Dave Keenan & Douglas Blumeyer's guide to RTT/Conventions for names, variables, units, and notations: Difference between revisions

Latest revision as of 01:44, 7 August 2025

This is an appendix to Dave Keenan & Douglas Blumeyer's guide to RTT. The tables in this article present our recommendations for communicating about regular temperament theory (RTT), in particular the names and notations for temperament matrices, tuning schemes, interval complexities, and measurement units.

Our recommendations are designed to make this topic easy to learn for musicians who do not have technical backgrounds, though we have generally deferred to established mathematical, scientific, and engineering conventions for the benefit of those who do.

See here for more information on our variation on extended bra-ket notation.

We've followed a variable styling convention, explained in the table below, which we hope serves as an aid to quickly identifying objects and remembering their properties and purposes, but at the least we hope our choices are unobtrusive. In short, the objects with simple units of primes, generators or cents, i.e. the things which are actually audible in our application, are distinguished by upright formatting, while other variables are italic as is conventional. This is crossed with the linear-algebra convention that objects of order-1 like vectors are bolded and order-2 like matrices are uppercased:


	Units →	Simple units	Compound or no units
↓ Order	↓ Style →	Roman (upright)	Italic
0	lowercase	scalar (with simple unit)	scalar (with no unit)
1	bold lowercase	vector	map (row vector)
2	UPPERCASE	BASIS or LIST (of vectors)	MATRIX

We present our conventions here in three separate sections, one for each level of this article series: basic, intermediate, and advanced. The basic section contains only information covered in the basic part of the series, the intermediate section contains both basic and intermediate, and the advanced section contains it all (that is to say, the sections are cumulative)^{[note 1]}. We expect that for most readers, the basic tier will be the best reference (this is the reference designed primarily for musicians interested in RTT, as opposed to scientists, engineers, mathematicians, or theoreticians), and so we've left the other two sections initially collapsed.

Basic

Objects


Equivalent expressions	Variable	Name	Units			Shape		Type		EBK notation		Subobjects				Notes
Equivalent expressions	Variable	Name	Unreduced	Reduced	Read as	Unreduced	Reduced	Numeric	Structural	Row-first	Col-first	Row	Column	Diagonal	Entry	Notes
Mapping
	[math]\displaystyle{ \textbf{i} }[/math]	(Just) interval		[math]\displaystyle{ \small 𝗽 }[/math]	Primes		[math]\displaystyle{ \scriptsize (d, 1) }[/math]	Integer	Vector		[...⟩				[math]\displaystyle{ \mathrm{i}_i }[/math]	Specific type: Vector (prime-count vector or PC-vector) Jargon name: Monzo
	[math]\displaystyle{ M }[/math]	(Temperament) mapping (matrix)		[math]\displaystyle{ \small 𝗴 }[/math]/[math]\displaystyle{ \small 𝗽 }[/math]	Generators per prime		[math]\displaystyle{ \scriptsize (r, d) }[/math]	Integer	Matrix	[⟨...] ...}	⟨[...} ...]	[math]\displaystyle{ 𝒎_i }[/math]			[math]\displaystyle{ m_{ij} }[/math]	Jargon name: Val list
[math]\displaystyle{ M\textbf{i} }[/math]	[math]\displaystyle{ \textbf{y} }[/math]	Mapped interval	[math]\displaystyle{ \scriptsize \begin{array} {c} M \\[-2pt] 𝗴 \hspace{-2mu} / \hspace{-2mu} \cancel{𝗽} \end{array} \begin{array} {c} \\[-2pt] · \end{array} \begin{array} {c} \textbf{i} \\[-2pt] \cancel{𝗽} \end{array} }[/math]	[math]\displaystyle{ \small 𝗴 }[/math]	Generators	[math]\displaystyle{ \scriptsize \! \! \begin{array} {c} M \\[-3pt] (r, \cancel{d}) \end{array} \! \! \begin{array} {c} \textbf{i} \\[-3pt] (\cancel{d}, 1) \end{array} \! \! }[/math]	[math]\displaystyle{ \scriptsize (r, 1) }[/math]	Integer	Vector		[...}					Specific type: Generator-count vector (GC-vector) Jargon name: tmonzo; mnemonic: [math]\displaystyle{ \textbf{y} }[/math]nterval
	[math]\displaystyle{ 𝒎 }[/math]	(Temperament) map		[math]\displaystyle{ \small 𝗴 }[/math]/[math]\displaystyle{ \small 𝗽 }[/math]	Generators per prime		[math]\displaystyle{ \scriptsize (1, d) }[/math]	Integer	Vector	⟨...]					[math]\displaystyle{ m_i }[/math]	Jargon name: val
	[math]\displaystyle{ d }[/math]	dimensionality					[math]\displaystyle{ \scriptsize (1, 1) }[/math]	Integer	Scalar
	[math]\displaystyle{ r }[/math]	Rank					[math]\displaystyle{ \scriptsize (1, 1) }[/math]	Integer	Scalar
Tuning
	[math]\displaystyle{ {\large\textbf{𝓁}}\hspace{2mu} }[/math]	Log-prime map		[math]\displaystyle{ \small\mathsf{oct} }[/math]/[math]\displaystyle{ \small 𝗽 }[/math]	Octaves per prime		[math]\displaystyle{ \scriptsize (1, d) }[/math]	Real	Vector	⟨...]					[math]\displaystyle{ {\large 𝓁}\hspace{2mu}_i }[/math]
[math]\displaystyle{ 1200×{\large\textbf{𝓁}}\hspace{2mu} }[/math]	[math]\displaystyle{ 𝒋 }[/math]	Just(-prime) tuning map		[math]\displaystyle{ \mathsf{¢} }[/math]/[math]\displaystyle{ \small 𝗽 }[/math]	Cents per prime		[math]\displaystyle{ \scriptsize (1, d) }[/math]	Real	Vector	⟨...]					[math]\displaystyle{ j_i }[/math]
	[math]\displaystyle{ 𝒈 }[/math]	Generator tuning map		[math]\displaystyle{ \mathsf{¢} }[/math]/[math]\displaystyle{ \small 𝗴 }[/math]	Cents per generator		[math]\displaystyle{ \scriptsize (1, r) }[/math]	Real	Vector	{...]					[math]\displaystyle{ g_i }[/math]
[math]\displaystyle{ 𝒈M }[/math]	[math]\displaystyle{ 𝒕 }[/math]	(Tempered-prime) tuning map	[math]\displaystyle{ \scriptsize \begin{array} {c} 𝒈 \\[-2pt] {\small\mathsf{¢}} \hspace{-2mu} / \hspace{-2mu} \cancel{𝗴} \end{array} \begin{array} {c} \\[-2pt] · \end{array} \begin{array} {c} 𝑀 \\[-2pt] \cancel{𝗴} \hspace{-2mu} / \hspace{-2mu} 𝗽 \end{array} }[/math]	[math]\displaystyle{ \mathsf{¢} }[/math]/[math]\displaystyle{ \small 𝗽 }[/math]	Cents per prime	[math]\displaystyle{ \scriptsize \! \! \begin{array} {c} 𝒈 \\[-3pt] \left(1, \cancel{r}\right) \end{array} \! \! \begin{array} {c} M \\[-3pt] \left(\cancel{r}, d\right) \end{array} \! \! }[/math]	[math]\displaystyle{ \scriptsize (1, d) }[/math]	Real	Vector	⟨...]					[math]\displaystyle{ t_i }[/math]
[math]\displaystyle{ 𝒕 - 𝒋 }[/math]	[math]\displaystyle{ 𝒓 }[/math]	Retuning (or mistuning) map		[math]\displaystyle{ \mathsf{¢} }[/math]/[math]\displaystyle{ \small 𝗽 }[/math]	Cents per prime		[math]\displaystyle{ \scriptsize (1, d) }[/math]	Real	Vector	⟨...]					[math]\displaystyle{ r_i }[/math]	Previous name: prime error map
[math]\displaystyle{ 𝒋\textbf{i} }[/math]	[math]\displaystyle{ \mathrm{o} }[/math]	(Just) (interval) size	[math]\displaystyle{ \scriptsize \begin{array} {c} 𝒋 \\[-2pt] {\small\mathsf{¢}} \hspace{-2mu} / \hspace{-2mu} \cancel{𝗽} \end{array} \begin{array} {c} \\[-2pt] · \end{array} \begin{array} {c} \textbf{i} \\[-2pt] \cancel{𝗽} \end{array} }[/math]	[math]\displaystyle{ \mathsf{¢} }[/math]	Cents	[math]\displaystyle{ \scriptsize \! \! \begin{array} {c} 𝒋 \\[-3pt] \left(1, \cancel{d}\right) \end{array} \! \! \begin{array} {c} \textbf{i} \\[-3pt] \left(\cancel{d}, 1\right) \end{array} \! \! }[/math]	[math]\displaystyle{ \scriptsize (1, 1) }[/math]	Real	Scalar							Mnemonic: [math]\displaystyle{ \mathrm{o} }[/math]riginal size
[math]\displaystyle{ 𝒈M\textbf{i} }[/math] [math]\displaystyle{ 𝒕\textbf{i} }[/math]	[math]\displaystyle{ \mathrm{a} }[/math]	Tempered (interval) size	[math]\displaystyle{ \scriptsize \begin{array} {c} 𝒕 \\[-2pt] {\small\mathsf{¢}} \hspace{-2mu} / \hspace{-2mu} \cancel{𝗽} \end{array} \begin{array} {c} \\[-2pt] · \end{array} \begin{array} {c} \textbf{i} \\[-2pt] \cancel{𝗽} \end{array} }[/math]	[math]\displaystyle{ \mathsf{¢} }[/math]	Cents	[math]\displaystyle{ \scriptsize \! \! \begin{array} {c} 𝒕 \\[-3pt] \left(1, \cancel{d}\right) \end{array} \! \! \begin{array} {c} \textbf{i} \\[-3pt] \left(\cancel{d}, 1\right) \end{array} \! \! }[/math]	[math]\displaystyle{ \scriptsize (1, 1) }[/math]	Real	Scalar							Mnemonic: [math]\displaystyle{ \mathrm{a} }[/math]ltered size
[math]\displaystyle{ 𝒕\textbf{i} - 𝒋\textbf{i} }[/math] [math]\displaystyle{ a - o }[/math] [math]\displaystyle{ 𝒓\textbf{i} }[/math]	[math]\displaystyle{ \mathrm{e} }[/math]	(Interval) error	[math]\displaystyle{ \scriptsize \begin{array} {c} 𝒓 \\[-2pt] {\small\mathsf{¢}} \hspace{-2mu} / \hspace{-2mu} \cancel{𝗽} \end{array} \begin{array} {c} \\[-2pt] · \end{array} \begin{array} {c} \textbf{i} \\[-2pt] \cancel{𝗽} \end{array} }[/math]	[math]\displaystyle{ \mathsf{¢} }[/math]	Cents	[math]\displaystyle{ \scriptsize \! \! \begin{array} {c} 𝒓 \\[-3pt] \left(1, \cancel{d}\right) \end{array} \! \! \begin{array} {c} \textbf{i} \\[-3pt] \left(\cancel{d}, 1\right) \end{array} \! \! }[/math]	[math]\displaystyle{ \scriptsize (1, 1) }[/math]	Real	Scalar
Optimization
	[math]\displaystyle{ p }[/math]	Optimization power					[math]\displaystyle{ \scriptsize (1, 1) }[/math]	Real	Scalar
	[math]\displaystyle{ \llangle\,·\,\rrangle_p }[/math]	Power mean ([math]\displaystyle{ p }[/math]-mean)					[math]\displaystyle{ \scriptsize (1, 1) }[/math]	Real	Scalar
Damage
	[math]\displaystyle{ c }[/math]	Complexity	[math]\displaystyle{ \small\mathsf{𝟙}\scriptsize\mathsf{(C)} }[/math]^{[note 2]}	[math]\displaystyle{ \small\mathsf{(C)} }[/math]	Complexity weight		[math]\displaystyle{ \scriptsize (1, 1) }[/math]	Real	Scalar
[math]\displaystyle{ \dfrac1c }[/math]	[math]\displaystyle{ s }[/math]	Simplicity	[math]\displaystyle{ \small\mathsf{𝟙}\scriptsize\mathsf{(S)} }[/math]	[math]\displaystyle{ \small\mathsf{(S)} }[/math]	Simplicity weight		[math]\displaystyle{ \scriptsize (1, 1) }[/math]	Real	Scalar
[math]\displaystyle{ c }[/math] or [math]\displaystyle{ s }[/math]	[math]\displaystyle{ w }[/math]	Weight	[math]\displaystyle{ \small\mathsf{𝟙}\scriptsize\mathsf{(C)} }[/math] or 𝟙[math]\displaystyle{ \small\mathsf{(S)} }[/math]	[math]\displaystyle{ \small\mathsf{(C)} }[/math] or [math]\displaystyle{ \small\mathsf{(S)} }[/math]	Complexity weight or simplicity weight		[math]\displaystyle{ \scriptsize (1, 1) }[/math]	Real	Scalar
[math]\displaystyle{ \abs{\mathrm{e}} w }[/math]	[math]\displaystyle{ \mathrm{d} }[/math]	Damage	[math]\displaystyle{ \scriptsize \begin{array} {c} \abs{\mathrm{e}} \\[-2pt] {\small\mathsf{¢}} \end{array} \begin{array} {c} \\[-2pt] · \end{array} \begin{array} {c} w \\[-2pt] \mathsf{(U, C, \text{or}\,S)} \end{array} }[/math]	[math]\displaystyle{ \mathsf{¢}\small\mathsf{(U)} }[/math] or [math]\displaystyle{ \mathsf{¢}\small\mathsf{(C)} }[/math] or [math]\displaystyle{ \mathsf{¢}\small\mathsf{(S)} }[/math]	(See damages table)	[math]\displaystyle{ \scriptsize \! \! \begin{array} {c} \abs{\mathrm{e}} \\[-3pt] \left(1, \cancel{1}\right) \end{array} \! \! \begin{array} {c} w \\[-3pt] \left(\cancel{1}, 1\right) \end{array} \! \! }[/math]	[math]\displaystyle{ \scriptsize (1, 1) }[/math]	Real	Scalar
Target-intervals
	[math]\displaystyle{ \mathrm{T} }[/math]	Target-interval list		[math]\displaystyle{ \small 𝗽 }[/math]	Primes		[math]\displaystyle{ \scriptsize (d, k) }[/math]	Integer	Matrix		[[...⟩ ...]		[math]\displaystyle{ \textbf{t}_i }[/math]		[math]\displaystyle{ \mathrm{t}_{ij} }[/math]
[math]\displaystyle{ M\mathrm{T} }[/math]	[math]\displaystyle{ \mathrm{Y} }[/math]	Mapped target-interval list	[math]\displaystyle{ \scriptsize \begin{array} {c} M \\[-2pt] 𝗴 \hspace{-2mu} / \hspace{-2mu} \cancel{𝗽} \end{array} \begin{array} {c} \\[-2pt] · \end{array} \begin{array} {c} \mathrm{T} \\[-2pt] \cancel{𝗽} \end{array} }[/math]	[math]\displaystyle{ \small 𝗴 }[/math]	Generators	[math]\displaystyle{ \scriptsize \! \! \begin{array} {c} M \\[-3pt] \left(r, \cancel{d}\right) \end{array} \! \! \begin{array} {c} \mathrm{T} \\[-3pt] \left(\cancel{d}, k\right) \end{array} \! \! }[/math]	[math]\displaystyle{ \scriptsize (r, k) }[/math]	Integer	Matrix		[[...} ...]		[math]\displaystyle{ \textbf{y}_i }[/math]		[math]\displaystyle{ \mathrm{y}_{ij} }[/math]	Mnemonic: looks like bent-up 'T', or cross between 'M' and 'T'
[math]\displaystyle{ 𝒋\mathrm{T} }[/math]	[math]\displaystyle{ \textbf{o} }[/math]	Target-interval (just) size list	[math]\displaystyle{ \scriptsize \begin{array} {c} 𝒋 \\[-2pt] {\small\mathsf{¢}} \hspace{-2mu} / \hspace{-2mu} \cancel{𝗽} \end{array} \begin{array} {c} \\[-2pt] · \end{array} \begin{array} {c} \mathrm{T} \\[-2pt] \cancel{𝗽} \end{array} }[/math]	[math]\displaystyle{ \mathsf{¢} }[/math]	Cents	[math]\displaystyle{ \scriptsize \! \! \begin{array} {c} 𝒋 \\[-3pt] \left(1, \cancel{d}\right) \end{array} \! \! \begin{array} {c} \mathrm{T} \\[-3pt] \left(\cancel{d}, k\right) \end{array} \! \! }[/math]	[math]\displaystyle{ \scriptsize (1, k) }[/math]	Real	List	[...]					[math]\displaystyle{ \mathrm{o}_i }[/math]	Mnemonic: [math]\displaystyle{ \textbf{o} }[/math]riginal size list
[math]\displaystyle{ 𝒕\mathrm{T} }[/math] [math]\displaystyle{ 𝒈M\mathrm{T} }[/math]	[math]\displaystyle{ \textbf{a} }[/math]	Tempered target-interval size list	[math]\displaystyle{ \scriptsize \begin{array} {c} 𝒕 \\[-2pt] {\small\mathsf{¢}} \hspace{-2mu} / \hspace{-2mu} \cancel{𝗽} \end{array} \begin{array} {c} \\[-2pt] · \end{array} \begin{array} {c} \mathrm{T} \\[-2pt] \cancel{𝗽} \end{array} }[/math]	[math]\displaystyle{ \mathsf{¢} }[/math]	Cents	[math]\displaystyle{ \scriptsize \! \! \begin{array} {c} 𝒕 \\[-3pt] \left(1, \cancel{d}\right) \end{array} \! \! \begin{array} {c} \mathrm{T} \\[-3pt] \left(\cancel{d}, k\right) \end{array} \! \! }[/math]	[math]\displaystyle{ \scriptsize (1, k) }[/math]	Real	List	[...]					[math]\displaystyle{ \mathrm{a}_i }[/math]	Mnemonic: [math]\displaystyle{ \textbf{a} }[/math]ltered size list
[math]\displaystyle{ 𝒕\mathrm{T} - 𝒋\mathrm{T} }[/math] [math]\displaystyle{ \textbf{a} - \textbf{o} }[/math] [math]\displaystyle{ 𝒓\mathrm{T} }[/math]	[math]\displaystyle{ \textbf{e} }[/math]	Target-interval error list	[math]\displaystyle{ \scriptsize \begin{array} {c} 𝒓 \\[-2pt] {\small\mathsf{¢}} \hspace{-2mu} / \hspace{-2mu} \cancel{𝗽} \end{array} \begin{array} {c} \\[-2pt] · \end{array} \begin{array} {c} \mathrm{T} \\[-2pt] \cancel{𝗽} \end{array} }[/math]	[math]\displaystyle{ \mathsf{¢} }[/math]	Cents	[math]\displaystyle{ \scriptsize \! \! \begin{array} {c} 𝒓 \\[-3pt] \left(1, \cancel{d}\right) \end{array} \! \! \begin{array} {c} \mathrm{T} \\[-3pt] \left(\cancel{d}, k\right) \end{array} \! \! }[/math]	[math]\displaystyle{ \scriptsize (1, k) }[/math]	Real	List	[...]					[math]\displaystyle{ \mathrm{e}_i }[/math]
[math]\displaystyle{ C }[/math] or [math]\displaystyle{ S }[/math]	[math]\displaystyle{ W }[/math]	Target-interval weight matrix	[math]\displaystyle{ \small\mathsf{𝟙}\scriptsize\mathsf{(C)} }[/math] or [math]\displaystyle{ \small\mathsf{𝟙}\scriptsize\mathsf{(S)} }[/math] or [math]\displaystyle{ \small\mathsf{𝟙}\scriptsize\mathsf{(U)} }[/math]	[math]\displaystyle{ \small\mathsf{(C)} }[/math] or [math]\displaystyle{ \small\mathsf{(S)} }[/math] or [math]\displaystyle{ \small\mathsf{(U)} }[/math]	Complexity weight or simplicity weight		[math]\displaystyle{ \scriptsize (k, k) }[/math]	Real	Matrix		[[...] ...]			[math]\displaystyle{ 𝒘 }[/math]	[math]\displaystyle{ w_i }[/math]
	[math]\displaystyle{ C }[/math]	Target-interval complexity weight matrix	[math]\displaystyle{ \small\mathsf{𝟙}\scriptsize\mathsf{(C)} }[/math]	[math]\displaystyle{ \small\mathsf{(C)} }[/math]	Complexity weight		[math]\displaystyle{ \scriptsize (k, k) }[/math]	Real	Matrix		[[...] ...]			[math]\displaystyle{ 𝒄 }[/math]	[math]\displaystyle{ c_i }[/math]
[math]\displaystyle{ \dfrac1C }[/math]	[math]\displaystyle{ S }[/math]	Target-interval simplicity weight matrix	[math]\displaystyle{ \small\mathsf{𝟙}\scriptsize\mathsf{(S)} }[/math]	[math]\displaystyle{ \small\mathsf{(S)} }[/math]	Simplicity weight		[math]\displaystyle{ \scriptsize (k, k) }[/math]	Real	Matrix		[[...] ...]			[math]\displaystyle{ 𝒔 }[/math]	[math]\displaystyle{ s_i }[/math]	Entry-wise reciprocal of [math]\displaystyle{ C }[/math]
[math]\displaystyle{ \abs{\textbf{e}} W }[/math]	[math]\displaystyle{ \textbf{d} }[/math]	Target-interval damage list^{[note 3]}	[math]\displaystyle{ \scriptsize \begin{array} {c} \abs{\textbf{e}} \\[-2pt] {\small\mathsf{¢}} \end{array} \begin{array} {c} \\[-2pt] · \end{array} \begin{array} {c} W \\[-2pt] (\mathsf{U, C, \text{or}\,S}) \end{array} }[/math]	[math]\displaystyle{ \mathsf{¢}\small\mathsf{(U)} }[/math], [math]\displaystyle{ \mathsf{¢}\small\mathsf{(C)} }[/math], or [math]\displaystyle{ \mathsf{¢}\small\mathsf{(S)} }[/math]	Weighted cents	[math]\displaystyle{ \scriptsize \! \! \begin{array} {c} \abs{\textbf{e}} \\[-3pt] \left(1, \cancel{k}\right) \end{array} \! \! \begin{array} {c} W \\[-3pt] \left(\cancel{k}, k\right) \end{array} \! \! }[/math]	[math]\displaystyle{ \scriptsize (1, k) }[/math]	Real	List	[...]					[math]\displaystyle{ \mathrm{d}_i }[/math]
	[math]\displaystyle{ k }[/math]	Target-interval count					[math]\displaystyle{ \scriptsize (1, 1) }[/math]	Integer	Scalar							Mnemonic: [math]\displaystyle{ k }[/math]ount
Held-intervals
	[math]\displaystyle{ \mathrm{H} }[/math]	Held-interval basis		[math]\displaystyle{ \small 𝗽 }[/math]	Primes		[math]\displaystyle{ \scriptsize (d, h) }[/math]		Matrix		[[...⟩ ...]		[math]\displaystyle{ \textbf{h}_i }[/math]		[math]\displaystyle{ \mathrm{h}_{ij} }[/math]
	[math]\displaystyle{ h }[/math]	Held-interval count					[math]\displaystyle{ \scriptsize (1, 1) }[/math]	Integer	Scalar
Exploring temperaments
	[math]\displaystyle{ \mathrm{C} }[/math]	Comma basis		[math]\displaystyle{ \small 𝗽 }[/math]	Primes		[math]\displaystyle{ \scriptsize (d, n) }[/math]	Integer	Matrix		[[...⟩ ...]		[math]\displaystyle{ \textbf{c}_i }[/math]		[math]\displaystyle{ \mathrm{c}_{ij} }[/math]	Jargon name: monzo list
	[math]\displaystyle{ \textbf{c} }[/math]	Comma		[math]\displaystyle{ \small 𝗽 }[/math]	Primes		[math]\displaystyle{ \scriptsize (d, 1) }[/math]	Integer	Vector		[...⟩				[math]\displaystyle{ \mathrm{c}_i }[/math]	Specific type: vector (prime-count vector or PC-vector)

