Ground's composition theory - Revision history

Ground at 23:42, 12 October 2026

2026-10-12T23:42:51Z

← Older revision		Revision as of 23:42, 12 October 2026
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	I believe xenharmony involves a balance of being unusual without being jarring. Neutral seconds around 150¢ are excellent for the former, but are more difficult to fit into a diatonic framework. When given the choice, I prefer to have neutral seconds around 135¢ to fit in place of a semitone and 165¢ to fit in place of a whole tone. Temperaments in small edos are Flattone for the former and Porcupine for the latter.		I believe xenharmony involves a balance of being unusual without being jarring. Neutral seconds around 150¢ are excellent for the former, but are more difficult to fit into a diatonic framework. When given the choice, I prefer to have neutral seconds around 135¢ to fit in place of a semitone and 165¢ to fit in place of a whole tone. Temperaments in small edos are Flattone for the former and Porcupine for the latter.

			When converting a simple subgroup to contain these intervals, it makes sense to use 2.3.5 because it's closer to neutral whereas 2.3.7 is closer to interordinal.
			* Making 16/15 larger requires a flatter 3 or 5, both of which are done by the more extreme tunings of Meantone.
			* Making 10/9 smaller requires a sharper 3 or flatter 5. Sharper 3 is better because it's squared, so the error is doubled.
			This is an excellent use case for straddle-3 temperaments. 37edo has mild Mavila and extreme Archy fifths, but their distance from 3/2 is somewhat masked in 5-limit chords due to the 5/4 anchor concordance.

	== Adaptive diatonic modification system ==		== Adaptive diatonic modification system ==

Ground: /* Neutral diachrome */

2026-10-12T13:58:10Z

Neutral diachrome

← Older revision		Revision as of 13:58, 12 October 2026
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	\|}		\|}

	=== Neutral ~~diachrome~~ ===		=== Neutral diatonic extensions ===

	Here's something I don't think we talk about enough: being raised on music that almost exclusively uses a diatonic framework makes that framework impossible to escape if we want to evoke any of the same emotions. I can use oneirotonic or smitonic for their melodic similarities or antidiatonic for its harmonic similarity, but none of them have a good approximation of 3/2 without using an extremely hard or soft tuning. Porcupine temperament is about as close as I can get to harmonically familiar yet melodically xen, but it's a tradeoff between sharp 6/5 and sharp 3/2. A solution to this that I've derived a few separate times is '''neutral diachrome''', which splits diatonic whole tones into quartertones and neutral seconds. This process can be extended to quasi-diatonic ternary scales like blackdye and diasem, especially when the neutral second splits the minor third equally.		Here's something I don't think we talk about enough: being raised on music that almost exclusively uses a diatonic framework makes that framework impossible to escape if we want to evoke any of the same emotions. I can use oneirotonic or smitonic for their melodic similarities or antidiatonic for its harmonic similarity, but none of them have a good approximation of 3/2 without using an extremely hard or soft tuning. Porcupine temperament is about as close as I can get to harmonically familiar yet melodically xen, but it's a tradeoff between sharp 6/5 and sharp 3/2. A solution to this that I've derived a few separate times is '''neutral diachrome''', which splits diatonic whole tones into quartertones and neutral seconds. This process can be extended to quasi-diatonic ternary scales like blackdye and diasem, especially when the neutral second splits the minor third equally.

			A simpler operation on ternary scales is splitting L into new L + s. The effectiveness of this varies widely depending on the aberrisma size.

			I believe xenharmony involves a balance of being unusual without being jarring. Neutral seconds around 150¢ are excellent for the former, but are more difficult to fit into a diatonic framework. When given the choice, I prefer to have neutral seconds around 135¢ to fit in place of a semitone and 165¢ to fit in place of a whole tone. Temperaments in small edos are Flattone for the former and Porcupine for the latter.

	== Adaptive diatonic modification system ==		== Adaptive diatonic modification system ==

Ground at 23:05, 11 October 2026

2026-10-11T23:05:29Z

← Older revision		Revision as of 23:05, 11 October 2026
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	I believe the most aesthetically ideal and widely useful aberrismic scales are Meantone septal diasem and Archy pental blackdye. See [[Monarch]] for further explanation.		I believe the most aesthetically ideal and widely useful aberrismic scales are Meantone septal diasem and Archy pental blackdye. See [[Monarch]] for further explanation.

