Planning Analytics

This post will hopefully get more developers using MDX within their sets and views.
The intention is to expose MDX commands that work in TM1, their syntax or usage and some examples or applications.

This is a guide and not gospel - I am sure there are many ways of doing the same thing as well as better ways.
You will see that some examples switch around certain functions - this may be by design or accidental.

There are also gaps as this project is a work in progress. Similarly, alignment of syntax needs to be reviewed and edited.

Most importantly was getting something out here to begin with. Just like with any TM1 model, something is better than nothing.
Expect errors and omissions but please feedback so that I can update/correct for everyone's benefit.

I am not going to try and replicate any websites or MDX books of which there are many.
My go-to reference is Multidimensional Expressions (MDX) Reference - SQL Server 2012 Books Online, Microsoft

My examples are based on a simple model with an Expense cube built with a Period, Cost Centre and other dimensions. Some examples may reference the cubes in the SData sample where I could not find a suitable example in the Period dimension.
My Period dimension is deliberately designed with leaf elements as YYYY-MMM e.g. 2021-JAN - these do not sort chronologically and is perfect for some examples.
Also, I have assumed a July start or Period 1.
My Period dimension has multiple rollups grouping Periods into Fiscal Years as well as Periods into Quarters, Halves and Fiscal Years.
These have also been configured in the }HierarchyProperties cube to drive some of the Level queries.

You can create your own Period dimension per below to play with the examples.


The Cost Centre dimension referenced is simple containing a Total with children. The leaf elements have two attributes that are used in the examples: Primary Cost Centre and Division.
You can configure your own dimension accordingly to test some of the examples.


I also created a basic Client Assumption cube to read the Current Period for the user in some examples.
You could create this per the below cube view.


That should suffice for most of the model needed to test the examples. You can create other objects as required based on the examples.

