To all the regular temperament lovers: An improvement in Scala

Hi tuners.

After some offlist communication with Manuel, I'd like to let you know that the most recent version of Scala has a new command very appropriate for all of us who have ever done something with "more than rank 1" temperaments. It's called "Mode/solve" and it can be used in the cases when the number of pure intervals equals the number of single-step sizes in the scale. Although it can be used on lots of weird temperaments as well, I'd like to give some pretty conventional examples to make it all easily understandable.

Let's say that we want to get a 12-tone scale of 2 different sizes of semitone, one of which will function as a minor second and the other will function as a chroma. Now we wish, for example, that octaves were pure and that augmented seconds were tuned to 6/5. In fact, we're requiring 7 minor seconds plus 5 chromas to make a 2/1 and also 1 minor second plus 2 chromas to make 6/5. Therefore, we do the following:
First, we store our list of desired intervals as a scale into one of Scala's memories using the "Input/line" command. For example, by typing "Input/line 1" on one line and "6/5 2/1" on the next one, we store our target intervals into scale memory #1.
Now we type "Mode/solve 1" and we're asked to enter a pattern for our 12-tone scale. If we label minor seconds as "1" and chromas and "2", then, for instance, a scale from C upwards with sharps only is expressed as "2 1 2 1 1 2 1 2 1 2 1 1", which is what we enter as the pattern.
Now we're asked to enter the step counts that should add up to 6/5 (which are 1 and 2, respectively) and 2/1 (which are 7 and 5), each on a separate line, making it a sequence of 5 lines (one for the pattern, four for the counts). So the full command sequence is then:
Input/line 1
6/5 2/1
Mode/solve 1
2 1 2 1 1 2 1 2 1 2 1 1
1
2
7
5
As a result, we get a 12-tone chain of 1/9-schisma helmholtz/grovenian temperament ranging from F to A#.

As our next example, suppose we want a 12-tone scale of some meantone temperament whose major and minor thirds are even closer to pure than in 2/7-comma. One such possible solution may be achieved by tuning major and minor tenths to exactly 5/2 and 12/5, respectively, which therefore makes 25/24 also pure as well as 6/1. This in turn results in stratched octaves, which can be a good solution in some situations just because of this particular fact (if we don't want pure octaves). And let's assume we want a scale with sharps only, similarly to the previous example. So we can enter something like this:
Input/line 1
25/24 5/2
Mode/solve 1
2 1 2 1 1 2 1 2 1 2 1 1
0
1
9
7

Now, obviously, this command is not limited to 2D temperaments. So maybe one day we'll be exploring temperaments like ragismatic in scales using three single-step sizes, who knows? :-)

So, happy "more-than-rank-1-tempering".

Petr

--- In tuning@yahoogroups.com, Petr Pařízek <petrparizek2000@...> wrote:
>
> Hi tuners.
>
> After some offlist communication with Manuel, I'd like to let you know that
> the most recent version of Scala has a new command very appropriate for all
> of us who have ever done something with "more than rank 1" temperaments.

I don't see any explanation of where your interval pattern comes from, and how you know it works.

Gene wrote:

> I don't see any explanation of where your interval pattern comes from, and > how you know it works.

If I want to make a scale of 7x+5y to an octave (without initially knowing whether x is larger than y or vice versa), I may easily convert the scale to standard notation and view it as 7 minor seconds + 5 chromas. If I then want the ascending scale to start on C and contain sharps only, the sequence of the two alternating step sizes necessarily has to go like "yxyxxyxyxyxx".

And how I know it works ... I've tested it.

Petr