	== 9-note ~~diatonic analogue~~ ==		== Diatonic analogues ==

			=== 9-note "diatygic" ===

	ModMOSes and ternary scales based on them are the best. I haven't used them extensively since my first two albums (2014-2015), so I'm going to challenge myself to use one as often as possible. It's easier if the scale being modified is very familiar, such as quasi-diatonic. There's actually nothing about ILD that prefers MOSes over any other type of scale. This will need to be a whole section eventually.		ModMOSes and ternary scales based on them are the best. I haven't used them extensively since my first two albums (2014-2015), so I'm going to challenge myself to use one as often as possible. It's easier if the scale being modified is very familiar, such as quasi-diatonic. There's actually nothing about ILD that prefers MOSes over any other type of scale. This will need to be a whole section eventually.
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	\|1200		\|1200
	\|}		\|}

			=== Neutral diachrome ===

			Here's something I don't think we talk about enough: being raised on music that almost exclusively uses a diatonic framework makes that framework impossible to escape if we want to evoke any of the same emotions. I can use oneirotonic or smitonic for their melodic similarities or antidiatonic for its harmonic similarity, but none of them have a good approximation of 3/2 without using an extremely hard or soft tuning. Porcupine temperament is about as close as I can get to harmonically familiar yet melodically xen, but it's a tradeoff between sharp 6/5 and sharp 3/2. A solution to this that I've derived a few separate times is '''neutral diachrome''', which splits diatonic whole tones into quartertones and neutral seconds. This process can be extended to quasi-diatonic ternary scales like blackdye and diasem, especially when the neutral second splits the minor third equally.

	== Adaptive diatonic modification system ==		== Adaptive diatonic modification system ==

Ground: /* Edo multiplication */

2026-10-09T18:34:07Z

Edo multiplication

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	* 36 has clearer concordances because it's so good at 2.3.7. It's good to have some anchor concordance in the base edo, but 24 also has 3/2. Having 2.3.7 outside the base edo naturally guides composition towards using other channels and makes it hard to forget about them. There's a nice symmetry with 24x6 putting 7/6 and 6/5 on the same channel as well as 9/7 and 5/4.		* 36 has clearer concordances because it's so good at 2.3.7. It's good to have some anchor concordance in the base edo, but 24 also has 3/2. Having 2.3.7 outside the base edo naturally guides composition towards using other channels and makes it hard to forget about them. There's a nice symmetry with 24x6 putting 7/6 and 6/5 on the same channel as well as 9/7 and 5/4.
	With all this in mind, 24x6 is clearly the better choice to start with, although it's close.		With all this in mind, 24x6 is clearly the better choice to start with, although it's close.

			=== Channel management ===

			Blackdye and diasem structures have a generator of a perfect fifth and some offset for certain notes. Because all of the offsets are in the same direction, using an offset that is part of a superset of the generator doubles the number of distinct channels required. This most notably results in scales where the generator is from the x2 edo and the offset is from the x3 or x6 edo only requiring 4 channels.

