Adaptive diatonic interval names - Revision history

Overthink: a few links

2026-05-25T01:45:41Z

a few links

Overthink: /* Step 1: Identify central intervals */ punctuation

2026-03-04T00:41:22Z

Step 1: Identify central intervals: punctuation

← Older revision		Revision as of 00:41, 4 March 2026
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	== Step 1: Identify central intervals ==		== Step 1: Identify central intervals ==
	For an EDO (let's say, 58edo), identify the "central intervals" for each category. These are the diatonic neutral intervals, which may be between edosteps,		For an EDO (let's say, 58edo), identify the "central intervals" for each category. These are the diatonic neutral intervals, which may be between edosteps.

	== Step 2: Identify anchors ==		== Step 2: Identify anchors ==

Inthar at 19:21, 8 January 2026

2026-01-08T19:21:36Z

← Older revision		Revision as of 19:21, 8 January 2026
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			{{Idiosyncratic terms}}
	[[File:22edo ADIN.png\|thumb\|291x291px\|22edo with adaptive diatonic interval names]]		[[File:22edo ADIN.png\|thumb\|291x291px\|22edo with adaptive diatonic interval names]]
	Adaptive diatonic interval names are Vector's attempt to characterize the labelling of certain EDOs' degrees of thirds in a manner inconsistent with conventional diatonic notation in a formal, systematic way.		Adaptive diatonic interval names are Vector's attempt to characterize the labelling of certain EDOs' degrees of thirds in a manner inconsistent with conventional diatonic notation in a formal, systematic way.

BudjarnLambeth: Uncategorised page

2025-12-28T00:13:40Z

Uncategorised page

← Older revision		Revision as of 00:13, 28 December 2025
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	[[File:Oneieh.png\|thumb\|18edo with oneirotonic vs. diatonic schemes compared. Note the lack of unison, octave, or perfect fourth/fifth in diatonic, and the tritone intervals in oneirotonic.]]		[[File:Oneieh.png\|thumb\|18edo with oneirotonic vs. diatonic schemes compared. Note the lack of unison, octave, or perfect fourth/fifth in diatonic, and the tritone intervals in oneirotonic.]]
	One possible extension to handle edos with an oneirotonic fifth (3, 6, 8, 13, and 18) is to use the neutralized oneirotonic scale as the basis instead of the neutralized diatonic scale. In this case, things function exactly the same as before, but based on oneirotonic instead of diatonic. The additional degree may be called a median or tritone - special tritone labels are not used as the semioctave is always the neutral tritone.		One possible extension to handle edos with an oneirotonic fifth (3, 6, 8, 13, and 18) is to use the neutralized oneirotonic scale as the basis instead of the neutralized diatonic scale. In this case, things function exactly the same as before, but based on oneirotonic instead of diatonic. The additional degree may be called a median or tritone - special tritone labels are not used as the semioctave is always the neutral tritone.

			[[Category:Interval naming]]

VectorGraphics at 10:53, 13 November 2025

2025-11-13T10:53:09Z

← Older revision		Revision as of 10:53, 13 November 2025
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	What interval qualities will label is distances from these "central intervals". For each interval degree, follow the given procedure:		What interval qualities will label is distances from these "central intervals". For each interval degree, follow the given procedure:

	* Find the smallest interval greater than or equal to ~~24c~~ above the neutral interval. Take the interval BEFORE this and label it "submajor" (if its offset is still positive, otherwise, interpret it as submajor but do not actually assign it that name).		* Find the smallest interval greater than or equal to 25c above the neutral interval. Take the interval BEFORE this and label it "submajor" (if its offset is still positive, otherwise, interpret it as submajor but do not actually assign it that name).
	* Find a) the closest interval to 85c above the neutral interval or b) the smallest interval greater than 75c above the neutral interval, whichever is higher. Label this interval "supermajor".		* Find a) the closest interval to 85c above the neutral interval or b) the smallest interval greater than 75c above the neutral interval, whichever is higher. Label this interval "supermajor".
	** If supermajor and submajor coincide, label the interval "major" and then label the next interval up "supermajor".		** If supermajor and submajor coincide, label the interval "major" and then label the next interval up "supermajor".
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	\|Functional.		\|Functional.
	\|}		\|}
	~~{{Todo\|Add info\|inline=1\|text=Find out what~~ edo ~~ADIN stops working~~ at.}}		The first edo that the current set of names is insufficient to cover is 152edo. If an extra name is added for an interval between sensamajor and ultramajor, then the first failure is at 156, and then at 159.