TM1 / Planning Analytics - MDX Reference Guide

ARITHMETIC OPERATORS	Description/Notes	Syntax	Example
+ Add, Positive
/ Divide
* Multiply
- Subtract, Negative
^ (Power)
BITWISE OPERATORS
AND	Performs a logical conjunction on two numeric expressions.	<Expression 1> AND <Expression 2>	{ FILTER( {TM1SUBSETALL( [Cost Centre] )}, [Cost Centre].CurrentMember.Properties("Primary Cost Centre") <> "" AND [Cost Centre].CurrentMember.Properties("Division") <> "" ) } Should give you Cost Centres where there is both a value in the Primary Cost Centre and Division attributes.
NOT	Performs a logical negation on a numeric expression.	NOT <Expression 1>	{ FILTER( {TM1SUBSETALL( [Cost Centre] )}, NOT [Cost Centre].CurrentMember.Properties("Primary Cost Centre") <> "" AND [Cost Centre].CurrentMember.Properties("Division") <> "" ) } Should give you Cost Centres where the Primary Cost Centre attribute is blank and Division attributes is not blank.
OR	Performs a logical disjunction on two numeric expressions.	<Expression 1> OR <Expression 2>	{ FILTER( {TM1SUBSETALL( [Cost Centre] )}, [Cost Centre].CurrentMember.Properties("Primary Cost Centre") = "" OR [Cost Centre].CurrentMember.Properties("Division") = "" ) } Should give you Cost Centres where Primary Cost Centre, Division attributes or both are blank.
XOR	Performs a logical exclusion on two numeric expressions. Returns True when only one expression evaluates to True. Either Expression 1 or Expression 2 is True, not both.	<Expression 1> XOR <Expression 2>	{ FILTER( {TM1SUBSETALL( [Cost Centre] )}, [Cost Centre].CurrentMember.Properties("Primary Cost Centre") = "" XOR [Cost Centre].CurrentMember.Properties("Division") = "" ) } Should give you Cost Centres where either the Primary Cost Centre or the Division attributes are blank, but not both.
IS	Performs a logical comparison on two object expressions. Use square brackets if your level contains a space e.g. [Fiscal Year] Best to fully qualify using dimension and value e.g. [Period].[Quarters] where the name may appear in other dimensions causing ambiguity.	<Expression 1> IS (<Expression 2> | NULL )	FILTER({TM1SUBSETALL( [Period] )}, [Period].CurrentMember.Level IS [Period].[Quarters]) Gives you Periods linked to the same level as which Quarters was defined.
COMPARISON OPERATORS
=	Is Equal To - Applies to numeric and string comparisons	<Expression 1> = <Expression 2>	{ FILTER( {TM1SUBSETALL( [Cost Centre] )}, [Cost Centre].CurrentMember.Properties("Primary Cost Centre") = "" ) } Returns a set of Cost Centres where the Primary Cost Centre attributes is blank.
<>	Is Not Equal to - Applies to numeric and string comparisons	<Expression 1> <> <Expression 2>	{ FILTER( {TM1SUBSETALL( [Cost Centre] )}, [Cost Centre].CurrentMember.Properties("Primary Cost Centre") <> "" ) } Returns a set of Cost Centres where the Primary Cost Centre attributes is not blank.
>	Is Greater Than	<Expression 1> > <Expression 2>	{ FILTER( {TM1SUBSETALL( [Cost Centre] )}, [Expense].(...,[Amount]) > 50000 ) } Returns a set of Cost Centres where specified value in the Expense cube is greater than 50,000
>=	Is Greater Than or Equal To	<Expression 1> >= <Expression 2>	{ FILTER( {TM1SUBSETALL( [Cost Centre] )}, [Expense].(...,[Amount]) >= 50000 ) } Returns a set of Cost Centres where specified value in the Expense cube is greater than or equal to 50,000
<	Is Less Than	<Expression 1> < <Expression 2>	{ FILTER( {TM1SUBSETALL( [Cost Centre] )}, [Expense].(...,[Amount]) < 0 ) } Returns a set of Cost Centres where specified value in the Expense cube is negative.
<=	Is Less Than or Equal To	<Expression 1> <= <Expression 2>	{ FILTER( {TM1SUBSETALL( [Cost Centre] )}, [Expense].(...,[Amount]) <= 0 ) } Returns a set of Cost Centres where specified value in the Expense cube is zero or negative.
TRUE	Not an operator but a literal used in comparisons/filters
FALSE	Not an operator but a literal used in comparisons/filters
CONCATENATION OPERATORS
+	Combine or join multiple strings	<String 1> + <String 2>	{StrToMember("[Period].[Period].[" + [Client Assumption].( StrToMember("[}Clients].[" + UserName + "]"), [Client Assumption Measures].[Current Period]) + "]")} Concatenates the value from an assumptions cube with the hierarchy to create a valid member.
SET OPERATORS
- (Except)	Returns the difference between two sets, removing duplicate members. This operator is functionally equivalent to the Except function.	<Set 1> - <Set 2>	Did not work in a Dimension set but may work with a SELECT statement
* (Crossjoin)	Returns the cross product of two sets. This operator is functionally equivalent to the Crossjoin function. Used in an MDX view where you have dimensions stacked e.g. Product within Customer.	<Set 1> * <Set 2>	SELECT {TM1SubsetToSet([Expense Measures].[Expense Measures],"Default","public")} ON 0, {TM1SubsetToSet([Cost Centre].[Cost Centre],"Default","public")} * {TM1SubsetToSet([Reporting Currency].[Reporting Currency],"Default","public")} ON 1 FROM [Expense] WHERE ...
