Adaptive diatonic interval names: Difference between revisions

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[[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 ==

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 ==

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 ~~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 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]]

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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.

* 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 also be one or more unlabelled steps below submajor. Follow the table:[[File:Qyrewywe.png|thumb|432x432px|Result after Step 3]]

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|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 ==

[[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.

[[Category:Interval naming]]

@@ Line 1: / Line 1: @@
+{{Idiosyncratic terms}}
 [[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 ==
-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 ==
-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 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 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]]
@@ Line 46: / Line 47: @@
 |}
 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 also be one or more unlabelled steps below submajor. Follow the table:[[File:Qyrewywe.png|thumb|432x432px|Result after Step 3]]
@@ Line 149: / Line 150: @@
 |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 ==
 [[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.
+[[Category:Interval naming]]