Fingerboard Diagrams

There are various articles across the web explaining the history and mathematics of temperaments. Some of these include tables detailing cent offsets which while very useful are difficult to visualise. This is the start of some work to help people see what different temperaments actually look like when fingered on a string instrument. Hopefully it may also prove useful to those performing or constructing instruments in different temperaments.

Temperaments for String Instruments

These diagrams show finger placement for stringed instruments. The blue circles indicate where the finger should be placed on a fretless instrument such as Violin, or where a slide should touch the string on guitar for example. The grey fret lines are for reference only as comparison to the tuning shown. The SVG versions are higher quality and should open directly in Firefox.

Violin, Viola, Cello, Double Bass

1/4 Comma Meantone for strings with fret lines indicating Equal Temperament (12-TET) - GIF or SVG
1/4 Comma Meantone for strings with fret lines indicating 31-TET - GIF or SVG

1/6 Comma Meantone for strings with fret lines indicating Equal Temperament (12-TET) - GIF or SVG
1/6 Comma Meantone for strings with fret lines indicating 55-TET - GIF or SVG

Stacked fifths in Meantone and Just Intonation with fret lines indicating 12-TET - GIF or SVG

Guitar

EADGBE tuning in Meantone and Just Intonation with fret lines indicating 12-TET  - GIF or SVG

Equal Temperaments Compared

This diagram shows how Equal Temperaments with increasing numbers of notes compare to Just Intonation, from 12-TET to 118-TET. The circles show the positions of important pure ratios while vertical lines show the Equal Temperament in question.

12, 19, 31, 34, 50, 53, 55, 56, 87, 91, 118 - GIF or SVG

Links

Dr. Ross W. Duffin
Kyle Gann - Information on Alternate Tunings
Bradley Lehman - Johann Sebastian Bach's tuning
Wikipedia - Musical temperament
Tonalsoft Encyclopedia of Microtal Music Theory - Limit Definition
Michael Harrison - My Work and Tunings
Dante Rosati - Just Intonation Guitars
Glen Peterson's Musical Instruments and Tuning Systems
Microtonal Guitar Gallery
True Temperament Guitar Necks

Diagrams created in SVG using Perl and then converted to GIF using Free Online Image Converter.

Last Update: 2nd March 2010