: (Range)	Returns a naturally ordered set, with the two specified members as endpoints and all members between the two specified members included as members of the set.	<Member 1> : <Member 2>	[Period].[Period].[2021-JAN] : [Period].[Period].[2021-DEC] Should return periods from Jan to Dec
+ (Union)	Returns a union of two sets, excluding duplicate members.	<Set 1> + <Set 2>	{[Period].[Period].[2020-JAN] : [Period].[Period].[2020-DEC]} + {[Period].[Period].[2022-JAN] : [Period].[Period].[2022-DEC]} Will return a set with the range of members from the first expression and second expression. Any overlaps do not result in duplicates.
STRING FUNCTIONS
Name	Returns a string containing the member name	<Member expression>.Name	FILTER({TM1SUBSETALL( [Period] )}, RIGHT([Period].CurrentMember.Name,1)="V") Returns elements where the Name of the member ends in a V e.g. 2021-NOV
Uniquename	Returns a string containing the member unique name. Values are enclosed in square brackets.	<Member expression>.UniqueName	FILTER({TM1SUBSETALL( [Period] )}, INSTR(1, [Period].CurrentMember.UniqueName, "^", 0) = 0) Returns members that are unique in the hierarchy i.e. do not form part of any other rollups and thus are not further qualified with a caret (^)
Properties	Returns a string, or a strongly-typed value, that contains a member property value i.e. Attribute value.	Member_Expression.Properties(Property_Name [, TYPED])	{ORDER( {TM1FILTERBYLEVEL( {TM1SUBSETALL( [Period] )}, 0)}, [Period].CurrentMember.Properties("Month"), BASC)} Returns a set of leaf level months orders by Month which is numeric. 2021-JAN, 2021-FEB etc. do not sort chronologically naturally.
Generate	Executes a string function on each member of the set, almost like a For Each Member statement.	Generate(<Set 1>, <Set 2> [, ALL])	{GENERATE( {[Period].[2023-MAR]}, {[Period].CurrentMember, StrToMember("[Period].[" + [Period].CurrentMember.Name + " YTD]"), [Period].CurrentMember.Parent, [Period].CurrentMember.LAG(12)} )} Should return 2023-MAR itself, being the CurrentMember then 2023.09 YTD, 2023.FY and 2022-APR
UserName	Returns the domain name and user name of the current connection.	UserName	{StrToMember("[Period].[Period].[" + [Client Assumption].( StrToMember("[}Clients].[" + UserName + "]"), [Client Assumption Measures].[Current Period]) + "]")} UserName is the string value the active client and used to lookup the current period in the assumption cube. In this case, my value in the cube is 2021-JAN and this is returned as a member.
Instr	Returns the position of the first occurrence of one string within another. NB: 4th parameter, compare in TM1 is used as 0 for case-sensitive, 1 for ignore case.	InStr([start, ]searched_string, search_string[, compare])	{FILTER( {[Period].[Period].Members}, InStr(1, [Period].[Period].CurrentMember.Name, "ju",1)>0 )} Returns periods containing JU, Ju, jU or ju - remember parameter 4 to manage case.
UCase	Convert a string to upper case	UCase(<string>)	{FILTER( {[Period].[Period].Members}, InStr(1, UCase([Period].[Period].CurrentMember.Name), "JU",0)>0 )} Returns periods containing JU e.g. 2021-JUL
LCase	Convert a string to lower case	LCase(<string>)	{FILTER( {[Period].[Period].Members}, InStr(1, LCase([Period].[Period].CurrentMember.Name), "ju",0)>0 )} Returns periods containing JU e.g. 2021-JUL
Left	Return n number of characters from the start of a string	Left(<string>,<count>)	{FILTER( {[Period].[Period].Members}, LEFT([Period].[Period].CurrentMember.Name, 4)="2022" )} Returns periods where the first 4 characters are 2022 - could be N or C or S elements.
Right	Return n number of characters from the end of a string	Right(<string>,<count>)	{FILTER( {[Period].[Period].Members}, RIGHT([Period].[Period].CurrentMember.Name, 3)="JUL" )} Returns periods where the last 3 characters are JUL - could be N or C or S elements. Does not appear case sensitive as it would include as a match 2021-Jul, 2021-jul too.
CASTING FUNCTIONS
MemberToStr	Return a string containing the uniquename of the member	MemberToStr(<Member>)	{FILTER( {[Period].[Period].Members}, MemberToStr([Period].[Period].CurrentMember)="[Period].[2022.FY^2022-JAN]" )}
StrToMember	Returns the member as specified in the string expression	StrToMember(<string expression> [, CONSTRAINED])	STRTOMEMBER("[Period].[Period].[" + SETTOSTR( TM1SubsetToSet([Period].[Period] , "_S-Current Year" , "public")) + "]" )
StrToValue	Return the value of a specified string. NB: Will fail on Nulls and my require the use of IIF() to trap	StrToValue(<string expression>)	{FILTER( {[Period].[Period].Members}, StrToValue([Period].[Period].CurrentMember.Properties("LEVEL_NUMBER"))=0 )}
SetToStr	Returns a string based on the set expression. Will bring back values with braces and a comma e.g. {2022-JAN}, you may need to trim these.	SetToStr(<Set> )	STRTOMEMBER("[Period].[Period].[" + SETTOSTR( TM1SubsetToSet([Period].[Period] , "_S-Current Fiscal Year" , "public")) + "]" ).NEXTMEMBER
