A way to improve your tuning skills

a)

After trying tuning a special temperament it is not so easy to judge how close to the idea one have come. How equal did I get the fifths, and so on?

(If it sounds good, then it's probably  an OK temperament.:)

But it can be useful to check the result with the original idea and see if the tuning contained unnecessary errors.

Examples:

Maybe one in passing  made a fifth wide instead of narrow. (Then the graph will go upward )

We also should be aware if a fifth is more impure than ca -180 TU. Such a fifth should have an function in the totality, in itself it should be avoided, and it may simply be a mistake that it became so.

A major third that is less than pure means that another third becomes unnecessarily impure, and the graphs are crossing each other (harmonic waste).

Maybe it's been a little «roller coaster» in the major thirds, Maybe Ab-C has been purer than both Db-F and Eb-G (each side in the circle of fifths).

It can be OK but also useful to know.

By studying the graphs, we can get an idea of ​​how we can improve the tuning.

Testing a tuning by ears is not a completely objective judgment....

Under "Play around with the temperaments" you will find a link to the free LibreOffice (or here  ).

(This is the program I started with, but did not come further with )

After you finish tuning, you can with an app measure  frequencies for the 12 tones of the scale, one-line octave or thereabouts.

If the app misses with 0.1 Hz it will only be a margin of error of <20 TU

If you click on the link "Tune your instrument .." (still under "Play around) and download the file «Check yourself..» and open it (or here ), you can`t use Googles spreadsheet.
so  you can there enter the frequencies. (E20-E31)

Then you will get a graph that is built on the same principle as in the blog, but the values ​​you have to find in the spreadsheet instead of in the diagram.

Green (E column) is fifths and red (J column) is major thirds. (Blue is the minor third in

a major triad)

Are you accustomed with cents you will get precise enough numbers by dividing with 30.

To interpret the graph it is the absolute best to read  INTRODUCTION Part I, at least the first part of it.

Now we will focus on fifths and major thirds.

A horizontal line means pure fifths. The steeper, the more impure is a fifth.
 The value you will find in column E (green).

To find the major third quality we have look at the vertical distance between the red and green graph.

The greater the distance, the more impure third.
 And the value is in column J (red).

Now we look at a hypothetical experiment with Vallotti.

Vallotti you will find originally under Play around / THE FILES (or here )
. (and of course in the blog with another layout)

And here is the result in our example :

It is a bit away from Vallotti. The errors you can see both in the green and red graph (red moved four fifths to the left, but the same curve).

We can see that the tuner has not quite succeeded in making equal fifths. It results in a bad fifth C-G (-200 TU) and G-D and D-A have been purer. A-E is also quite bad.

F-C is correct -120 and this steepness should be the same from F to B.

The major third G-H has been 260 TU instead of 180 TU. But not so bad that it is not good for anything: Eb-G have been purer, but maybe that was not the intention ....

..................................

b)  A guessing game

Another good tip is to not necessarily tune a special temperament, but create something passable and so listen carefully to all the fifths and write down your guesses for all of them.

Is this fifth a 1/4 comma  ? (- 165 TU / -180 TU) 

or

is it a 1/6 comma  ? (-110 TU / -120 TU) ?

You get the TU by dividing -720 TU for Pythagorean comma (or -660 for syntonic comma,nearly the same , I think you will not hear the difference).

Once you've written down your guesses: measure the frequencies and put them into the spreadsheet («Check yourself») in E20-E31. You will then see the «set answer» in column E.

To be able to guess you must have some notions about fifth qualities. But I think this is a good method to get these notions if you not have them already. This is also a good way to get to know different values of the third quality. Even though it is more common to count beats ?

Now you can start this guessing game and improve yourself.

This has in any case been useful for me. :)

..................

c)

I presume many here have their own personal touch on a temperement.

It can be fun and useful to see  such a tuning visualized, see the different intervals relative to each other . You are following the same procedure.

I have created a link to «cembalists own tunings» on my blog. You are welcome to give me your data . And I will post a diagram there with your name into it.

...............

In this spreadsheet you can also play around with the graphs with column B and C . In column B, you can adjust a single tone.

In column C, you can enter the fifth quality. Just beware of interaction between B and C.

It is therefore important to relate to column E (green) as the correct numbers .

And extremely important: the sum in     E13 must always be -720 TU (pyth.comma)
If E13 is not -720, E14 will show you which value have to put in column B.

It is also important to know that the numbers in E20-31 generates numbers in B20-31 which in turn generates the C1-C12

giving the numbers in the colored columns.

 It means that if you eg enter  numbers in C1-C12 so you can no longer use B20-31 and E20-31 . If you need it you must download the file again.

Good luck!