User:Ganaram inukshuk/Methodologies

This page is for describing how I approach various xen-related topics. It's neither definitive nor pedagogical, rather it's insight into how I understand certain concepts and put them to use. (Mileage may vary.)

The default mode of a mos

By convention, the two main scales that most musicians talk about are the major and minor scales, or the ionian and aeolian modes. This convention is not something most musicians may agree on, but it provides a starting point when talking about music in a more general sense or in a context that is not as technical. Thus, when looking at a mos that falls outside the familiar diatonic scale (5L 2s), can this notion of a major and minor scale be generalized? This section shows my attempt at answering this question, with justification as to why.

Examples using heptatonic mosses

As an example, let's use all six more heptatonic mosses: 1L 6s (anti-archeotonic), 2L 5s (antidiatonic), 3L 4s (mosh), 4L 3s (smitonic), 5L 2s (diatonic), and 6L 1s (archeotonic) to get the table below. All modes are sorted by modal brightness. The familiar major and minor scales are shown in bold.

Anti-archeotonic			Antidiatonic			Mosh			Smitonic			Diatonic			Archeotonic
Mode Name	UDP	Step Pattern	Mode Name	UDP	Step Pattern	Mode Name	UDP	Step Pattern	Mode Name	UDP	Step Pattern	Mode Name	UDP	Step Pattern	Mode Name	UDP	Step Pattern
Antizokalaraian	6|0	Lssssss	Antilocrian	6|0	LssLsss	Dril	6|0	LsLsLss	Nerevarine	6|0	LLsLsLs	Lydian	6|0	LLLsLLs	Ryonian	6|0	LLLLLLs
Antitamashian	5|1	sLsssss	Antiphrygian	5|1	LsssLss	Gil	5|1	LsLssLs	Vivecan	5|1	LsLLsLs	Ionian (major)	5|1	LLsLLLs	Karakalian	5|1	LLLLLsL
Anti-oukranian	4|2	ssLssss	Anti-aeolian	4|2	sLssLss	Kleeth	4|2	LssLsLs	Lorkhanic	4|2	LsLsLLs	Mixolydian	4|2	LLsLLsL	Lobonian	4|2	LLLLsLL
Anti-horthathian	3|3	sssLsss	Antidorian	3|3	sLsssLs	Bish	3|3	sLsLsLs	Sothic	3|3	LsLsLsL	Dorian	3|3	LsLLLsL	Horthathian	3|3	LLLsLLL
Antilobonian	2|4	ssssLss	Antimixolydian	2|4	ssLssLs	Fish	2|4	sLsLssL	Kagrenacan	2|4	sLLsLsL	Aeolian (minor)	2|4	LsLLsLL	Oukranian	2|4	LLsLLLL
Antikarakalian	1|5	sssssLs	Anti-ionian	1|5	ssLsssL	Jwl	1|5	sLssLsL	Almalexian	1|5	sLsLLsL	Phrygian	1|5	sLLLsLL	Tamashian	1|5	LsLLLLL
Anti-ryonian	0|6	ssssssL	Antilydian	0|6	sssLssL	Led	0|6	ssLsLsL	Dagothic	0|6	sLsLsLL	Locrian	0|6	sLLsLLL	Zokalarian	0|6	sLLLLLL

There are a few ways to answer the default mode question. Looking at the scale pattern for ionian may provide some clues. Since it's the second-darkest mode, an easy answer is that it's the second-brightest mode. However, a more interesting answer is to say that the default bright mode is the darkest mode whose step pattern starts with L and ends with s.

As of the default dark mode, a similar easy answer is to say it's the third-darkest mode. However, a more interesting answer is to say it's the mode that starts with an L and ends with an L. However, this definition does not work with scales that more s's than L's; 1L 6s, 2L 5s, and 3L 4s have no such modes that fit this description. This definition can be amended to say that the default dark mode is the darkest mode whose step pattern starts and ends with the same step size.

Using this assumption as a guide, we can then identify the corresponding major and minor modes of these mosses in bold.

Anti-archeotonic			Antidiatonic			Mosh			Smitonic			Diatonic			Archeotonic
Mode Name	UDP	Step Pattern	Mode Name	UDP	Step Pattern	Mode Name	UDP	Step Pattern	Mode Name	UDP	Step Pattern	Mode Name	UDP	Step Pattern	Mode Name	UDP	Step Pattern
Antizokalaraian	6|0	Lssssss	Antilocrian	6|0	LssLsss	Dril	6|0	LsLsLss	Nerevarine	6|0	LLsLsLs	Lydian	6|0	LLLsLLs	Ryonian	6|0	LLLLLLs
Antitamashian	5|1	sLsssss	Antiphrygian	5|1	LsssLss	Gil	5|1	LsLssLs	Vivecan	5|1	LsLLsLs	Ionian (major)	5|1	LLsLLLs	Karakalian	5|1	LLLLLsL
Anti-oukranian	4|2	ssLssss	Anti-aeolian	4|2	sLssLss	Kleeth	4|2	LssLsLs	Lorkhanic	4|2	LsLsLLs	Mixolydian	4|2	LLsLLsL	Lobonian	4|2	LLLLsLL
Anti-horthathian	3|3	sssLsss	Antidorian	3|3	sLsssLs	Bish	3|3	sLsLsLs	Sothic	3|3	LsLsLsL	Dorian	3|3	LsLLLsL	Horthathian	3|3	LLLsLLL
Antilobonian	2|4	ssssLss	Antimixolydian	2|4	ssLssLs	Fish	2|4	sLsLssL	Kagrenacan	2|4	sLLsLsL	Aeolian (minor)	2|4	LsLLsLL	Oukranian	2|4	LLsLLLL
Antikarakalian	1|5	sssssLs	Anti-ionian	1|5	ssLsssL	Jwl	1|5	sLssLsL	Almalexian	1|5	sLsLLsL	Phrygian	1|5	sLLLsLL	Tamashian	1|5	LsLLLLL
Anti-ryonian	0|6	ssssssL	Antilydian	0|6	sssLssL	Led	0|6	ssLsLsL	Dagothic	0|6	sLsLsLL	Locrian	0|6	sLLsLLL	Zokalarian	0|6	sLLLLLL

It's important to note that there are many ways to settle on a mos's default mode, and which mode is decided on may vary between musicians and their musical goals. This is just one way to answer the default mode question.

Example using a mos with far more notes

wip

Justification and comparison

Justification

Personal experiments with 2L 5s had led me to believe that anti-aeolian is not the default bright mode, but rather antiphrygian. (wip: examples)

Additionally, 19edo (and 31edo) supports both the diatonic and mosh mosses, where the generating interval for 3L 4s is 5L 2s's major third. This means that 3L 4s is, in a sense, 19edo's equivalent of an augmented scale. Constructing a tertian chord with C as the root results in the chord C-E-G#, an augmented chord, but constructing a tertian chord where C is the highest note requires the notes Fb and Ab. This is reached by starting at C and going down two major thirds, which matches the description of mode 4|2 of mosh (up 4 generators and down 2 generators), which is the exact mode that is described as the default mode.

Comparison with other methods

Interestingly, this definition of a default mode has some overlap with Jake Freivald's method of enumerating a mos's modes.