Here I show how to use a homemade computer to compute any of the diatonic scales.  Instructions for building such a computer can be found at https://fiddlerman.com/forum/s.....-any-mode/

The best known of the diatonic scales are the usual major and minor scales.  Every major scale follows the same pattern of whole and half steps to climb an octave.  The minor scales (meaning the natural minor scales) have their own pattern too, distinct from, but related to, that of the major scales.  Major and minor are called modes, and there are five other modes---seven modes in all.  The general concept of mode includes the concept of relative major/relative minor.

The computer has two stiff paper disks.  The inner disk is able to rotate relative to the outer one.  Around the outer margin of the outer disk are names of the twelve pitches of the chromatic scale.  The outer margin of the inner disk is marked at seven points, one point for each of the seven modes.  There are 84 diatonic scales.

The first photo shows how the computer is set for computing any of the seven scales of the C-Major key signature.  "Ionian (Major)" on the inner disk is aligned with "C" of the outer disk.  The sequence of notes of the C-Major scale are read clockwise as the seven pitches aligned with the marks on the inner wheel.  Starting at the mark for "Ionian (Major)", you would read: C D E F G A B.  Staying with the same setting, the sequence for the A-minor scale is read starting at "Aeolian (minor)" and going clockwise: A B C D E F G.  Again with the same setting, the D-Dorian scale is read as D E F G A B C, and the G-Mixolydian as G A B C D E F.  

In the second photo, we change to the key signature of G.  "Ionian (Major)" on the inner disk is aligned with "G" on the outer disk.  Some of the scales of the key signature of G are: G-Major: G A B C D E F#; E-Minor: E F# G A B C D; B-Phrygian: B C D E F# G A.

Suppose you want to find a specific scale, say C-Minor.  You would align the name of the scale's tonic, "C", with the name of the mode, "minor".  Then you would read the names of the pitches aligned with the marks, starting with the tonic: C D Eb F G Ab Bb.  C-minor is a mode of the key of Eb.  Other modes of Eb include Bb-Mixolydian and F-Dorian.

The computer can also be used to find pentatonic scales.  These five-note scales are simply diatonic scales with two certain scale degrees left out.  The scale degrees to be left out are distinguished by shorter marks at the margin of the inner disk.  You can verify that the pentatonic C-Major scale is C D E G A, that pentatonic A-Dorian is A B D E G, and that pentatonic Bb-Mixolydian is Bb C Eb F G.