Units

We recommend using a narrow no-break space (U+202F) between quantities and their units.^{[note 4]} For how to type this, see the WinCompose section below.


Symbol	Name	Vectorized
[math]\displaystyle{ \small 𝗴 }[/math]	Generators	Yes
[math]\displaystyle{ \small 𝗽 }[/math]	Primes	Yes
[math]\displaystyle{ \mathsf{¢} }[/math]^{[note 5]}	Cents
[math]\displaystyle{ \mathsf{¢}\small\mathsf{(U)} }[/math]	Unity-weighted cents
[math]\displaystyle{ \mathsf{¢}\small\mathsf{(C)} }[/math]	Complexity-weighted cents
[math]\displaystyle{ \mathsf{¢}\small\mathsf{(S)} }[/math]	Simplicity-weighted cents
[math]\displaystyle{ \small\mathsf{oct} }[/math]	Octaves
[math]\displaystyle{ \small\mathsf{(C)} }[/math]	Complexity weight
[math]\displaystyle{ \small\mathsf{(S)} }[/math]	Simplicity weight

Tuning schemes

Copied from Systematic tuning scheme names.


Damage weight	Optimization power	Systematic name
<none>	∞	Minimax-U
Complexity		Minimax-C
1/Complexity		Minimax-S
<none>	2	MiniRMS-U
Complexity		MiniRMS-C
1/Complexity		MiniRMS-S
<none>	1	Miniaverage-U
Complexity		Miniaverage-C
1/Complexity		Miniaverage-S

Damages


Quantity		Unit
Abbreviation	Name	Symbol	Name
U-damage	Unity-weight damage	[math]\displaystyle{ \mathsf{¢}\small\mathsf{(U)} }[/math]	Unity-weighted cents
C-damage	Complexity-weight damage	[math]\displaystyle{ \mathsf{¢}\small\mathsf{(C)} }[/math]	Complexity-weighted cents
S-damage	Simplicity-weight damage	[math]\displaystyle{ \mathsf{¢}\small\mathsf{(S)} }[/math]	Simplicity-weighted cents

Complexity and simplicity


Quantity		Unit
Abbreviation	Name	Symbol	Name
C	Complexity	[math]\displaystyle{ \small\mathsf{(C)} }[/math]	Complexity weight
S	Simplicity	[math]\displaystyle{ \small\mathsf{(S)} }[/math]	Simplicity weight

Intermediate

Objects


Equivalent expressions	Variable	Name	Units			Shape		Type		EBK notation		Subobjects				Notes
Equivalent expressions	Variable	Name	Unreduced	Reduced	Read as	Unreduced	Reduced	Numeric	Structural	Row-first	Col-first	Row	Col	Diag	Entry	Notes
Mapping
	[math]\displaystyle{ \textbf{i} }[/math]	(Just) interval		[math]\displaystyle{ \small 𝗽 }[/math]	Primes		[math]\displaystyle{ \scriptsize (d, 1) }[/math]	Integer	Vector		[...⟩				[math]\displaystyle{ \mathrm{i}_i }[/math]	Specific type: vector (prime-count vector or PC-vector) Jargon name: monzo
	[math]\displaystyle{ M }[/math]	(Temperament) mapping (matrix)		[math]\displaystyle{ \small 𝗴 }[/math]/[math]\displaystyle{ \small 𝗽 }[/math]	Generators per prime		[math]\displaystyle{ \scriptsize (r, d) }[/math]	Integer	Matrix	[⟨...] ...}	⟨[...} ...]	[math]\displaystyle{ 𝒎_i }[/math]			[math]\displaystyle{ m_{ij} }[/math]	Jargon name: val list
[math]\displaystyle{ M\textbf{i} }[/math]	[math]\displaystyle{ \textbf{y} }[/math]	Mapped interval	[math]\displaystyle{ \scriptsize \begin{array} {c} M \\[-2pt] 𝗴 \hspace{-2mu} / \hspace{-2mu} \cancel{𝗽} \end{array} \begin{array} {c} \\[-2pt] · \end{array} \begin{array} {c} \textbf{i} \\[-2pt] \cancel{𝗽} \end{array} }[/math]	[math]\displaystyle{ \small 𝗴 }[/math]	Generators	[math]\displaystyle{ \scriptsize \! \! \begin{array} {c} M \\[-3pt] \left(r, \cancel{d}\right) \end{array} \! \! \begin{array} {c} \textbf{i} \\[-3pt] \left(\cancel{d}, 1\right) \end{array} \! \! }[/math]	[math]\displaystyle{ \scriptsize (r, 1) }[/math]	Integer	Vector		[...}					Specific type: generator-count vector (GC-vector) Jargon name: tmonzo; mnemonic: [math]\displaystyle{ \textbf{y} }[/math]nterval
	[math]\displaystyle{ 𝒎 }[/math]	(Temperament) map		[math]\displaystyle{ \small 𝗴 }[/math]/[math]\displaystyle{ \small 𝗽 }[/math]	Generators per prime		[math]\displaystyle{ \scriptsize (1, d) }[/math]	Integer	Vector	⟨...]					[math]\displaystyle{ m_i }[/math]	Jargon name: val
[math]\displaystyle{ n + r }[/math]	[math]\displaystyle{ d }[/math]	Dimensionality					[math]\displaystyle{ \scriptsize (1, 1) }[/math]	Integer	Scalar
[math]\displaystyle{ d - n }[/math]	[math]\displaystyle{ r }[/math]	Rank					[math]\displaystyle{ \scriptsize (1, 1) }[/math]	Integer	Scalar
[math]\displaystyle{ d - r }[/math]	[math]\displaystyle{ n }[/math]	Nullity					[math]\displaystyle{ \scriptsize (1, 1) }[/math]	Integer	Scalar
Tuning
	[math]\displaystyle{ {\large\textbf{𝓁}}\hspace{2mu} }[/math]	Log-prime map		[math]\displaystyle{ \small\mathsf{oct} }[/math]/[math]\displaystyle{ \small 𝗽 }[/math]	Octaves per prime		[math]\displaystyle{ \scriptsize (1, d) }[/math]	Real	Vector	⟨...]					[math]\displaystyle{ {\large 𝓁}\hspace{2mu}_i }[/math]
[math]\displaystyle{ 1200×{\large\textbf{𝓁}}\hspace{2mu} }[/math]	[math]\displaystyle{ 𝒋 }[/math]	Just(-prime) tuning map		[math]\displaystyle{ \mathsf{¢} }[/math]/[math]\displaystyle{ \small 𝗽 }[/math]	Cents per prime		[math]\displaystyle{ \scriptsize (1, d) }[/math]	Real	Vector	⟨...]					[math]\displaystyle{ j_i }[/math]
	[math]\displaystyle{ 𝒈 }[/math]	Generator tuning map		[math]\displaystyle{ \mathsf{¢} }[/math]/[math]\displaystyle{ \small 𝗴 }[/math]	Cents per generator		[math]\displaystyle{ \scriptsize (1, r) }[/math]	Real	Vector	{...]					[math]\displaystyle{ g_i }[/math]
	[math]\displaystyle{ 𝒕 }[/math]	(Tempered-prime) tuning map		[math]\displaystyle{ \mathsf{¢} }[/math]/[math]\displaystyle{ \small 𝗽 }[/math]	Cents per prime		[math]\displaystyle{ \scriptsize (1, d) }[/math]	Real	Vector	⟨...]					[math]\displaystyle{ t_i }[/math]
[math]\displaystyle{ 𝒕 - 𝒋 }[/math] [math]\displaystyle{ 1200×\slant{\mathbf{1}}L(P - I) }[/math]	[math]\displaystyle{ 𝒓 }[/math]	Retuning (or mistuning) map		[math]\displaystyle{ \mathsf{¢} }[/math]/[math]\displaystyle{ \small 𝗽 }[/math]	Cents per prime		[math]\displaystyle{ \scriptsize (1, d) }[/math]	Real	Vector	⟨...]					[math]\displaystyle{ r_i }[/math]	Previous name: prime error map
[math]\displaystyle{ 𝒋\textbf{i} }[/math]	[math]\displaystyle{ \mathrm{o} }[/math]	(Just) (interval) size	[math]\displaystyle{ \scriptsize \begin{array} {c} 𝒋 \\[-2pt] {\small\mathsf{¢}} \hspace{-2mu} / \hspace{-2mu} \cancel{𝗽} \end{array} \begin{array} {c} \\[-2pt] · \end{array} \begin{array} {c} \textbf{i} \\[-2pt] \cancel{𝗽} \end{array} }[/math]	[math]\displaystyle{ \mathsf{¢} }[/math]	Cents	[math]\displaystyle{ \scriptsize \! \! \begin{array} {c} 𝒋 \\[-3pt] \left(1, \cancel{d}\right) \end{array} \! \! \begin{array} {c} \mathbf{i} \\[-3pt] \left(\cancel{d}, 1\right) \end{array} \! \! }[/math]	[math]\displaystyle{ \scriptsize (1, 1) }[/math]	Real	Scalar							Mnemonic: [math]\displaystyle{ \mathrm{o} }[/math]riginal size
[math]\displaystyle{ 𝒈M\textbf{i} }[/math] [math]\displaystyle{ 𝒕\textbf{i} }[/math]	[math]\displaystyle{ \mathrm{a} }[/math]	Tempered (interval) size	[math]\displaystyle{ \scriptsize \begin{array} {c} 𝒕 \\[-2pt] {\small\mathsf{¢}} \hspace{-2mu} / \hspace{-2mu} \cancel{𝗽} \end{array} \begin{array} {c} \\[-2pt] · \end{array} \begin{array} {c} \textbf{i} \\[-2pt] \cancel{𝗽} \end{array} }[/math]	[math]\displaystyle{ \mathsf{¢} }[/math]	Cents	[math]\displaystyle{ \scriptsize \! \! \begin{array} {c} 𝒕 \\[-3pt] \left(1, \cancel{d}\right) \end{array} \! \! \begin{array} {c} \textbf{i} \\[-3pt] \left(\cancel{d}, 1\right) \end{array} \! \! }[/math]	[math]\displaystyle{ \scriptsize (1, 1) }[/math]	Real	Scalar							Mnemonic: [math]\displaystyle{ \mathrm{a} }[/math]ltered size
[math]\displaystyle{ 𝒕\textbf{i} - 𝒋\textbf{i} }[/math] [math]\displaystyle{ a - o }[/math] [math]\displaystyle{ 𝒓\textbf{i} }[/math]	[math]\displaystyle{ \mathrm{e} }[/math]	(Interval) error	[math]\displaystyle{ \scriptsize \begin{array} {c} 𝒓 \\[-2pt] {\small\mathsf{¢}} \hspace{-2mu} / \hspace{-2mu} \cancel{𝗽} \end{array} \begin{array} {c} \\[-2pt] · \end{array} \begin{array} {c} \textbf{i} \\[-2pt] \cancel{𝗽} \end{array} }[/math]	[math]\displaystyle{ \mathsf{¢} }[/math]	Cents	[math]\displaystyle{ \scriptsize \! \! \begin{array} {c} 𝒓 \\[-3pt] \left(1, \cancel{d}\right) \end{array} \! \! \begin{array} {c} \textbf{i} \\[-3pt] \left(\cancel{d}, 1\right) \end{array} \! \! }[/math]	[math]\displaystyle{ \scriptsize (1, 1) }[/math]	Real	Scalar
Optimization
	[math]\displaystyle{ p }[/math]	Optimization power					[math]\displaystyle{ \scriptsize (1, 1) }[/math]	Real	Scalar
	[math]\displaystyle{ \llangle\,·\,\rrangle_p }[/math]	Power mean ([math]\displaystyle{ p }[/math]-mean)					[math]\displaystyle{ \scriptsize (1, 1) }[/math]	Real	Scalar
Damage
	[math]\displaystyle{ c }[/math]	Complexity	(See complexities section of complexities and simplicities table)				[math]\displaystyle{ \scriptsize (1, 1) }[/math]	Real	Scalar
[math]\displaystyle{ \dfrac1c }[/math]	[math]\displaystyle{ s }[/math]	Simplicity	(See simplicities section of complexities and simplicities table)				[math]\displaystyle{ \scriptsize (1, 1) }[/math]	Real	Scalar
[math]\displaystyle{ c }[/math] or [math]\displaystyle{ s }[/math]	[math]\displaystyle{ w }[/math]	weight	(See complexities and simplicities table)				[math]\displaystyle{ \scriptsize (1, 1) }[/math]	Real	Scalar
[math]\displaystyle{ \abs{\mathrm{e}} w }[/math]	[math]\displaystyle{ \mathrm{d} }[/math]	Damage	(See damages table)				[math]\displaystyle{ \scriptsize (1, 1) }[/math]	Real	Scalar
Target-intervals
	[math]\displaystyle{ \mathrm{T} }[/math]	Target-interval list		[math]\displaystyle{ \small 𝗽 }[/math]	Primes		[math]\displaystyle{ \scriptsize (d, k) }[/math]	Integer	Matrix		[[...⟩ ...]		[math]\displaystyle{ \textbf{t}_i }[/math]		[math]\displaystyle{ \mathrm{t}_{ij} }[/math]
[math]\displaystyle{ M\mathrm{T} }[/math]	[math]\displaystyle{ \mathrm{Y} }[/math]	Mapped target-interval list	[math]\displaystyle{ \scriptsize \begin{array} {c} M \\[-2pt] 𝗴 \hspace{-2mu} / \hspace{-2mu} \cancel{𝗽} \end{array} \begin{array} {c} \\[-2pt] · \end{array} \begin{array} {c} \mathrm{T} \\[-2pt] \cancel{𝗽} \end{array} }[/math]	[math]\displaystyle{ \small 𝗴 }[/math]	Generators	[math]\displaystyle{ \scriptsize \! \! \begin{array} {c} M \\[-3pt] \left(r, \cancel{d}\right) \end{array} \! \! \begin{array} {c} \mathrm{T} \\[-3pt] \left(\cancel{d}, k\right) \end{array} \! \! }[/math]	[math]\displaystyle{ \scriptsize (r, k) }[/math]	Integer	Matrix		[[...} ...]		[math]\displaystyle{ \textbf{y}_i }[/math]		[math]\displaystyle{ \mathrm{y}_{ij} }[/math]	Mnemonic: looks like bent-up 'T', or cross between 'M' and 'T'
[math]\displaystyle{ 𝒋\mathrm{T} }[/math]	[math]\displaystyle{ \textbf{o} }[/math]	Target-interval (just) size list	[math]\displaystyle{ \scriptsize \begin{array} {c} 𝒋 \\[-2pt] {\small\mathsf{¢}} \hspace{-2mu} / \hspace{-2mu} \cancel{𝗽} \end{array} \begin{array} {c} \\[-2pt] · \end{array} \begin{array} {c} \mathrm{T} \\[-2pt] \cancel{𝗽} \end{array} }[/math]	[math]\displaystyle{ \mathsf{¢} }[/math]	Cents	[math]\displaystyle{ \scriptsize \! \! \begin{array} {c} 𝒋 \\[-3pt] \left(1, \cancel{d}\right) \end{array} \! \! \begin{array} {c} \mathrm{T} \\[-3pt] \left(\cancel{d}, k\right) \end{array} \! \! }[/math]	[math]\displaystyle{ \scriptsize (1, k) }[/math]	Real	List	[...]					[math]\displaystyle{ \mathrm{o}_i }[/math]	Mnemonic: [math]\displaystyle{ \textbf{o} }[/math]riginal size list
[math]\displaystyle{ 𝒕\mathrm{T} }[/math]	[math]\displaystyle{ \textbf{a} }[/math]	Tempered target-interval size list	[math]\displaystyle{ \scriptsize \begin{array} {c} 𝒕 \\[-2pt] {\small\mathsf{¢}} \hspace{-2mu} / \hspace{-2mu} \cancel{𝗽} \end{array} \begin{array} {c} \\[-2pt] · \end{array} \begin{array} {c} \mathrm{T} \\[-2pt] \cancel{𝗽} \end{array} }[/math]	[math]\displaystyle{ \mathsf{¢} }[/math]	Cents	[math]\displaystyle{ \scriptsize \! \! \begin{array} {c} 𝒕 \\[-3pt] \left(1, \cancel{d}\right) \end{array} \! \! \begin{array} {c} \mathrm{T} \\[-3pt] \left(\cancel{d}, k\right) \end{array} \! \! }[/math]	[math]\displaystyle{ \scriptsize (1, k) }[/math]	Real	List	[...]					[math]\displaystyle{ \mathrm{a}_i }[/math]	Mnemonic: [math]\displaystyle{ \textbf{a} }[/math]ltered size list
[math]\displaystyle{ 𝒕\mathrm{T} - 𝒋\mathrm{T} }[/math] [math]\displaystyle{ 𝒓\mathrm{T} }[/math] [math]\displaystyle{ \textbf{a} - \textbf{o} }[/math]	[math]\displaystyle{ \textbf{e} }[/math]	Target-interval error list	[math]\displaystyle{ \scriptsize \begin{array} {c} 𝒓 \\[-2pt] {\small\mathsf{¢}} \hspace{-2mu} / \hspace{-2mu} \cancel{𝗽} \end{array} \begin{array} {c} \\[-2pt] · \end{array} \begin{array} {c} \mathrm{T} \\[-2pt] \cancel{𝗽} \end{array} }[/math]	[math]\displaystyle{ \mathsf{¢} }[/math]	Cents	[math]\displaystyle{ \scriptsize \! \! \begin{array} {c} 𝒓 \\[-3pt] \left(1, \cancel{d}\right) \end{array} \! \! \begin{array} {c} \mathrm{T} \\[-3pt] \left(\cancel{d}, k\right) \end{array} \! \! }[/math]	[math]\displaystyle{ \scriptsize (1, k) }[/math]	Real	List	[...]					[math]\displaystyle{ \mathrm{e}_i }[/math]
[math]\displaystyle{ C }[/math] or [math]\displaystyle{ S }[/math]	[math]\displaystyle{ W }[/math]	Target-interval weight matrix	(See complexities and simplicities table)				[math]\displaystyle{ \scriptsize (k, k) }[/math]	Real	Matrix		[[...] ...]			[math]\displaystyle{ 𝒘 }[/math]	[math]\displaystyle{ w_i }[/math]
	[math]\displaystyle{ C }[/math]	Target-interval complexity weight matrix	(See complexities section of complexities and simplicities table)				[math]\displaystyle{ \scriptsize (k, k) }[/math]	Real	Matrix		[[...] ...]			[math]\displaystyle{ 𝒄 }[/math]	[math]\displaystyle{ c_i }[/math]
[math]\displaystyle{ \dfrac1C }[/math]	[math]\displaystyle{ S }[/math]	Target-interval simplicity weight matrix	(See simplicities section of complexities and simplicities table)				[math]\displaystyle{ \scriptsize (k, k) }[/math]	Real	Matrix		[[...] ...]			[math]\displaystyle{ 𝒔 }[/math]	[math]\displaystyle{ s_i }[/math]	Entry-wise reciprocal of [math]\displaystyle{ C }[/math]
[math]\displaystyle{ \abs{\textbf{e}} W }[/math]	[math]\displaystyle{ \textbf{d} }[/math]	Target-interval damage list	(See damages table)				[math]\displaystyle{ \scriptsize (1, k) }[/math]	Real	List	[...]					[math]\displaystyle{ \mathrm{d}_i }[/math]
	[math]\displaystyle{ k }[/math]	Target-interval count					[math]\displaystyle{ \scriptsize (1, 1) }[/math]	Integer	Scalar							Mnemonic: [math]\displaystyle{ k }[/math]ount
Held-intervals
	[math]\displaystyle{ \mathrm{H} }[/math]	Held-interval basis		[math]\displaystyle{ \small 𝗽 }[/math]	Primes		[math]\displaystyle{ \scriptsize (d, h) }[/math]		Matrix		[[...⟩ ...]		[math]\displaystyle{ \textbf{h}_i }[/math]		[math]\displaystyle{ \mathrm{h}_{ij} }[/math]
	[math]\displaystyle{ h }[/math]	Held-interval count					[math]\displaystyle{ \scriptsize (1, 1) }[/math]	Integer	Scalar
Exploring temperaments
	[math]\displaystyle{ \mathrm{C} }[/math]	Comma basis		[math]\displaystyle{ \small 𝗽 }[/math]	Primes		[math]\displaystyle{ \scriptsize (d, n) }[/math]	Integer	Matrix		[[...⟩ ...]		[math]\displaystyle{ \textbf{c}_i }[/math]		[math]\displaystyle{ \mathrm{c}_{ij} }[/math]	Jargon name: monzo list
	[math]\displaystyle{ \textbf{c} }[/math]	Comma		[math]\displaystyle{ \small 𝗽 }[/math]	primes		[math]\displaystyle{ \scriptsize (d, 1) }[/math]	Integer	Vector		[...⟩				[math]\displaystyle{ \mathrm{c}_i }[/math]	Specific type: vector (prime-count vector or PC-vector)
Computation
	ꗨ⁠ ⁠ꗨ[math]\displaystyle{ \,·\, }[/math]ꗨ⁠ ⁠ꗨ[math]\displaystyle{ _p }[/math]	Power sum ([math]\displaystyle{ p }[/math]-sum)					[math]\displaystyle{ \scriptsize (1, 1) }[/math]	Real	Scalar
All-interval tuning schemes
[math]\displaystyle{ \mathrm{I} }[/math]	[math]\displaystyle{ \mathrm{T}_{\text{p}} }[/math]	Prime proxy target-interval list		[math]\displaystyle{ \small 𝗽 }[/math]	Primes		[math]\displaystyle{ \scriptsize (d, d) }[/math]	Integer	Matrix		⟨[...⟩ ...]			[math]\displaystyle{ \mathbf{1} }[/math]
	[math]\displaystyle{ X }[/math]	Complexity prescaler	[math]\displaystyle{ \small\mathsf{𝟙}\scriptsize\mathsf{(C)} }[/math]	[math]\displaystyle{ \small\mathsf{(C)} }[/math]	Complexity weight		[math]\displaystyle{ \scriptsize (d, d) }[/math]	Real	Matrix	[⟨...] ...⟩				[math]\displaystyle{ 𝒙 }[/math]	[math]\displaystyle{ x_i }[/math]
[math]\displaystyle{ \text{diag}({\large\textbf{𝓁}}\hspace{2mu}) }[/math]	[math]\displaystyle{ L }[/math]	Log-prime matrix		[math]\displaystyle{ \small\mathsf{oct} }[/math]/[math]\displaystyle{ \small 𝗽 }[/math]	Octaves per prime		[math]\displaystyle{ \scriptsize (d, d) }[/math]	Real	Matrix	[⟨...] ...⟩	⟨[...⟩ ...]	[math]\displaystyle{ {\large\textbf{𝓁}}\hspace{2mu}_i }[/math]		[math]\displaystyle{ {\large\textbf{𝓁}}\hspace{2mu} }[/math]	[math]\displaystyle{ {\large 𝓁}\hspace{2mu}_{ij} }[/math]
	[math]\displaystyle{ q }[/math]	Interval complexity norm power					[math]\displaystyle{ \scriptsize (1, 1) }[/math]	Real	Scalar
	[math]\displaystyle{ \norm{·}_q }[/math]	Power norm ([math]\displaystyle{ p }[/math]-norm)					[math]\displaystyle{ \scriptsize (1, 1) }[/math]	Real	Scalar
[math]\displaystyle{ \dfrac1{1-\frac1q} }[/math]	[math]\displaystyle{ \text{dual}(q) }[/math]	Dual norm power					[math]\displaystyle{ \scriptsize (1, 1) }[/math]	Real	Scalar
	[math]\displaystyle{ \norm{X\mathbf{i}}_q }[/math]	interval complexity		[math]\displaystyle{ \small\mathsf{(C)} }[/math]			[math]\displaystyle{ \scriptsize (1, 1) }[/math]	Real	Scalar
	[math]\displaystyle{ \norm{𝒓X^{-1}}_{\text{dual}(q)} }[/math]	Retuning magnitude		[math]\displaystyle{ \mathsf{¢}\small\mathsf{(C^{-1})} }[/math]			[math]\displaystyle{ \scriptsize (1, 1) }[/math]	Real	Scalar

