)
   - Dec section: 6 RS rows = 12 rows ≈ 2"
   - Work even: remaining rows to reach shoulder
   
   Total back length from underarm: Let's say armhole depth = 7.5"
   7.5" × 6 rows/inch = 45 rows
   
   Back length from CO to underarm: Let's say total length = 20" → body = 20" - 7.5" = 12.5" to underarm. That seems reasonable for a tank top.

   Actually, let me think about total length:
   - Short tank: 18-20" from shoulder to hem (or ~12-14" from underarm down)
   - The body worked in round = length from hem to underarm
   - Let's set:
     * Body length (hem to underarm): 13" 
     * Armhole depth: 8" (generous for a tank, allows good armhole finish)
     * Total length: 21" from shoulder to hem

   That seems a bit long. For a standard tank:
   - Total length ~19-20" for most sizes
   - Hem to underarm: 12"
   - Armhole depth: 7.5" (back) / longer for front due to lower neck
   
   Let me use:
   - Hem to underarm: 12" 
   - Armhole depth: 7.5"
   - Total: ~19.5" ≈ 20" — good for a standard tank

   Now BACK NECK shaping:
   Back neck is usually higher than front. For a tank with scoop front, the back can be a simple bind off with slight shaping or just a straight bind off.
   
   Back neck width: slightly narrower than front
   After armhole shaping:
   - XS: 76 - 20 = 56 sts remain
   - Back neck: bind off center 20 sts (20/4.5 = 4.4"), then each shoulder = (56-20)/2 = 18 sts
   
   Hmm, but shoulder sts should match front:
   - XS front shoulder = 16 sts, XS back shoulder = 18 sts — these don't match!
   
   This is because I calculated different amounts. Let me reconcile.
   
   The total sts removed through armhole shaping should be the same for front and back (since the armhole is symmetric). After armhole shaping:
   - XS: 76 - 20 = 56 sts active for both front and back
   
   For the BACK: bind off center X sts, shoulder bind off = remaining sts each side
   For the FRONT: larger neck opening (scoop), bind off center 32 sts + decreases, shoulder = 16 sts

   So back shoulders must also = 16 sts each (to match for seaming)
   Back: 56 sts total → 16 sts (shoulder) + back neck + 16 sts (shoulder) = 32 sts shoulders
   Back neck bind off = 56 - 32 = 24 sts (24/4.5 = 5.3") — reasonable for back neck ✓

   But wait — I said front has 16 shoulder sts (after 6 neck decreases from 22 sts each side). Let me re-examine:
   
   Front after armhole shaping (XS): 56 sts
   Center bind off: 32 sts
   Each side: (56-32)/2 = 12 sts each side remaining for neck dec + shoulder
   Neck decreases: 6 times
   Shoulder: 12 - 6 = 6 sts 

   That's only 6 shoulder stitches — way too narrow! I made an error earlier. Let me redo this.

   The issue: I was calculating on the original piece sts (76) for front neck, but I need to calculate on the POST-armhole-shaping sts.

   Let me redo armhole and neck calculations:

   POST-armhole sts per piece:
   - XS: 56 sts
   - S: 66 sts
   - M: 74 sts
   - L: 84 sts
   - XL: 92 sts

   SHOULDER width: ~3.5-4.5" per shoulder
   - XS: 3.5" × 4.5 = ~16 sts → 16 sts each shoulder
   - S: 3.75" × 4.5 = ~17 sts → 18 sts (round up to even)
   - M: 4" × 4.5 = 18 sts
   - L: 4.25" × 4.5 = ~19 sts → 20 sts
   - XL: 4.5" × 4.5 = ~20 sts → 20 sts

   BACK neck width (= post-armhole sts - 2 × shoulder sts):
   - XS: 56 - 32 = 24 sts (24/4.5 = 5.3") ✓
   - S: 66 - 36 = 30 sts (30/4.5 = 6.7") ✓
   - M: 74 - 36 = 38 sts (38/4.5 = 8.4") — hmm, that's quite wide for back neck
   - L: 84 - 40 = 44 sts (44/4.5 = 9.8") — too wide for back neck!
   - XL: 92 - 40 = 52 sts (52/4.5 = 11.6") — definitely too wide

   I need to increase shoulder sts for larger sizes or decrease armhole shaping removal. Let me reconsider.

