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This is an essay I have written and released on Discord, and I will reiterate it here for the benefit of those who are not on the Discord.
This is an essay I have written and released on Discord, and I will reiterate it here for the benefit of those who are not on the Discord. (MMTM, if you are reading this, please give feedback on my talk page!)
 
(EDIT 5/9/24: added clarification)


== Deconstructing MMTM’s Theory ==
== Deconstructing MMTM’s Theory ==
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The simplest variety of these MOSses are taking segments from parent scales and checking if they are MOS.
The simplest variety of these MOSses are taking segments from parent scales and checking if they are MOS.
e.g.  
e.g.  
2L 1s <4/3> is from LLsLLLs,
*2L 1s <4/3> is from '''LLs'''LLLs,
3L1s <3/2> is from LLsLLLs, and  
*3L 1s <3/2> is from LLs'''LLLs''', and  
8L3s <3/1> is from LLsLLLsLLsLLLs.
*8L 3s <3/1> is from '''LLsLLLsLLsL'''LLs.
Keep in mind that one can obtain these segments from any part of the scale, as long as it is MOS. These are highly generalizable, as MMTM himself demonstrated in an obscure table in his soid-family scales article In this table, he extends this procedure to 7L 2s, 10L 2s, and 12L 2s scales.
Keep in mind that one can obtain these segments from any part of the scale, as long as it is MOS. These are highly generalizable, as MMTM himself demonstrated in an obscure table in his soid-family scales article In this table, he extends this procedure to 7L 2s, 10L 2s, and 12L 2s scales.


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One can preserve the L and s sizes while still making nonoctave MOSses. In this case, 5L 3s with diatonic L and s sizes has a period of about 8\7~6\5. This is the basis of MMTM’s logic, which I call ‘EDOs within EDOs’.
One can preserve the L and s sizes while still making nonoctave MOSses. In this case, 5L 3s with diatonic L and s sizes has a period of about 8\7~6\5. This is the basis of MMTM’s logic, which I call ‘EDOs within EDOs’.


Alternatively, one can use a just equave, obtained by taking just ratios within the diatonic scale. Unlike much of MMTM’s theory, this is completely arbitrary.  
Alternatively, one can use a just equave, obtained by taking just ratios within the diatonic scale. Unlike much of MMTM’s theory, this is completely arbitrary. (EDIT 5/9/24: this is not really arbitrary. The just equaves he picks are close to the interval category he is using as his equave, and there are different 'flavours' of this equave depending on whether one would like a meantone-like or a superpyth-like temperament.)


The chords he uses, much like the just equaves, are completely arbitrary. But there is a kernel of unarbitrariness to his chords and just equaves! He picks the simplest chords one could potentially use (‘simplest’ being up to MMTM’s discretion). They are usually triads.
The chords he uses, much like the just equaves, are completely arbitrary. But there is a kernel of unarbitrariness to his chords and just equaves! He picks the simplest chords one could potentially use (‘simplest’ being up to MMTM’s discretion). They are usually triads.
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