Units

Same as the basic level.

Tuning schemes


Retuning (or mistuning) magnitude			Damage									Target intervals	Systematic name		Previously named tuning schemes that are specific types of this tuning scheme	Of interest?
			Weight						Optimization
			Interval complexity			Slope			Initial	Name	Power
Initial	Name	Power	Initial	Name	Power	Initial	Name	Multiplier	Initial	Name	Power		Abbreviated	Read ("____ tuning scheme")
<n/a>	Maximum	∞	(t)	Taxicab	1	S	Simplicity-weight	1/Complexity	<n/a>	Minimax	∞	All	Minimax-S	Minimax simplicity-weight damage	"TOP"/"T1"/"TIPTOP", "CTOP", "POTOP"/"POTT", "BOP", "Weil", "Kees"	Yes
<n/a>	Euclidean	2	E	Euclidean	2	S	Simplicity-weight	1/Complexity				All	Minimax-ES	Minimax Euclideanized-simplicity-weight damage	"TE"/"T2"/"TOP-RMS", "CTE", "POTE", "Frobenius", "BE", "WE", "KE"
<n/a>			<n/a>			U	Unity-weight	<none>				<set>	<set> Minimax-U	<set> Minimax unity-weight-damage	" minimax"	yes
			(t)	taxicab	1	S	Simplicity-weight	1/Complexity					<set> Minimax-S	<set> Minimax simplicity-weight damage		Yes
			E	Euclidean	2	S	Simplicity-weight	1/Complexity					<set> Minimax-ES	<set> Minimax Euclideanized-simplicity-weight damage
			(t)	Taxicab	1	C	Complexity-weight	Complexity					<set> Minimax-C	<set> Minimax complexity-weight damage		Yes
			E	Euclidean	2	C	Complexity-weight	Complexity					<set> Minimax-EC	<set> Minimax Euclideanized-complexity-weight damage
			<n/a>			U	Unity-weight	<none>		MiniRMS	2		<set> MiniRMS-U	<set> MiniRMS unity-weight damage	"Least squares"	Yes
			(t)	Taxicab	1	S	Simplicity-weight	1/Complexity					<set> MiniRMS-S	<set> MiniRMS simplicity-weight damage		Yes
			E	Euclidean	2	S	Simplicity-weight	1/Complexity					<set> MiniRMS-ES	<set> MiniRMS Euclideanized-simplicity-weight damage
			(t)	Taxicab	1	C	Complexity-weight	Complexity					<set> MiniRMS-C	<set> MiniRMS complexity-weight damage		Yes
			E	Euclidean	2	C	Complexity-weight	Complexity					<set> MiniRMS-EC	<set> MiniRMS Euclideanized-complexity-weight damage
			<n/a>			U	Unity-weight	<none>		Miniaverage	1		<set> Miniaverage-U	<set> Miniaverage unity-weight damage		Yes
			(t)	Taxicab	1	S	Simplicity-weight	1/Complexity					<set> Miniaverage-S	<set> Miniaverage simplicity-weight damage		Yes
			E	Euclidean	2	S	Simplicity-weight	1/Complexity					<set> Miniaverage-ES	<set> Miniaverage Euclideanized-simplicity-weight damage
			(t)	Taxicab	1	C	Complexity-weight	Complexity					<set> Miniaverage-C	<set> Miniaverage complexity-weight damage		Yes
			E	Euclidean	2	C	Complexity-weight	Complexity					<set> Miniaverage-EC	<set> Miniaverage Euclideanized-complexity-weight damage

Damages


Quantity		Unit
Abbreviation	Name	Symbol	Name
U-damage	Unity-weight damage	[math]\displaystyle{ \mathsf{¢}\small\mathsf{(U)} }[/math]	Unity-weighted cents
C-damage	Complexity-weight damage	[math]\displaystyle{ \mathsf{¢}\small\mathsf{(C)} }[/math]	Complexity-weighted cents
EC-damage	Euclideanized-complexity-weight damage	[math]\displaystyle{ \mathsf{¢} }[/math][math]\displaystyle{ \small\mathsf{(EC)} }[/math]	Euclideanized-complexity-weighted cents
S-damage	Simplicity-weight damage	[math]\displaystyle{ \mathsf{¢}\small\mathsf{(S)} }[/math]	Simplicity-weighted cents
ES-damage	Euclideanized-simplicity-weight damage	[math]\displaystyle{ \mathsf{¢} }[/math][math]\displaystyle{ \small\mathsf{(ES)} }[/math]	Euclideanized-simplicity-weighted cents

Complexity and simplicity


Quantity		Unit
Abbreviation	Name	Symbol	Name
C	Complexity	[math]\displaystyle{ \small\mathsf{(C)} }[/math]	Complexity weight
EC	Euclideanized complexity	[math]\displaystyle{ \small\mathsf{(EC)} }[/math]	Euclideanized-complexity weight
S	Simplicity	[math]\displaystyle{ \small\mathsf{(S)} }[/math]	Simplicity weight
ES	Euclideanized simplicity	[math]\displaystyle{ \small\mathsf{(ES)} }[/math]	Euclideanized-simplicity weight

