Converged Generator MOS Scales

how to get started

2 options *{change any of the A,B,C,or D inputs}
or alternatively *{click on one of the inputs and click off}

this will trigger a sequence generation

you should see a bit of info about G and a list of numbers the list of numbers with rectangles around them is the recurrent sequence

next select a [scale size] when you a:hover over or click in the scale size input , a dropdown menu of MOS scale sizes appears. one of the MOS scale sizes can be clicked on to change the scale size or you can type in scale size.

next select a [seed]
all ones is self explanatory.
F-Seed is the seed as it would be if drawn on pascals triangle.
P-Seed is round(G^n).
S-Seed is round(x*G^n). selecting S-Seed brings up a dialog with an input for x, the [x] input must be blurred(clicked on and edited(or not) then clicked off) to set the [seed] input to round(x*G^n). when [x] is blurred a list of x*G^n is displayed , this is handy for finding x with least rounding so the sequence starts out near convergence. to recalculate the sequence with the [seed] , the seed input must be blurred.

next select a scale *{click on any number in the recurrent sequence list } lets call the list of numbers harmonics the clicked harmonic becomes the scale starting point

[scale size] number of harmonics will be hilighted this will generate a table with the scale sorted to octave reduced column also a plot of the scale around a circle you can select a different starting point if not satisfied

next *{select a row on the table}, clicked row and rows of the corresponding fibonacci triplet will be hilighted in the table. orange =c, lightorange=b, yellow=a a+b=c lines will be drawn on the graph between the fibonacci triplet. orange=a,b , lightorange= c,b, yellow=c,a if a fibonacci triplet member is missing(signified by -value in a or b column) a row is highligted brightpink as if the -index wrapped around the top of the scale , if the sequence were converged this is where the missing fibonacci triplet member would be, also on the graph, the line from c to a or c to b or both will be bright pink instead of lightorange or yellow. when you select another row the previously selected triplet gets unhilighted and a new triplet gets highlighted, the triplet lines onnthe graph remain , so you can show the entire set on the graph, the way to erase the lines is to click on a row twice.

what can go wrong?
scale start and scale size you can select a starting point that is too far down the list, of this happens, you can edit the scale start input , change to 0, then you can select a different starting point.

octave repeats, if your sequence has octave repeats the resulting scale will be jarbled, if the bottom row n column is not = 0 then more than likely you have an octave repeat if ypu only get part of a scale around the circle plot more thsn likely you have an octave repeat
how to fix octave repeats?
select a different starting point or change the seed

what else can go wrong?
you can input C > D this is not valid

ideally D and C should be coprime, else you get 2 or more? independent sequences

seed must have D number of elements separated by one space

ideally your scale size should be the same as cardinality of any MOS with generator = G
how do you know cardinalities of MOS with generator=G
you can use Erv Wilson's 1/x zig zags.
my fav walkthrough is http://anaphoria.com/LucyRecurrent.pdf
where Erv shows Charles Lucy how to 1/x and zigzag down the scale tree.

You can copy and paste G into the 1/x Zig-Zag calculator here. https://anaphoria.com/zigzag-calculator.html

alternatively you can copy and paste G cents value into Mike Battaglias flat horogram app to see a list of MOS, number of notes in MOS = cardinality = scale size.
https://mikebattagliamusic.com/MOS/flathorogram.html


sometimes you might want to go ahead and see what happens when you have octave repeats, you would then need to increase scale size by the number of octave repeats.