More than 1600 diagrams , 175 tunings !

(Pinned post ) IMPORTANT :

For those of you who are familiar with cent values in several temperaments, please use the diagram called «Minor cent» in the beginning.

Here you will find cent values for fifths, major thirds and minor thirds within the same graph.

The red vectors is deviation from pure major third and blue vectors for minor third.

In the other diagrams I am using TU, but simply divide values by 30 to get a precise enough cent value.

Pythagorean comma = 23.46 cents = 720 TU

Syntonic comma = 21.51 cents = 660 TU.

(These numbers are easy to divide in 2,3,4,5,6...)

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The easiest way to get an overview of historical and newer tunings ! Read the Introduction (1) carefully and the diagrams will tell you much more than all the cent tables on the web.
Many of those who have found the key to the diagrams use this webside a lot.
If you have questions , let me hear, click HERE

III OTHER DIAGRAMS


On the diagram "Beats" I have stretched the diagram horizontally to gain more space for the numbers.
Otherwise in all diagrams I have the same relationship between x and y axis even at the extreme tunings, although it is very small and cramped.



This diagram is similar to the diagram   vs equal  with blue values ​​for the minor thirds at the bottom.
The difference is that here we are talking about beats per second
The numbers in a line vertically are the numbers for the three intervals in a major triad .
Since an interval beats twice as fast for each octave we go upwards it is very important to define in which octave the intervals are.
The border runs between E major and Fmajor.
F major has F3 as the lowest tone.
Emajor has E4 as the lowest tone.
Beats are calculated with 415 HZ as the concert pitch.
Do you want beats for A=440 HZ multiply the numbers with 1.06.


The «Cent» diagram I have made to show how the cent values are revealed by the difference between the fifth-chain to a choosen tuning (the marked line) and the fifth-chain to equal tempered
(dotted line) which is like the cent values always are calculated. We recognize the simple shape of Vallotti and the red cents value can now be placed in an tuning-app and be used to tune an instrument.
I also publish a "Table" where we instead follow the chromatic scale that is the order the most apps follow. You will also find frequencies here.

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