   Actually, for larger sizes, the armhole shaping needs to remove more stitches (wider armhole for a bigger body). Let me scale the armhole shaping:

   Armhole shaping (BO + dec per side):
   - XS: BO 4 + 4 dec = 8 sts per side (16 total removed per piece) — revised from before
   - S: BO 4 + 5 dec = 9 sts per side (18 total)
   - M: BO 4 + 6 dec = 10 sts per side (20 total)
   - L: BO 5 + 7 dec = 12 sts per side (24 total)
   - XL: BO 5 + 8 dec = 13 sts per side (26 total)

   POST-armhole sts per piece:
   - XS: 76 - 16 = 60 sts
   - S: 86 - 18 = 68 sts
   - M: 94 - 20 = 74 sts
   - L: 104 - 24 = 80 sts (actually wait, BO at underarm happens once at the start of working flat — BO is on both sides of the piece. Let me clarify: for flat armhole shaping, at start of row BO 4 sts, start of next row BO 4 sts = 8 sts removed, then dec 1 each side every RS = 2 sts per dec row)

   For flat working:
   - BO at start of first RS: removes sts from right armhole side
   - BO at start of next WS: removes sts from left armhole side
   - Then dec at each end of RS rows

   So total removed = 2 × BO + 2 × dec_rows
   - XS: 2×4 + 2×4 = 8+8 = 16 sts → 76-16 = 60 remaining ✓
   - S: 2×4 + 2×5 = 8+10 = 18 → 86-18 = 68 ✓
   - M: 2×4 + 2×6 = 8+12 = 20 → 94-20 = 74 ✓
   - L: 2×5 + 2×7 = 10+14 = 24 → 104-24 = 80 ✓
   - XL: 2×5 + 2×8 = 10+16 = 26 → 112-26 = 86 ✓

   Now shoulder sts:
   - XS: 60 sts → shoulders 17 each... want even numbers. Let me use 18 each = 36
     Back neck = 60 - 36 = 24 sts (5.3") ✓
   - S: 68 sts → shoulders 18 each = 36
     Back neck = 68 - 36 = 32 sts (7.1") — acceptable but wide. Use 20 each = 40? Back neck = 28 (6.2") still wide. Hmm.
   
   Actually for a tank top with a scoop front, the back neck can be fairly wide — it's a tank! The back neck doesn't need to be as structured as a sweater. Let me just accept wider back necks and make them look intentional (wide back neck is fine for a tank).

   But I need shoulder sts to be consistent (so the front and back shoulders match for seaming).

   Let me set shoulder sts:
   - XS: 18 sts each (4.0") → back neck = 60-36 = 24 sts (5.3")
   - S: 20 sts each (4.4") → back neck = 68-40 = 28 sts (6.2")
   - M: 20 sts each (4.4") → back neck = 74-40 = 34 sts (7.6") — quite wide
   - L: 22 sts each (4.9") → back neck = 80-44 = 36 sts (8.0") — wide
   - XL: 24 sts each (5.3") → back neck = 86-48 = 38 sts (8.4") — wide

   These back neck widths are wider than typical but acceptable for a tank top style. However, the front will be even wider (scoop). Let me check front:

   FRONT NECK (scoop):
   After armhole shaping, front has same sts as back. 
   Scoop neck should be wider than back neck and have a lower curve.
   Front scoop center bind off + decreases:
   - XS: 60 sts total → 2 × 18 shoulder = 36, remaining = 24 sts
     Center bind off: 14 sts, then dec 5 each side → 14 + 10 = 24 ✓
     Shoulder after all shaping: 18 - 5 = 13 sts... wait that doesn't work.
     
   Hmm, I need to rethink. The front needs:
   - Shoulder sts = same as back = 18 sts (XS)
   - Neck sts must also total 60 - 36 = 24 sts to be distributed among center BO + dec
   - So center BO + 2 × dec = 24 sts
   - If 5 dec each side: center BO = 24 - 10 = 14 sts
   - Front neck total width: (14 + 5 + 5) sts = 24 sts, but that's in stitches
   - Front neck actual width INCLUDING decrease area: Since decreases bring the neck inward gradually, the visual width of the neck opening is approximately: center BO width + the dec sts at either side
   - Center BO: 14 sts = 14/4.5 = 3.1" — that seems narrow for a scoop
   
   I think my armhole shaping is removing too few stitches, making the piece too narrow for proper neck + shoulder distribution.

