# A geometric analysis of the lyra pegbox (part 1)

Recently, I checked out a copy of Geometry, Proportion and the Art of Lutherie (review here) and was inspired to analyze some historical lyras to look for design patterns.

Tracing old instruments is useful for drawing inspiration when setting out to make a new instrument. However, in each step there is a risk of introducing errors (when tracing the lyra, using the tracing the create a template, projecting the template onto a piece of wood). In addition, old instruments may be slightly asymmetric, either because they were built that way or because of dimensional change in the wood over time.

To begin, we normalize the images so that all have a 40mm height difference in string lengths. Although this changes the absolute dimensions, I am most concerned in this analysis with relative proportions. These photos are not distortion-free, but I selected the ones that are most straight relative to the top of each instrument. Each string is ~15mm apart from the next.

First, we create a bounding box around each pegbox. We immediately see integer and root proportions emerge: 4/3, sqrt(2), and sqrt(φ), from left to right. These rectangular proportions are commonly found in art and architecture.

Next, let’s draw some circles. Today we’ll focus on 2003.378, and we draw a circle with a 92mm diameter (shown in blue):

Generate another circle by multiplying the diameter by sqrt(φ): 92 x 1.272 = 117mm. This ratio nicely mirrors the proportion of the bounding box. The larger circle is tangent to the smaller one, and is shown in red:

A nice result is that the (right) red circle’s center is at the left edge of the pegbox, and vice versa. In other words, the two circles’ centers are one radius apart. The resulting shape is called vesica piscis

Note that you can scale this analysis as you like, by beginning with the desired width of the instrument and choosing this as the radius of the red circle, computing the others according to the proportions here.

Finally, we create a circle whose diameter is 1/3 that of the 92mm circle, or 30.7mm (shown in green). This small circle is tangent to the two red circles, outlines the top curve of the instrument, while the top of the vesica marks the top of the ornament. In addition, the tangents of the green and red circles mark the start of the ornament.
A matching 30.7mm circle may be added to bound the curvature of the ornament (shown in orange).
The bottom pegs are centered 3/4 of the way down on the bounding box; strings are spaced 15mm apart and pegs are roughly 7mm in diameter. This is enough to reconstruct the pegbox from scratch:
The one variable I’m not sure about: at what height to place the lower (blue) circles, relative to the red?  Here, I matched the height of the red circles’ centers, but this results in a slightly wider neck than on the original instrument. In either case, though, it’s a very close match.
The other pegboxes will follow in a future post. Feedback welcome!

# MMA (1889b)

89.4.418 is a very different piece than the first four. Also acquired in 1889, it appears to be older and probably predates the standardization of the lyra’s dimensions led by Baron. The contours of the body are simpler, more rounded, without the refined inflection points of the newer design. The soundboard is also much flatter, and has a bit of decoration and inlay.

How do we know it’s still an Istanbul lyra? It has the same general shape and length; three long pegs and no nut on the middle string; and the fingerboard’s shape and size is consistent with other lyras. We might speculate that this predates the kemençe’s entry into Ottoman court music, and perhaps was used in the köçekçeler ensembles of Beyoğlu´s wine taverns, where the environment was rowdy and required some power. But a bit of restoration, replacement of the two broken tuning pegs and fitting of a suitable bridge would be invaluable towards assessing the volume and timbre of this lyra in comparison with the others in the collection.

# MMA (1889a)

89.4.416, acquired in 1889, is very unusual because of its painted soundboard. Because of the acoustic significance of the soundboard, it is usually not ornamented. The colorful motifs are reminiscent of Greek folk painting, but the Arabic script at the bottom says “El Cezayir” or “Al Jeza’ir”, which means “Algeria”. This is clearly an Istanbul lyra from the mid-to-late 19th century and the Ottoman rule in Algeria ended in 1830, so it is difficult to speculate about the reasons for this.

In addition, the body is well-constructed and has the standard Baron dimensions, so it may have been a very good instrument that was decorated by someone other than the maker. The tuning pegs are in much better condition than the instrument, but still appear to be in the late 19th-century style, so they may have been replaced (before the lyra’s acquisition by the Met).

The bottom two gut strings appear quite old. This is the only lyra which has a bow. The bow is extremely short (shorter than the lyra!), and the stick’s curvature is extremely high. The stick is held in place by a strip of metal, possibly iron.

Condition:
• At least two large cracks running down the body
• Mother-of-pearl inlay around edges of fingerboard is missing some pieces
• Wood on bow is very fragile

# MMA (2003)

A visually stunning piece in the collection is 2003.378, acquired in June 2003 through a European auction house.

Notable features:
• The most ornate of the five instruments, yet in the best condition. The entire body is covered in tortoiseshell strips inlaid with mother-of-pearl. Even the tuning pegs are exquisitely inlaid with a matching pattern.
• Lateral curvature somewhat flatter than the first two.
It is not possible to confirm the maker, but the extreme inlay and the slender construction suggest Küçük İzmitli. A very similar instrument is on display at the Museum of Greek Folk Instruments in Athens, Greece, and appears briefly in this video, around the 6:50 mark.
Dimensions:
• 147mm max width
• 42mm min width (at bottom of pegbox)
• 53mm width (at bottom of fingerboard)

# MMA (1906)

06.1309 was donated to the museum in 1906 by one of the Hewitt sisters and is also in the classic “Baron style”. In Ben Hume’s notes from 1987, he describes it as the “best playing of the three”, but I am not sure which two instruments he compared. In addition, the reconstructed bridges are surely not optimized for each lyra.

Notable features:
• Tortoiseshell fingerboard grip with mother-of-pearl inlay
• Mother-of-pearl inlay around perimeter of soundboard
• Small filling on back of fingerboard, in region where other lyras have a possible hole for a fourth peg
Condition:
• Tuning pegs are loose
• Inlay on fingerboard is cracked. Missing pieces of inlay around soundboard.
• Body is in excellent condition
Dimensions:
• 147mm max width
• 38mm min width (at bottom of pegbox)
• 49mm width (at bottom of fingerboard)

# MMA (1946)

Currently on display in the musical instrument gallery is 46.34.37. The instrument was collected by Henry Harrison Getty sometime before 1919, and donated to the Met by his daughter Alice in 1946. Notable features include:

• Significant lateral curvature on the soundboard
• Small hole above bass tuning peg
• Ivory tuning pegs and fingerboard/grip. Fingerboard is inlaid with wood decorations.
Condition:
• Small crack in side of body
• Slight warping in decoration across top edge of soundboard
• Gut strings appear new
• Otherwise excellent condition
Dimensions:
• 142mm max width
• 39mm min width (at bottom of pegbox)
• 47mm width (at bottom of fingerboard)