StrToSet	Return a set as specified by the string in the set specification. MS MDX has CONSTRAINED as an optional 2nd parameter which is not supported in TM1	StrToSet(<set specification> [, CONSTRAINED])	StrToSet( "[Period].[Period].Members" )
StrToTuple	Returns a tuple as specified in the string expression	StrToTuple(<string expression> [, CONSTRAINED])	Need an example using SELECT
TupleToStr	Returns a string containing tuples. Could be used to parse in other functions	StrToTuple(<tuple expression>)	Need an example using SELECT
NameToSet	Returns a set based on a member name	NameToSet(<member name>)	{NameToSet( "[Period].[Period].[2022.FY^2022-JAN]")}
LOGICAL FUNCTIONS
IS	Performs a logical comparison on two object expressions to see if they are exactly the same.	<Expression1> IS <Expression2>	No useful example of how to use: FILTER( {TM1SUBSETALL( [Period] )}, [Period].CurrentMember IS [Period].[2020-JUL]))
IIF	Returns one of two values determined by a logical test.	IIf(Logical_Expression, Expression1, Expression2)	FILTER( {TM1SUBSETALL( [Period] )}, StrToValue( IIF([Period].CurrentMember.Properties("Period Index")="", "0", [Period].CurrentMember.Properties("Period Index")))>0)
Case, When, Else, End	Lets you conditionally return specific values from multiple comparisons.	CASE <expression> WHEN <case 1> then <expression 1> WHEN.. ELSE <expression> END	{ STRTOMEMBER("[Period].[" + CASE LEFT( RIGHT( SetToStr( {[Period].[Period].[_S-Current Period].Item(0)} ), 10), 8) WHEN "2022-JAN" then "2021.Q1" WHEN "2021-APR" then "2021.Q2" ELSE SetToStr( {[Period].[Period].[_S-Current Period].Item(0)} ) END +"]") }
IsLeaf	Test is a member is a Leaf element	IsLeaf(<Member>)	FILTER( {TM1SUBSETALL( [Period] )}, IsLeaf([Period].CurrentMember))
IsAncestor	Test if a specified member is an Ancestor of another specified member.	IsAncestor(<Member1>,<Member2>)	FILTER( {TM1SUBSETALL( [Period] )}, IsAncestor([Period].CurrentMember,[Period].[2022.Q3])) Returns all Ancestors of 2022.Q3
IsEmpty	Test if a cell, property or value is empty	IsEmpty(<Expression>)	FILTER( {TM1SUBSETALL( [Period] )}, IsEmpty([Sales].([...]))
IsSibling	Test if a member is a sibling of another specified member.	IsSibling(<Member>,<Sibling Member>)	FILTER( {TM1SUBSETALL( [Period] )}, IsSibling([Period].CurrentMember,[Period].[2022.Q3]))
IsGeneration	Test if the specified Member is in the specified Generation (Level)	IsGeneration(<Member>,<Generation>)	FILTER( {TM1SUBSETALL( [Period] )}, IsGeneration([Period].CurrentMember,2))
IsNull	Not supported yet	ISNULL(MDX_expression,value_if_null)	Would be useful to set blanks to "0" etc. avoids IIF()
*Boolean values returned
MEMBER FUNCTIONS AND EXPRESSIONS
AllMembers	Returns a set that contains all members of the specified hierarchy or level. Will include all calculated members in that hierarchy or level.	<hierarchy expression>.AllMembers <level expression>.AllMembers	[Period].AllMembers or [Period].[level000].AllMembers or [Period].[Halves].AllMembers
Members	Returns the set of members in a dimension, level, or hierarchy. Returns Members, not Elements i.e. will repeat where element is in multiple rollups	<dimension expression>.Members <hierarchy expression>.Members <level expression>.Members	[Period].Members
DefaultMember	Return the default member for the dimension/hierarchy as specified in the }HierarchyProperties cube.	<dimension expression>.DefaultMember	{[Period].DefaultMember}
Current	Returns the current tuple from a set during iteration.	<Set>.Current	Need a useful example
CurrentMember	Returns the current member along a specified hierarchy during iteration.	Hierarchy_Expression.CurrentMember	FILTER( {TM1SUBSETALL( [Period] )}, IsLeaf([Period].CurrentMember))
NextMember	Returns the next member in the level that contains a specified member.	Member_Expression.NextMember	{[Period].[2020-JUN].NextMember} gives you 2020-JUL
PrevMember	Returns the previous member in the level that contains a specified member.	Member_Expression.PrevMember	{[Period].[2020-JUN].PrevMember} gives you 2020-MAY
Parent	Returns the parent of a member.	Member_Expression.Parent	Returns the first parent of the member {TM1Member([Period].[Current Month].Item(0),0).Parent}
Root
Level	Returns the Level of a member	Member_Expression.Level	[Period].[2021-Q3].Level
Levels	Returns members from a specified Level using the Level Name or number	Hierarchy_Expression.Levels( Level_Number ) or Hierarchy_Expression.Levels( Level_Name )	[Period].[Period].LEVELS("Quarters").MEMBERS or [Period].[Period].LEVELS(1).MEMBERS
This
Ancestor	A function that returns the ancestor of a specified member at a specified level or at a specified distance from the member.	Ancestor(Member_Expression, Level_Expression) or Ancestor(Member_Expression, Distance)	Returns an Ancestor from n levels higher. This returns Total Years which is the parent of 2021 {Ancestor(TM1Member([Period].[Current Month].Item(0),0),2)} or Returns the Half that the period is in: {Ancestor([Period].[2021-Q3^2021/07],[Period].[Halves])}