   Let me step back and approach this differently with cleaner numbers.

   APPROACH: Define desired measurements first, then calculate sts.

   For each size:
   FINISHED BUST (half circumference per piece):
   - XS: 17" per piece
   - S: 19" per piece
   - M: 21" per piece
   - L: 23" per piece
   - XL: 25" per piece

   That gives finished bust: 34" (XS), 38" (S), 42" (M), 46" (L), 50" (XL)
   With 2" ease: fits 30-32" (XS), 34-36" (S), 38-40" (M), 42-44" (L), 46-48" (XL) ✓

   Stitch counts per piece at bust:
   - XS: 17 × 4.5 = 76.5 → 76 sts
   - S: 19 × 4.5 = 85.5 → 86 sts
   - M: 21 × 4.5 = 94.5 → 94 sts
   - L: 23 × 4.5 = 103.5 → 104 sts
   - XL: 25 × 4.5 = 112.5 → 112 sts

   Total CO sts (front + back):
   - XS: 152 / S: 172 / M: 188 / L: 208 / XL: 224

   Now, desired measurements at shoulder/neck:

   SHOULDER WIDTH (each side): about 4-5" 
   - XS: 4.0" = 18 sts
   - S: 4.25" = 19 → 20 sts
   - M: 4.5" = 20 sts (actually 20.25, round to 20)
   - L: 4.75" = 21 → 22 sts
   - XL: 5.0" = 22 sts (actually 22.5, round to 22)

   ARMHOLE WIDTH (horizontal, per side) = piece width - 2×shoulder - neck
   Let me define armhole removal per side = BO + dec stitches

   I'll work it out differently. Let me define:
   - Front neck width (center BO for scoop): approximately 7" for all sizes (consistent scoop feel)
     7" × 4.5 = 31.5 → 32 sts for all sizes — but that seems too uniform. Let me scale slightly:
     - XS: 6.5" = 29 → 30 sts
     - S: 7" = 31.5 → 32 sts
     - M: 7.5" = 33.75 → 34 sts
     - L: 8" = 36 sts
     - XL: 8.5" = 38 sts (38.25 → 38)

   FRONT NECK decreases per side (for scoop curve): 4-6 decreases
   Let's use 4 dec each side for all sizes (keeps it simple for beginner)

   Now check: front neck sts total = center BO + 2×dec = (sts needed)
   Sts available for neck + shoulders after armhole:
   = piece sts - armhole removal sts
   = sts available total = 2×shoulder + front neck BO + 2×neck dec

   Let me call armhole removal per side = A (BO + dec)

   piece sts - 2A = 2×shoulder + center BO + 2×neck dec

   Solving for A:
   - XS: 76 - 2A = 2×18 + 30 + 2×4 = 36 + 30 + 8 = 74 → 2A = 2 → A = 1 — that's way too small!

   This means my piece sts are too small to accommodate all these elements. The problem is that 76 sts at 4.5 sts/inch is only 16.9" wide per piece, and I'm trying to fit 4" shoulder + 6.5" neck + 4" shoulder = 14.5" plus some armhole shaping. That would only leave 16.9" - 14.5" = 2.4" for armhole width total (1.2" per side) — which is essentially no armhole shaping.

   The issue is that the armhole shaping is meant to create a proper armhole (removing stitches to narrow the top of the piece), not to be measured from the total width. The piece gets NARROWER at the top due to armhole shaping, and that narrowing IS the armhole.

   So the proper way to think about it:
   - FULL WIDTH of piece at bust = shoulder + neck + shoulder + armhole (armhole goes away to the side/seam)
   - After armhole shaping: remaining sts = should + neck + shoulder
   - The armhole sts are REMOVED (not measured in width at top)

   So: shoulder + neck/2 + neck/2 + shoulder = post-armhole sts
   And: pre-armhole sts = post-armhole sts + 2A (where A = sts removed per side for armhole)

   For the width to work out:
   - post-armhole sts (back) = 2×shoulder + back neck BO
   - XS: 2×18 + 24 = 60 sts post-armhole back
   - XS: 76 - 60 = 16 sts removed for armhole → 8 per side

   - post-armhole sts (front) = 2×shoulder + center neck BO + 2×neck dec
   - XS: 2×18 + 30 + 2×4 = 36 + 30 + 8 = 74 sts needed post-armhole front
   - But back post-armhole = 60. Front post-armhole must equal back post-armhole (same armhole shaping)!
   
