Creating Scala scl files for rank two temperaments

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The first step for creating a Scala file for your temperament is assembling the required tuning data. A good place to find that out are Graham Breed's temperament finder pages, which can be found by clicking the link.

For instance, taking the temperament finder from ETs page, put in two (it must be two, for a rank two temperament) integers representing equal divisions of the octave in the top box, and the prime limit you want in the bottom box. For instance, for pajara temperament, we might put in 12 and 22 in the "list of steps to the octave" box, and if 7-limit will suffice, we put 7 in the "limit" box. This brings up a new page with various kinds of information on it. In the "Generator Tunings (cents)" box, we find two numbers, in this case 598.859 and 106.844. The first number is the period, and the second number is the generator. If you want to use a slightly compressed octave for your tuning, these are the numbers you will need. Otherwise, go to where it say "Reduced Mapping", and look at the top row; in this case it will be [<2 3 5 6]. Take the first number, in this case 2. This is the number of periods in an octave, call it "n". If "P" is the first number, in the "Generator Tunings (cents)" box, the period, and "G" is the second number, the generator, then instead of P and G you may use 1200.0/n and (1200.0G/nP) for the period and generator, which will give pure octaves. In this case, we get 600.0 for the period and 107.48 for the generator.

You can also start from the unison vector search page. In this case, you get a box telling you to put your commas in the box. For a rank two temperament with a prime limit containing n primes, you need to put in n-2 commas. For instance, in the 7-limit there are four primes, 2, 3, 5, and 7. Putting in 4-2=2 7-limit commas will work: for instance putting in 50/49 and 64/63 and scrolling down to rank two temperaments we see pajara again.

Another starting point, of course, is this wiki. In an article on the temperament, find the POTE generator listing; you may use that. You also can look at edo tunings; in N-edo you may find g\N as a generator tuning, meaning g steps of N-edo, or the g/N fraction of an octave.

Now take the two numbers you obtained from the temperament finder, and start Scala. In the box at the bottom of the screen, type in "lineartemp". It will ask for a size; enter the number of steps you want in your scale, divided by n, the number of periods in an octave. For instance if you want ten steps, and are using the pajara generators we obtained, put in 5. Then it says "enter formal octave (2/1)". Put in the period, making sure to include the decimal point. That is, put in 598.859 if you want to use octave compression; otherwise put in 600.0. Now it will say "enter fifth degree, 0 for monotonic scale [0]" and you hit return. Then it will say "enter formal fifth [$0]", and you enter the correct generator. For instance, if before you had entered 600.0, now you enter 107.48 to go with it. Then it says "enter count downwards" and again you can just hit return, or you might try putting in a positive integer and seeing where that gets you. If you have an edo tuning in the form g\N, you can enter 2^g\N (with no parentheses around "g\N") as the formal fifth.

Next, if the number of periods in an octave "n" was greater than 1, type in "extend m" at the bottom, where m is however many steps you want in an octave; it should be n times the number you entered when it asked for size. In this case, we entered 5 for size and n=2, so we type in "extend 10".

Now, apparently, nothing has happened. Don't panic; if you hit the show button it should show you your new scale. Now on the pull down menu under file use "save scale as" and save your scale!

If you want to be sure to end up with a MOS, start the process by typing "lineartemp /wellformed" at the beginning, instead of just "lineartemp". Later, instead of "extend m", type in "extend /absolute 1200.0" if you are using pure octaves. If you are using adjusted octaves, use the first number of "Tuning Map (cents)" on Grahams's page; in the example we are using, that would be 1197.719, so you'd type in "extend /absolute 1198.719".

see also