Ancestors	Returns a set of ALL ancestors	Ancestors(Member_Expression, Level_Expression) Ancestors(Member_Expression, Distance)	Returns Ascendants without the current member {TM1Member([Period].[Current Month].Item(0),0).Ancestors}
Ascendants	Returns all of the ancestors of a member from the member itself up to the top of the member’s hierarchy	Ascendants(Member_Expression)	Returns the Current Month and parent then its parent {Ascendants(TM1Member([Period].[Current Month].Item(0),0))}
FirstSibling	Returns the first child of the parent of a member.	Member_Expression.FirstSibling	Returns the first child in the rollup that the member is in i.e. 2021/01 in this case {TM1Member([Period].[Current Month].Item(0),0).FirstSibling}
LastSibling	Returns the last child of the parent of a specified member.	Member_Expression.LastSibling	Returns the first child in the rollup that the member is in i.e. 2021/12 in this case {TM1Member([Period].[Current Month].Item(0),0).LastSibling}
FirstChild	Returns the first child of a specified member.	Member_Expression.FirstChild	Returns 2021/01 given 2021 {[Period].[2021].FirstChild}
LastChild	Returns the last child of a specified member.	Member_Expression.LastChild	Returns 2021/12 given 2021 {[Period].[2021].FirstChild}
Cousin	Returns the child member with the same relative position under a parent member as the specified child member.	Cousin( Member_Expression , Ancestor_Member_Expression )	Returns the same month in the specified year i.e. 2023/06: {Cousin([Period].[Period].[2021/06], [Period].[Period].[2023])}
OpeningPeriod	Returns the first sibling among the descendants of a specified level, optionally at a specified member.	OpeningPeriod( [ Level_Expression [ , Member_Expression ] ] )	{OpeningPeriod([Period].[Period].[Quarters],[Period].[Period].[2022-H2])} Returns 2022-Q3 as this is the first Quarter in 2022-H2
ClosingPeriod	Returns the member that is the last sibling among the descendants of a specified member at a specified level.	ClosingPeriod( [ Level_Expression [ ,Member_Expression ] ] )	{ClosingPeriod([Period].[Period].[Quarters],[Period].[Period].[2022-H2])} Returns 2022-Q4 being the last Quarter in 2022-H2.
ParallelPeriod	Returns a member from a prior period in the same relative position as a specified member.	ParallelPeriod( [ Level_Expression [ ,Index [ , Member_Expression ] ] ] )	{ParallelPeriod([Period].[Period].[Quarters],4,[Period].[Period].[2022-Q4])} Returns 2021-Q4 which is 4 quarters prior
Head	Returns the first specified number of elements in a set, while retaining duplicates.	Head(<Set> [ ,Count ] )	{HEAD([Period].[2020.FY].Children,6)}
Tail	Returns a subset from the end of a set.	Tail(<Set> [ ,Count ] )	{TAIL([Period].[2020.FY].Children,6)}
Lead	Returns the member that is a specified number of positions following a specified member along the member's level.	Member_Expression.Lead( Index )	{[Period].[2020-JUL].LEAD(6)} Gives you 2021-JAN
Lag	Returns the member that is a specified number of positions before a specified member at the member's level.	Member_Expression.Lag(Index)	{[Period].[2020-JUL].LAG(6)} Gives you 2020-JAN
Value	Default property of a member
TUPLE FUNCTIONS
Current	Returns the current tuple from a set during iteration.
Item	The Item function returns a member from the specified tuple.		TM1Member([Period].[Current Year].ITEM(1),0 )
SET FUNCTIONS AND EXPRESSIONS
AddCalculatedMembers	Returns a set generated by adding calculated members to that specified set.		Example needed
Children	Returns the set of children of a specified member.	Member_Expression.Children	Returns the months in the quarter in this case: [Period].[2021-Q3].Children
Siblings	Returns the siblings of a specified member, including the member itself.	Member_Expression.Siblings	Return all periods in the year based on current month. {TM1Member([Period].[Current Month].Item(0),0).Siblings}
Descendants	Review parameters e.g. SELF, ABOVE, LEAVES etc.	Descendants(Member_Expression [ , Level_Expression [ ,Desc_Flag ] ] )	Descendants(TM1SubsetToSet([Period].[Period], "FiscalPeriods" , "public" ),4,Leaves)
Members	Retrieves a set containing all of the members from a dimension, hierarchy, or level.	Dimension_Expression.Members Hierarchy_Expression.Members Level_Expression.Members	{[Period].Members} {[Period].[Halves].Members} In the first MDX, all members in the Period dimension are returned. In the second, members in the Halves level are returned.
Distinct	Evaluates a specified set, removes duplicate tuples from the set, and returns the resulting set.	Distinct(<Set>)	DISTINCT({[Period].[2020.FY].Children,[Period].[2020.Q3].Children}) The set would have repeated 2020-JAN, 2020-FEB and 2020-MAR but removed using Distinct