Advanced

Objects


Equivalent expressions	Variable	Name	Units			Shape		Type		EBK notation		Subobjects				Notes
Equivalent expressions	Variable	Name	Unreduced	Reduced	Read as	Unreduced	Reduced	Numeric	Structural	Row-first	Col-first	Row	Column	Diagonal	Entry	Notes
Mapping
	[math]\displaystyle{ \textbf{i} }[/math]	(Just) interval		[math]\displaystyle{ \small 𝗽 }[/math]	Primes		[math]\displaystyle{ \scriptsize (d, 1) }[/math]	Integer	Vector		[...⟩				[math]\displaystyle{ \mathrm{i}_i }[/math]	Specific type: vector (prime-count vector or PC-vector) Jargon name: monzo
	[math]\displaystyle{ M }[/math]	(Temperament) mapping (matrix)		[math]\displaystyle{ \small 𝗴 }[/math]/[math]\displaystyle{ \small 𝗽 }[/math]	Generators per prime		[math]\displaystyle{ \scriptsize (r, d) }[/math]	Integer	Matrix	[⟨...] ...}	⟨[...} ...]	[math]\displaystyle{ 𝒎_i }[/math]			[math]\displaystyle{ m_{ij} }[/math]	Jargon name: val list
[math]\displaystyle{ M\textbf{i} }[/math]	[math]\displaystyle{ \textbf{y} }[/math]	Mapped interval	[math]\displaystyle{ \scriptsize \begin{array} {c} M \\[-2pt] 𝗴 \hspace{-2mu} / \hspace{-2mu} \cancel{𝗽} \end{array} \begin{array} {c} \\[-2pt] · \end{array} \begin{array} {c} \textbf{i} \\[-2pt] \cancel{𝗽} \end{array} }[/math]	[math]\displaystyle{ \small 𝗴 }[/math]	generators	[math]\displaystyle{ \scriptsize \! \! \begin{array} {c} M \\[-3pt] \left(r, \cancel{d}\right) \end{array} \! \! \begin{array} {c} \textbf{i} \\[-3pt] \left(\cancel{d}, 1\right) \end{array} \! \! }[/math]	[math]\displaystyle{ \scriptsize (r, 1) }[/math]	Integer	Vector		[...}					Specific type: generator-count vector (GC-vector) Jargon name: tmonzo; mnemonic: [math]\displaystyle{ \textbf{y} }[/math]nterval
	[math]\displaystyle{ 𝒎 }[/math]	(Temperament) map		[math]\displaystyle{ \small 𝗴 }[/math]/[math]\displaystyle{ \small 𝗽 }[/math]	Generators per prime		[math]\displaystyle{ \scriptsize (1, d) }[/math]	Integer	Vector	⟨...]					[math]\displaystyle{ m_i }[/math]	Jargon name: val
[math]\displaystyle{ n + r }[/math]	[math]\displaystyle{ d }[/math]	Dimensionality					[math]\displaystyle{ \scriptsize (1, 1) }[/math]	Integer	Scalar
[math]\displaystyle{ d - n }[/math]	[math]\displaystyle{ r }[/math]	Rank					[math]\displaystyle{ \scriptsize (1, 1) }[/math]	Integer	Scalar
[math]\displaystyle{ d - r }[/math]	[math]\displaystyle{ n }[/math]	Nullity					[math]\displaystyle{ \scriptsize (1, 1) }[/math]	Integer	Scalar
Tuning
[math]\displaystyle{ \slant{\mathbf{1}}L }[/math]	[math]\displaystyle{ {\large\textbf{𝓁}}\hspace{2mu} }[/math]	Log-prime map		[math]\displaystyle{ \small\mathsf{oct} }[/math]/[math]\displaystyle{ \small 𝗽 }[/math]	Octaves per prime		[math]\displaystyle{ \scriptsize (1, d) }[/math]	Real	Vector	⟨...]					[math]\displaystyle{ {\large 𝓁}\hspace{2mu}_i }[/math]
[math]\displaystyle{ 1200×\slant{\mathbf{1}}LG_{\text{j}}M_{\text{j}} }[/math] [math]\displaystyle{ 1200×\slant{\mathbf{1}}L }[/math] [math]\displaystyle{ 𝒈_{\text{j}}M_{\text{j}} }[/math]	[math]\displaystyle{ 𝒋 }[/math]	Just(-prime) tuning map	[math]\displaystyle{ \scriptsize \begin{array} {c} 1200 \\[-2pt] {\small\mathsf{¢}} \hspace{-2mu} / \hspace{-2mu} \cancel{\mathsf{oct}} \end{array} \begin{array} {c} \\[-2pt] · \end{array} \begin{array} {c} \slant{\mathbf{1}} \\[-2pt] \cancel{\mathsf{oct}} \hspace{-2mu} / \hspace{-2mu} \cancel{\mathsf{oct}} \end{array} \begin{array} {c} \\[-2pt] · \end{array} \begin{array} {c} L \\[-2pt] \cancel{\mathsf{oct}} \hspace{-2mu} / \hspace{-2mu} \cancel{𝗽} \end{array} \begin{array} {c} \\[-2pt] · \end{array} \\ \scriptsize \quad \begin{array} {c} G_{\text{j}} \\[-2pt] \cancel{𝗽} \hspace{-2mu} / \hspace{-2mu} \cancel{𝗴} \end{array} \begin{array} {c} \\[-2pt] · \end{array} \begin{array} {c} M_{\text{j}} \\[-2pt] \cancel{𝗴} \hspace{-2mu} / \hspace{-2mu} 𝗽 \end{array} }[/math]	[math]\displaystyle{ \mathsf{¢} }[/math]/[math]\displaystyle{ \small 𝗽 }[/math]	Cents per prime	[math]\displaystyle{ \scriptsize \! \! \begin{array} {c} 1200 \\[-3pt] \left(1, \cancel{1}\right) \end{array} \! \! \begin{array} {c} \slant{\mathbf{1}} \\[-3pt] \left(\cancel{1}, \cancel{d}\right) \end{array} \! \! \begin{array} {c} L \\[-3pt] \left(\cancel{d}, \cancel{d}\right) \end{array} \\ \scriptsize \quad \! \! \begin{array} {c} G_{\text{j}} \\[-3pt] \left(\cancel{d}, \cancel{r}\right) \end{array} \! \! \begin{array} {c} M_{\text{j}} \\[-3pt] \left(\cancel{r}, d\right) \end{array} \! \! }[/math]	[math]\displaystyle{ \scriptsize \left(1, d_{\text{p}}\right) }[/math]	Real	Vector	⟨...]					[math]\displaystyle{ j_i }[/math]
[math]\displaystyle{ 1200×\slant{\mathbf{1}}LG }[/math]	[math]\displaystyle{ 𝒈 }[/math]	Generator tuning map	[math]\displaystyle{ \scriptsize \begin{array} {c} 1200 \\[-2pt] {\small\mathsf{¢}} \hspace{-2mu} / \hspace{-2mu} \cancel{\mathsf{oct}} \end{array} \begin{array} {c} \\[-2pt] · \end{array} \begin{array} {c} \slant{\mathbf{1}} \\[-2pt] \cancel{\mathsf{oct}} \hspace{-2mu} / \hspace{-2mu} \cancel{\mathsf{oct}} \end{array} \begin{array} {c} \\[-2pt] · \end{array} \begin{array} {c} L \\[-2pt] \cancel{\mathsf{oct}} \hspace{-2mu} / \hspace{-2mu} \cancel{𝗽} \end{array} \begin{array} {c} \\[-2pt] · \end{array} \\ \scriptsize \quad \begin{array} {c} G \\[-2pt] \cancel{𝗽} \hspace{-2mu} / \hspace{-2mu} 𝗴 \end{array} }[/math]	[math]\displaystyle{ \mathsf{¢} }[/math]/[math]\displaystyle{ \small 𝗴 }[/math]	Cents per generator	[math]\displaystyle{ \scriptsize \! \! \begin{array} {c} 1200 \\[-3pt] (1, \cancel{1}) \end{array} \! \! \begin{array} {c} \slant{\mathbf{1}} \\[-3pt] (\cancel{1}, \cancel{d}) \end{array} \! \! \begin{array} {c} L \\[-3pt] (\cancel{d}, \cancel{d}) \end{array} \\ \scriptsize \quad \! \! \begin{array} {c} G \\[-3pt] (\cancel{d}, r) \end{array} \! \! }[/math]	[math]\displaystyle{ \scriptsize (1, r) }[/math]	Real	Vector	{...]					[math]\displaystyle{ g_i }[/math]
[math]\displaystyle{ 1200×\slant{\mathbf{1}}LGM }[/math] [math]\displaystyle{ 1200×\slant{\mathbf{1}}LP }[/math] [math]\displaystyle{ 𝒈M }[/math]	[math]\displaystyle{ 𝒕 }[/math]	(Tempered-prime) tuning map	[math]\displaystyle{ \scriptsize \begin{array} {c} 1200 \\[-2pt] {\small\mathsf{¢}} \hspace{-2mu} / \hspace{-2mu} \cancel{\mathsf{oct}} \end{array} \begin{array} {c} \\[-2pt] · \end{array} \begin{array} {c} \slant{\mathbf{1}} \\[-2pt] \cancel{\mathsf{oct}} \hspace{-2mu} / \hspace{-2mu} \cancel{\mathsf{oct}} \end{array} \begin{array} {c} \\[-2pt] · \end{array} \begin{array} {c} L \\[-2pt] \cancel{\mathsf{oct}} \hspace{-2mu} / \hspace{-2mu} \cancel{𝗽} \end{array} \begin{array} {c} \\[-2pt] · \end{array} \\ \scriptsize \quad \begin{array} {c} G \\[-2pt] \cancel{𝗽} \hspace{-2mu} / \hspace{-2mu} \cancel{𝗴} \end{array} \begin{array} {c} \\[-2pt] · \end{array} \begin{array} {c} M \\[-2pt] \cancel{𝗴} \hspace{-2mu} / \hspace{-2mu} 𝗽 \end{array} }[/math]	[math]\displaystyle{ \mathsf{¢} }[/math]/[math]\displaystyle{ \small 𝗽 }[/math]	Cents per prime	[math]\displaystyle{ \scriptsize \! \! \begin{array} {c} 1200 \\[-3pt] \left(1, \cancel{1}\right) \end{array} \! \! \begin{array} {c} \slant{\mathbf{1}} \\[-3pt] \left(\cancel{1}, \cancel{d}\right) \end{array} \! \! \begin{array} {c} L \\[-3pt] \left(\cancel{d}, \cancel{d}\right) \end{array} \\ \scriptsize \quad \! \! \begin{array} {c} G \\[-3pt] \left(\cancel{d}, \cancel{r}\right) \end{array} \! \! \begin{array} {c} M \\[-3pt] \left(\cancel{r}, d\right) \end{array} \! \! }[/math]	[math]\displaystyle{ \scriptsize (1, d) }[/math]	Real	Vector	⟨...]					[math]\displaystyle{ t_i }[/math]
[math]\displaystyle{ 𝒕 - 𝒋 }[/math] [math]\displaystyle{ 1200×\slant{\mathbf{1}}L(P - I) }[/math]	[math]\displaystyle{ 𝒓 }[/math]	Retuning (or mistuning) map		[math]\displaystyle{ \mathsf{¢} }[/math]/[math]\displaystyle{ \small 𝗽 }[/math]	Cents per prime		[math]\displaystyle{ \scriptsize (1, d) }[/math]	Real	Vector	⟨...]					[math]\displaystyle{ r_i }[/math]	Previous name: prime error map
[math]\displaystyle{ 𝒋\textbf{i} }[/math]	[math]\displaystyle{ \mathrm{o} }[/math]	(Just) (interval) size	[math]\displaystyle{ \scriptsize \begin{array} {c} 𝒋 \\[-2pt] {\small\mathsf{¢}} \hspace{-2mu} / \hspace{-2mu} \cancel{𝗽} \end{array} \begin{array} {c} \\[-2pt] · \end{array} \begin{array} {c} \textbf{i} \\[-2pt] \cancel{𝗽} \end{array} }[/math]	[math]\displaystyle{ \mathsf{¢} }[/math]	Cents	[math]\displaystyle{ \scriptsize \! \! \begin{array} {c} 𝒋 \\[-3pt] \left(1, \cancel{d}\right) \end{array} \! \! \begin{array} {c} \textbf{i} \\[-3pt] \left(\cancel{d}, 1\right) \end{array} \! \! }[/math]	[math]\displaystyle{ \scriptsize (1, 1) }[/math]	Real	Scalar							Mnemonic: [math]\displaystyle{ \mathrm{o} }[/math]riginal size
[math]\displaystyle{ 𝒈M\textbf{i} }[/math] [math]\displaystyle{ 𝒕\textbf{i} }[/math]	[math]\displaystyle{ \mathrm{a} }[/math]	Tempered (interval) size	[math]\displaystyle{ \scriptsize \begin{array} {c} 𝒕 \\[-2pt] {\small\mathsf{¢}} \hspace{-2mu} / \hspace{-2mu} \cancel{𝗽} \end{array} \begin{array} {c} \\[-2pt] · \end{array} \begin{array} {c} \textbf{i} \\[-2pt] \cancel{𝗽} \end{array} }[/math]	[math]\displaystyle{ \mathsf{¢} }[/math]	cents	[math]\displaystyle{ \scriptsize \! \! \begin{array} {c} 𝒕 \\[-3pt] \left(1, \cancel{d}\right) \end{array} \! \! \begin{array} {c} \textbf{i} \\[-3pt] \left(\cancel{d}, 1\right) \end{array} \! \! }[/math]	[math]\displaystyle{ \scriptsize (1, 1) }[/math]	Real	Scalar							Mnemonic: [math]\displaystyle{ \mathrm{a} }[/math]ltered size
[math]\displaystyle{ 𝒕\textbf{i} - 𝒋\textbf{i} }[/math] [math]\displaystyle{ a - o }[/math] [math]\displaystyle{ 𝒓\textbf{i} }[/math]	[math]\displaystyle{ \mathrm{e} }[/math]	(Interval) error	[math]\displaystyle{ \scriptsize \begin{array} {c} 𝒓 \\[-2pt] {\small\mathsf{¢}} \hspace{-2mu} / \hspace{-2mu} \cancel{𝗽} \end{array} \begin{array} {c} \\[-2pt] · \end{array} \begin{array} {c} \textbf{i} \\[-2pt] \cancel{𝗽} \end{array} }[/math]	[math]\displaystyle{ \mathsf{¢} }[/math]	Cents	[math]\displaystyle{ \scriptsize \! \! \begin{array} {c} 𝒓 \\[-3pt] \left(1, \cancel{d}\right) \end{array} \! \! \begin{array} {c} \textbf{i} \\[-3pt] \left(\cancel{d}, 1\right) \end{array} \! \! }[/math]	[math]\displaystyle{ \scriptsize (1, 1) }[/math]	Real	Scalar
Optimization
	[math]\displaystyle{ p }[/math]	Optimization power					[math]\displaystyle{ \scriptsize (1, 1) }[/math]	Real	Scalar
	[math]\displaystyle{ \llangle\,·\,\rrangle_p }[/math]	Power mean ([math]\displaystyle{ p }[/math]-mean)					[math]\displaystyle{ \scriptsize (1, 1) }[/math]	Real	Scalar
Damage
	[math]\displaystyle{ c }[/math]	complexity	(See complexities section of complexities and simplicities table)				[math]\displaystyle{ \scriptsize (1, 1) }[/math]	Real	Scalar
[math]\displaystyle{ \dfrac1c }[/math]	[math]\displaystyle{ s }[/math]	Simplicity	(See simplicities section of complexities and simplicities table)				[math]\displaystyle{ \scriptsize (1, 1) }[/math]	Real	Scalar
[math]\displaystyle{ c }[/math] or [math]\displaystyle{ s }[/math]	[math]\displaystyle{ w }[/math]	Weight	(See complexities and simplicities table)				[math]\displaystyle{ \scriptsize (1, 1) }[/math]	Real	Scalar
[math]\displaystyle{ \abs{\mathrm{e}} w }[/math]	[math]\displaystyle{ \mathrm{d} }[/math]	Damage	(See damages table)				[math]\displaystyle{ \scriptsize (1, 1) }[/math]	Real	Scalar
Target-intervals
	[math]\displaystyle{ \mathrm{T} }[/math]	Target-interval list		[math]\displaystyle{ \small 𝗽 }[/math]	Primes		[math]\displaystyle{ \scriptsize (d, k) }[/math]	Integer	Matrix		[[...⟩ ...]		[math]\displaystyle{ \textbf{t}_i }[/math]		[math]\displaystyle{ \mathrm{t}_{ij} }[/math]
[math]\displaystyle{ M\mathrm{T} }[/math]	[math]\displaystyle{ \mathrm{Y} }[/math]	Mapped target-interval list	[math]\displaystyle{ \scriptsize \begin{array} {c} M \\[-2pt] 𝗴 \hspace{-2mu} / \hspace{-2mu} \cancel{𝗽} \end{array} \begin{array} {c} \\[-2pt] · \end{array} \begin{array} {c} \mathrm{T} \\[-2pt] \cancel{𝗽} \end{array} }[/math]	[math]\displaystyle{ \small 𝗴 }[/math]	Generators	[math]\displaystyle{ \scriptsize \! \! \begin{array} {c} M \\[-3pt] \left(r, \cancel{d}\right) \end{array} \! \! \begin{array} {c} \mathrm{T} \\[-3pt] \left(\cancel{d}, k\right) \end{array} \! \! }[/math]	[math]\displaystyle{ \scriptsize (r, k) }[/math]	Integer	Matrix		[[...} ...]		[math]\displaystyle{ \textbf{y}_i }[/math]		[math]\displaystyle{ \mathrm{y}_{ij} }[/math]	Mnemonic: looks like bent-up 'T', or cross between 'M' and 'T'
[math]\displaystyle{ 𝒋\mathrm{T} }[/math]	[math]\displaystyle{ \textbf{o} }[/math]	Target-interval (just) size list	[math]\displaystyle{ \scriptsize \begin{array} {c} 𝒋 \\[-2pt] {\small\mathsf{¢}} \hspace{-2mu} / \hspace{-2mu} \cancel{𝗽} \end{array} \begin{array} {c} \\[-2pt] · \end{array} \begin{array} {c} \mathrm{T} \\[-2pt] \cancel{𝗽} \end{array} }[/math]	[math]\displaystyle{ \mathsf{¢} }[/math]	Cents	[math]\displaystyle{ \scriptsize \! \! \begin{array} {c} 𝒋 \\[-3pt] \left(1, \cancel{d}\right) \end{array} \! \! \begin{array} {c} \mathrm{T} \\[-3pt] \left(\cancel{d}, k\right) \end{array} \! \! }[/math]	[math]\displaystyle{ \scriptsize (1, k) }[/math]	Real	List	[...]					[math]\displaystyle{ \mathrm{o}_i }[/math]	Mnemonic: [math]\displaystyle{ \textbf{o} }[/math]riginal size list
[math]\displaystyle{ 𝒕\mathrm{T} }[/math]	[math]\displaystyle{ \textbf{a} }[/math]	Tempered target-interval size list	[math]\displaystyle{ \scriptsize \begin{array} {c} 𝒕 \\[-2pt] {\small\mathsf{¢}} \hspace{-2mu} / \hspace{-2mu} \cancel{𝗽} \end{array} \begin{array} {c} \\[-2pt] · \end{array} \begin{array} {c} \mathrm{T} \\[-2pt] \cancel{𝗽} \end{array} }[/math]	[math]\displaystyle{ \mathsf{¢} }[/math]	Cents	[math]\displaystyle{ \scriptsize \! \! \begin{array} {c} 𝒕 \\[-3pt] \left(1, \cancel{d}\right) \end{array} \! \! \begin{array} {c} \mathrm{T} \\[-3pt] \left(\cancel{d}, k\right) \end{array} \! \! }[/math]	[math]\displaystyle{ \scriptsize (1, k) }[/math]	Real	List	[...]					[math]\displaystyle{ \mathrm{a}_i }[/math]	Mnemonic: [math]\displaystyle{ \textbf{a} }[/math]ltered size list
[math]\displaystyle{ 𝒕\mathrm{T} - 𝒋\mathrm{T} }[/math] [math]\displaystyle{ 𝒓\mathrm{T} }[/math] [math]\displaystyle{ \textbf{a} - \textbf{o} }[/math]	[math]\displaystyle{ \textbf{e} }[/math]	target-interval error list	[math]\displaystyle{ \scriptsize \begin{array} {c} 𝒓 \\[-2pt] {\small\mathsf{¢}} \hspace{-2mu} / \hspace{-2mu} \cancel{𝗽} \end{array} \begin{array} {c} \\[-2pt] · \end{array} \begin{array} {c} \mathrm{T} \\[-2pt] \cancel{𝗽} \end{array} }[/math]	[math]\displaystyle{ \mathsf{¢} }[/math]	Cents	[math]\displaystyle{ \scriptsize \! \! \begin{array} {c} 𝒕 \\[-3pt] \left(1, \cancel{d}\right) \end{array} \! \! \begin{array} {c} \mathrm{T} \\[-3pt] \left(\cancel{d}, k\right) \end{array} \! \! }[/math]	[math]\displaystyle{ \scriptsize (1, k) }[/math]	Real	List	[...]					[math]\displaystyle{ \mathrm{e}_i }[/math]
[math]\displaystyle{ C }[/math] or [math]\displaystyle{ S }[/math]	[math]\displaystyle{ W }[/math]	Target-interval weight matrix	(See complexities and simplicities table)				[math]\displaystyle{ \scriptsize (k, k) }[/math]	Real	Matrix		[[...] ...]			[math]\displaystyle{ 𝒘 }[/math]	[math]\displaystyle{ w_i }[/math] or [math]\displaystyle{ w_{ij} }[/math]