	== Oneirotonic extension ==		== Oneirotonic extension ==
	[[File:Oneieh.png\|thumb\|18edo with oneirotonic vs. diatonic schemes compared. Note the lack of unison, octave, or perfect fourth/fifth in diatonic, and the tritone intervals in oneirotonic.]]		[[File:Oneieh.png\|thumb\|18edo with oneirotonic vs. diatonic schemes compared. Note the lack of unison, octave, or perfect fourth/fifth in diatonic, and the tritone intervals in oneirotonic.]]
	One possible extension to handle edos with an oneirotonic fifth (3, 6, 8, 13, and 18) is to use the neutralized oneirotonic scale as the basis instead of the neutralized diatonic scale. In this case, things function exactly the same as before, but based on oneirotonic instead of diatonic. The additional degree may be called a median or tritone - special tritone labels are not used as the semioctave is always the neutral tritone.		One possible extension to handle edos with an oneirotonic fifth (3, 6, 8, 13, and 18) is to use the neutralized oneirotonic scale as the basis instead of the neutralized diatonic scale. In this case, things function exactly the same as before, but based on oneirotonic instead of diatonic. The additional degree may be called a median or tritone - special tritone labels are not used as the semioctave is always the neutral tritone.

VectorGraphics at 10:20, 13 November 2025

2025-11-13T10:20:03Z

← Older revision		Revision as of 10:20, 13 November 2025
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	What interval qualities will label is distances from these "central intervals". For each interval degree, follow the given procedure:		What interval qualities will label is distances from these "central intervals". For each interval degree, follow the given procedure:

	* Find the smallest interval greater than ~~25c~~ above the neutral interval. Take the interval BEFORE this and label it "submajor" (if its offset is still positive, otherwise, interpret it as submajor but do not actually assign it that name).		* Find the smallest interval greater than or equal to 24c above the neutral interval. Take the interval BEFORE this and label it "submajor" (if its offset is still positive, otherwise, interpret it as submajor but do not actually assign it that name).
	* Find a) the closest interval to 85c above the neutral interval or b) the smallest interval greater than 75c above the neutral interval, whichever is higher. Label this interval "supermajor".		* Find a) the closest interval to 85c above the neutral interval or b) the smallest interval greater than 75c above the neutral interval, whichever is higher. Label this interval "supermajor".
	** If supermajor and submajor coincide, label the interval "major" and then label the next interval up "supermajor".		** If supermajor and submajor coincide, label the interval "major" and then label the next interval up "supermajor".

VectorGraphics at 10:06, 13 November 2025

2025-11-13T10:06:04Z

← Older revision		Revision as of 10:06, 13 November 2025
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	\|6		\|6
	\|magimajor, pentamajor, novamajor, trimajor, neomajor, shrubmajor		\|magimajor, pentamajor, novamajor, trimajor, neomajor, shrubmajor
			\|-
			\|7
			\|magimajor, pentamajor, novamajor, dodecamajor, trimajor, neomajor, shrubmajor
	\|}		\|}
	This might lead to nonsensical assignments of "pentamajor" in edos like 17 (in fact, 17 is the only edo to have this property) - but do not worry! Those will be cleaned up in later steps.		This might lead to nonsensical assignments of "pentamajor" in edos like 17 (in fact, 17 is the only edo to have this property) - but do not worry! Those will be cleaned up in later steps.