   So: 60 = 2×18 + 30 + 2×neck dec
   60 = 66 + 2×neck dec
   2×neck dec = -6 — impossible!

   The center BO is too wide. The neck BO + decreases must fit within the available post-armhole stitches (minus shoulders).

   Available for front neck sts = post-armhole sts - 2×shoulders = 60 - 36 = 24 sts
   These 24 sts are distributed as: center BO + 2×neck dec
   
   If 4 neck dec each side: center BO = 24 - 8 = 16 sts (16/4.5 = 3.6") — quite narrow for scoop
   If 6 neck dec each side: center BO = 24 - 12 = 12 sts (12/4.5 = 2.7") — very narrow
   
   A scoop neck that's only 3.6" wide doesn't look like a scoop... 

   The fundamental issue: the shoulders are too wide and leaving too little for the neck. OR I need more armhole removal to make the piece wider relative to shoulder + neck.

   Wait — I think I'm confusing myself. Let me re-read the armhole shaping:

   The total piece width (sts) is the FULL width including where the armhole will be. The armhole shaping removes sts from the SIDES of the piece, narrowing it. The remaining sts include BOTH shoulders and the neck area.

   So if I want:
   - Left shoulder: 3"  = 13.5 → 14 sts
   - Neck: 9"  = 40.5 → 40 sts  
   - Right shoulder: 3" = 13.5 → 14 sts
   - Total needed at top: 68 sts post-armhole shaping
   - Total at bust: 76 sts
   - Armhole removal: 76 - 68 = 8 sts → 4 per side

   That works better! The key insight is that the shoulders don't need to be as wide on a TANK TOP because there are no sleeves — the shoulder seam is narrow (just the strap width essentially).

   Let me redefine with narrower shoulders (tank top straps):
   
   TANK TOP SHOULDERS (strap width): 
   - A tank top strap is typically 2.5-4" wide
   - XS: 3" = 13.5 → 14 sts
   - S: 3" = 14 sts
   - M: 3.25" = 14.6 → 14 sts  
   - L: 3.5" = 15.75 → 16 sts
   - XL: 3.5" = 16 sts

   Hmm actually for a standard tank top (not a spaghetti strap), shoulder straps of 3-4" are common. Let me use:
   - All sizes: 3.5" shoulder strap = 3.5 × 4.5 = 15.75 → 16 sts per shoulder

   Actually tank top shoulders are usually the shoulder seam width, which for a fitted tank is typically 3-4.5" per side. Let me use a modest scaling:
   - XS: 14 sts (3.1")
   - S: 16 sts (3.6")
   - M: 16 sts (3.6")
   - L: 18 sts (4.0")
   - XL: 18 sts (4.0")

   Now: post-armhole = 2×shoulder + neck available
   Front neck available = post-armhole - 2×shoulder = center BO + 2×dec

   Let me define target scoop neck widths:
   Total front neck visual width (center BO + decrease sections at sides):
   - XS: 8" total → 8 × 4.5 = 36 sts
   - S: 9" → 40.5 → 40 sts
   - M: 9.5" → 42.75 → 42 sts (using 44 for even? let me just round naturally)
   - L: 10" → 45 sts
   - XL: 10.5" → 47.25 → 46 sts

   Post-armhole per piece = 2×shoulder + neck sts:
   - XS: 28 + 36 = 64 sts
   - S: 32 + 40 = 72 sts
   - M: 32 + 44 = 76 sts
   - L: 36 + 46 = 82 sts
   - XL: 36 + 48 = 84 sts

   Armhole removal (per piece total = piece sts - post-armhole sts):
   - XS: 76 - 64 = 12 sts → 6 per side (BO 3 + dec 3 each side, or BO 4 + dec 2)
   - S: 86 - 72 = 14 → 7 per side (BO 3 + dec 4, or BO 4 + dec 3)
   - M: 94 - 76 = 18 → 9 per side (BO 4 + dec 5)
   - L: 104 - 82 = 22 → 11 per side (BO 4 + dec 7, or BO 5 + dec 6)
   - XL: 112 - 84 = 28 → 14 per side (BO 5 + dec 9, or BO 6 + dec 8)

   Back neck (= post-armhole - 2×shoulders):
   Same post-armhole sts as front:
   - XS: 64 - 28 = 36 sts back neck? Wait, back shoulder = same as front shoulder.
   