	== Anchor concordances ==		== Anchor concordances ==

Ground: /* Tertian categorization */

2026-10-09T18:22:40Z

Tertian categorization

← Older revision		Revision as of 18:22, 9 October 2026
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	\|?		\|?
	\|"Septal"		\|"Septal"
	\|"~~Eridian~~"		\|"Eridial"
	\|"Novemdecal"		\|"Novemdecal"
	\|Pental		\|Pental
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	The diatonic scale and its tertian harmony are the framework of all Western music. It makes sense that using the lowest prime as the period and second lowest prime as the generator would produce a versatile scale, and the fact that it clusters around 12edo rather than 3edo in the case of prime 5 produces more useful step sizes. Modifying this into an aberrismic scale containing the simplest tertian triad 4:5:6 and its retroversion in as many places as possible produces blackdye, and doing the same with 6:7:9 produces diasem. These are the main scales I use to represent my take on Western music: melodically interesting, harmonically pure, and not far from diatonic. However, there are other tunings of them that are useful in different places. These are generalized forms and their aberrismas may be tempered out for a true diatonic scale. 64/63 and 81/80 are common, but 736/729 and especially 513/512 are smaller and make more sense to temper out. If not, inflating them is recommended to keep the melodic significance of the aberrisma.		The diatonic scale and its tertian harmony are the framework of all Western music. It makes sense that using the lowest prime as the period and second lowest prime as the generator would produce a versatile scale, and the fact that it clusters around 12edo rather than 3edo in the case of prime 5 produces more useful step sizes. Modifying this into an aberrismic scale containing the simplest tertian triad 4:5:6 and its retroversion in as many places as possible produces blackdye, and doing the same with 6:7:9 produces diasem. These are the main scales I use to represent my take on Western music: melodically interesting, harmonically pure, and not far from diatonic. However, there are other tunings of them that are useful in different places. These are generalized forms and their aberrismas may be tempered out for a true diatonic scale. 64/63 and 81/80 are common, but 736/729 and especially 513/512 are smaller and make more sense to temper out. If not, inflating them is recommended to keep the melodic significance of the aberrisma.

	'''~~Eridian~~''' diasem is a term I coined for diasem with shrub- or sometimes neo- major/minor thirds. It is named for Eris, ~~who~~ is probably one of the most goth deities of Ancient Greece and is also associated with the number 23 by Discordians. It targets 18:23:27, a little-known and surprisingly concordant tertian triad. Many microtonalists contend that 12edo pop music, while historically tracing back to Meantone, tends to sound better in Pythagorean tuning. I can really hear it after comparing different quasi-diatonic options for retuning my melodies. I've taken a particular liking to gentle/neogothic diatonic scales in the past for this reason, but I believe eridian diasem is a further refinement. As with diasem in general, I prefer this with the 3 tuned slightly flat to inflate the aberrisma, although it is especially important in this case because 736/729 has a size of only 17¢. When inflated in tunings such as 43edo, the aberrisma is subtle enough to not disturb the Pythagorean sound much, but impactful in cases like the subminor seventh, which is tuned close to 7/4. Its melody is not particularly xenharmonic, but it's one of my default scales when available because it works for almost everything. It works well as an extension to [[Septimal meantone]]. {{adv\|The difference between eridian diasem's analogous 2.3.25 and 2.3.17/5 thirds (e.g. 75/64 and 20/17) is 256/255, also the difference between 16/15 and 17/16, supporting it as one of the most important 17-limit commas.}}		'''Eridial''' diasem is a term I coined for diasem with shrub- or sometimes neo- major/minor thirds. It is named after "eridian", the demonym for Eris, with the -al suffix of subgroups. Eris is probably one of the most goth deities of Ancient Greece and is also associated with the number 23 by Discordians. It targets 18:23:27, a little-known and surprisingly concordant neogothic tertian triad. Many microtonalists contend that 12edo pop music, while historically tracing back to Meantone, tends to sound better in Pythagorean tuning. I can really hear it after comparing different quasi-diatonic options for retuning my melodies. I've taken a particular liking to gentle/neogothic diatonic scales in the past for this reason, but I believe eridian diasem is a further refinement. As with diasem in general, I prefer this with the 3 tuned slightly flat to inflate the aberrisma, although it is especially important in this case because 736/729 has a size of only 17¢. When inflated in tunings such as 43edo, the aberrisma is subtle enough to not disturb the Pythagorean sound much, but impactful in cases like the subminor seventh, which is tuned close to 7/4. Its melody is not particularly xenharmonic, but it's one of my default scales when available because it works for almost everything. It works well as an extension to [[Septimal meantone]]. {{adv\|The difference between eridian diasem's analogous 2.3.25 and 2.3.17/5 thirds (e.g. 75/64 and 20/17) is 256/255, also the difference between 16/15 and 17/16, supporting it as one of the most important 17-limit commas.}}

