Here is a description of the geometric design method of the neck that can be generally used regardless of the size of the instrument, for violin, viola, and cello. It starts with the ⌜length of the string⌟ and is designed using the ⌜position of notes on the fingerboard and the intervals between notes⌟.
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The purpose of this study is to establish a geometric design method for the neck that can be used generally regardless of the size of the instrument, for violin, viola, and cello. If such a universal design method exists, the value calculated by the method can be ⌜a standard value⌟, and in some cases, the value can be modified slightly according to the intention of the maker. The existence of such a universal design method can increase the reliability of the instrument by enabling consistent work.
In this study, I design the neck using geometric principles. However, since the shape of the neck must be determined by the rigidity and playability of the instrument, there is a contradiction that it cannot be determined geometrically. The only way to resolve this contradiction is ⌜to find a geometric method that can obtain values that are as close as possible to empirical values⌟. Therefore, I would like to state in advance that this report is based on past data.
In this report, ⌜the length of the string (vibrating part)⌟ is taken as the starting point for all calculations. If the length of the string becomes longer, the tension of the string also increases, requiring a thicker neck. Also, as the string becomes longer, the distance between semitones on the fingerboard becomes longer, which causes changes in the left-hand position. In other words, the neck design must change according to the length of the string. The ⌜stop length⌟ can also be considered as a candidate for the starting point, but it has a slightly different dimension from the length of the string. If the stop length becomes longer, both the neck length and the length of the string become longer, and thus the neck thickness and the left-hand position also change, as shown above. However, there are cases where the stop length does not change, but only the length of the string changes. This is the case when the height of the bridge changes or the position of the bridge moves. Therefore, the fundamental starting point of the neck design must be ⌜the length of the string⌟.
When the player holds the first position (the upper part of the neck), the index finger should be able to quickly find the position of the first semitone, and when the player holds the fourth position (the lower part of the neck), the index finger should be able to quickly find the position of the seventh semitone. These two are determined by the shape of the curve of the upper and lower parts of the neck and the position of that curve. In other words, from the player’s point of view, the design of the neck is determined by the position of the semitone on the fingerboard. Since the position of such semitone on the fingerboard is determined by the length of the string, this study will use the length of the string as the starting point and ⌜the position of each semitone on the fingerboard and the interval between the semitones⌟.
Since the violin (viola) and the cello have very different geometry, I will explain them separately. The viola without cheeks uses exactly the same method as the violin, and the upper neck curve of the viola with cheeks can be referenced from the cello.
Lastly, in this report, all values are expressed to two decimal places to increase accuracy, but in actual work, they can be rounded to one decimal place and applied. Also, the length unit, mm, is omitted and only numbers are expressed.
Table of Contents
(For details, see PDF...)
1. Violin and Viola (model without cheeks)
1.1. Preparation
1.2. Button size
1.3. Neck thickness and measurement location
1.4. Neck thickness including fingerboard
1.5. Upper curve
1.6. Lower curve
1.7. Cross-sectional shape of the neck
1.8. Angle of neck end
2. Cello
2.1. Preparation
2.2. Button size
2.3. Neck thickness and measurement location
2.4. Neck thickness including fingerboard
2.5. Upper curve
2.6. Lower curve
2.7. Cross-sectional shape of the neck
2.8. Angle of neck end
I'm adding this because there's a misunderstanding.
The purpose of this report is to provide a starting point for neck design by establishing a universal method that uses the string length as a starting point and uses the pitch distance to design. (It is not the best finished result.)
The issues raised about this report are as follows:
- The thickness line should not be a straight line.
- The head end should not be on the same line as the upper end of the fingerboard.
- The neck cross-section shape should not be oval.
- The lower curve of the neck has a large radius.
All of the above are either very difficult problems to simplify geometrically or cases…