Reading the Charts

The charts display thirteen major triads in a cycle of fifths, starting with the C3E3G3 triad at the left and proceeding up by fifths and down by fourths until you reach C4E4G4 at the right.


The bars indicate cents; the numbers represent beats.


Fifths are blue; major thirds are red; minor thirds are green. [Technically, the minor third bars should be shown below zero, since minor thirds are contracted (not expanded like thirds and fourths). But I think they look better behind the major thirds.]


Therefore, in the example C major triad shown at the left, the blue CG fifth is contracted by about 3 cents and beats at 0.7 beats per second (bps). The red CE major third is expanded by a little more than 5 cents, and beats at 2.0 bps. The green EG minor third is contracted by about 8 cents and beats at 4.9 bps. 


The fifth CG, minor third of EG, and major third of CE are thus seen together. The "feeling" of C Major is represented in the mingling beat rates of these three intervals. When those beats are synchronous (equal or in whole-number ratios such as 3:2) ... so that they are beating together ... there is something that happens in the soul of the listener.


Immediately below each triad is the offset for the fundamental of that triad. (In the example triad shown on this page, C is offset by 6.20 cents sharp.) There is a red "horizon" line (ET reference line) representing 13.7 cents, the amount by which Equally Tempered major thirds are expanded. Likewise there is a blue ET horizon representing equally-tempered fifths, which are all contracted by 1.96 cents. The dotted curves are polynomial trendlines that help to show the degree of balance in the temperament.


The large red numbers in the upper right of the chart indicate the minimum and maximum size of the Major Thirds (in cents). This can serve as a quick guide to the degree of key coloring in the temperament.


These are busy charts, and there is some overlapping data. Below the graph is a data table that shows every number in the graph. Watch this space for an announcement of a printed reference guide containing all these charts (and more) in high-resolution, 11 x 8.5 format.