   For back: post-armhole sts = 2×shoulder + back neck BO
   But post-armhole sts for back = same as front (same armhole shaping on both)
   - XS: 64 sts post-armhole → 2×14 + back neck = 28 + 36 = 64 ✓ → back neck = 36 sts (8")
   - S: 72 → 32 + 40 = 72 → back neck = 40 sts (8.9")
   
   Wait, that means the back neck IS the same as the front neck width?! That seems odd. The back neck should be narrower.

   Oh! I see the issue. The front neck has DECREASES — so the front neck area is wider in sts (more sts removed from each side piece) but the ACTUAL final shoulder width is the same. Let me re-examine:

   For the FRONT:
   - After armhole shaping: say 64 sts (XS)
   - Work even for a bit, then:
   - Bind off center sts for neck: say 24 sts
   - Two sections remain: (64-24)/2 = 20 sts each
   - Each section: dec at neck edge 6 times → 20-6 = 14 sts shoulder ✓

   Total neck width = center BO + both dec sections = 24 + 6 + 6 = 36 sts (but this is the number of sts in the neck zone, not the same as the visual width being constant)
   Center BO visible width = 24/4.5 = 5.3"
   The decreases taper from 20 sts to 14 sts on each side → the curved portion adds visual width

   For the BACK:
   - After armhole shaping: also 64 sts (XS)
   - Back neck: simpler shaping. Let's say just BO center sts, no dec (or maybe 2 dec per side for slight curve)
   - If shoulder = 14 sts: back neck BO = 64 - 28 = 36 sts straight bind off, no extra shaping needed
   - Back neck = 36/4.5 = 8" — that's WIDE for a back neck but remember this is a TANK TOP, so it can have a wider, lower back — that actually looks good!

   OR — if I want the back neck to be narrower (more modest):
   - Back shoulder slightly wider: say 18 sts each (4") for XS
   - Back neck = 64 - 36 = 28 sts (6.2")
   - Front shoulder must also = 18 sts: 20 sts each side after armhole, dec 2 times → 20-2 = 18 ✓ but only 2 neck dec per side means less of a scoop curve

   I keep going in circles. Let me just commit to clean, workable numbers and verify the math once.

   FINAL DECISION — keeping it simple for a beginner pattern:

   Let me use a clean, simple approach:
   - Define stitch counts at cast-on
   - Define armhole shaping (BO + dec)
   - Whatever remains: split between shoulder and neck, with neck being the "remainder" after shoulders

   GAUGE: 4.5 sts/inch, 6 rows/inch (worsted on US 7)

   SIZES (finished bust):
   - XS: 34" | S: 38" | M: 42" | L: 46" | XL: 50"
   These give 2" ease for standard body measurements.

   CO STITCHES (for in the round, full circumference):
   - XS: 34 × 4.5 = 153 → round to 152 (76/76 per piece)
   - S: 38 × 4.5 = 171 → round to 172 (86/86 per piece)
   - M: 42 × 4.5 = 189 → round to 188 (94/94 per piece)
   - L: 46 × 4.5 = 207 → round to 208 (104/104 per piece)
   - XL: 50 × 4.5 = 225 → round to 224 (112/112 per piece)

   Verification of bust measurements:
   - XS: 152/4.5 = 33.8" ≈ 34" ✓
   - S: 172/4.5 = 38.2" ≈ 38" ✓
   - M: 188/4.5 = 41.8" ≈ 42" ✓
   - L: 208/4.5 = 46.2" ≈ 46" ✓
   - XL: 224/4.5 = 49.8" ≈ 50" ✓

   ARMHOLE SHAPING (per piece, both sides):
   Keep it simple: BO 4 sts each side, then dec 1 st each side every RS row, X times.
   
   I want the final piece to be wide enough for reasonable shoulders + neck.
   
   Target: shoulder = 3" each = 14 sts (rounded down from 3×4.5=13.5)
   
   With 4 sts BO + X dec each side:
   Post-armhole sts = piece sts - 2×(4+X)
   = piece sts - 8 - 2X
   
   This must = 2×14 + front neck section
   = 28 + neck sts needed
   
   Front neck target: ~8-9" wide total (including dec portions) → ~36-40 sts
   
   For XS: 76 - 8 - 2X = 28 + 36 → 76 - 8 - 2X = 64 → 2X = 4 → X = 2 dec per side
   That's very few decreases. Armhole would be almost straight.