	[math]\displaystyle{ C }[/math]	Target-interval complexity weight matrix	(See complexities section of complexities and simplicities table)				[math]\displaystyle{ \scriptsize (k, k) }[/math]	Real	Matrix		[[...] ...]			[math]\displaystyle{ 𝒄 }[/math]	[math]\displaystyle{ c_i }[/math]
[math]\displaystyle{ \dfrac1C }[/math]	[math]\displaystyle{ S }[/math]	Target-interval simplicity weight matrix	(See simplicities section of complexities and simplicities table)				[math]\displaystyle{ \scriptsize (k, k) }[/math]	Real	Matrix		[[...] ...]			[math]\displaystyle{ 𝒔 }[/math]	[math]\displaystyle{ s_i }[/math]	Entry-wise reciprocal of [math]\displaystyle{ C }[/math]
[math]\displaystyle{ \abs{\textbf{e}} W }[/math] [math]\displaystyle{ 1200×\slant{\mathbf{1}}L\abs{P - I} \mathrm{T}W }[/math]	[math]\displaystyle{ \textbf{d} }[/math]	Target-interval damage list	(See damages table)				[math]\displaystyle{ \scriptsize (1, k) }[/math]	Real	List	[...]					[math]\displaystyle{ \mathrm{d}_i }[/math]
	[math]\displaystyle{ k }[/math]	Target-interval count					[math]\displaystyle{ \scriptsize (1, 1) }[/math]	Integer	Scalar							Mnemonic: [math]\displaystyle{ k }[/math]ount
Held-intervals
	[math]\displaystyle{ \mathrm{H} }[/math]	Held-interval basis		[math]\displaystyle{ \small 𝗽 }[/math]	Primes		[math]\displaystyle{ \scriptsize (d, h) }[/math]		Matrix		[[...⟩ ...]		[math]\displaystyle{ \textbf{h}_i }[/math]		[math]\displaystyle{ \mathrm{h}_{ij} }[/math]
	[math]\displaystyle{ h }[/math]	Held-interval count					[math]\displaystyle{ \scriptsize (1, 1) }[/math]	Integer	Scalar
Exploring temperaments
	[math]\displaystyle{ \mathrm{C} }[/math]	Comma basis		[math]\displaystyle{ \small 𝗽 }[/math]	Primes		[math]\displaystyle{ \scriptsize (d, n) }[/math]	Integer	Matrix		[[...⟩ ...]		[math]\displaystyle{ \textbf{c}_i }[/math]		[math]\displaystyle{ \mathrm{c}_{ij} }[/math]	Jargon name: monzo list
	[math]\displaystyle{ \textbf{c} }[/math]	Comma		[math]\displaystyle{ \small 𝗽 }[/math]	Primes		[math]\displaystyle{ \scriptsize (d, 1) }[/math]	Integer	Vector		[...⟩				[math]\displaystyle{ \mathrm{c}_i }[/math]	Specific type: vector (prime-count vector or PC-vector)
Computation
	ꗨ⁠ ⁠ꗨ[math]\displaystyle{ \,·\, }[/math]ꗨ⁠ ⁠ꗨ[math]\displaystyle{ _p }[/math]	Power sum ([math]\displaystyle{ p }[/math]-sum)					[math]\displaystyle{ \scriptsize (1, 1) }[/math]	Real	Scalar
All-interval tuning schemes
[math]\displaystyle{ \mathrm{I} }[/math]	[math]\displaystyle{ \mathrm{T}_{\text{p}} }[/math]	Prime proxy target-interval list		[math]\displaystyle{ \small 𝗽 }[/math]	Primes		[math]\displaystyle{ \scriptsize (d, d) }[/math]	Integer	Matrix		⟨[...⟩ ...]			[math]\displaystyle{ \slant{\mathbf{1}} }[/math]
	[math]\displaystyle{ X }[/math]	Complexity pretransformer	[math]\displaystyle{ \small\mathsf{𝟙}\scriptsize\mathsf{(C)} }[/math] or [math]\displaystyle{ \small\mathsf{𝟙}\scriptsize\mathsf{(} }[/math]<alt>-[math]\displaystyle{ \scriptsize\mathsf{C)} }[/math]^{[note 6]}	[math]\displaystyle{ \small\mathsf{(C)} }[/math] or [math]\displaystyle{ \small\mathsf{(} }[/math]<alt>-[math]\displaystyle{ \small\mathsf{C)} }[/math]	Complexity weight or <alternative>-complexity weight		[math]\displaystyle{ \scriptsize (d, d) }[/math] or [math]\displaystyle{ \scriptsize (d+1, d+1) }[/math]	Real	Matrix	[⟨...] ...⟩		[math]\displaystyle{ 𝒙_i }[/math]		[math]\displaystyle{ 𝒙 }[/math]	[math]\displaystyle{ x_i }[/math] or [math]\displaystyle{ x_{ij} }[/math]
[math]\displaystyle{ \text{diag}({\large\textbf{𝓁}}\hspace{2mu}) }[/math]	[math]\displaystyle{ L }[/math]	Log-prime matrix		[math]\displaystyle{ \small\mathsf{oct} }[/math]/[math]\displaystyle{ \small 𝗽 }[/math]	Octaves per prime		[math]\displaystyle{ \scriptsize (d, d) }[/math]	Real	Matrix	[⟨...] ...⟩	⟨[...⟩ ...]	[math]\displaystyle{ {\large\textbf{𝓁}}\hspace{2mu}_i }[/math]		[math]\displaystyle{ {\large\textbf{𝓁}}\hspace{2mu} }[/math]	[math]\displaystyle{ {\large 𝓁}\hspace{2mu}_{ij} }[/math]
	[math]\displaystyle{ q }[/math]	Interval complexity norm power					[math]\displaystyle{ \scriptsize (1, 1) }[/math]	Real	Scalar
	[math]\displaystyle{ \norm{·}_q }[/math]	Power norm ([math]\displaystyle{ p }[/math]-norm)					[math]\displaystyle{ \scriptsize (1, 1) }[/math]	Real	Scalar
[math]\displaystyle{ \dfrac1{1-\frac1q} }[/math]	[math]\displaystyle{ \text{dual}(q) }[/math]	Dual norm power					[math]\displaystyle{ \scriptsize (1, 1) }[/math]	Real	Scalar
	[math]\displaystyle{ \norm{X\mathbf{i}}_q }[/math]	Interval complexity		[math]\displaystyle{ \small\mathsf{(C)} }[/math] or [math]\displaystyle{ \small\mathsf{(} }[/math]<alt>-[math]\displaystyle{ \small\mathsf{C)} }[/math]			[math]\displaystyle{ \scriptsize (1, 1) }[/math]	Real	Scalar
	[math]\displaystyle{ \norm{𝒓X^{-1}}_{\text{dual}(q)} }[/math]	Retuning magnitude		[math]\displaystyle{ \mathsf{¢}\small\mathsf{(C^{-1})} }[/math] or [math]\displaystyle{ \mathsf{¢}\small\mathsf{(} }[/math]<alt>-[math]\displaystyle{ \small\mathsf{C^{-1})} }[/math]			[math]\displaystyle{ \scriptsize (1, 1) }[/math]	Real	Scalar
Alternative complexities
	[math]\displaystyle{ 𝒑 }[/math]	Prime list^{[note 7]}					[math]\displaystyle{ \scriptsize (1, d) }[/math]	Integer	List	[...]					[math]\displaystyle{ p_i }[/math]
	[math]\displaystyle{ \slant{\mathbf{1}} }[/math]	Summation map					[math]\displaystyle{ \scriptsize (1, d) }[/math]	Integer	Vector	⟨...]					[math]\displaystyle{ 1 }[/math]
	[math]\displaystyle{ 1200 }[/math]	Octaves-to-cents conversion		¢/oct	Cents per octave		[math]\displaystyle{ \scriptsize (1, 1) }[/math]	Integer	Scalar
	[math]\displaystyle{ Z }[/math]	Size-sensitizing matrix					[math]\displaystyle{ \scriptsize (d+1, d) }[/math]	Real	Matrix	[⟨…]...]		[math]\displaystyle{ 𝒛_i }[/math]			[math]\displaystyle{ z_{ij} }[/math]
Non-standard domain bases
	[math]\displaystyle{ B_s }[/math]	(Domain) basis (change) matrix		[math]\displaystyle{ \small 𝗽 }[/math]/[math]\displaystyle{ \small 𝗯 }[/math]	Primes per nonprime basis elements		[math]\displaystyle{ \scriptsize (d_p, d_b) }[/math]	Integer	Matrix	[[...] ...]	[[...] ...]		[math]\displaystyle{ b_i }[/math]		[math]\displaystyle{ b_{ij} }[/math]
	[math]\displaystyle{ B_{Ls} }[/math]	(Domain) basis (change) matrix		[math]\displaystyle{ \small 𝗕 }[/math]/[math]\displaystyle{ \small 𝗯 }[/math]	Superspace basis elements per (subspace) basis elements		[math]\displaystyle{ \scriptsize (d_L, d_s) }[/math]	Integer	Matrix	[[...] ...]	[[...] ...]		[math]\displaystyle{ b_i }[/math]		[math]\displaystyle{ b_{ij} }[/math]
Embedding and projection
	[math]\displaystyle{ G }[/math]	Generator embedding (matrix)		[math]\displaystyle{ \small 𝗽 }[/math]/[math]\displaystyle{ \small 𝗴 }[/math]	Primes per generator		[math]\displaystyle{ \scriptsize (d, r) }[/math]	Real	Matrix	[{...] ...⟩	{[...⟩ ...]	[math]\displaystyle{ 𝒈_i }[/math]			[math]\displaystyle{ g_{ij} }[/math]
[math]\displaystyle{ G_cF^{-1}FM_c }[/math] [math]\displaystyle{ \mathrm{V}\textit{Λ}\mathrm{V}^{-1} }[/math]	[math]\displaystyle{ P }[/math]	Projection (matrix)	[math]\displaystyle{ \scriptsize \begin{array} {c} G \\[-2pt] 𝗽 \hspace{-2mu} / \hspace{-2mu} \cancel{𝗴} \end{array} \begin{array} {c} \\[-2pt] · \end{array} \begin{array} {c} M \\[-2pt] \cancel{𝗴} \hspace{-2mu} / \hspace{-2mu} 𝗽 \end{array} }[/math]	[math]\displaystyle{ \small 𝗽 }[/math]/[math]\displaystyle{ \small 𝗽 }[/math]	Primes per prime	[math]\displaystyle{ \scriptsize \! \! \begin{array} {c} G \\[-3pt] \left(d, \cancel{r}\right) \end{array} \! \! \begin{array} {c} M \\[-3pt] \left(\cancel{r}, d\right) \end{array} \! \! }[/math]	[math]\displaystyle{ \scriptsize (d, d) }[/math]	Real	Matrix	[⟨...] ...⟩	⟨[...⟩ ...]	[math]\displaystyle{ 𝒑_i }[/math]			[math]\displaystyle{ p_i }[/math]
[math]\displaystyle{ GM\textbf{i} }[/math]	[math]\displaystyle{ P\textbf{i} }[/math]	Projected interval	[math]\displaystyle{ \scriptsize \begin{array} {c} G \\[-2pt] 𝗽 \hspace{-2mu} / \hspace{-2mu} \cancel{𝗴} \end{array} \begin{array} {c} \\[-2pt] · \end{array} \begin{array} {c} M \\[-2pt] \cancel{𝗴} \hspace{-2mu} / \hspace{-2mu} \cancel{𝗽} \end{array} \begin{array} {c} \\[-2pt] · \end{array} \begin{array} {c} \textbf{i} \\[-2pt] \cancel{𝗽} \end{array} }[/math]	[math]\displaystyle{ \small 𝗽 }[/math]	Primes	[math]\displaystyle{ \scriptsize \! \! \begin{array} {c} G \\[-3pt] \left(d, \cancel{r}\right) \end{array} \! \! \begin{array} {c} M \\[-3pt] \left(\cancel{r}, \cancel{d}\right) \end{array} \! \! \begin{array} {c} \textbf{i} \\[-3pt] \left(\cancel{d}, 1\right) \end{array} \! \! }[/math]	[math]\displaystyle{ \scriptsize (d, 1) }[/math]	Real	Vector		[...⟩					Specific type: vector (prime-count vector or PC-vector)
	[math]\displaystyle{ \mathrm{U} }[/math]	Unchanged-interval basis		[math]\displaystyle{ \small 𝗽 }[/math]	Primes		[math]\displaystyle{ \scriptsize (d, r) }[/math]		Matrix		[[...⟩ ...]		[math]\displaystyle{ \textbf{u}_i }[/math]		[math]\displaystyle{ \mathrm{u}_{ij} }[/math]	Jargon name: eigenmonzo list
	[math]\displaystyle{ \textit{Λ} }[/math]	Scaling factor (eigenvalue) matrix					[math]\displaystyle{ \scriptsize (d, d) }[/math]		Matrix	[⟨…] …⟩	⟨[…⟩ …]			[math]\displaystyle{ 𝝀 }[/math]	[math]\displaystyle{ λ_i }[/math]	Mnemonic: [math]\displaystyle{ \mathrm{V} }[/math] is mirrored of [math]\displaystyle{ \textit{Λ} }[/math] which it combines with to create the projection matrix; previous name: eigenvalue matrix
	[math]\displaystyle{ \mathrm{V} }[/math]	Unrotated vector (eigenvector) list		[math]\displaystyle{ \small 𝗽 }[/math]	Primes		[math]\displaystyle{ \scriptsize (d, d) }[/math]		Matrix		⟨[...⟩ ...]		[math]\displaystyle{ \textbf{v}_i }[/math]		[math]\displaystyle{ \mathrm{v}_{ij} }[/math]	Mnemonic: [math]\displaystyle{ \mathrm{V} }[/math] is mirrored of [math]\displaystyle{ \textit{Λ} }[/math] which it combines with to create the projection matrix; jargon name: eigenmonzo and comma list
	[math]\displaystyle{ F }[/math]	Generator form matrix					[math]\displaystyle{ \scriptsize (r, r) }[/math]		Matrix	[{...] …}			[math]\displaystyle{ 𝒇_i }[/math]		[math]\displaystyle{ f_{ij} }[/math]
[math]\displaystyle{ I }[/math]	[math]\displaystyle{ M_{\text{j}} }[/math]	JI mapping (matrix)		[math]\displaystyle{ \small 𝗴 }[/math]/[math]\displaystyle{ \small 𝗽 }[/math]	Generators per prime		[math]\displaystyle{ \scriptsize (d, d) }[/math]	Integer	Matrix	[⟨...] ...}	⟨[...} ...]			[math]\displaystyle{ \slant{\mathbf{1}} }[/math]
[math]\displaystyle{ I }[/math]	[math]\displaystyle{ G_{\text{j}} }[/math]	JI generator embedding (matrix)		[math]\displaystyle{ \small 𝗽 }[/math]/[math]\displaystyle{ \small 𝗴 }[/math]	Primes per generator		[math]\displaystyle{ \scriptsize (d, d) }[/math]	Integer	Matrix	[{...] ...⟩	{[...⟩ ...]			[math]\displaystyle{ \slant{\mathbf{1}} }[/math]
	[math]\displaystyle{ K }[/math]	Constraint (matrix)					[math]\displaystyle{ \scriptsize (k, r) }[/math]	[math]\displaystyle{ \scriptsize \{0, +1, -1\} }[/math]	Matrix	[[...] ...]		[math]\displaystyle{ 𝒌_i }[/math]			[math]\displaystyle{ k_{ij} }[/math]	Mnemonic: [math]\displaystyle{ K }[/math]onstraint
	[math]\displaystyle{ 𝒃 }[/math]	(Generator tuning map) blend map					[math]\displaystyle{ \scriptsize (1, τ-1) }[/math]	Real	Vector	[...]					[math]\displaystyle{ b_i }[/math]
	[math]\displaystyle{ B }[/math]	(Generator tuning map) blend matrix					[math]\displaystyle{ \scriptsize (d, τ-1) }[/math]	Real	Matrix	[[...⟩...]			[math]\displaystyle{ 𝒃_{i} }[/math]		[math]\displaystyle{ b_{ij} }[/math]
	[math]\displaystyle{ D }[/math]	(Generator tuning map) deltas matrix		[math]\displaystyle{ \mathsf{¢} }[/math]/[math]\displaystyle{ \small 𝗴 }[/math]	Cents per generator		[math]\displaystyle{ \scriptsize (τ-1,r) }[/math]	Real	Matrix	[{...] ...]		[math]\displaystyle{ 𝜹_i }[/math]			[math]\displaystyle{ 𝛿_{ij} }[/math]
	[math]\displaystyle{ τ }[/math]	Tied basic minimax tuning count						Integer	Scalar
Exterior algebra
	[math]\displaystyle{ 𝕞 }[/math]	Multimap		[math]\displaystyle{ \small 𝗴 }[/math]/[math]\displaystyle{ \small 𝗽 }[/math]	Generators per prime		[math]\displaystyle{ \scriptsize (1, d) }[/math]	Integer	Multivector	⟨...] or ⟨⟨...]] or ⟨⟨⟨...]]] ...					[math]\displaystyle{ 𝕞_i }[/math]
	[math]\displaystyle{ 𝕔 }[/math]	Multicomma		[math]\displaystyle{ \small 𝗽 }[/math]	Primes		[math]\displaystyle{ \scriptsize (1, n) }[/math]	Integer	Multivector		[...⟩ or [[...⟩⟩ or [[[...⟩⟩⟩ ...				[math]\displaystyle{ 𝕔_i }[/math]
	[math]\displaystyle{ 𝕧 }[/math]	(Generic temperament multivector)					[math]\displaystyle{ \scriptsize (1, {{d}\choose{r}}) }[/math] or [math]\displaystyle{ \scriptsize (1, {{d}\choose{n}}) }[/math]	Integer	Multivector	⟨...] or ⟨⟨...]] or ⟨⟨⟨...]]] ...	[...⟩ or [[...⟩⟩ or [[[...⟩⟩⟩ ...				[math]\displaystyle{ 𝕧_i }[/math]
	[math]\displaystyle{ A }[/math]	(Generic temperament matrix)					[math]\displaystyle{ \scriptsize (g, d) }[/math] or [math]\displaystyle{ \scriptsize (d, g) }[/math]	Integer	Matrix	[⟨...] ...}	⟨[...} ...] or [[...⟩ ...]	[math]\displaystyle{ 𝒂_i }[/math]	[math]\displaystyle{ 𝒂_i }[/math]	[math]\displaystyle{ 𝒂 }[/math]	[math]\displaystyle{ a_{ij} }[/math]
	[math]\displaystyle{ v }[/math]	Variance
	[math]\displaystyle{ g }[/math]	Grade					[math]\displaystyle{ \scriptsize (1, 1) }[/math]	Integer	Scalar
Temperament addition
[math]\displaystyle{ \min(r, n) }[/math]	[math]\displaystyle{ g_\text{min} }[/math]	Min-grade					[math]\displaystyle{ \scriptsize (1, 1) }[/math]	Integer	Scalar
[math]\displaystyle{ \max(r, n) }[/math]	[math]\displaystyle{ g_\text{max} }[/math]	Max-grade					[math]\displaystyle{ \scriptsize (1, 1) }[/math]	Integer	Scalar
	[math]\displaystyle{ L_\text{dep} }[/math]	Linear-dependence basis					[math]\displaystyle{ \scriptsize \left(l_\text{dep}, d\right) }[/math] or [math]\displaystyle{ \scriptsize \left(d, l_\text{dep}\right) }[/math]	Integer	Matrix	[⟨...]] or [[...] ...⟩	⟨[...]] or [[...⟩ ...]	[math]\displaystyle{ {\large\textbf{𝓁}}\hspace{2mu}_{\text{dep}i} }[/math]	[math]\displaystyle{ {\large\textbf{𝓁}}\hspace{2mu}_{\text{dep}i} }[/math]	[math]\displaystyle{ {\large\textbf{𝓁}}\hspace{2mu}_\text{dep} }[/math]	[math]\displaystyle{ {\large 𝓁}\hspace{2mu}_{\text{dep}ij} }[/math]
	[math]\displaystyle{ L_\text{ind} }[/math]	Linear-independence basis					[math]\displaystyle{ \scriptsize \left(l_\text{ind}, d\right) }[/math] or [math]\displaystyle{ \scriptsize \left(d, l_\text{ind}\right) }[/math]	Integer	Matrix	[⟨...]] or [[...] ...⟩	⟨[...]] or [[...⟩ ...]	[math]\displaystyle{ {\large\textbf{𝓁}}\hspace{2mu}_{\text{ind}i} }[/math]	[math]\displaystyle{ {\large\textbf{𝓁}}\hspace{2mu}_{\text{ind}i} }[/math]	[math]\displaystyle{ {\large\textbf{𝓁}}\hspace{2mu}_\text{ind} }[/math]	[math]\displaystyle{ {\large 𝓁}\hspace{2mu}_{\text{ind}ij} }[/math]
[math]\displaystyle{ \dim(L_\text{dep}) }[/math]	[math]\displaystyle{ l_\text{dep} }[/math]	Linear-dependence					[math]\displaystyle{ \scriptsize (1, 1) }[/math]	Integer	Scalar
[math]\displaystyle{ \dim(L_\text{ind}) }[/math]	[math]\displaystyle{ l_\text{ind} }[/math]	Linear-independence					[math]\displaystyle{ \scriptsize (1, 1) }[/math]	Integer	Scalar