VectorGraphics: VectorGraphics moved page User:Adaptive diatonic interval names to Adaptive diatonic interval names

2025-10-18T08:46:28Z

VectorGraphics moved page User:Adaptive diatonic interval names to Adaptive diatonic interval names

← Older revision	Revision as of 08:46, 18 October 2025
(No difference)

VectorGraphics: VectorGraphics moved page User:VectorGraphics/Adaptive diatonic interval names to User:Adaptive diatonic interval names

2025-10-18T08:46:18Z

VectorGraphics moved page User:VectorGraphics/Adaptive diatonic interval names to User:Adaptive diatonic interval names

← Older revision	Revision as of 08:46, 18 October 2025
(No difference)

VectorGraphics at 08:34, 10 October 2025

2025-10-10T08:34:49Z

← Older revision		Revision as of 08:34, 10 October 2025
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	If there is only one type of major or minor (not including submajor or supraminor), the qualifier on major or minor (i.e. penta- or magi-) is removed.		If there is only one type of major or minor (not including submajor or supraminor), the qualifier on major or minor (i.e. penta- or magi-) is removed.
	[[File:Composite 2.png\|thumb\|420x420px\|See? Nonsensical penta- names are all gone!]]		[[File:Composite 2.png\|thumb\|420x420px\|See? Nonsensical penta- names are all gone!]]

			== Functioning for various edos ==
			{\| class="wikitable"
			\|+
			!EDO
			!Notes
			\|-
			\|1
			\|Functional: unison and octave.
			\|-
			\|2
			\|Mostly functional: unison, octave, and tritone, which is read as a perfect fifth and perfect fourth simultaneously.
			\|-
			\|3
			\|Oneirotonic; switches places of fifth and fourth and no perfect intervals. Neutral fifth is 400c; neutral fourth is 800c.
			\|-
			\|4
			\|Extreme case: 300c and 900c intervals are neutral fourth and fifth respectively. Alternatively, neutral third and sixth respectively.
			\|-
			\|5
			\|Functional as in standard notation. 4ths and fifths have exact same priority.
			\|-
			\|6
			\|Oneirotonic; 600c interval is "supermajor" fifth.
			\|-
			\|7
			\|Functional as in standard notation.
			\|-
			\|8
			\|Oneirotonic; switches places of fifth and fourth and no perfect intervals.
			\|-
			\|9
			\|Functional. Major second and minor third coincide.
			\|-
			\|10
			\|Functional. 5edo + neutrals.
			\|-
			\|11
			\|Functional. Most intervals are neutral.
			\|-
			\|12
			\|Functional as in standard notation.
			\|-
			\|13
			\|Oneirotonic; switches places of fifth and fourth and no perfect intervals.
			\|-
			\|14
			\|Functional. 7edo + major/minor intervals which are also perfect interordinals.
			\|-
			\|15
			\|Functional.
			\|-
			\|16
			\|Functional.
			\|-
			\|17
			\|Functional. Contains the nonsensical pentamajor that's resolved by the compositing process.
			\|-
			\|18
			\|Oneirotonic; switches places of fifth and fourth and no perfect intervals.
			\|-
			\|19+
			\|Functional.
			\|}
			{{Todo\|Add info\|inline=1\|text=Find out what edo ADIN stops working at.}}

			== Oneirotonic extension ==
			[[File:Oneieh.png\|thumb\|18edo with oneirotonic vs. diatonic schemes compared. Note the lack of unison, octave, or perfect fourth/fifth in diatonic, and the tritone intervals in oneirotonic.]]
			One possible extension to handle edos with an oneirotonic fifth (3, 6, 8, 13, and 18) is to use the neutralized oneirotonic scale as the basis instead of the neutralized diatonic scale. In this case, things function exactly the same as before, but based on oneirotonic instead of diatonic. The additional degree may be called a median or tritone - special tritone labels are not used as the semioctave is always the neutral tritone.

← Older revision		Revision as of 01:45, 25 May 2026
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	{{Idiosyncratic terms}}		{{Idiosyncratic terms}}
	[[File:22edo ADIN.png\|thumb\|291x291px\|22edo with adaptive diatonic interval names]]		[[File:22edo ADIN.png\|thumb\|291x291px\|22edo with adaptive diatonic interval names]]
	Adaptive diatonic interval names are Vector's attempt to characterize the labelling of certain ~~EDOs~~' degrees of thirds in a manner inconsistent with conventional diatonic notation in a formal, systematic way.		Adaptive diatonic interval names are Vector's attempt to characterize the labelling of certain [[EDO]]s' degrees of thirds in a manner inconsistent with conventional [[diatonic]] notation in a formal, systematic way.

	They replace Walker Brightness Notation, which is now deprecated.		They replace [[Walker Brightness Notation]], which is now deprecated.