	The default set of qualities to consider is septal and pental due to their simplicity, possibly with a Pythagorean diatonic scale in the middle as found in Aberschismic edos. But I've found that I particularly like shifting both septal and pental towards neutral, to eridian and exaggerated pental. This is probably because it puts both of them about an equal distance from diatonic when using a prime 3 within a few cents of just. Eridian provides a more versatile sound and pental sounds more interesting while still working about the same. In some edos that do this such as 48 and 86, the pental tuning is Negri, meaning that semiquartal is also available.		The default set of qualities to consider is septal and pental due to their simplicity, possibly with a Pythagorean diatonic scale in the middle as found in Aberschismic edos. But I've found that I particularly like shifting both septal and pental towards neutral, to eridian and exaggerated pental. This is probably because it puts both of them about an equal distance from diatonic when using a prime 3 within a few cents of just. Eridian provides a more versatile sound and pental sounds more interesting while still working about the same. In some edos that do this such as 48 and 86, the pental tuning is Negri, meaning that semiquartal is also available.
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	</div>		</div>
	27/23 is close enough to 32/27 that it can be replaced and result in another 2.3.23 blackdye scale with 32/27*23/18 = 368/243 triads. The fifth is the same as the existing Eridian wolf fifth, which is barely diatonic in JI. I might call this '''~~hiberidian~~''' because it applies the principle of [[Hibernal]] to the eridian subgroup. 82edo is the near-perfect 2.3.23 tuning, but 20 and 37edo have a close approximation of the scale despite not being good for the subgroup. Switching thirds to 32/27 or 81/64 to remain in the subgroup with a wolf fifth as the main one can be applied to other scales in the table.		27/23 is close enough to 32/27 that it can be replaced and result in another 2.3.23 blackdye scale with 32/27*23/18 = 368/243 triads. The fifth is the same as the existing Eridian wolf fifth, which is barely diatonic in JI. I might call this '''hiberidial''' because it applies the principle of [[Hibernal]] to the eridian subgroup. 82edo is the near-perfect 2.3.23 tuning, but 20 and 37edo have a close approximation of the scale despite not being good for the subgroup. Switching thirds to 32/27 or 81/64 to remain in the subgroup with a wolf fifth as the main one can be applied to other scales in the table.

	I have a lot more to write about how blackdye and diasem work harmonically.		I have a lot more to write about how blackdye and diasem work harmonically.

Ground at 12:24, 19 September 2026

2026-09-19T12:24:41Z

← Older revision		Revision as of 12:24, 19 September 2026
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	Edos that are multiples of 6 usually have more than one reasonable way to split them. I will use 144edo to explain my thought process in deciding whether to use 24x6 or 36x4.		Edos that are multiples of 6 usually have more than one reasonable way to split them. I will use 144edo to explain my thought process in deciding whether to use 24x6 or 36x4.
	* The most important consideration is which base edo the composer enjoys the most. Both options have features that are important to me, but I've written a good amount in 24 because I believe its lack of a good 5 is less important.		* The most important consideration is which base edo the composer enjoys the most. Both options have features that are important to me, but I've written a good amount in 24 because I believe its lack of a good 5 is less important, so it's been proven by time.
	* In terms of the number of useful scales available, 36 is superior. To some extent, this comes with having more notes in general.		* In terms of the number of useful scales available, 36 is superior. To some extent, this comes with having more notes in general.
	* x6 has more channels overall, but contains both the x2 and x3 subsets. x4 requires a larger base edo and has only the option to use x2 and x4 notes. Because of the distribution of the number of channels I typically use, I expect x6 to have more practical options.		* x6 has more channels overall, but contains both the x2 and x3 subsets. x4 requires a larger base edo and has only the option to use x2 and x4 notes. Because of the distribution of the number of channels I typically use, I expect x6 to have more practical options.
	* x6 is more of a standard for me, so I'm set up better for that.		* x6 is more of a standard for me, so I'm set up better for that.
	* I mentioned how I like to make clear switches between x2 and x3 to make it easier to read my piano roll notes. ~~24x6~~ is better for this because ~~using x2 and~~ x4 has ~~less distinction between~~ the ~~two~~.		* I mentioned how I like to make clear switches between x2 and x3 to make it easier to read my piano roll notes. x6 is better for this because x4 has only one distinct subset besides the base edo, x2.
	* 36x2 makes accessing 72edo especially convenient because fewer channels is easier. It wins for 11-limit stuff.		* 36x2 makes accessing 72edo especially convenient because fewer channels is easier. It wins for 11-limit stuff.
	* Two important subsets of 144 are 16 and 18. 24x6 has them as x2 and x3, but 36x4 has them as x4 and x1. This is a tie.		* Two important subsets of 144 are 16 and 18. 24x6 has them as x2 and x3, but 36x4 has them as x4 and x1. This is a tie.
	* I use 5-form structures a lot, and some of my favorite edos are 43 and 67. Add 5 to bring their 3/2 closer to just, resulting in 48 and 72, 24x2 and x3. This is an elegant way to approximate both 43 and 67.		* I use 5-form structures a lot, and some of my favorite edos are 43 and 67. Add 5 to bring their 3/2 closer to just, resulting in 48 and 72, 24x2 and x3. This is an elegant way to approximate both 43 and 67.
	* Using a smaller edo gets more range in the piano roll, which is useful for quick creative writing.		* Using a smaller edo gets more range in the piano roll, which is useful for quick creative writing.
			* 36 has clearer concordances because it's so good at 2.3.7. It's good to have some anchor concordance in the base edo, but 24 also has 3/2. Having 2.3.7 outside the base edo naturally guides composition towards using other channels and makes it hard to forget about them. There's a nice symmetry with 24x6 putting 7/6 and 6/5 on the same channel as well as 9/7 and 5/4.
	With all this in mind, 24x6 is clearly the better choice to start with, although it's close.		With all this in mind, 24x6 is clearly the better choice to start with, although it's close.