Units


Symbol	Name	Vectorized
[math]\displaystyle{ \small 𝗴 }[/math]	Generators	Yes
[math]\displaystyle{ \small 𝗽 }[/math]	Primes	Yes
[math]\displaystyle{ \small 𝗯 }[/math]	(Subspace) basis elements	Yes
[math]\displaystyle{ \small 𝗕 }[/math]	Superspace basis elements	Yes
[math]\displaystyle{ \mathsf{¢} }[/math]	Cents
[math]\displaystyle{ \mathsf{¢}\small{(} }[/math]<weight>[math]\displaystyle{ \small\mathsf{)} }[/math]	Weighted cents
[math]\displaystyle{ \small\mathsf{oct} }[/math]	Octaves

Tuning schemes


Retuning (or mistuning) magnitude						Damage												Target intervals	Systematic name		Previously named tuning schemes that are specific types of this tuning scheme	Of interest?
						Weight									Optimization
						Interval complexity						Slope			Initial	Name	Power
Norm pretransformer			Norm power			Norm pretransformer			Norm power			Initial	Name	Multiplier
Initial	Name	Multiplier	Initial	Name	Power	Initial	Name	Multiplier	Initial	Name	Power	Initial	Name	Multiplier					Abbreviated	Read ("____ tuning scheme")
<none>			<n/a>	Maximum	∞	<none>			(t)	Taxicab	1	S	Simplicity-weight	1/Complexity	<n/a>	Minimax	∞	All	Minimax-S	Minimax simplicity-weight damage	"TOP"/"T1"/"TIPTOP", "CTOP", "POTOP"/"POTT"	yes
<various>				Maximum	∞	<various>			(t)	Taxicab	1								Minimax-<alt>-S	Minimax <alternative>-simplicity-weight damage	"BOP", "Weil", "Kees"	yes
<none>				Euclidean	2	<none>			E	Euclidean	2								Minimax-ES	Minimax Euclideanized-simplicity-weight damage	"TE"/"T2"/"TOP-RMS", "CTE", "POTE"	yes
<various>				Euclidean	2	<various>			E	Euclidean	2								Minimax-E-<alt>-S	Minimax Euclideanized-<alternative>-simplicity-weight damage	"Frobenius", "BE", "WE", "KE"	Yes
<n/a>						<n/a>						U	Unity-weight	<none>				<set>	<set> Minimax-U	<set> Minimax unity-weight damage	"Minimax"	yes
						<none>			(t)	Taxicab	1	S	Simplicity-weight	1/Complexity					<set> Minimax-S	<set> Minimax simplicity-weight damage		Yes
						<various>			(t)	Taxicab	1								<set> Minimax-<alt>-S	<set> Minimax <alternative>-simplicity-weight damage
						<none>			E	Euclidean	2								<set> Minimax-ES	<set> Minimax Euclideanized-simplicity-weight damage
						<various>			E	Euclidean	2								<set> Minimax-E-<alt>-S	<set> Minimax Euclideanized-<alternative>-simplicity-weight damage
						<none>			(t)	Taxicab	1	C	Complexity-weight	Complexity					<set> Cinimax-C	<set> Cinimax complexity-weight damage		Yes
						<various>			(t)	Taxicab	1								<set> Minimax-<alt>-C	<set> Minimax <alternative>-complexity-weight damage
						<none>			E	Euclidean	2								<set> Minimax-EC	<set> Minimax Euclideanized-complexity-weight damage
						<various>			E	Euclidean	2								<set> Minimax-E-<alt>-C	<set> Minimax Euclideanized-<alternative>-complexity-weight damage
						<n/a>						U	Unity-weight	<none>		MiniRMS	2		<set> MiniRMS-U	<set> MiniRMS unity-weight damage	"Least squares"	yes
						<none>			(t)	Taxicab	1	S	Simplicity-weight	1/Complexity					<set> MiniRMS-S	<set> MiniRMS simplicity-weight damage		Yes
						<various>			(t)	Taxicab	1								<set> MiniRMS-<alt>-S	<set> MiniRMS <alternative>-simplicity-weight damage
						<none>			E	Euclidean	2								<set> MiniRMS-ES	<set> MiniRMS Euclideanized-simplicity-weight damage
						<various>			E	Euclidean	2								<set> MiniRMS-E-<alt>-S	<set> MiniRMS Euclideanized-<alternative>-simplicity-weight damage
						<none>			(t)	Taxicab	1	C	Complexity-weight	Complexity					<set> MiniRMS-C	<set> MiniRMS complexity-weight damage		yes
						<various>			(t)	Taxicab	1								<set> MiniRMS-<alt>-C	<set> MiniRMS <alternative>-complexity-weight damage
						<none>			E	Euclidean	2								<set> MiniRMS-EC	<set> MiniRMS Euclideanized-complexity-weight damage
						<various>			E	Euclidean	2								<set> MiniRMS-E-<alt>-C	<set> MiniRMS Euclideanized-<alternative>-complexity-weight damage
						<n/a>						U	Unity-weight	<none>		Miniaverage	1		<set> Miniaverage-U	<set> Miniaverage unity-weight damage		yes
						<none>			(t)	Taxicab	1	S	Simplicity-weight	1/Complexity					<set> Miniaverage-S	<set> Miniaverage simplicity-weight damage		Yes
						<various>			(t)	Taxicab	1								<set> Miniaverage-<alt>-S	<set> Miniaverage <alternative>-simplicity-weight damage
						<none>			E	Euclidean	2								<set> Miniaverage-ES	<set> Miniaverage Euclideanized-simplicity-weight damage
						<various>			E	Euclidean	2								<set> Miniaverage-E-<alt>-S	<set> Miniaverage Euclideanized-<alternative>-simplicity-weight damage
						<none>			(t)	Taxicab	1	C	Complexity-weight	Complexity					<set> Miniaverage-C	<set> Miniaverage complexity-weight damage		Yes
						<various>			(t)	Taxicab	1								<set> Miniaverage-<alt>-C	<set> Miniaverage <alternative>-complexity-weight damage
						<none>			E	Euclidean	2								<set> Miniaverage-EC	<set> Miniaverage Euclideanized-complexity-weight damage
						<various>			E	Euclidean	2								<set> Miniaverage-E-<alt>-C	<set> Miniaverage Euclideanized-<alternative>-complexity-weight damage