	== Step 1: Identify central intervals ==		== Step 1: Identify central intervals ==
	For an EDO (let's say, 58edo), identify the "central intervals" for each category. These are the diatonic neutral intervals, which may be between edosteps.		For an EDO (let's say, [[58edo]]), identify the "central intervals" for each category. These are the diatonic [[neutral (interval quality)\|neutral intervals]], which may be between edosteps.

	== Step 2: Identify anchors ==		== Step 2: Identify anchors ==
	What interval qualities will label is distances from these "central intervals". For each interval degree, follow the given procedure:		What [[interval quality\|interval qualities]] will label is distances from these "central intervals". For each interval degree, follow the given procedure:

	* Find the smallest interval greater than or equal to ~~25c~~ above the neutral interval. Take the interval BEFORE this and label it "submajor" (if its offset is still positive, otherwise, interpret it as submajor but do not actually assign it that name).		* Find the smallest interval greater than or equal to 25{{c}} above the neutral interval. Take the interval BEFORE this and label it "submajor" (if its offset is still positive, otherwise, interpret it as submajor but do not actually assign it that name).
	* Find a) the closest interval to ~~85c~~ above the neutral interval or b) the smallest interval greater than ~~75c~~ above the neutral interval, whichever is higher. Label this interval "supermajor".		* Find a) the closest interval to 85{{c}} above the neutral interval or b) the smallest interval greater than 75{{c}} above the neutral interval, whichever is higher. Label this interval "supermajor".
	** If supermajor and submajor coincide, label the interval "major" and then label the next interval up "supermajor".		** If supermajor and submajor coincide, label the interval "major" and then label the next interval up "supermajor".
	** If there are no unlabelled steps between submajor and supermajor, label whichever is closer to ~~50c~~ above the neutral interval "major". If this is supermajor, label the next interval up "supermajor"; if this is submajor, label the next interval down "submajor" if its offset is still positive.		** If there are no unlabelled steps between submajor and supermajor, label whichever is closer to 50{{c}} above the neutral interval "major". If this is supermajor, label the next interval up "supermajor"; if this is submajor, label the next interval down "submajor" if its offset is still positive.
	[[File:Qetqet.png\|thumb\|434x434px\|Result after Step 2]]		[[File:Qetqet.png\|thumb\|434x434px\|Result after Step 2]]

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	\|}		\|}
	This might lead to nonsensical assignments of "pentamajor" in edos like 17 (in fact, 17 is the only edo to have this property) - but do not worry! Those will be cleaned up in later steps.		This might lead to nonsensical assignments of "pentamajor" in edos like 17 (in fact, 17 is the only edo to have this property) - but do not worry! Those will be cleaned up in later steps.
	* Find the closest otherwise unlabelled interval to 103c above the neutral interval which is higher than ~~75c~~; call it "ultramajor". (Note: you may be ending up with this interval being many semitones above the neutral, that's okay because extraneous names will be clipped off once we actually apply everything to interval classes.) Label the step above ultramajor "tendo" if it is at most 1/6 of the size of the perfect fifth above neutral - otherwise, treat tendo as synonymous with the largest step that is at most 1/6 the size of the perfect fifth above neutral.		* Find the closest otherwise unlabelled interval to 103c above the neutral interval which is higher than 75{{c}}; call it "ultramajor". (Note: you may be ending up with this interval being many semitones above the neutral, that's okay because extraneous names will be clipped off once we actually apply everything to interval classes.) Label the step above ultramajor "tendo" if it is at most 1/6 of the size of the perfect fifth above neutral - otherwise, treat tendo as synonymous with the largest step that is at most 1/6 the size of the perfect fifth above neutral.
	* There may now be one or more unlabelled steps between supermajor and ultramajor (ignoring tendo): this scheme currently supports one interval between these two points, which is labelled "sensamajor".		* There may now be one or more unlabelled steps between supermajor and ultramajor (ignoring tendo): this scheme currently supports one interval between these two points, which is labelled "sensamajor".
	* There may also be one or more unlabelled steps below submajor. Follow the table:[[File:Qyrewywe.png\|thumb\|432x432px\|Result after Step 3]]		* There may also be one or more unlabelled steps below submajor. Follow the table:[[File:Qyrewywe.png\|thumb\|432x432px\|Result after Step 3]]