Ground at 04:32, 19 September 2026

2026-09-19T04:32:29Z

← Older revision		Revision as of 04:32, 19 September 2026
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	* In terms of the number of useful scales available, 36 is superior. To some extent, this comes with having more notes in general.		* In terms of the number of useful scales available, 36 is superior. To some extent, this comes with having more notes in general.
	* x6 has more channels overall, but contains both the x2 and x3 subsets. x4 requires a larger base edo and has only the option to use x2 and x4 notes. Because of the distribution of the number of channels I typically use, I expect x6 to have more practical options.		* x6 has more channels overall, but contains both the x2 and x3 subsets. x4 requires a larger base edo and has only the option to use x2 and x4 notes. Because of the distribution of the number of channels I typically use, I expect x6 to have more practical options.
			* x6 is more of a standard for me, so I'm set up better for that.
	* I mentioned how I like to make clear switches between x2 and x3 to make it easier to read my piano roll notes. 24x6 is better for this because using x2 and x4 has less distinction between the two.		* I mentioned how I like to make clear switches between x2 and x3 to make it easier to read my piano roll notes. 24x6 is better for this because using x2 and x4 has less distinction between the two.
	* 36x2 makes accessing 72edo especially convenient because fewer channels is easier. It wins for 11-limit stuff.		* 36x2 makes accessing 72edo especially convenient because fewer channels is easier. It wins for 11-limit stuff.

Ground at 04:27, 19 September 2026

2026-09-19T04:27:58Z

← Older revision		Revision as of 04:27, 19 September 2026
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	When using edo multiples, it's important to keep better track of the intervals in use and minimize the effect of the added complexity to compose efficiently. I do this by switching between discrete scales in the multiples (rather than flowing freely between structures and selecting all notes by ear as in the base edo) and by primarily using notes of the base edo as the tonic to minimize the versions of each scale to keep track of when I modulate. No matter what, the things I write will always be filtered through the base edo. It's natural that the extra precision and features of multiples won't be necessary most of the time, and the freedom of a reasonably sized base edo will outweigh them.		When using edo multiples, it's important to keep better track of the intervals in use and minimize the effect of the added complexity to compose efficiently. I do this by switching between discrete scales in the multiples (rather than flowing freely between structures and selecting all notes by ear as in the base edo) and by primarily using notes of the base edo as the tonic to minimize the versions of each scale to keep track of when I modulate. No matter what, the things I write will always be filtered through the base edo. It's natural that the extra precision and features of multiples won't be necessary most of the time, and the freedom of a reasonably sized base edo will outweigh them.

