User:2^67-1/Deconstructing MMTM’s Theory - Revision history

2^67-1 at 01:24, 5 September 2024

2024-09-05T01:24:15Z

← Older revision		Revision as of 01:24, 5 September 2024
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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. (MMTM, if you are reading this, please give feedback on my talk page!)		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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	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.

2^67-1 at 12:23, 4 September 2024

2024-09-04T12:23:50Z

← Older revision		Revision as of 12:23, 4 September 2024
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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.

2^67-1 at 12:14, 4 September 2024

2024-09-04T12:14:44Z

← Older revision		Revision as of 12:14, 4 September 2024
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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 LLsLLLs,
	3L1s <3/2> is from LLsLLLs, and		*3L1s <3/2> is from LLsLLLs, and
	8L3s <3/1> is from LLsLLLsLLsLLLs.		*8L3s <3/1> is from LLsLLLsLLsLLLs.
	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.

2^67-1 at 12:07, 4 September 2024

2024-09-04T12:07:58Z

← Older revision		Revision as of 12:07, 4 September 2024
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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!)

	== Deconstructing MMTM’s Theory ==		== Deconstructing MMTM’s Theory ==

2^67-1 at 12:05, 4 September 2024

2024-09-04T12:05:27Z

← Older revision		Revision as of 12:05, 4 September 2024
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	Now, most of these scales will be inevitably stretched or compressed. Here, all four scales would be noticeably stretched and as such will not give very diatonic-like interval qualities.		Now, most of these scales will be inevitably stretched or compressed. Here, all four scales would be noticeably stretched and as such will not give very diatonic-like interval qualities.

	~~In this part we will be looking at EDONOIs, and his very enigmatic modal qualities.~~

	EDONOIs are particularly simple to derive from the MOSses. If a MOS is aLbs<c> then the corresponding EDONOI is (a+b)EDc. Rather unpleasantly, MMTM likes to give them fancy names like White Oak and Roccocavallo. These all distract from his actual theory, which, as I have shown previously, is ridiculously simple when you take out all the technobabble.		EDONOIs are particularly simple to derive from the MOSses. If a MOS is aLbs<c> then the corresponding EDONOI is (a+b)EDc. Rather unpleasantly, MMTM likes to give them fancy names like White Oak and Roccocavallo. These all distract from his actual theory, which, as I have shown previously, is ridiculously simple when you take out all the technobabble.

2^67-1: Created page with "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. == Deconstructing MMTM’s Theory =..."

2024-09-04T12:03:20Z

Created page with "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. == Deconstructing MMTM’s Theory =..."

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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.

== Deconstructing MMTM’s Theory ==

This theory (the LCP, or Long Common Practice) is a theory developed by Joseph Ruhf, or Moremajorthanmajor. Most of you who have been on the wiki might know about him sparking controversy for his poor explanations. I will try to demystify them for people who would like to learn more.

In this part we will cover how he derived his MOSses.

The derivation of nonoctave MOSses which bear a similar structure to their parent is quite simple. No, we are not talking about the same MOS but with a different equave, that’s cheating.

The simplest variety of these MOSses are taking segments from parent scales and checking if they are MOS.
e.g.
2L 1s <4/3> is from LLsLLLs,
3L1s <3/2> is from LLsLLLs, and
8L3s <3/1> is from LLsLLLsLLsLLLs.
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.

“But wait,”, you’ll say, “the segment of 5L 3s, LLsLLsLs is not in any part of the diatonic scale!” Yes, and you are right. This scale is part of the second category of MOS scales.

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.

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.

Now, how to select the subgroup? It is very simple. The subgroup is a.b.c where a is the equave, and b and c are the chord’s intervals from the root.

There is one way he creates his temperaments. It is usually true that if you pick two random EDOs in any subgroup (say a and b) a MOS will be created that has the shape aLbs or bLas. This logic is followed here. Let’s use the 9/4 equave as an example.

Here, MMTM uses the 6L 2s MOSS, which he calls ‘macroshrutis’. This is admittedly a bad name, but let’s forget about that. What is important is that he uses the 5:6:8 chord as the main chord in this system, and that the q6p&q2p temperament in the 9/4.6/5.8/5 subgroup has a 6L 2s MOSS!

The way he gets his branches is by trying out all possible partitions of the number of notes in the scale with two elements (usually each element is greater than 1, but sometimes, he breaks this pattern). For the ED9/4s, we have 5L 3s, 4L 4s, 3L 5s, and 2L 6s. Usually, MMTM puts aLbs and bLas under the same category, which he calls a&b (for some a and b). It’s easy when you think about it!

Now, most of these scales will be inevitably stretched or compressed. Here, all four scales would be noticeably stretched and as such will not give very diatonic-like interval qualities.

In this part we will be looking at EDONOIs, and his very enigmatic modal qualities.

EDONOIs are particularly simple to derive from the MOSses. If a MOS is aLbs<c> then the corresponding EDONOI is (a+b)EDc. Rather unpleasantly, MMTM likes to give them fancy names like White Oak and Roccocavallo. These all distract from his actual theory, which, as I have shown previously, is ridiculously simple when you take out all the technobabble.

Modal qualities are named, obviously, after the intervals in the scale, be it a MOS or EDONOI. Admittedly, most such designations are arbitrary, except for some of his designations which are surprisingly useful.

For example, in his hierarchy of soid-family modes page, he calls scales with an equave of about an octave plus a semitone ‘Phrygian’. This all makes sense until you consider that he calls scales with an equave of about an octave plus a tone ‘Aeolian’. It could be practically any mode other than Phrygian or Locrian, so it was probably because of his earlier, coarser designation of ‘Perfect Minor’, so it apparently makes sense.

Or consider the temperaments with equave equal to about an octave and a minor 3rd. In his coarser designation he calls them ‘Melodic’, and in his finer one he calls them ‘Dorian’. Makes sense? Yes! This is because the first hexachord of the Dorian scale is the same as that of the melodic minor!

Thankfully, his chord progression translations are equally arbitrary, and a less arbitrary solution could be used instead. Had he not had a bias toward otonal chords the chord progression translations could be less arbitrary, using both otonal and utonal chords.

== Another way to conceptualize the soid-family modes page ==

And of course, in ambiguous qualities he uses two modal designations. Since the neutral scale sounds ‘between’ Dorian and Mixolydian, it makes sense to call the scales with an equave equal to an octave plus a neutral-third-ish interval Dorian-Mixolydian.

The 2nd degree changes when we change the mode from Phrygian to Aeolian, and vice versa, the 3rd degree changes when we go from Dorian to Mixolydian, and vice versa.
Hence

ambiguous ed(8\7)s have a Phrygian-Aeolian quality, with the brightness increasing as the equave increases around that range,

ambiguous ed(9\7)s have a Dorian-Mixolydian quality, with the brightness increasing as the equave increases around that range,

etc, etc.