User:Ganaram inukshuk/Methodologies - Revision history

Ganaram inukshuk: /* My approach to descendant mosses */

2023-04-24T20:16:07Z

My approach to descendant mosses

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Ganaram inukshuk: /* My approach to descendant mosses */

2023-04-24T05:30:16Z

My approach to descendant mosses

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Ganaram inukshuk: /* My approach to diatonic descendant mosses */ Chroma/diesis rules generalized to any mos; 3rd descendants are wip

2023-04-23T21:20:11Z

My approach to diatonic descendant mosses: Chroma/diesis rules generalized to any mos; 3rd descendants are wip

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Ganaram inukshuk: /* My approach to diatonic descendant mosses */ 45edo and the triesis

2022-11-25T10:18:37Z

My approach to diatonic descendant mosses: 45edo and the triesis

← Older revision		Revision as of 10:18, 25 November 2022
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	The following list is some commentary on some of the basic edos shown in the table:		The following list is some commentary on some of the basic edos shown in the table:

	* '''19edo''': I've seen one musician describe it as a baby version of 31edo, and I'm inclined to agree in that it's basically an equalized 12L 7s.		* '''19edo''': I've seen one musician describe it as a baby version of 31edo, and I'm inclined to agree in that it's basically an equalized 12L 7s. It also introduces the idea that a note raised by two chromas can fall short of the next note one whole tone above it (for example, Cx falling short of D).
	* '''31edo''': This, and 50edo to an extent, is currently my go-to edo for meantone temperament. Generally speaking, I like the mellow sound of meantone, which explains why I do absolutely nothing to date with 17edo and friends. It's also compatible with half-sharp and half-flat notation, so "quartertone" compositions are possible.		* '''31edo''': This, and 50edo to an extent, is currently my go-to edo for meantone temperament. Generally speaking, I like the mellow sound of meantone, which explains why I do absolutely nothing to date with 17edo and friends. It's also compatible with half-sharp and half-flat notation, so "quartertone" compositions are possible.
			* '''45edo''': Like 19edo but more extreme. Whereas 19edo has Cx falling short of D but C#x being equivalent to D, in 45edo, C#x falls short of D, but the interval between C#x and D is its own smaller interval I'm dubbing the '''triesis''' for the purposes of this page.

	=== 7L 5s ===		=== 7L 5s and 12L 7s ===
	Given a chroma is the absolute difference between a large and small step (c = \| L - s \|), mathematically speaking, the large steps can be broken into a chroma and small step, the small and large steps of 7L 5s. Depending on the order, this produces two ways each of the seven modes can be broken down into the m-chromatic modes, with some overlap.		Given a chroma is the absolute difference between a large and small step (c = \| L - s \|), mathematically speaking, the large steps can be broken into a chroma and small step, the small and large steps of 7L 5s. Depending on the order, this produces two ways each of the seven modes can be broken down into the m-chromatic modes, with some overlap. Basically, a chroma and small step are not the same size, more commonly described with the terms "diatonic and chromatic semitones". This unevenness manifests itself as the m-chromatic scale, a scale I admittedly don't use as often compared to 12L 7s. I see this mos as an incomplete form of 12L 7s. Nonetheless, a mode table is still provided, providing a guide as to how these 12 modes relate back to the more familiar 7 modes.
	{\| class="wikitable"		{\| class="wikitable"
	!		!
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	\|SC Locrian		\|SC Locrian
	\|}		\|}
	Basically, a chroma and small step are not the same size, more commonly described with the terms "diatonic and chromatic semitones". This unevenness manifests itself as the m-chromatic scale, a scale I admittedly don't use as often compared to 12L 7s. The mode "CS ionian" is basically an incomplete form of one of my favorite modes in 12L 7s.		This breakdown can be taken one step further by breaking down small steps into a chroma and diesis, where a diesis is defined as such: d = \| L - 2s \|. Ultimately, the large steps of 5L 2s are broken down into two chromas and a diesis, in some order. This produces the modes of 12L 7s and introduces an additional 7 modes on top of the previous 12. In either case, it's easier to think of these modes as some sort of extension of the seven modes of 5L 2s. There are, for example, 13 modes of 12L 7s that contain ionian as a subset (UDPs 17\|1 to 5\|13), so it's confusing and unhelpful to say there are 13 ionian modes. Therefore, saying that the large steps break down in a specific order (chroma-chroma-diesis, chroma-diesis-chroma, or diesis-chroma-chroma, or simply CCD, CDC, and DCC) helps to narrow down ionian-containing modes to 3 specific modes.

	~~=== 12L 7s ===~~
	This breakdown can be taken one step further by breaking down small steps into a chroma and diesis, where a diesis is defined as such: d = \| L - 2s \|. Ultimately, the large steps of 5L 2s are broken down into two chromas and a diesis, in some order. This produces the modes of 12L 7s and introduces an additional 7 modes. In either case, it's easier to think of these modes as some sort of extension of the seven modes of 5L 2s. ~~The use of "CS/SC" and "CCD/CDC/DCC" is to enforce how these modes are broken down; there~~ are 13 modes of 12L 7s that contain ionian as a subset (UDPs 17\|1 to 5\|13), so it's confusing to say there are 13 ionian modes.
	{\| class="wikitable"		{\| class="wikitable"
	!		!
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	todo:examples		todo:examples

			=== 19L 7s ===
			Whereas a diesis is defined as d = \| L - 2s \|, a triesis is defined as t = \| L - 3s \|. As a summary, 19L 7s contains all the super-leading tone goodness I expect from 12L 7s, but with an additional step (literally) to get there.