			Edos that are multiples of 6 usually have more than one reasonable way to split them. I will use 144edo to explain my thought process in deciding whether to use 24x6 or 36x4.
			* The most important consideration is which base edo the composer enjoys the most. Both options have features that are important to me, but I've written a good amount in 24 because I believe its lack of a good 5 is less important.
			* In terms of the number of useful scales available, 36 is superior. To some extent, this comes with having more notes in general.
			* x6 has more channels overall, but contains both the x2 and x3 subsets. x4 requires a larger base edo and has only the option to use x2 and x4 notes. Because of the distribution of the number of channels I typically use, I expect x6 to have more practical options.
			* I mentioned how I like to make clear switches between x2 and x3 to make it easier to read my piano roll notes. 24x6 is better for this because using x2 and x4 has less distinction between the two.
			* 36x2 makes accessing 72edo especially convenient because fewer channels is easier. It wins for 11-limit stuff.
			* Two important subsets of 144 are 16 and 18. 24x6 has them as x2 and x3, but 36x4 has them as x4 and x1. This is a tie.
			* I use 5-form structures a lot, and some of my favorite edos are 43 and 67. Add 5 to bring their 3/2 closer to just, resulting in 48 and 72, 24x2 and x3. This is an elegant way to approximate both 43 and 67.
			* Using a smaller edo gets more range in the piano roll, which is useful for quick creative writing.
			With all this in mind, 24x6 is clearly the better choice to start with, although it's close.

	== Anchor concordances ==		== Anchor concordances ==

Ground at 19:23, 9 September 2026

2026-09-09T19:23:06Z

← Older revision		Revision as of 19:23, 9 September 2026
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	* x3: 8%		* x3: 8%
	* x6: 4%		* x6: 4%

			This should show just how important the base edo is. No matter how many intervals you have, large edos or edo multiplication will never be as efficient to write in as an elegant mid-sized edo that does what you want the most. Everything is filtered through the base edo's structure. Because of this, there's no such thing as the perfect edo. At this point, I use whatever I feel like at the time and multiply it by 6 to fill any gaps that might come up.

	When using edo multiples, it's important to keep better track of the intervals in use and minimize the effect of the added complexity to compose efficiently. I do this by switching between discrete scales in the multiples (rather than flowing freely between structures and selecting all notes by ear as in the base edo) and by primarily using notes of the base edo as the tonic to minimize the versions of each scale to keep track of when I modulate. No matter what, the things I write will always be filtered through the base edo. It's natural that the extra precision and features of multiples won't be necessary most of the time, and the freedom of a reasonably sized base edo will outweigh them.		When using edo multiples, it's important to keep better track of the intervals in use and minimize the effect of the added complexity to compose efficiently. I do this by switching between discrete scales in the multiples (rather than flowing freely between structures and selecting all notes by ear as in the base edo) and by primarily using notes of the base edo as the tonic to minimize the versions of each scale to keep track of when I modulate. No matter what, the things I write will always be filtered through the base edo. It's natural that the extra precision and features of multiples won't be necessary most of the time, and the freedom of a reasonably sized base edo will outweigh them.

Ground at 00:02, 4 September 2026

2026-09-04T00:02:51Z

← Older revision		Revision as of 00:02, 4 September 2026
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	The diatonic scale and its tertian harmony are the framework of all Western music. It makes sense that using the lowest prime as the period and second lowest prime as the generator would produce a versatile scale, and the fact that it clusters around 12edo rather than 3edo in the case of prime 5 produces more useful step sizes. Modifying this into an aberrismic scale containing the simplest tertian triad 4:5:6 and its retroversion in as many places as possible produces blackdye, and doing the same with 6:7:9 produces diasem. These are the main scales I use to represent my take on Western music: melodically interesting, harmonically pure, and not far from diatonic. However, there are other tunings of them that are useful in different places. These are generalized forms and their aberrismas may be tempered out for a true diatonic scale. 64/63 and 81/80 are common, but 736/729 and especially 513/512 are smaller and make more sense to temper out. If not, inflating them is recommended to keep the melodic significance of the aberrisma.		The diatonic scale and its tertian harmony are the framework of all Western music. It makes sense that using the lowest prime as the period and second lowest prime as the generator would produce a versatile scale, and the fact that it clusters around 12edo rather than 3edo in the case of prime 5 produces more useful step sizes. Modifying this into an aberrismic scale containing the simplest tertian triad 4:5:6 and its retroversion in as many places as possible produces blackdye, and doing the same with 6:7:9 produces diasem. These are the main scales I use to represent my take on Western music: melodically interesting, harmonically pure, and not far from diatonic. However, there are other tunings of them that are useful in different places. These are generalized forms and their aberrismas may be tempered out for a true diatonic scale. 64/63 and 81/80 are common, but 736/729 and especially 513/512 are smaller and make more sense to temper out. If not, inflating them is recommended to keep the melodic significance of the aberrisma.