Hierarchize	Organize members into the Hierarchical order.	Hierarchize(<Set> [ , POST ] )	{Hierarchize([Period].[Halves].Members + [Period].[Fiscal Years].Members,POST)}
Union	Returns a set that is generated by the union of two sets, optionally retaining duplicate members.	Union(<Set 1>, <Set 2>[, ALL])	{UNION( [Period].[2020.FY].Children,[Period].[2021.FY].Children )} Combines set 1 and set 2 {UNION( [Period].[2020.FY].Children, {[Period].[2020-JAN]}, ALL )} Will combine the sets and in this case have a duplicate entry for 2020-JAN
Intersect	Returns members appearing in both sets. Duplicates can optionally be retained using the ALL parameter	Intersect(<Set>1 , Set_Expression2 [ , ALL ] )	INTERSECT( TM1SUBSETALL( [Period] ), TM1SubsetToSet( [Period], "_S-Quarter", "Public" ), ALL )
Except	Evaluates two sets and removes those tuples in the first set that also exist in the second set, optionally retaining duplicates.		{Except( {[Period].[2020.FY].Children}, {[Period].[2019-NOV],[Period].[2019-DEC]} )} Will return all months then exclude Nov and Dec
Extract	This is the opposite of the CrossJoin function and returns a set of tuples from the extracted hierarchy elements.	Extract(<Set>, Hierarchy_Expression1 [,Hierarchy_Expression2, ...n] )	Need an example using a Select statement
Filter	Exclude members based on criteria		FILTER( {TM1SUBSETALL( [Scenario] )}, VAL([Scenario].CurrentMember.Properties("Flag"))=1)
Order	Order contents of a set ASC, DESC, BASC, BDESC Note that ASC and DESC sorts within the member's parent. BASC and BDESC breaks the hierarchies and sort the elements like a flat list.		{ORDER( {TM1FILTERBYLEVEL( {TM1SUBSETALL( [Period] )}, 0)}, [Period].CurrentMember.Properties("Month"), BASC)} Returns a set of leaf level months orders by Month which is numeric. 2021-JAN, 2021-FEB etc. do not sort chronologically naturally.
Subset	Skip N number of members and returns the remainder like the MID function for characters. Position is zero-based.	Subset(<Set>, Start [ ,Count ] )	SUBSET( {TM1SubsetToSet([Period],"_S-All N","public")},5,4) In this example element 5 is 2019-May, so 2019-May and the next 3 elements are returned.
LastPeriods	Returns a set of members up to and including a specified member.	LastPeriods(Index [ ,Member_Expression ] )	LastPeriods(4,[Period].[Period].[2022/08]) Returns 2022/08 and the prior 3 periods - 4 members in all
PeriodsToDate	Returns a set of sibling members from the same level as a given member, starting with the first sibling and ending with the given member, as constrained by a specified level in the Time dimension.	PeriodsToDate( [ Level_Expression [ ,Member_Expression ] ] )	PeriodsToDate([Period].[Period].[Years],[Period].[Period].[2022-Q3^2022/08]) Returns 2022/01 and all periods to 2022/08
BottomCount	Sorts a set in ascending order, and returns the specified number of tuples in the specified set with the lowest values.	BottomCount(<Set>, Count [,Numeric_Expression])	BOTTOMCOUNT( TM1SubsetToSet([model].[model] , "_S-All N" , "public") , 10.0 , [SalesCube].([actvsbud].[Actual], [region].[Argentina], [account1].[Units], [Month].[1 Quarter])) Sorts and returns bottom 10 models based on units sold - lowest sales (SData)
BottomPercent	Sorts a set in ascending order, and returns a set of tuples with the lowest values whose cumulative total is equal to or greater than a specified percentage.	BottomPercent(<Set>, Percentage, Numeric_Expression)	BOTTOMPERCENT( TM1SubsetToSet([model].[model] , "_S-All N" , "public") , 10 , [SalesCube].([actvsbud].[Actual], [region].[Argentina], [account1].[Units], [Month].[1 Quarter])) Returns models where the aggregate value is within 10% of the total for all models
BottomSum	Sorts a set and returns the bottom most elements whose cumulative total is at most a specified value.	BottomSum(<Set>, Value, Numeric_Expression)	BOTTOMSUM( TM1SubsetToSet([model].[model] , "_S-All N" , "public") , 1000 , [SalesCube].([actvsbud].[Actual], [region].[Argentina], [account1].[Units], [Month].[1 Quarter])) Returns all members where the sum of units is 1000 or less
TopCount	Sorts a set in descending order and returns the specified number of elements with the highest values.	TopCount(<Set>,Count [ ,Numeric_Expression ] )	TOPCOUNT( TM1SubsetToSet([model].[model] , "_S-All N" , "public") , 10.0 , [SalesCube].([actvsbud].[Actual], [region].[Argentina], [account1].[Units], [Month].[1 Quarter])) Sorts and returns top 10 models based on units sold (SData)
TopPercent	Sorts a set in descending order, and returns a set of tuples with the highest values whose cumulative total is equal to or greater than a specified percentage.	TopPercent(<Set>, Percentage, Numeric_Expression)	TOPPERCENT( TM1SubsetToSet([model].[model] , "_S-All N" , "public") , 10 , [SalesCube].([actvsbud].[Actual], [region].[Argentina], [account1].[Units], [Month].[1 Quarter])) Returns models where the aggregate value contributes 10% of the total for all models