Damages


Quantity		Unit
Abbreviation	Name	Symbol	Name
U-damage	Unity-weight damage	[math]\displaystyle{ \mathsf{¢}\small\mathsf{(U)} }[/math]	Unity-weighted cents
C-damage	Complexity-weight damage	[math]\displaystyle{ \mathsf{¢}\small\mathsf{(C)} }[/math]	Complexity-weighted cents
<alt>-C-damage	<alternative>-complexity-weight damage	[math]\displaystyle{ \mathsf{¢} }[/math][math]\displaystyle{ \small\mathsf{(} }[/math]<alt>-[math]\displaystyle{ \small\mathsf{C)} }[/math]	<alternative>-complexity-weighted cents
EC-damage	Euclideanized-complexity-weight damage	[math]\displaystyle{ \mathsf{¢} }[/math][math]\displaystyle{ \small\mathsf{(EC)} }[/math]	Euclideanized-complexity-weighted cents
E-<alt>-C-damage	Euclideanized-<alternative>-complexity-weight damage	[math]\displaystyle{ \mathsf{¢} }[/math][math]\displaystyle{ \small\mathsf{(E} }[/math]-<alt>-[math]\displaystyle{ \small\mathsf{C)} }[/math]	Euclideanized-<alternative>-complexity-weighted cents
S-damage	Simplicity-weight damage	[math]\displaystyle{ \mathsf{¢}\small\mathsf{(S)} }[/math]	Simplicity-weighted cents
<alt>-S-damage	<alternative>-simplicity-weight damage	[math]\displaystyle{ \mathsf{¢} }[/math][math]\displaystyle{ \small\mathsf{(} }[/math]<alt>-[math]\displaystyle{ \small\mathsf{S)} }[/math]	<alternative>-simplicity-weighted cents
ES-damage	Euclideanized-simplicity-weight damage	[math]\displaystyle{ \mathsf{¢} }[/math][math]\displaystyle{ \small\mathsf{(ES)} }[/math]	Euclideanized-simplicity-weighted cents
E-<alt>-S-damage	Euclideanized-<alternative>-simplicity-weight damage	[math]\displaystyle{ \mathsf{¢} }[/math][math]\displaystyle{ \small\mathsf{(E} }[/math]-<alt>-[math]\displaystyle{ \small\mathsf{S)} }[/math]	Euclideanized-<alternative>-simplicity-weighted cents

Complexity and simplicity


Quantity		Unit
Abbreviation	Name	Unit	Name
C	Complexity	[math]\displaystyle{ \small\mathsf{𝟙}\scriptsize\mathsf{(C)} }[/math] = [math]\displaystyle{ \small\mathsf{(C)} }[/math]	Complexity weight
<alt>-C	<alternative> complexity	[math]\displaystyle{ \small\mathsf{𝟙}\scriptsize\mathsf{(} }[/math]<alt>-[math]\displaystyle{ \scriptsize\mathsf{C)} }[/math] = [math]\displaystyle{ \small\mathsf{(} }[/math]<alt>-[math]\displaystyle{ \small\mathsf{C)} }[/math]	<alternative>-complexity weight
EC	Euclideanized complexity	[math]\displaystyle{ \small\mathsf{𝟙}\scriptsize\mathsf{(EC)} }[/math] = [math]\displaystyle{ \small\mathsf{(EC)} }[/math]	Euclideanized-complexity weight
E-<alt>-C	Euclideanized-<alternative> complexity	[math]\displaystyle{ \small\mathsf{𝟙}\scriptsize\mathsf{(E} }[/math]-<alt>-[math]\displaystyle{ \scriptsize\mathsf{C)} }[/math] = [math]\displaystyle{ \small\mathsf{(E} }[/math]-<alt>-[math]\displaystyle{ \small\mathsf{C)} }[/math]	Euclideanized-<alternative>-complexity weight
S	Simplicity	[math]\displaystyle{ \small\mathsf{𝟙}\scriptsize\mathsf{(S)} }[/math] = [math]\displaystyle{ \small\mathsf{(S)} }[/math]	Simplicity weight
<alt>-S	<alternative> simplicity	[math]\displaystyle{ \small\mathsf{𝟙}\scriptsize\mathsf{(} }[/math]<alt>-[math]\displaystyle{ \scriptsize\mathsf{S)} }[/math] = [math]\displaystyle{ \small\mathsf{(} }[/math]<alt>-[math]\displaystyle{ \small\mathsf{S)} }[/math]	<alternative>-simplicity weight
ES	Euclideanized simplicity	[math]\displaystyle{ \small\mathsf{𝟙}\scriptsize\mathsf{(ES)} }[/math] = [math]\displaystyle{ \small\mathsf{(ES)} }[/math]	Euclideanized-simplicity weight
E-<alt>-S	Euclideanized-<alternative> simplicity	[math]\displaystyle{ \small\mathsf{𝟙}\scriptsize\mathsf{(E} }[/math]-<alt>-[math]\displaystyle{ \scriptsize\mathsf{S)} }[/math] = [math]\displaystyle{ \small\mathsf{(E} }[/math]-<alt>-[math]\displaystyle{ \small\mathsf{S)} }[/math]	Euclideanized-<alternative>-simplicity weight

WinCompose

Are you tired of every time web-searching for and copy-pasting special characters that you use over and over in RTT discussions, or would like to use if only it were easy, such as ♯, ♭, ¢, √, °, ₂, ×, ⁻¹, ⟩, ∞, and ϕ? Well, try WinCompose! This tool lets you communicate about these ideas without disrupting your train of thought, by typing these characters with simple and memorable key sequences. These sequences always begin with your chosen Compose-key, which defaults to being your right Alt key. When describing these sequences we represent this key with the symbol ⎄. So for example, you type ♯ as ⎄##, ♭ as ⎄bb, ¢ as ⎄c/, √ as ⎄v/, ° as ⎄00, ₂ as ⎄-2, × as ⎄xx, ⁻¹ as ⎄11, ⟩ as ⎄>>, ∞ as ⎄88, and ϕ as ⎄8f.

For Windows users, install WinCompose then copy-paste the contents of this file: https://dkeenan.com/XCompose.txt into your user sequences (Show sequences → User-defined sequences → Edit). Then save and reload. You can always choose to override or add alternatives to our sequences if you find others to be more intuitive.

For Mac users, we refer you to this repo, which gives tools and instructions for setting up key bindings as compose rules in Mac OS, and even comes pre-packaged with our rules: https://github.com/cmloegcmluin/compose2keybindings

Table of noteworthy sequences

Dave Keenan & Douglas Blumeyer's compose-key sequences
Compose-key sequence	Resulting text	Description
Keyboard key symbols
⎄⎄⎄	⎄	Compose key symbol (the right alt key by default)
⎄\␣	␣	Spacebar symbol
⎄\▶︎ etc.	▶︎ etc.	Right etc. arrow key symbols
⎄\A or ⎄\O	⌥	Alt or option key symbol
⎄\B	⌫	Backspace key symbol
⎄\C	✲	Control key symbol
⎄\D	⌦	Delete key symbol
⎄\E	⎋	Escape key symbol
⎄\L	⇪	Caps lock key symbol
⎄\R or ⎄\.E	⏎	Return or enter key symbol
⎄\S	⇧	Shift key symbol
⎄\T	⭾	Tab key symbol
⎄()	◌	Dotted circle, represents any character (such as the character preceding a combining mark)
Double key sequences
⎄␣␣		Narrow no-break space (used between quantities and their units)
⎄..	·	Middle dot (used to multiply units when juxtaposition is ambiguous)
⎄::	÷	Divide sign
⎄;;	◌̲̅	Combining overline and low line (undirected value)
⎄\| \|	‖	Power norm bracket
⎄<<	⟨	Left angle bracket
⎄>>	⟩	Right angle bracket
⎄~~	≈	Approximately equal
⎄**	★	Black star
⎄''	′	prime mark
⎄11	⁻¹	Power of −1 or inverse
⎄22 through ⎄77	² ³ ⁴ ⁵ ⁶ ⁷	Squared, cubed, fourth through seventh power
⎄88	∞	Infinity
⎄00	°	Degree sign
⎄nn	ⁿ	Superscript small n
⎄--	₋	Subscript minus sign
⎄__	◌̲	Combining low line (underline)
⎄==	≡	Modular congruence
⎄//	⁄	Fraction slash (use with super and subscripts to create fractions)
⎄##	♯	Musical sharp
⎄bb	♭	Musical flat
⎄dd	∂	Partial derivative
⎄ff	ϕ	Small phi symbol
⎄gg	ɡ	Single-storey (opentail) small g
⎄ll	ℓ	Script small L
⎄uu	µ	Micro sign
⎄xx	×	Multiplication sign
⎄DD	∆	Delta (small difference) operator
⎄FF	Φ	Greek capital phi
⎄QQ	Ϙ	Greek capital letter archaic qoppa (small quotient operator)
⎄TT	ᵀ	Superscript capital T (matrix transpose)
⎄++	⁺	Superscript plus sign (matrix pseudoinverse)
⎄▶︎▶︎ etc.	→ etc.	Right etc. arrows
Multiplication operators
⎄xx	×	Multiplication sign
⎄Xx or ⎄xX	⨯	Vector or cross product (barely distinguishable from multiplication sign)
⎄XX	✕	Large multiplication sign (a better symbol for cross product)
⎄x*	⋆	Star operator (prefix: tensor complement, Hodge)
⎄X*	∗	Asterisk operator (infix: scalar product, Dorst)
⎄x.	⋅	Dot (product) operator
⎄X.	•	Bullet (infix: fat dot product, Dorst)
Other operators
⎄v/	√	Square root sign
⎄3v/	∛	Cube root sign
⎄4v/	∜	Fourth root sign
⎄-+	₊	Subscript plus sign
⎄--	₋	Subscript minus sign
⎄-=	₌	Subscript equals sign
⎄++	⁺	Superscript plus sign (matrix pseudoinverse)
⎄+- or ⎄+=	±	Plus or minus sign
⎄=+	∓	Minus or plus sign
⎄=-	−	Minus sign
⎄==	≡	Modular congruence
⎄/\	∧	Logical AND, wedge product, progressive product
⎄\/	∨	Logical OR, vee product, regressive product
⎄⎄/\	⋀	Larger logical AND, wedge product, progressive product
⎄⎄\/	⋁	Larger logical OR, vee product, regressive product
⎄\| _	⌊	Left floor (infix: right contraction, Dorst)
⎄_\|	⌋	Right floor (infix: left contraction, Dorst)
⎄\| ^	⌈	Left ceiling
⎄^\|	⌉	Right ceiling
⎄'-	⨽	Righthand interior product
⎄-'	⨼	(Left-hand) interior product
⎄-,	¬	Not sign (prefix: multivector complement)
⎄⎄<>	⋄	Diamond operator (prefix: multivector dual)
⎄(.)	⨀	Entry-wise vector multiplication operator
⎄(..)	⊙	Alternative entry-wise vector multiplication operator
⎄(/)	⊘	Entry-wise vector division operator
Mathematical letter and digit prefixes
⎄3◌	я	Cyrillic, ⎄3q is ya (example)
⎄4◌	ℵ	Hebrew, ⎄4a is aleph (example)
⎄5◌	𝔞	Fraktur, ⎄5a
⎄6◌	ᵃ ¹  ᪲ ⁸	Superscripts, ⎄6a ⎄61 ⎄688 ⎄68␣ (not all letters, some only approximate) (same key as ^ but without shift)
⎄68◌	ᵝ	Superscript greek, ⎄68b is superscript beta (only a few)
⎄7◌	𝒶	Script, ⎄7a
⎄8◌	α	Greek, ⎄8a is alpha (by sound where possible otherwise letter-shape)
⎄8.◌	ς	Greek variants, ⎄8.s is final sigma
⎄9◌	𝐚 𝟏 𝟓 𝟕 𝟖 𝟎	Bold, ⎄9a ⎄91 ⎄95␣ ⎄97␣ ⎄98␣ ⎄90␣
⎄95◌	𝖆	Bold fraktur, ⎄95a
⎄97◌	𝓪	Bold script, ⎄97a
⎄98◌	𝛂	Bold greek, ⎄98a is bold alpha
⎄90◌	𝒂	Bold italic, ⎄90a
⎄908◌	𝜶	Bold italic greek, ⎄908a is bold italic alpha
⎄0◌	𝑎	Italic, ⎄0a
⎄08◌	𝛼	Italic greek, ⎄08a is italic alpha
⎄-◌	ₐ ᴀ  ͚ ₈	Subscripts and small caps, ⎄-a ⎄-A ⎄-88 ⎄-8␣ (not all letters, some only approximate) (same key as _ but without shift)
⎄-8◌	ᵦ	Subscript greek, ⎄-8b is subscript beta (only a few)
⎄{◌	𝖺 𝟣 𝟫	Sans-serif, ⎄{a ⎄{1 ⎄{9␣
⎄{9◌	𝗮 𝟭	Sans-serif bold, ⎄{9a ⎄{91
⎄}◌	𝚊 𝟷	Monospace, ⎄}a ⎄}1
⎄\| ◌	𝕒 𝟙 𝟠 𝟘	Double-struck, ⎄\| a ⎄\| 1 ⎄\| 8␣ ⎄\| 0␣
⎄\| 8◌	ℼ	Double-struck greek, ⎄\| 8p (only a few)
⎄\| 0◌	ⅇ ⅈ	Double-struck italic, ⎄\| 0e ⎄\| i (only a few)
Power statistics brackets
⎄\| \|	‖	Power-norm bracket
⎄\|-1	‖₁	1-Norm right bracket
⎄\|-2	‖₂	2-Norm right bracket
⎄\|-8	‖ ͚	∞-Norm right bracket
⎄⎄<<	⟪	Left power-mean bracket
⎄⎄>>	⟫	Right power-mean bracket
⎄⎄{{	⧛	Left power-sum bracket (substitute for ꗨ⁠ ⁠ꗨ when HTML is not available)
⎄⎄}}	⧚	Right power-sum bracket (substitute for ꗨ⁠ ⁠ꗨ when HTML is not available)
Combining marks
⎄\-	◌̶	Combining strike-thru
⎄^_	◌̅	Combining overline
⎄__	◌̲	Combining low line
⎄;; or ⎄-_ or ⎄_^	◌̲̅	Combining overline and low line (undirected value)

Keyboard map

Footnotes

↑ The advanced section also contains conventions collected from other RTT-related articles Dave and Douglas have contributed to but are outside the main guide to RTT series.
↑ For educational purposes, we use the 𝟙 symbol here to represent the implicit dimensionless unit that the weighting annotation "(C)" is attached to. But this symbol should not be shown in the reduced result. Another way to understand how we arrive at a bare annotation for the units of this quantity is to consider that w = d/|e| whose units are ¢(W) / ¢ and the cents cancel.
↑ You may sometimes see annotated units without parentheses, such as "dBA", but this is not compliant with SI standards, so we always keep the parentheses.
↑ Per https://physics.nist.gov/cuu/Units/checklist.html and https://academia.stackexchange.com/questions/54885/should-there-be-a-space-between-a-value-and-the-units-used .
↑ It seems there is no standard symbol for a musical cent, except the word spelled in full (see https://en.wikipedia.org/wiki/Cent_(music)). But it seems unlikely anyone will interpret the cent currency symbol "¢" following a number in a musical context as anything other than musical cents.
↑ In these tables, "alternative" means any complexity other than the default of log-product complexity, and "alt" stands for its abbreviation.
↑ May be used for a prime-limit or for any prime-only list.

[1] The advanced section also contains conventions collected from other RTT-related articles Dave and Douglas have contributed to but are outside the main guide to RTT series.

[2] For educational purposes, we use the 𝟙 symbol here to represent the implicit dimensionless unit that the weighting annotation "(C)" is attached to. But this symbol should not be shown in the reduced result. Another way to understand how we arrive at a bare annotation for the units of this quantity is to consider that w = d/|e| whose units are ¢(W) / ¢ and the cents cancel.

[3] You may sometimes see annotated units without parentheses, such as "dBA", but this is not compliant with SI standards, so we always keep the parentheses.

[4] Per https://physics.nist.gov/cuu/Units/checklist.html and https://academia.stackexchange.com/questions/54885/should-there-be-a-space-between-a-value-and-the-units-used .

[5] It seems there is no standard symbol for a musical cent, except the word spelled in full (see https://en.wikipedia.org/wiki/Cent_(music)). But it seems unlikely anyone will interpret the cent currency symbol "¢" following a number in a musical context as anything other than musical cents.

[6] In these tables, "alternative" means any complexity other than the default of log-product complexity, and "alt" stands for its abbreviation.

[7] May be used for a prime-limit or for any prime-only list.