   Hmm. The issue is that for a tank top with wide neck, there's less width needed at the top, so armhole shaping is minimal. This actually makes sense — a basic tank top doesn't have dramatic armhole shaping.

   Let me verify: 76 sts (17" wide) for XS:
   - Shoulder 3" each: 13.5 → 14 sts each × 2 = 28 sts
   - Front neck center BO + dec area: 76 - 28 (shoulders) - 8 (2 × BO 4) - 2×2 (2 dec per side) = 76 - 28 - 8 - 4 = 36 sts neck section
   - Front neck: BO 24 center (24/4.5 = 5.3"), each side: (76-8-4-24)/2... wait let me redo this.

   POST-armhole sts for XS:
   - BO 4 each side: 76 - 8 = 68 sts
   - Dec 2 each side: 68 - 4 = 64 sts remaining

   Front: 64 sts. Shoulders = 14 each (28 total). Available for neck = 64 - 28 = 36 sts.
   
   Center BO: 24 sts (24/4.5 = 5.3") 
   Each side remaining after center BO: (64-24)/2 = 20 sts
   Neck dec: 20 - 14 = 6 dec each side
   
   Check: center BO 24 + 2×6 dec = 24 + 12 = 36 sts ✓ (neck zone accounts for 36 sts)
   
   Front neck visual width:
   - Center BO: 24 sts = 5.3" (the flat bottom of the scoop)
   - The dec sections taper from 20 sts to 14 sts — these form the curved sides of the scoop
   - Total neck width at top = 24 + 6 + 6 = 36 sts = 8" ✓ — yes this makes a nice scoop!

   Back: 64 sts. Shoulders = 14 each. Back neck = 64 - 28 = 36 sts straight BO.
   Back neck width = 36/4.5 = 8" — That's quite wide for a back neck but for a low-back tank it's actually fine! Or I could add 1-2 dec per side for back neck too.

   Actually, let me use 3" shoulder width but increase it slightly per size to give natural scaling:

   Let me set:
   - Shoulder sts (each side): 14, 14, 16, 16, 18 for XS, S, M, L, XL

   And let me define armhole shaping:
   - XS, S: BO 4 each side, dec 2 each side (8 + 4 = 12 total removed per piece)
   - M, L: BO 4 each side, dec 3 each side (8 + 6 = 14 total removed per piece)  
   - XL: BO 4 each side, dec 4 each side (8 + 8 = 16 total removed per piece)

   POST-armhole sts:
   - XS: 76 - 12 = 64 sts
   - S: 86 - 12 = 74 sts
   - M: 94 - 14 = 80 sts
   - L: 104 - 14 = 90 sts
   - XL: 112 - 16 = 96 sts

   Back neck (no extra shaping, simple straight BO):
   - XS: 64 - 2×14 = 36 sts (8")
   - S: 74 - 2×14 = 46 sts (10.2") — too wide!
   - M: 80 - 2×16 = 48 sts (10.7") — too wide!
   - L: 90 - 2×16 = 58 sts (12.9") — way too wide!
   - XL: 96 - 2×18 = 60 sts (13.3") — absurd!

   Something is seriously wrong. The larger sizes have way too many stitches post-armhole relative to shoulder + neck needs.

   The issue: Larger body = larger piece width = but neck and shoulder don't scale proportionally as much. For larger sizes, the armhole needs to remove MORE stitches because the EXCESS comes from the body width.

   Let me dramatically increase armhole removal for larger sizes:

   Think about it physically: 
   - XS: 76 sts piece. Want: 14 shoulder + 14 shoulder + 36 neck region = 64 sts top. Remove: 76-64 = 12 sts (6 per side: BO 4 + dec 2)
   - S: 86 sts piece. Want: 14 shoulder + 14 shoulder + 40 neck = 68 sts top. Remove: 86-68 = 18 sts (9 per side: BO 4 + dec 5, or BO 5 + dec 4)
   - M: 94 sts piece. Want: 16 shoulder + 16 shoulder + 44 neck = 76 sts. Remove: 94-76 = 18 sts (9 per side: BO 4 + dec 5)
   - L: 104 sts. Want: 16+16+48 = 80 sts. Remove: 24 sts (12 per side: BO 4 + dec 8, or BO 5 + dec 7)
   - XL: 112 sts. Want: 18+18+52 = 88 sts. Remove: 24 sts (12 per side: BO 4 + dec 8, or BO 5 + dec 7)