TopSum	Sorts a set and returns the topmost elements whose cumulative total is at least a specified value.	TopSum(<Set>, Value, Numeric_Expression)	TOPSUM( TM1SubsetToSet([model].[model] , "_S-All N" , "public") , 40000000, [SalesCube].([actvsbud].[Actual], [region].[Argentina], [account1].[Units], [Month].[1 Quarter])) Returns members where the sum is at least 40,000,000 - 3 members returned as the first 2 members was below 40 mil and needed a 3rd member to take it over the threshold.
DrilldownLevel	Drills down the members of a set to one level below the lowest level represented in the set, or to one level below an optionally specified level of a member represented in the set.	DrilldownLevel(<Set> [ , , Index ] ) DrilldownLevel(<Set> [ , Level_Expression ] )	DrilldownLevel( {[Period].[Quarters].Members}) Expands each member of quarters, only to 1 level, not recursive. Similarly DrilldownLevel({[Period].[2020.FY]}) expands the year showing the year and month. DrilldownLevel({[Period].[2020.FY HQ]},,0) will drill into the first hierarchy of the expression.
DrilldownLevelTop	Drills down the topmost members of a set, at a specified level, to one level below.	DrilldownLevelTop(<Set>, <count> [,[<level_expression>] [,[<numeric_expression>][,INCLUDE_CALC_MEMBERS]]])	DrilldownLevelTop( {[Period].[2020.FY HQ]}, 1, [FISCAL YEAR]) Will return 2020.FY HQ and the first half as we specified a count of 1. If we changed this to 2, would get the year and both Halves
DrilldownLevelBottom	Drills down the bottommost members of a set, at a specified level, to one level below.	DrilldownLevelBottom(<Set>, Count [ , Level_Expression [ ,Numeric_Expression ] ] )	Example needed - seems to behave like DrilldownLevelTop
DrilldownMember	Drills down the members in a specified set that are present in a second specified set.	DrillDownMember(<Set 1>, <Set 2> [,[<target_hierarchy>]] [,[RECURSIVE][,INCLUDE_CALC_MEMBERS]])	DrillDownMember({[Period].[Fiscal Periods].Children},{[Period].[2020.FY]}) Will return all Fiscal years and all periods for 2020.FY
DrilldownMemberTop	Drills down the members in a Set 1 that are present in Set 2. You can limit the result set to a specified number of members using the count parameter.	DrillDownMemberTop(<Set 1>, <Set 2>, <Count> [,[<Numeric_Expression>] [,[<Hierarchy>]] [,[RECURSIVE][,INCLUDE_CALC_MEMBERS]]])	DrillDownMemberTop({[Period].[Fiscal Periods].Children},{[Period].[2020.FY]},5) Will return all Fiscal years and first 5 periods for 2020.FY
DrillupLevel	Drill members that are below a certain level up	DrillupLevel(<Set>[, [level expression])	DrillUpLevel( {TM1SubsetAll([Period])}, [Halves]) Will return the top levels rolling down until Halves. All levels below Halves are removed i.e. Quarters and Leaves
DrillupMember	Returns members from Set 1 that are not descendants of members in Set 2	DrillupMember(<Set 1>, <Set 2>)	DrillUpMember( {Descendants([Period].[Fiscal Periods])}, {[Period].[2020.FY]}) Set 1 would have the Fiscal Periods total, each Fiscal Year and its Periods. Set 2 has the one Fiscal Year. The result is that for all Fiscal Years, all months are shown, except for those in 2020.FY, only the 2020.FY parent is shown as descendants are drilled up to this member.
DrilldownMemberBottom	Returns a specified number of members from Set 1 that exist in Set 2. Function can also be used to drill down on a hierarchy. Not sure if <hierarchy> is supported - not tested.	DrillDownMemberBottom(<Set 1>, <Set 2>, <count> [,[<numeric_expresion>] [,[<hierarchy>]] [,[RECURSIVE][,INCLUDE_CALC_MEMBERS]]])	DrilldownMemberBottom( {[Period].[Fiscal Periods].Children}, {[Period].[2020.FY]},5) Returns the Fiscal Years 2020.FY, 2021.FY etc. but drills down 2020.FY showing the first 5 children.
ToggleDrillState	Per TM1ToggleDrillState
DIMENSION, HIERARCHY and LEVEL FUNCTIONS
Dimension.Name	Intrinsic DIMENSION_NAME
Hierarchy.Name	Intrinsic HIERARCHY_NAME
Level.Name	Intrinsic LEVEL_NAME
* Used in conjunction with other functions to obtain information about the members of a dimension, hierarchy, or level.
COMMENTING
//	Inline comments or own line
--	Inline comments or own line
/*…*/	Blocked comments
NUMERIC FUNCTIONS
LEN	Returns the length of a string		FILTER({TM1SUBSETALL( [Period] )}, LEN([Period].CurrentMember.Name)=4)
VAL	Returns the value of a string (Nulls evaluate to 0)		FILTER( {TM1SUBSETALL( [Scenario] )}, VAL([Scenario].CurrentMember.Properties("Flag"))=1)
CoalesceEmpty	Converts an Empty but not Null value to a specified value	CoalesceEmpty( <Numeric_Expression> [ ,<Replacement_Numeric_Expression>,...n] )
Aggregate		Need examples using SELECT
Avg		Need examples using SELECT
Count			FILTER({TM1FILTERBYLEVEL({TM1SUBSETALL( [Period] )},0)}, COUNT({ Intersect({[Period].Members},{[Period].CurrentMember},ALL) })>5) Returns all members that appear in the hierarchy more than 5 times. This is due to multiple rollups like Quarters, YTD etc. Could be used to find members with multiple parents where they should only have one.