Ganaram inukshuk: /* My approach to 7L 5s and 12L 7s */ super-leading tone

2022-11-25T08:07:41Z

My approach to 7L 5s and 12L 7s: super-leading tone

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Ganaram inukshuk: Added a section for 7L 5s and 12L 7s

2022-11-23T22:51:01Z

Added a section for 7L 5s and 12L 7s

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Ganaram inukshuk: X-pattern with the default modes. Also added other possible "default modes".

2022-11-23T06:07:41Z

X-pattern with the default modes. Also added other possible "default modes".

← Older revision		Revision as of 06:07, 23 November 2022
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	=== Examples using heptatonic mosses ===		=== 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'''.		As an example, let's use all six more heptatonic mosses: [[1L 6s]] (onyx), [[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'''.
	{\| class="wikitable"		{\| class="wikitable"
	! colspan="2" \|~~Anti-archeotonic~~		! colspan="2" \|Onyx
	! colspan="2" \|Antidiatonic		! colspan="2" \|Antidiatonic
	! colspan="2" \|Mosh		! colspan="2" \|Mosh
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	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'''.		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 below in '''bold'''.		Using this assumption as a guide, we can then identify the corresponding major and minor modes of these mosses below in '''bold'''. Here, an emergent pattern starts to appear.
	{\| class="wikitable"		{\| class="wikitable"
	! colspan="2" \|~~Anti-archeotonic~~		! colspan="2" \|Onyx
	! colspan="2" \|Antidiatonic		! colspan="2" \|Antidiatonic
	! colspan="2" \|Mosh		! colspan="2" \|Mosh
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	\|sLLLLLL		\|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.'''		'''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. (Also, that X-pattern.)'''

	=== Example using a mos with far more notes ===		=== Example using a mos with far more notes ===
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	Teasing out the properties of the diatonic minor scale is admittedly harder to justify. The current assumption is that the leading tone is lost, but the interval between the first and second degrees is still in its large form as seen diatonic major. This property only works for mosses that have more L's than s's, hence the amended definition described above. This currently remains untested.		Teasing out the properties of the diatonic minor scale is admittedly harder to justify. The current assumption is that the leading tone is lost, but the interval between the first and second degrees is still in its large form as seen diatonic major. This property only works for mosses that have more L's than s's, hence the amended definition described above. This currently remains untested.

			===== Other possible answers =====
			It's also possible to default to a mos's brightest mode, or its middle mode (such as the dorian mode for diatonic). This doesn't work with mosses with an even number of steps, since there will be two middle modes.

	==== Comparison with other methods ====		==== Comparison with other methods ====
	Interestingly, this definition of a default mode has some overlap with [[Naming Rank-2 Scales\|Jake Freivald's method]] of enumerating a mos's modes.		Interestingly, this definition of a default mode has some overlap with [[Naming Rank-2 Scales\|Jake Freivald's method]] of enumerating a mos's modes.

Ganaram inukshuk: /* Biases */ Some clarification

2022-07-27T22:44:02Z

Biases: Some clarification

← Older revision		Revision as of 22:44, 27 July 2022
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	==== Biases ====		==== Biases ====
	I'm admittedly biased at the idea that unfamiliar scales necessarily need some form of familiar ground. The diatonic major scale is said to contain a leading tone (the "s" at the end of its step pattern), hence preserving this property was deemed necessary for how I explore (and play with) unfamiliar mosses.		I'm admittedly biased at the idea that unfamiliar scales necessarily need some form of familiar ground. The diatonic major scale is said to contain a leading tone (the "s" at the end of its step pattern), hence preserving this property was deemed necessary for how I explore (and play with) unfamiliar mosses. For this reason, my notion of a mos's "default mode" is whatever its equivalent of a major scale is.

	Teasing out the properties of the diatonic minor scale is admittedly harder to justify. The current assumption is that the leading tone is lost, but the interval between the first and second degrees is still in its large form as seen diatonic major. This property only works for mosses that have more L's than s's, hence the amended definition described above. This currently remains untested.		Teasing out the properties of the diatonic minor scale is admittedly harder to justify. The current assumption is that the leading tone is lost, but the interval between the first and second degrees is still in its large form as seen diatonic major. This property only works for mosses that have more L's than s's, hence the amended definition described above. This currently remains untested.

Ganaram inukshuk: /* Justification */ Added biases

2022-07-27T06:00:27Z

Justification: Added biases

← Older revision		Revision as of 06:00, 27 July 2022
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	wip		wip

	=== ~~Justification and comparison~~ ===		=== Other notes ===

	==== Justification ====		==== Justification ====
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	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.		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.

			==== Biases ====
			I'm admittedly biased at the idea that unfamiliar scales necessarily need some form of familiar ground. The diatonic major scale is said to contain a leading tone (the "s" at the end of its step pattern), hence preserving this property was deemed necessary for how I explore (and play with) unfamiliar mosses.

			Teasing out the properties of the diatonic minor scale is admittedly harder to justify. The current assumption is that the leading tone is lost, but the interval between the first and second degrees is still in its large form as seen diatonic major. This property only works for mosses that have more L's than s's, hence the amended definition described above. This currently remains untested.

	==== Comparison with other methods ====		==== Comparison with other methods ====
	Interestingly, this definition of a default mode has some overlap with [[Naming Rank-2 Scales\|Jake Freivald's method]] of enumerating a mos's modes.		Interestingly, this definition of a default mode has some overlap with [[Naming Rank-2 Scales\|Jake Freivald's method]] of enumerating a mos's modes.

Ganaram inukshuk: /* Examples using heptatonic mosses */ Removed the UDP columns because it was confusing me

2022-07-27T04:53:11Z

Examples using heptatonic mosses: Removed the UDP columns because it was confusing me

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