   Hmm, 8-9 decreases per side seems like a lot for a beginner pattern armhole. Let me reconsider by widening the neck:

   For larger sizes, the neck SHOULD be wider. A size XL tank can have a much wider neck than XS. Let me scale neck widths more aggressively:

   Front neck total width (center BO + dec sts each side):
   - XS: 36 sts (8.0") → center BO 24, dec 6 each
   - S: 46 sts (10.2") → center BO 28, dec 9 each... hmm 9 is a lot

   Actually wait — I realize I need to think about this differently again. The "neck region" in my calculation above is all the stitches between the two shoulder sections. This includes BOTH the center bind-off AND the decreasing sections. So a wide "neck region" in my arithmetic means the total visual width of the neckline opening is wide — which is fine for a scoop!

   Let me recalculate back neck with this understanding. Back neck = all stitches not in the shoulders = what gets bound off. For the back of a tank, this CAN be wide — a wide back neck on a tank is a design feature!

   Let me reconsider: what if for the back, the shoulder sts are wider (more like a regular sweater), and for the front, the shoulders are the same width but the front neck is wider/lower?

   OR — what if I just have the same back "neck" width as front? For an open back tank, the back neck could be as wide as the front scoop. But that's a specific design.

   OR — more practically: let me use different shoulder widths for back vs front...

   NO. For seaming at the shoulder, the back and front shoulder widths MUST match.

   OK. Let me try a completely different approach and use MUCH wider shoulders (like a regular top):
   
   For a tank top (NOT a spaghetti strap), shoulder widths of 4-5" per side are typical.

   Shoulder sts (each side): 
   - XS: 18 sts (4.0")
   - S: 20 sts (4.4")
   - M: 22 sts (4.9")  
   - L: 24 sts (5.3")
   - XL: 26 sts (5.8")

   Target back neck width (reasonable for a back neck):
   - All sizes: approximately 6-7"
   - 6" = 27 → 28 sts; 6.5" = 29.25 → 30 sts; 7" = 31.5 → 32 sts
   
   Post-armhole sts (back) = 2×shoulder + back neck:
   - XS: 36 + 28 = 64 sts
   - S: 40 + 32 = 72 sts
   - M: 44 + 32 = 76 sts
   - L: 48 + 32 = 80 sts
   - XL: 52 + 32 = 84 sts

   Armhole removal:
   - XS: 76 - 64 = 12 → 6 per side (BO 4 + dec 2)
   - S: 86 - 72 = 14 → 7 per side (BO 4 + dec 3 OR BO 3 + dec 4)
   - M: 94 - 76 = 18 → 9 per side (BO 4 + dec 5)
   - L: 104 - 80 = 24 → 12 per side (BO 4 + dec 8)
   - XL: 112 - 84 = 28 → 14 per side (BO 5 + dec 9)

   8-9 decreases per side for L/XL is still a lot. This is realistic for a larger garment's armhole shaping, but for a BEGINNER pattern it might be daunting. However, it's just repeating the same dec row... I'll keep it but explain clearly.

   Front neck: post-armhole sts same as back.
   Each side remaining after center neck BO = (post-armhole - center BO) / 2
   After neck dec = shoulder sts
   
   So: center BO + 2 × neck dec = post-armhole - 2×shoulder = back neck BO
   
   That means center BO + 2×neck dec = back neck sts!
   
   So front neck ZONE (center BO + dec area) = same total sts as back neck BO
   
   The DIFFERENCE between front and back neck is that front distributes those sts between a center BO and curved decreases, while back just BOs them all.

   So:
   - XS: Front neck zone = 28 sts: center BO = 16 sts (3.6"), remaining each side = (64-16)/2 = 24 sts, dec 24-18 = 6 times. Check: 16 + 6+6 = 28 ✓
   
   Hmm, 16 sts center BO = 3.6" — not very scoopy. But with 6 dec each side forming the curve, the visual scoop is wider. The actual opening at the top of the neck is: 18 shoulder + curved section + 18 shoulder — the neck opening is from shoulder seam to shoulder seam minus the shoulder widths = neck visual width at knitting = center BO width at bottom of scoop + the curved sides. This gives maybe 8" total? That's reasonable.