Correlation
Covariance
CovarianceN
DistinctCount
LinRegIntercept
LinRegPoint
LinRegR2
LinRegSlope
LinRegVariance
LookupCube
Max
Min
Median
Rank
StdDev	Same as StDev - Alias
StDev
StdDevP	Same as StDevP - Alias
StDevP
Sum
Var
Variance	Same as Var - Alias
VarP
VarianceP	Same as VarP - Alias
TM1 Specific MDX Functions	https://www.ibm.com/docs/en/planning-analytics/2.0.0?topic=mfs-tm1-specific-mdx-functions-1
TM1Member	Returns a member from a specified tuple/subset. Avoid using as PAW translates any subset with TM1Member to underlying code.	TM1Member	TM1Member([Period].[_S-Current Recharge Quarter].ITEM(1),0 ),
TM1FilterbyPattern	Returns members matching a specified pattern. An asterisk is used for any characters before or after, a question mark to indicate a particular position only.	TM1FILTERBYPATTERN( <set>, <pattern_str> ) Undocumented is the 3rd parameter for an attribute: TM1FILTERBYPATTERN( <set>, <pattern_str>[, <attribute>] )	{TM1FILTERBYPATTERN( {TM1SUBSETALL( [Period] )}, "*JUN*")} Returns all members containing JUN e.g. 2020-JUN, 2021-JUN {TM1FILTERBYPATTERN( {TM1SUBSETALL( [Period] )}, "202?-JUN")} Returns all Jun members in the 2020's, excludes 2019-JUN
TM1FilterByLevel	Returns members matching a level number (0=Leaf)	TM1FILTERBYLEVEL( <set>, <level_number>)	{TM1FILTERBYLEVEL( {TM1SUBSETALL( [Period] )}, 0)} Returns all Leaf elements i.e. those at the lowest level. May include String and Numeric, not only Numeric.
TM1DrillDownMember	Drills down a member like the expand button in TM1 but for each Member in Set 2. Seems to behave exactly like DrillDownMember above.	TM1DRILLDOWNMEMBER( <set1>, <set2>|ALL [,RECURSIVE] )	TM1DrillDownMember({[Period].[Fiscal Periods].Children},{[Period].[2020.FY]}) Will return all Fiscal years and all periods for 2020.FY
TM1Sort	Sorts a set alphabetically, ignores hierarchies	TM1SORT( <set>, ASC|DESC )	TM1SORT( {TM1SUBSETALL( [Period] )}, ASC)} Will sort all elements alphabetically returning a mix of N and C levels
TM1SortByIndex	Sorts a set by index/ordinal	TM1SORTBYINDEX( <set>, ASC|DESC )	TM1SORTINDEX( {TM1SUBSETALL( [Period] )}, ASC)} Will sort all elements based on their ordinal position or Index in the hierarchy
TM1SubsetAll	Returns all Elements in a dimension, distinct, not all members. Where an element appears in multiple rollups, only the first occurrence is returned, like using DISTINCT()	TM1SUBSETALL([<dimname>])	{TM1SUBSETALL( [Period] )} Will return all elements from Period without duplicates.
TM1SubsetToSet	Inserts the elements of a set into the current set	TM1SubsetToSet(<Dimension>,<Hierarchy>,<SubsetName>[,<Public|Private])	TM1SubsetToSet([Period], "_S-All N", "public") Returns all the members from the underlying public subset.
TM1TupleSize	A count of members in the set/tuple	TM1TupleSize
TM1SubsetBasis	A placeholder generated by the MDX recorded in Architect/Perspectives. Replace with a valid tuple.		Not giving an example - if you see it, fix your code.
TM1RollUp	Rollup members from Set 1 to their parents if specified in Set 2	TM1Rollup(<Set 1>, <Set 2>)	TM1ROLLUP({[Period].[2020.FY].Children},{[Period].[2020-FEB],[Period].[2020-MAR]}) Will return all months and then roll up to the parents of 2020-FEB and 2020-MAR
TM1ToggleDrillState	Per MS MDX - Toggles the drill state of members between drilldown and drillllup modes. Need a better example on this.	TM1TOGGLEDRILLSTATE(<Set 1>,<Set 2>,EXPAND_ABOVE|EXPAND_BELOW,RECURSIVE) )	TM1TOGGLEDRILLSTATE( {[Period].[FISCAL PERIODS].Children}, {DESCENDANTS([Period].[2021.FY])}, EXPAND_BELOW, RECURSIVE )
TM1ToggleExpandMode	Used to Expand Above or Below	{TM1ToggleExpandMode(<set>,EXPAND_ABOVE|EXPAND_BELOW)}	{TM1ToggleExpandMode({Descendants([Period].[2021.FY])},EXPAND_ABOVE)}
MDX VIEW RELATED KEYWORDS
With	WITH MEMBER...
Member
As
On
Select
From
Rows
Columns
Pages
Sections
Chapters
NonEmpty	Returns the set of tuples that are not empty from a specified set, based on the cross product of the specified set with a second set.	NONEMPTY(<Set>1 [,set_expression2])
CrossJoin	It returns a set of tuples representing the cartesian product of the sets passed into it as parameters. Enables you to create 'nested' or 'crosstabbed' axes in queries, same as using *	Crossjoin(<Set>1 ,Set_Expression2 [,...n] )
NonEmptyCrossJoin	Deprecated - Do not use - Use Non Empty
Where
Solve_Order
Format_String
Clear	CLEAR CALCULATIONS
RollupChildren
TM1Ignore_BadTuples
TM1Format_String
TM1RuleDerived
TM1Subset_Ident
TM1Update
TM1Updateable
TM1BangPrefix

The MDX View related functions and related keywords above still need some expansion and some examples which will follow in the future.

As mentioned at the outset, please feedback to improve this post for everyone and let me know of any errors that need correction, examples that need updating etc. etc.

Thanks to Wim, Adam, Declan, Ryan and others who have added input along the way.

#PlanningAnalyticswithWatson