	'''Eridian''' diasem is a term I coined for diasem with shrub- or sometimes neo- major/minor thirds. It is named for Eris, who is probably one of the most goth deities of Ancient Greece and is also associated with the number 23 by Discordians. It targets 18:23:27, a little-known and surprisingly concordant tertian triad. Many microtonalists contend that 12edo pop music, while historically tracing back to Meantone, tends to sound better in Pythagorean tuning. I can really hear it after comparing different quasi-diatonic options for retuning my melodies. I've taken a particular liking to gentle/neogothic diatonic scales in the past for this reason, but I believe eridian diasem is a further refinement. As with diasem in general, I prefer this with the 3 tuned slightly flat to inflate the aberrisma, although it is especially important in this case because 736/729 has a size of only 17¢. When inflated in tunings such as 43edo, the aberrisma is subtle enough to not disturb the Pythagorean sound much, but impactful in cases like the subminor seventh, which is tuned close to 7/4. Its melody is not particularly xenharmonic, but it's one of my default scales when available because it works for almost everything. It works well as an extension to [[Septimal meantone]].		'''Eridian''' diasem is a term I coined for diasem with shrub- or sometimes neo- major/minor thirds. It is named for Eris, who is probably one of the most goth deities of Ancient Greece and is also associated with the number 23 by Discordians. It targets 18:23:27, a little-known and surprisingly concordant tertian triad. Many microtonalists contend that 12edo pop music, while historically tracing back to Meantone, tends to sound better in Pythagorean tuning. I can really hear it after comparing different quasi-diatonic options for retuning my melodies. I've taken a particular liking to gentle/neogothic diatonic scales in the past for this reason, but I believe eridian diasem is a further refinement. As with diasem in general, I prefer this with the 3 tuned slightly flat to inflate the aberrisma, although it is especially important in this case because 736/729 has a size of only 17¢. When inflated in tunings such as 43edo, the aberrisma is subtle enough to not disturb the Pythagorean sound much, but impactful in cases like the subminor seventh, which is tuned close to 7/4. Its melody is not particularly xenharmonic, but it's one of my default scales when available because it works for almost everything. It works well as an extension to [[Septimal meantone]]. {{adv\|The difference between eridian diasem's analogous 2.3.25 and 2.3.17/5 thirds (e.g. 75/64 and 20/17) is 256/255, also the difference between 16/15 and 17/16, supporting it as one of the most important 17-limit commas.}}

	The default set of qualities to consider is septal and pental due to their simplicity, possibly with a Pythagorean diatonic scale in the middle as found in Aberschismic edos. But I've found that I particularly like shifting both septal and pental towards neutral, to eridian and exaggerated pental. This is probably because it puts both of them about an equal distance from diatonic when using a prime 3 within a few cents of just. Eridian provides a more versatile sound and pental sounds more interesting while still working about the same. In some edos that do this such as 48 and 86, the pental tuning is Negri, meaning that semiquartal is also available.		The default set of qualities to consider is septal and pental due to their simplicity, possibly with a Pythagorean diatonic scale in the middle as found in Aberschismic edos. But I've found that I particularly like shifting both septal and pental towards neutral, to eridian and exaggerated pental. This is probably because it puts both of them about an equal distance from diatonic when using a prime 3 within a few cents of just. Eridian provides a more versatile sound and pental sounds more interesting while still working about the same. In some edos that do this such as 48 and 86, the pental tuning is Negri, meaning that semiquartal is also available.
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