   Actually you know what, for a beginner pattern for a tank top, a neck that starts with a 3.6" bind off and then curves up is perfectly fine. Let me just go with it and note it as a "moderate scoop neck."

   Let me also reconsider — maybe I should just go with a CREW NECK for simplicity at the beginner level. Or a wider scoop where I bind off more center sts and do fewer dec. For beginner, simpler neck shaping is better!

   For beginner-friendly neck: bind off most of the neck stitches at once, then just 2-3 dec per side. That's much simpler to execute.

   Let me try: center BO = 18 sts, dec 2 per side, shoulder = post-armhole/2 - center_BO/2... let me just work forward:

   XS (64 sts post-armhole):
   - Center BO: 20 sts
   - Each side: (64-20)/2 = 22 sts
   - Neck dec: 2 per side
   - Shoulder: 22-2 = 20 sts ← but back shoulder = 18! Mismatch!

   This shows: if I want shoulder to match back (18 sts), I need to remove 4 sts through neck dec + armhole, which is already done. Center BO must = 64 - 2×18 - 2×neck_dec.

   If neck dec = 4: center BO = 64 - 36 - 8 = 20 sts (20/4.5 = 4.4"). Moderate scoop. Each side after BO: 22 sts, dec 4 times = 18 shoulder ✓

   If neck dec = 2: center BO = 64 - 36 - 4 = 24 sts (24/4.5 = 5.3"). Nicer scoop. Each side: 20, dec 2 = 18 shoulder ✓

   For beginner: fewer decreases = easier. Let me use neck dec = 4 per side for all sizes (slight scoop) to give a bit more curve. But let me check bigger sizes:

   S (72 sts post-armhole): shoulder = 20 each
   Center BO = 72 - 2×20 - 2×4 = 72 - 40 - 8 = 24 sts (5.3") Each side: 26, dec 4 = 22... but shoulder should be 20. That doesn't work.
   
   Oh wait: each side after BO: (72-24)/2 = 24 sts, dec 4 = 20 shoulder ✓

   M (76 sts post-armhole): shoulder = 22 each
   Center BO = 76 - 44 - 8 = 24 sts (5.3") Each side: (76-24)/2 = 26, dec 4 = 22 ✓

   L (80 sts post-armhole): shoulder = 24 each
   Center BO = 80 - 48 - 8 = 24 sts (5.3") Each side: (80-24)/2 = 28, dec 4 = 24 ✓

   XL (84 sts post-armhole): shoulder = 26 each
   Center BO = 84 - 52 - 8 = 24 sts (5.3") Each side: (84-24)/2 = 30, dec 4 = 26 ✓

   This works! Let me verify the back neck:
   Back: same post-armhole sts. Shoulder same. Back neck BO = post-armhole - 2×shoulder.
   - XS: 64 - 36 = 28 sts (6.2") back neck — reasonable
   - S: 72 - 40 = 32 sts (7.1") — wide-ish but okay for a tank
   - M: 76 - 44 = 32 sts (7.1") ✓
   - L: 80 - 48 = 32 sts (7.1") ✓
   - XL: 84 - 52 = 32 sts (7.1") ✓

   These work! Back neck bind-off of 28-32 sts for a tank is absolutely fine.

   Now let me re-examine armhole shaping to make sure the dec numbers are reasonable:
   - XS: 6 per side → BO 4 + dec 2 (2 RS rows of dec)
   - S: 7 per side → BO 4 + dec 3 (3 RS rows)
   - M: 9 per side → BO 5 + dec 4 (4 RS rows)
   - L: 12 per side → BO 4 + dec 8 (8 RS rows)
   - XL: 14 per side → BO 5 + dec 9 (9 RS rows)

   8-9 RS rows of decreases for L/XL is a lot. This corresponds to 16-18 rows = about 2.7-3". For a tank armhole, this seems excessive. The armhole would be very curved at the top.

   Let me increase the armhole BO to reduce the number of dec rows:
   - L: BO 6 + dec 6 = 12 per side (6 RS rows)
   - XL: BO 7 + dec 7 = 14 per side (7 RS rows)

   Updated:
   - L: BO 6 + dec 6 per side → total removed: 2×12 = 24 ✓
   - XL: BO 7 + dec 7