Fashioning the Fab Four (Part 10): We Can Work It Out

 At first, I could not work it out. Why were my instruments out of proportion?

In Fashioning the Fab Four (Part 8): Tools of the Trade, it was noted that
“gauge is not critical for this project” but I am here to tell you that it is!

 

Warning: this post contains mathematics!

Bass drum ("big drum" in pattern)
New DK version (3.5 mm hook)

The pattern did not specify the finished dimensions of any of the instruments except the bass drum’s diameter: approximately 12.5 cm or 5 inches. That measurement is only relevant if one is making the same specifications as the pattern (which I wasn’t) so I was working without heeding final dimensions.

I was using a lighter yarn than prescribed by the pattern with a smaller hook, so my finished product was going to be smaller. That made sense.

I figured that as long as the tension was consistent, and each instrument used the same yarn and hook, all of the instruments would be in the similar proportions to each other as in the original pattern, wouldn’t they? (This worked for the dolls.)



Snare drum ("small drum" in pattern)
DK Version (3.5 mm hook)

Except when it came to the side of the smaller drums, the number of rows specified in the pattern did not match up to the circumference of the drum ‘skin’. 

(My theory is that this happened because the row gauge did not match the stitch gauge and circles are involved. Any other ideas?)

I could have worked the rows until they reached right around the edge, but how many stitches long should I make each row to keep to the scale of the original design?  Mathematics is one way to work this out, using the tension measurements and gauge specifications to guide me.

The only size information I had was the gauge specification given in the pattern, plus the dimensions of the finished dolls and the bass drum.

	Original Pattern (Aran + 4 mm hook)	My version (DK +3.5 mm hook)	Difference in size of DK version compared to Aran version
Gauge/Tension	14 sc & 12 rows over 4x4” / 10x10cm	38 rows over 9.625” / 24.5 cm OR (jacket) 28 sts & 12 rows over 6x3” / 15.24 x 7.62 cm
Stitch tension (4”/ 10 cm ÷ 14 sts)	1 sc = 0.285” / 0.714 cm	1 sc = 0.21” / 0.54 cm	76% of original
Row tension (4”/ 10 cm ÷ 12 rows)	1 row = 0.33” / 0.833 cm	1 row = 0.25” / 0.65 cm	78% of original
Doll height	Approx 11.5” / 29 cm	7.5–8” / 19–20 cm	66–69% of original
Large (bass) drum diameter	Approx 5” / 12.5 cm (6 rounds)	2.75” / 7 cm (6 rounds)	55–56% of original
Height of bass drum in relation to height of doll	43–44% height of doll	35–37% height of doll

Floor Tom ("medium drum" in pattern)
DK version (3.5 mm hook)

It confused me that the reduction in size of the drum was a different percentage to the reduction in size of the dolls by more than 10%.  No wonder the scale looked a little odd to me. There wasn’t enough size difference between the bass and snare. The bass drum did not look big enough compared to the dolls even though I had worked 6 rounds as instructed by the pattern.

When I scaled down by yarn weight and hook size, the stitch and row gauges reduced by different amounts (%) also. 

 

If the DK dolls were 70% of the size of the Aran ones, I would expect the DK drums to be 70% of the Aran instrument sizes too, but they were not. This confused and intrigued me. If you have any ideas as to why this might be, please let me know.



Drumkit seat
DK version (3.5 mm hook)

I reviewed the original pattern to compare the original sizes of things. I only had the gauge specifications to guide me. Because the specifications were in rows, I calculated the sides of the drums first.

I have rounded the values in these tables but when doing the calculations, I always use the non-rounded values of the stitch and row gauges; e.g. 4"÷14 sc=0.2857142 for each sc then x 8 sc (for bass drum) = 2.2857136" and then round off the answer (2.29").

It is up to you how many decimal places you round to. Two decimal places are practical but three are more accurate.

Instrument section	Stitches/Rows required by original pattern	Approximate Measurement based on 14 sc & 12 rows over 4x4”/10x10cm
Big Bass Drum side	8 sc (x 0.29”/0.714 cm =)	2.29” wide	5.71 cm wide
	48 rows (x 0.33”/0.833 cm =)	16” long	40 cm long
Medium Drum side Floor Tom	10 sc	2.85”	7.14 cm
	32 rows	10.67”	26.67 cm
Small Snare Drum side	7 sc	1.99”	4.99 cm
	30 rows	9.99”	24.99 cm
Seat side	5 sc	1.43”	3.57 cm
	27 rows	8.99”	22.5 cm

The length of a drum side in rows = the circumference of the circle.

If we know the circumference (C), we can work out the diameter (D) using the formula*:

 

C = D x π.   (or C = 2 πr where r = radius)

In which case:

Diameter = Circumference ÷ π.

 *(π = 3.1415927)

Instrument	Length of side = Circumference	Original Diameter (Aran version)
Big Bass Drum	16” / 40 cm	5.09” /12.73 cm
Medium Drum Floor Tom	10.67” /26.67 cm	3.39” / 8.49 cm
Small Snare Drum	9.99” / 24.99 cm	3.18” / 7.95 cm
Seat	8.99” / 22.5 cm	2.86” / 7.16 cm

Once I had decided upon the new diameters of the drums, I grabbed a compass and drew the circles onto a piece of paper and used that as a guide while working the rounds. 

It turned out that the bass drum needed extra rounds to make it ‘fit the circle’ and be in correct proportion to the dolls and other drums.  Instead of working 6 rounds as the pattern instructed, I worked 8 rounds.  These can be seen in the photograph.

Much better!

Summary

·       Find out the original pattern sizes of instruments and compare them to the original pattern's doll size.

·       Work out the ratios of instrument size:doll height according to the original pattern

·       The tension/gauge specifications indicate how long and wide the sides of each drum should be.

·       The lengths of the drum sides (no. of rows) will be the same as the circumferences which can help calculate the diameters of the circles.

·       Once I have the diameters of the original Aran circles, I can calculate the new DK diameters by reducing them by a certain percentage and/or comparing them to the smaller DK doll. Then work my version of the circles, adding or omitting rounds until the circles match the new diameters.

·       From the new diameter I can work out the circumference which will be the length of the sides in rows.

·       I can use my own tension specifications to work out how many rows I need to make to match the circumference, and also how many stitches long each row should be to maintain the correct scale.

·       I could have just worked the sides until they were the right length to work around the new circumferences, but I like the precision and double-checking that the maths provides. Knowing in advance how many rows will be required saves time by not having to frequently stop and check the rows against the circumference.