[note 1]

[note 2]

[note 3]

[note 4]

[note 5]

[note 6]

[note 7]

Dave Keenan & Douglas Blumeyer's guide to RTT/Conventions for names, variables, units, and notations: Difference between revisions

Latest revision as of 01:44, 7 August 2025

Contents

Basic

Objects

Units

Tuning schemes

Damages

Complexity and simplicity

Intermediate

Objects

Units

Tuning schemes

Damages

Complexity and simplicity

Advanced

Objects

Units

Tuning schemes

Damages

Complexity and simplicity

WinCompose

Table of noteworthy sequences

Keyboard map

Footnotes

Navigation menu

@@ Line 1: / Line 1: @@
-This is an appendix to [[Dave Keenan]] & [[Douglas Blumeyer]]'s guide to RTT, or "[[D&D's guide]]" for short. The tables in this article present our recommendations for communicating about [[regular temperament theory]] (RTT), in particular the names and notations for temperament matrices, tuning schemes, interval complexities, and measurement units.
+{{breadcrumb}}{{texops}}{{texmap}}{{texzz}}
+This is an appendix to [[Dave Keenan]] & [[Douglas Blumeyer]]'s guide to RTT. The tables in this article present our recommendations for communicating about [[regular temperament theory]] (RTT), in particular the names and notations for temperament matrices, tuning schemes, interval complexities, and measurement units.
 Our recommendations are designed to make this topic easy to learn for musicians who do not have technical backgrounds, though we have generally deferred to established mathematical, scientific, and engineering conventions for the benefit of those who do.
-For more information on our variation on extended bra-ket notation, please see [[Extended_bra-ket_notation#Variant_including_curly_and_square_brackets|Extended bra-ket notation: Variant including curly and square brackets]].
+See [[Extended bra-ket notation#Variant including curly and square brackets|here]] for more information on our variation on extended bra-ket notation.
-We've followed a symbol formatting pattern, explained by the table below, which we hope serves as an aid to quickly identifying objects and remembering their properties and purposes, but at the least we hope our choices are unobtrusive. In short, the objects with simple units of primes, generators or cents, i.e. the things which are actually audible in our application, are distinguished by upright formatting, while other variables are italic as is conventional. This is crossed with the mathematical convention that objects of order-1 like vectors are bolded and order-2 like matrices are uppercased:
+We've followed a variable styling convention, explained in the table below, which we hope serves as an aid to quickly identifying objects and remembering their properties and purposes, but at the least we hope our choices are unobtrusive. In short, the objects with simple units of primes, generators or cents, i.e. the things which are actually audible in our application, are distinguished by upright formatting, while other variables are italic as is conventional. This is crossed with the linear-algebra convention that objects of order-1 like vectors are bolded and order-2 like matrices are uppercased:
 {| class="wikitable center-all"
-|+
+|-
 !
-|    units →
+| Units &rarr;
-! rowspan="2" |
+! rowspan="2" | &nbsp;
-|simple units
+| Simple units
-|compound or no units
+| Compound or no units
 |-
-| ↓ order
+| &darr; Order
-|  ↓ style →
+| &darr; Style &rarr;
-|upright
+| Roman (upright)
-|''italic''
+| ''Italic''
 |-
 ! scope="col" height="8px" ! colspan="2" |
@@ Line 25: / Line 25: @@
 ! colspan="2" |
 |-
-|0
+| 0
-|plain
+| lowercase
-! rowspan="3" |
+! rowspan="3" | &nbsp;
-|scalar with simple unit
+| scalar (with simple unit)
-|''scalar'' with no unit
+| ''scalar'' (with no unit)
 |-
-|1
+| 1
-|'''bold'''
+| '''bold lowercase'''
-|'''vector'''
+| '''vector'''
-|'''''map''''' (covector)
+| '''''map''''' (row vector)
 |-
-|2
+| 2
-|UPPERCASE
+| UPPERCASE
-|LIST or BASIS
+| BASIS or LIST (of vectors)
-|true ''MATRIX''
+| ''MATRIX''
 |}
-We present our conventions here in three separate sections, one for each level of this article series: '''basic''', '''intermediate''', and '''advanced'''. The basic section contains only information covered in the basic part of the series, the intermediate section contains both basic and intermediate, and the advanced section contains it all (that is to say, the sections are cumulative)<ref>The advanced section also contains conventions collected from other RTT-related articles Dave and Douglas have contributed to but are outside the main guide to RTT series.</ref>. We expect that for most readers, the basic tier will be the best reference (this is the reference designed primarily for musicians interested in RTT, as opposed to scientists, engineers, mathematicians, or theoreticians), and so we've left the other two sections initially collapsed.
+We present our conventions here in three separate sections, one for each level of this article series: '''basic''', '''intermediate''', and '''advanced'''. The basic section contains only information covered in the basic part of the series, the intermediate section contains both basic and intermediate, and the advanced section contains it all (that is to say, the sections are cumulative)<ref group="note">The advanced section also contains conventions collected from other RTT-related articles Dave and Douglas have contributed to but are outside the main guide to RTT series.</ref>. We expect that for most readers, the basic tier will be the best reference (this is the reference designed primarily for musicians interested in RTT, as opposed to scientists, engineers, mathematicians, or theoreticians), and so we've left the other two sections initially collapsed.
-==Basic==
-===Objects===
+== Basic ==
+=== Objects ===
 {| class="wikitable mw-collapsible"
-|+
+|+ style="font-size: 105%;" |
-! rowspan="2" |equivalent expressions
+|-
-! rowspan="2" |variable
+! rowspan="2" | Equivalent<br />expressions
-! rowspan="2" |name
+! rowspan="2" | Variable
-! colspan="3" |units
+! rowspan="2" | Name
-! colspan="2" |shape
+! colspan="3" | Units
-! colspan="2" |type
+! colspan="2" | Shape
-! colspan="2" |EBK notation
+! colspan="2" | Type
-! colspan="4" |subobjects
+! colspan="2" | EBK notation
-! rowspan="2" |notes
+! colspan="4" | Subobjects
+! rowspan="2" | Notes
 |-
-!unreduced
+! Unreduced
-!reduced
+! Reduced
-!read as
+! Read as
-!unreduced
+! Unreduced
-!reduced
+! Reduced
-!numeric
+! Numeric
-!structural
+! Structural
-!row-first
+! Row-first
-!col-first
+! Col-first
-!row
+! Row
-!col
+! Column
-!diag
+! Diagonal
-!entry
+! Entry
 |-
-! colspan="17" |mapping
+! colspan="17" | Mapping
 |-
 |
-|<math>\textbf{i}</math>
+| <math>\textbf{i}</math>
-|[[interval|(just) interval]]
+| [[interval|(Just) interval]]
 |
-|<math>\small 𝗽</math>
+| <math>\small 𝗽</math>
-|primes
+| Primes
 |
-|<math>\scriptsize (d, 1)</math>
+| <math>\scriptsize (d, 1)</math>
-|integer
+| Integer
-|vector
+| Vector
 |
-|[...⟩
+| [...⟩
 |
 |
 |
-|<math>\mathrm{i}_i</math>
+| <math>\mathrm{i}_i</math>
-|specific type: [[prime-count vector]] (PC-vector)
+| Specific type: Vector ([[prime-count vector]] or PC-vector)
-jargon name: monzo
+Jargon name: Monzo
 |-
 |
-|<math>M</math>
+| <math>M</math>
-|[[Mapping|(temperament) mapping (matrix)]]
+| [[Mapping|(Temperament) mapping (matrix)]]
 |
-|<math>\small 𝗴</math>/<math>\small 𝗽</math>
+| <math>\small 𝗴</math>/<math>\small 𝗽</math>
-|generators per prime
+| Generators per prime
 |
-|<math>\scriptsize (r, d)</math>
+| <math>\scriptsize (r, d)</math>
-|integer
+| Integer
-|matrix
+| Matrix
-|[⟨...] ...}
+| [⟨...] ...}
-|⟨[...} ...]
+| ⟨[...} ...]
-|<math>𝒎_i</math>
+| <math>𝒎_i</math>
 |
 |
-|<math>m_{ij}</math>
+| <math>m_{ij}</math>
-|jargon name: val list
+| Jargon name: Val list
 |-
-|<math>M\textbf{i}</math>
+| <math>M\textbf{i}</math>
-|<math>\textbf{y}</math>
+| <math>\textbf{y}</math>
-|[[mapped interval]]
+| [[Mapped interval]]
-|<math>\scriptsize
+| <math>\scriptsize
 \begin{array} {c} M \\[-2pt] 𝗴 \hspace{-2mu} / \hspace{-2mu} \cancel{𝗽} \end{array}
 \begin{array} {c} \\[-2pt] · \end{array}
 \begin{array} {c} \textbf{i} \\[-2pt] \cancel{𝗽} \end{array}
 </math>
-|<math>\small 𝗴</math>
+| <math>\small 𝗴</math>
-|generators
+| Generators
-|<math>\scriptsize
+| <math>\scriptsize
-\!\!
+\! \!
 \begin{array} {c} M \\[-3pt] (r, \cancel{d}) \end{array}
-\!\!
+\! \!
 \begin{array} {c} \textbf{i} \\[-3pt] (\cancel{d}, 1) \end{array}
-\!\!
+\! \!
 </math>
-|<math>\scriptsize (r, 1)</math>
+| <math>\scriptsize (r, 1)</math>
-|integer
+| Integer
-|vector
+| Vector
 |
-|[...}
+| [...}
 |
 |
 |
 |
-|specific type: [[generator-count vector]] (GC-vector)
+| Specific type: [[Generator-count vector]] (GC-vector)
-jargon name: tmonzo; mnemonic: <math>\textbf{y}</math>nterval
+Jargon name: tmonzo; mnemonic: <math>\textbf{y}</math>nterval
 |-
 |
-|<math>𝒎</math>
+| <math>𝒎</math>
-|[[map|(temperament) map]]
+| [[map|(Temperament) map]]
 |
-|<math>\small 𝗴</math>/<math>\small 𝗽</math>
+| <math>\small 𝗴</math>/<math>\small 𝗽</math>
-|generators per prime
+| Generators per prime
 |
-|<math>\scriptsize (1, d)</math>
+| <math>\scriptsize (1, d)</math>
-|integer
+| Integer
-|vector
+| Vector
-|⟨...]
+| ⟨...]
 |
 |
 |
 |
-|<math>m_i</math>
+| <math>m_i</math>
-|jargon name: val
+| Jargon name: val
 |-
 |
-|<math>d</math>
+| <math>d</math>
-|[[dimensionality]]
+| [[dimensionality]]
 |
 |
 |
 |
-|<math>\scriptsize (1, 1)</math>
+| <math>\scriptsize (1, 1)</math>
-|integer
+| Integer
-|scalar
+| Scalar
 |
 |
 |
 |
 |
 |
 |
 |-
 |
-|<math>r</math>
+| <math>r</math>
-|[[rank]]
+| [[Rank]]
 |
 |
 |
 |
-|<math>\scriptsize (1, 1)</math>
+| <math>\scriptsize (1, 1)</math>
-|integer
+| Integer
-|scalar
+| Scalar
 |
 |
 |
 |
 |
 |
 |
 |-
-! colspan="17" |tuning
+! colspan="17" | Tuning
 |-
 |
-|<math>𝒋</math>
+| <math>{\large\textbf{𝓁}}\hspace{2mu}</math>
-|[[just tuning map|just(-prime) tuning map]]
+| [[Log-prime map]]
 |
-|<math>\mathsf{¢}</math>/<math>\small 𝗽</math>
+| <math>\small\mathsf{oct}</math>/<math>\small 𝗽</math>
-|cents per prime
+| Octaves per prime
 |
-|<math>\scriptsize (1, d)</math>
+| <math>\scriptsize (1, d)</math>
-|real
+| Real
-|vector
+| Vector
-|⟨...]
+| ⟨...]
 |
 |
 |
 |
-|<math>j_i</math>
+| <math>{\large 𝓁}\hspace{2mu}_i</math>
 |
 |-
-|
+| <math>1200×{\large\textbf{𝓁}}\hspace{2mu}</math>
-|<math>𝒈</math>
+| <math>𝒋</math>
-|[[generator tuning map]]
+| [[just tuning map|Just(-prime) tuning map]]
 |
-|<math>\mathsf{¢}</math>/<math>\small 𝗴</math>
+| <math>\mathsf{¢}</math>/<math>\small 𝗽</math>
-|cents per generator
+| Cents per prime
 |
-|<math>\scriptsize (1, r)</math>
+| <math>\scriptsize (1, d)</math>
-|real
+| Real
-|vector
+| Vector
-|{...]
+| ⟨...]
 |
 |
 |
 |
-|<math>g_i</math>
+| <math>j_i</math>
 |
 |-
-|<math>𝒈M</math>
+|
-|<math>𝒕</math>
+| <math>𝒈</math>
-|[[tuning map|(tempered-prime) tuning map]]
+| [[Generator tuning map]]
-|<math>\scriptsize
+|
+| <math>\mathsf{¢}</math>/<math>\small 𝗴</math>
+| Cents per generator
+|
+| <math>\scriptsize (1, r)</math>
+| Real
+| Vector
+| {...]
+|
+|
+|
+|
+| <math>g_i</math>
+|
+|-
+| <math>𝒈M</math>
+| <math>𝒕</math>
+| [[tuning map|(Tempered-prime) tuning map]]
+| <math>\scriptsize
 \begin{array} {c} 𝒈 \\[-2pt] {\small\mathsf{¢}} \hspace{-2mu} / \hspace{-2mu} \cancel{𝗴} \end{array}
 \begin{array} {c} \\[-2pt] · \end{array}
 \begin{array} {c} 𝑀 \\[-2pt] \cancel{𝗴} \hspace{-2mu} / \hspace{-2mu} 𝗽 \end{array}
 </math>
-|<math>\mathsf{¢}</math>/<math>\small 𝗽</math>
+| <math>\mathsf{¢}</math>/<math>\small 𝗽</math>
-|cents per prime
+| Cents per prime
-|<math>\scriptsize
+| <math>\scriptsize
-\!\!
+\! \!
-\begin{array} {c} 𝒈 \\[-3pt] (1, \cancel{r}) \end{array}
+\begin{array} {c} 𝒈 \\[-3pt] \left(1, \cancel{r}\right) \end{array}
-\!\!
+\! \!
-\begin{array} {c} M \\[-3pt] (\cancel{r}, d) \end{array}
+\begin{array} {c} M \\[-3pt] \left(\cancel{r}, d\right) \end{array}
-\!\!
+\! \!
 </math>
-|<math>\scriptsize (1, d)</math>
+| <math>\scriptsize (1, d)</math>
-|real
+| Real
-|vector
+| Vector
-|⟨...]
+| ⟨...]
 |
 |
 |
 |
-|<math>t_i</math>
+| <math>t_i</math>
 |
 |-
-|<math>𝒕 - 𝒋</math>
+| <math>𝒕 - 𝒋</math>
-|<math>𝒓</math>
+| <math>𝒓</math>
-|[[retuning map|retuning (or mistuning) map]]
+| [[retuning map|Retuning (or mistuning) map]]
 |
-|<math>\mathsf{¢}</math>/<math>\small 𝗽</math>
+| <math>\mathsf{¢}</math>/<math>\small 𝗽</math>
-|cents per prime
+| Cents per prime
 |
-|<math>\scriptsize (1, d)</math>
+| <math>\scriptsize (1, d)</math>
-|real
+| Real
-|vector
+| Vector
-|⟨...]
+| ⟨...]
 |
 |
 |
 |
-|<math>r_i</math>
+| <math>r_i</math>
-|previous name: prime error map
+| Previous name: prime error map
 |-
-|<math>𝒋\textbf{i}</math>
+| <math>𝒋\textbf{i}</math>
-|<math>\mathrm{o}</math>
+| <math>\mathrm{o}</math>
-|[[interval span|(just) (interval) size]]
+| [[interval span|(Just) (interval) size]]
-|<math>\scriptsize
+| <math>\scriptsize
 \begin{array} {c} 𝒋 \\[-2pt] {\small\mathsf{¢}} \hspace{-2mu} / \hspace{-2mu} \cancel{𝗽} \end{array}
 \begin{array} {c} \\[-2pt] · \end{array}
 \begin{array} {c} \textbf{i} \\[-2pt] \cancel{𝗽} \end{array}
 </math>
-|<math>\mathsf{¢}</math>
+| <math>\mathsf{¢}</math>
-|cents
+| Cents
-|<math>\scriptsize
+| <math>\scriptsize
-\!\!
+\! \!
-\begin{array} {c} 𝒋 \\[-3pt] (1, \cancel{d}) \end{array}
+\begin{array} {c} 𝒋 \\[-3pt] \left(1, \cancel{d}\right) \end{array}
-\!\!
+\! \!
-\begin{array} {c} \textbf{i} \\[-3pt] (\cancel{d}, 1) \end{array}
+\begin{array} {c} \textbf{i} \\[-3pt] \left(\cancel{d}, 1\right) \end{array}
-\!\!
+\! \!
 </math>
-|<math>\scriptsize (1, 1)</math>
+| <math>\scriptsize (1, 1)</math>
-|real
+| Real
-|scalar
+| Scalar
 |
 |
 |
 |
 |
 |
-|mnemonic: <math>\mathrm{o}</math>riginal size
+| Mnemonic: <math>\mathrm{o}</math>riginal size
 |-
-|<math>𝒈M\textbf{i} \\
+| <math>𝒈M\textbf{i}</math><br />
-𝒕\textbf{i}</math>
+<math>𝒕\textbf{i}</math>
-|<math>\mathrm{a}</math>
+| <math>\mathrm{a}</math>
-|[[Dave_Keenan_%26_Douglas_Blumeyer%27s_guide_to_RTT:_tuning_fundamentals#Example_3|tempered (interval) size]]
+| {{subpage|tuning_fundamentals|uprev|s=Example 3|text=Tempered (interval) size}}
-|<math>\scriptsize
+| <math>\scriptsize
 \begin{array} {c} 𝒕 \\[-2pt] {\small\mathsf{¢}} \hspace{-2mu} / \hspace{-2mu} \cancel{𝗽} \end{array}
 \begin{array} {c} \\[-2pt] · \end{array}
 \begin{array} {c} \textbf{i} \\[-2pt] \cancel{𝗽} \end{array}
 </math>
-|<math>\mathsf{¢}</math>
+| <math>\mathsf{¢}</math>
-|cents
+| Cents
-|<math>\scriptsize
+| <math>\scriptsize
-\!\!
+\! \!
-\begin{array} {c} 𝒕 \\[-3pt] (1, \cancel{d}) \end{array}
+\begin{array} {c} 𝒕 \\[-3pt] \left(1, \cancel{d}\right) \end{array}
-\!\!
+\! \!
-\begin{array} {c} \textbf{i} \\[-3pt] (\cancel{d}, 1) \end{array}
+\begin{array} {c} \textbf{i} \\[-3pt] \left(\cancel{d}, 1\right) \end{array}
-\!\!
+\! \!
 </math>
-|<math>\scriptsize (1, 1)</math>
+| <math>\scriptsize (1, 1)</math>
-|real
+| Real
-|scalar
+| Scalar
 |
 |
 |
 |
 |
 |
-|mnemonic: <math>\mathrm{a}</math>ltered size
+| Mnemonic: <math>\mathrm{a}</math>ltered size
 |-
-|<math>𝒕\textbf{i} - 𝒋\textbf{i} \\
+| <math>𝒕\textbf{i} - 𝒋\textbf{i}</math><br />
-a - o \\
+<math>a - o</math><br />
-𝒓\textbf{i}</math>
+<math>𝒓\textbf{i}</math>
-|<math>\mathrm{e}</math>
+| <math>\mathrm{e}</math>
-|[[error|(interval) error]]
+| [[error|(Interval) error]]
-|<math>\scriptsize
+| <math>\scriptsize
 \begin{array} {c} 𝒓 \\[-2pt] {\small\mathsf{¢}} \hspace{-2mu} / \hspace{-2mu} \cancel{𝗽} \end{array}
 \begin{array} {c} \\[-2pt] · \end{array}
 \begin{array} {c} \textbf{i} \\[-2pt] \cancel{𝗽} \end{array}
 </math>
-|<math>\mathsf{¢}</math>
+| <math>\mathsf{¢}</math>
-|cents
+| Cents
-|<math>\scriptsize
+| <math>\scriptsize
-\!\!
+\! \!
-\begin{array} {c} 𝒓 \\[-3pt] (1, \cancel{d}) \end{array}
+\begin{array} {c} 𝒓 \\[-3pt] \left(1, \cancel{d}\right) \end{array}
-\!\!
+\! \!
-\begin{array} {c} \textbf{i} \\[-3pt] (\cancel{d}, 1) \end{array}
+\begin{array} {c} \textbf{i} \\[-3pt] \left(\cancel{d}, 1\right) \end{array}
-\!\!
+\! \!
 </math>
-|<math>\scriptsize (1, 1)</math>
+| <math>\scriptsize (1, 1)</math>
-|real
+| Real
-|scalar
+| Scalar
 |
 |
 |
 |
 |
 |
 |
 |-
-! colspan="17" |optimization
+! colspan="17" | Optimization
 |-
 |
-|<math>p</math>
+| <math>p</math>
-|[[optimization power]]
+| [[Optimization power]]
 |
 |
 |
 |
-|<math>\scriptsize (1, 1)</math>
+| <math>\scriptsize (1, 1)</math>
-|real
+| Real
-|scalar
+| Scalar
 |
 |
 |
 |
 |
 |
 |
 |-
 |
-|<math>⟪\,·\,⟫_p</math>
+| <math>\llangle\,·\,\rrangle_p</math>
-|[[power mean]] (<math>p</math>-mean)
+| [[Power mean]] (<math>p</math>-mean)
 |
 |
 |
 |
-|<math>\scriptsize (1, 1)</math>
+| <math>\scriptsize (1, 1)</math>
-|real
+| Real
-|scalar
+| Scalar
 |
 |
 |
 |
 |
 |
 |
 |-
-! colspan="17" |damage
+! colspan="17" | Damage
 |-
 |
-|<math>c</math>
+| <math>c</math>
-|[[Dave_Keenan_%26_Douglas_Blumeyer%27s_guide_to_RTT:_tuning_fundamentals#Complexity|complexity]]
+| {{subpage|tuning_fundamentals|uprev|s=Complexity}}
-|<math>\small\mathsf{𝟙}\scriptsize\mathsf{(C)}</math><ref>For educational purposes, we use the 𝟙 symbol here to represent the implicit [[Wikipedia:Dimensionless_quantity|dimensionless unit]] that the weighting annotation "(C)" is attached to. But this symbol should not be shown in the reduced result. Another way to understand how we arrive at a bare annotation for the units of this quantity is to consider that ''w'' = ''d'' / |''e''| whose units are ¢(W) / ¢ and the cents cancel.</ref>
+| <math>\small\mathsf{𝟙}\scriptsize\mathsf{(C)}</math><ref group="note">For educational purposes, we use the 𝟙 symbol here to represent the implicit [[Wikipedia:Dimensionless_quantity| dimensionless unit]] that the weighting annotation "(C)" is attached to. But this symbol should not be shown in the reduced result. Another way to understand how we arrive at a bare annotation for the units of this quantity is to consider that {{nowrap|''w'' {{=}} ''d''/{{!}}''e''{{!}}}} whose units are {{nowrap|¢(W) / ¢}} and the cents cancel.</ref>
-|<math>\small\mathsf{(C)}</math>
+| <math>\small\mathsf{(C)}</math>
-|complexity weight
+| Complexity weight
 |
-|<math>\scriptsize (1, 1)</math>
+| <math>\scriptsize (1, 1)</math>
-|real
+| Real
-|scalar
+| Scalar
 |
 |
 |
 |
 |
 |
 |
 |-
-|<math>\dfrac1c</math>
+| <math>\dfrac1c</math>
-|<math>s</math>
+| <math>s</math>
-|[[simplicity]]
+| [[Simplicity]]
-|<math>\small\mathsf{𝟙}\scriptsize\mathsf{(S)}</math>
+| <math>\small\mathsf{𝟙}\scriptsize\mathsf{(S)}</math>
-|<math>\small\mathsf{(S)}</math>
+| <math>\small\mathsf{(S)}</math>
-|simplicity weight
+| Simplicity weight
 |
-|<math>\scriptsize (1, 1)</math>
+| <math>\scriptsize (1, 1)</math>
-|real
+| Real
-|scalar
+| Scalar
 |
 |
 |
 |
 |
 |
 |
 |-
-|<math>c</math> or <math>s</math>
+| <math>c</math> or <math>s</math>
-|<math>w</math>
+| <math>w</math>
-|[[weight]]
+| [[Weight]]
-|<math>\small\mathsf{𝟙}\scriptsize\mathsf{(C)}</math> or 𝟙<math>\small\mathsf{(S)}</math>
+| <math>\small\mathsf{𝟙}\scriptsize\mathsf{(C)}</math> or 𝟙<math>\small\mathsf{(S)}</math>
-|<math>\small\mathsf{(C)}</math> or <math>\small\mathsf{(S)}</math>
+| <math>\small\mathsf{(C)}</math> or <math>\small\mathsf{(S)}</math>
-|complexity weight or simplicity weight
+| Complexity weight or simplicity weight
 |
-|<math>\scriptsize (1, 1)</math>
+| <math>\scriptsize (1, 1)</math>
-|real
+| Real
-|scalar
+| Scalar
 |
 |
 |
 |
 |
 |
 |
 |-
-|<math>|\mathrm{e}|w</math>
+| <math>\abs{\mathrm{e}} w</math>
-|<math>\mathrm{d}</math>
+| <math>\mathrm{d}</math>
-|[[damage]]
+| [[Damage]]
-|<math>\scriptsize
+| <math>\scriptsize
-\begin{array} {c} |\mathrm{e}| \\[-2pt] {\small\mathsf{¢}} \end{array}
+\begin{array} {c} \abs{\mathrm{e}} \\[-2pt] {\small\mathsf{¢}} \end{array}
 \begin{array} {c} \\[-2pt] · \end{array}
-\begin{array} {c} w \\[-2pt] \mathsf{(U, C, or\,S)} \end{array}
+\begin{array} {c} w \\[-2pt] \mathsf{(U, C, \text{or}\,S)} \end{array}
 </math>
 | <math>\mathsf{¢}\small\mathsf{(U)}</math> or <math>\mathsf{¢}\small\mathsf{(C)}</math> or <math>\mathsf{¢}\small\mathsf{(S)}</math>
-| (see damages table)
+| (See damages table)
-|<math>\scriptsize
+| <math>\scriptsize
-\!\!
+\! \!
-\begin{array} {c} |\mathrm{e}| \\[-3pt] (1, \cancel{1}) \end{array}
+\begin{array} {c} \abs{\mathrm{e}} \\[-3pt] \left(1, \cancel{1}\right) \end{array}
-\!\!
+\! \!
-\begin{array} {c} w \\[-3pt] (\cancel{1}, 1) \end{array}
+\begin{array} {c} w \\[-3pt] \left(\cancel{1}, 1\right) \end{array}
-\!\!
+\! \!
 </math>
-|<math>\scriptsize (1, 1)</math>
+| <math>\scriptsize (1, 1)</math>
-|real
+| Real
-|scalar
+| Scalar
 |
 |
 |
 |
 |
 |
 |
 |-
-! colspan="17" |target-intervals
+! colspan="17" | Target-intervals
 |-
 |
-|<math>\mathrm{T}</math>
+| <math>\mathrm{T}</math>
-|[[target-interval list]]
+| [[Target-interval list]]
 |
-|<math>\small 𝗽</math>
+| <math>\small 𝗽</math>
-|primes
+| Primes
 |
-|<math>\scriptsize (d, k)</math>
+| <math>\scriptsize (d, k)</math>
-|integer
+| Integer
-|matrix
+| Matrix
 |
-|[[...⟩ ...]
+| [[...⟩ ...]
 |
-|<math>\textbf{t}_i</math>
+| <math>\textbf{t}_i</math>
 |
-|<math>\mathrm{t}_{ij}</math>
+| <math>\mathrm{t}_{ij}</math>
 |
 |-
-|<math>M\mathrm{T}</math>
+| <math>M\mathrm{T}</math>
-|<math>\mathrm{Y}</math>
+| <math>\mathrm{Y}</math>
-|[[mapped target-interval list]]
+| [[Mapped target-interval list]]
-|<math>\scriptsize
+| <math>\scriptsize
 \begin{array} {c} M \\[-2pt] 𝗴 \hspace{-2mu} / \hspace{-2mu} \cancel{𝗽} \end{array}
 \begin{array} {c} \\[-2pt] · \end{array}
 \begin{array} {c} \mathrm{T} \\[-2pt] \cancel{𝗽} \end{array}
 </math>
-|<math>\small 𝗴</math>
+| <math>\small 𝗴</math>
-|generators
+| Generators
-|<math>\scriptsize
+| <math>\scriptsize
-\!\!
+\! \!
-\begin{array} {c} M \\[-3pt] (r, \cancel{d}) \end{array}
+\begin{array} {c} M \\[-3pt] \left(r, \cancel{d}\right) \end{array}
-\!\!
+\! \!
-\begin{array} {c} \mathrm{T} \\[-3pt] (\cancel{d}, k) \end{array}
+\begin{array} {c} \mathrm{T} \\[-3pt] \left(\cancel{d}, k\right) \end{array}
-\!\!
+\! \!
 </math>
-|<math>\scriptsize (r, k)</math>
+| <math>\scriptsize (r, k)</math>
-|integer
+| Integer
-|matrix
+| Matrix
 |
-|[[...} ...]
+| [[...} ...]
 |
-|<math>\textbf{y}_i</math>
+| <math>\textbf{y}_i</math>
 |
-|<math>\mathrm{y}_{ij}</math>
+| <math>\mathrm{y}_{ij}</math>
-|mnemonic: looks like bent-up 'T', or cross between 'M' and 'T'
+| Mnemonic: looks like bent-up 'T', or cross between 'M' and 'T'
 |-
-|<math>𝒋\mathrm{T}</math>
+| <math>𝒋\mathrm{T}</math>
-|<math>\textbf{o}</math>
+| <math>\textbf{o}</math>
-|[[Dave_Keenan_%26_Douglas_Blumeyer%27s_guide_to_RTT:_tuning_fundamentals#Primes|target-interval (just) size list]]
+| {{subpage|tuning_fundamentals|uprev|s=primes|text=Target-interval (just) size list}}
-|<math>\scriptsize
+| <math>\scriptsize
 \begin{array} {c} 𝒋 \\[-2pt] {\small\mathsf{¢}} \hspace{-2mu} / \hspace{-2mu} \cancel{𝗽} \end{array}
 \begin{array} {c} \\[-2pt] · \end{array}
 \begin{array} {c} \mathrm{T} \\[-2pt] \cancel{𝗽} \end{array}
 </math>
-|<math>\mathsf{¢}</math>
+| <math>\mathsf{¢}</math>
-|cents
+| Cents
-|<math>\scriptsize
+| <math>\scriptsize
-\!\!
+\! \!
-\begin{array} {c} 𝒋 \\[-3pt] (1, \cancel{d}) \end{array}
+\begin{array} {c} 𝒋 \\[-3pt] \left(1, \cancel{d}\right) \end{array}
-\!\!
+\! \!
-\begin{array} {c} \mathrm{T} \\[-3pt] (\cancel{d}, k) \end{array}
+\begin{array} {c} \mathrm{T} \\[-3pt] \left(\cancel{d}, k\right) \end{array}
-\!\!
+\! \!
 </math>
-|<math>\scriptsize (1, k)</math>
+| <math>\scriptsize (1, k)</math>
-|real
+| Real
-|list
+| List
-|[...]
+| [...]
 |
 |
 |
 |
-|<math>\mathrm{o}_i</math>
+| <math>\mathrm{o}_i</math>
-|mnemonic: <math>\textbf{o}</math>riginal size list
+| Mnemonic: <math>\textbf{o}</math>riginal size list
 |-
-|<math>𝒕\mathrm{T} \\
+| <math>𝒕\mathrm{T}</math><br />
-𝒈M\mathrm{T}</math>
+<math>𝒈M\mathrm{T}</math>
-|<math>\textbf{a}</math>
+| <math>\textbf{a}</math>
-|[[tempered target-interval size list]]
+| [[Tempered target-interval size list]]
-|<math>\scriptsize
+| <math>\scriptsize
 \begin{array} {c} 𝒕 \\[-2pt] {\small\mathsf{¢}} \hspace{-2mu} / \hspace{-2mu} \cancel{𝗽} \end{array}
 \begin{array} {c} \\[-2pt] · \end{array}
 \begin{array} {c} \mathrm{T} \\[-2pt] \cancel{𝗽} \end{array}
 </math>
-|<math>\mathsf{¢}</math>
+| <math>\mathsf{¢}</math>
-|cents
+| Cents
-|<math>\scriptsize
+| <math>\scriptsize
-\!\!
+\! \!
-\begin{array} {c} 𝒕 \\[-3pt] (1, \cancel{d}) \end{array}
+\begin{array} {c} 𝒕 \\[-3pt] \left(1, \cancel{d}\right) \end{array}
-\!\!
+\! \!
-\begin{array} {c} \mathrm{T} \\[-3pt] (\cancel{d}, k) \end{array}
+\begin{array} {c} \mathrm{T} \\[-3pt] \left(\cancel{d}, k\right) \end{array}
-\!\!
+\! \!
 </math>
-|<math>\scriptsize (1, k)</math>
+| <math>\scriptsize (1, k)</math>
-|real
+| Real
-|list
+| List
-|[...]
+| [...]
 |
 |
 |
 |
-|<math>\mathrm{a}_i</math>
+| <math>\mathrm{a}_i</math>
-|mnemonic: <math>\textbf{a}</math>ltered size list
+| Mnemonic: <math>\textbf{a}</math>ltered size list
 |-
-|<math>𝒕\mathrm{T} - 𝒋\mathrm{T}\\
+| <math>𝒕\mathrm{T} - 𝒋\mathrm{T}</math><br />
-\textbf{a} - \textbf{o} \\
+<math>\textbf{a} - \textbf{o}</math><br />
-𝒓\mathrm{T}
+<math>𝒓\mathrm{T}</math>
-</math>
+| <math>\textbf{e}</math>
-|<math>\textbf{e}</math>
+| [[Target-interval error list]]
-|[[target-interval error list]]
+| <math>\scriptsize
-|<math>\scriptsize
 \begin{array} {c} 𝒓 \\[-2pt] {\small\mathsf{¢}} \hspace{-2mu} / \hspace{-2mu} \cancel{𝗽} \end{array}
 \begin{array} {c} \\[-2pt] · \end{array}
 \begin{array} {c} \mathrm{T} \\[-2pt] \cancel{𝗽} \end{array}
 </math>
-|<math>\mathsf{¢}</math>
+| <math>\mathsf{¢}</math>
-|cents
+| Cents
-|<math>\scriptsize
+| <math>\scriptsize
-\!\!
+\! \!
-\begin{array} {c} 𝒓 \\[-3pt] (1, \cancel{d}) \end{array}
+\begin{array} {c} 𝒓 \\[-3pt] \left(1, \cancel{d}\right) \end{array}
-\!\!
+\! \!
-\begin{array} {c} \mathrm{T} \\[-3pt] (\cancel{d}, k) \end{array}
+\begin{array} {c} \mathrm{T} \\[-3pt] \left(\cancel{d}, k\right) \end{array}
-\!\!
+\! \!
 </math>
-|<math>\scriptsize (1, k)</math>
+| <math>\scriptsize (1, k)</math>
-|real
+| Real
-|list
+| List
-|[...]
+| [...]
 |
 |
 |
 |
-|<math>\mathrm{e}_i</math>
+| <math>\mathrm{e}_i</math>
 |
 |-
-|<math>C</math> or <math>S</math>
+| <math>C</math> or <math>S</math>
-|<math>W</math>
+| <math>W</math>
-|[[target-interval weight matrix]]
+| [[Target-interval weight matrix]]
-|<math>\small\mathsf{𝟙}\scriptsize\mathsf{(C)}</math> or <math>\small\mathsf{𝟙}\scriptsize\mathsf{(S)}</math> or <math>\small\mathsf{𝟙}\scriptsize\mathsf{(U)}</math>
+| <math>\small\mathsf{𝟙}\scriptsize\mathsf{(C)}</math> or <math>\small\mathsf{𝟙}\scriptsize\mathsf{(S)}</math> or <math>\small\mathsf{𝟙}\scriptsize\mathsf{(U)}</math>
-|<math>\small\mathsf{(C)}</math> or <math>\small\mathsf{(S)}</math> or <math>\small\mathsf{(U)}</math>
+| <math>\small\mathsf{(C)}</math> or <math>\small\mathsf{(S)}</math> or <math>\small\mathsf{(U)}</math>
-|complexity weight or simplicity weight
+| Complexity weight or simplicity weight
 |
-|<math>\scriptsize (k, k)</math>
+| <math>\scriptsize (k, k)</math>
-|real
+| Real
-|matrix
+| Matrix
 |
-|[[...] ...]
+| [[...] ...]
 |
 |
-|<math>𝒘</math>
+| <math>𝒘</math>
-|<math>w_i</math>
+| <math>w_i</math>
 |
 |-
 |
-|<math>C</math>
+| <math>C</math>
-|[[Dave_Keenan_%26_Douglas_Blumeyer%27s_guide_to_RTT:_tuning_fundamentals#Complexity-weight_damage|target-interval complexity weight matrix]]
+| {{subpage|tuning_fundamentals|uprev|s=complexity-weight_damage|text=Target-interval complexity weight matrix}}
-|<math>\small\mathsf{𝟙}\scriptsize\mathsf{(C)}</math>
+| <math>\small\mathsf{𝟙}\scriptsize\mathsf{(C)}</math>
-|<math>\small\mathsf{(C)}</math>
+| <math>\small\mathsf{(C)}</math>
-|complexity weight
+| Complexity weight
 |
-|<math>\scriptsize (k, k)</math>
+| <math>\scriptsize (k, k)</math>
-|real
+| Real
-|matrix
+| Matrix
 |
-|[[...] ...]
+| [[...] ...]
 |
 |
-|<math>𝒄</math>
+| <math>𝒄</math>
-|<math>c_i</math>
+| <math>c_i</math>
 |
 |-
-|<math>\dfrac1C</math>
+| <math>\dfrac1C</math>
-|<math>S</math>
+| <math>S</math>
-|[[Dave_Keenan_%26_Douglas_Blumeyer%27s_guide_to_RTT:_tuning_fundamentals#Complexity-weight_damage|target-interval simplicity weight matrix]]
+| {{subpage|tuning fundamentals|uprev|s=complexity-weight_damage|text=Target-interval simplicity weight matrix}}
-|<math>\small\mathsf{𝟙}\scriptsize\mathsf{(S)}</math>
+| <math>\small\mathsf{𝟙}\scriptsize\mathsf{(S)}</math>
-|<math>\small\mathsf{(S)}</math>
+| <math>\small\mathsf{(S)}</math>
-|simplicity weight
+| Simplicity weight
 |
-|<math>\scriptsize (k, k)</math>
+| <math>\scriptsize (k, k)</math>
-|real
+| Real
-|matrix
+| Matrix
 |
-|[[...] ...]
+| [[...] ...]
 |
 |
-|<math>𝒔</math>
+| <math>𝒔</math>
-|<math>s_i</math>
+| <math>s_i</math>
-|entrywise reciprocal of <math>C</math>
+| Entry-wise reciprocal of <math>C</math>
 |-
-|<math>|\textbf{e}|W</math>
+| <math>\abs{\textbf{e}} W</math>
-|<math>\textbf{d}</math>
+| <math>\textbf{d}</math>
-|[[target-interval damage list]]<ref>You may sometimes see annotated units without parentheses, such as "dBA", but this is not compliant with SI standards, so we always keep the parentheses.</ref>
+| [[Target-interval damage list]]<ref group="note">You may sometimes see annotated units without parentheses, such as "dBA", but this is not compliant with SI standards, so we always keep the parentheses.</ref>
-|<math>\scriptsize
+| <math>\scriptsize
-\begin{array} {c} |\textbf{e}| \\[-2pt] {\small\mathsf{¢}} \end{array}
+\begin{array} {c} \abs{\textbf{e}} \\[-2pt] {\small\mathsf{¢}} \end{array}
 \begin{array} {c} \\[-2pt] · \end{array}
-\begin{array} {c} W \\[-2pt] (\mathsf{U, C, or\,S}) \end{array}
+\begin{array} {c} W \\[-2pt] (\mathsf{U, C, \text{or}\,S}) \end{array}
 </math>
-|<math>\mathsf{¢}\small\mathsf{(U)}</math>, <math>\mathsf{¢}\small\mathsf{(C)}</math>, or <math>\mathsf{¢}\small\mathsf{(S)}</math>
+| <math>\mathsf{¢}\small\mathsf{(U)}</math>, <math>\mathsf{¢}\small\mathsf{(C)}</math>, or <math>\mathsf{¢}\small\mathsf{(S)}</math>
-|weighted cents
+| Weighted cents
-|<math>\scriptsize
+| <math>\scriptsize
-\!\!
+\! \!
-\begin{array} {c} |\textbf{e}| \\[-3pt] (1, \cancel{k}) \end{array}
+\begin{array} {c} \abs{\textbf{e}} \\[-3pt] \left(1, \cancel{k}\right) \end{array}
-\!\!
+\! \!
-\begin{array} {c} W \\[-3pt] (\cancel{k}, k) \end{array}
+\begin{array} {c} W \\[-3pt] \left(\cancel{k}, k\right) \end{array}
-\!\!
+\! \!
 </math>
-|<math>\scriptsize (1, k)</math>
+| <math>\scriptsize (1, k)</math>
-|real
+| Real
-|list
+| List
-|[...]
+| [...]
 |
 |
 |
 |
-|<math>\mathrm{d}_i</math>
+| <math>\mathrm{d}_i</math>
 |
 |-
 |
-|<math>k</math>
+| <math>k</math>
-|[[target-interval count]]
+| [[Target-interval count]]
 |
 |
 |
 |
-|<math>\scriptsize (1, 1)</math>
+| <math>\scriptsize (1, 1)</math>
-|integer
+| Integer
-|scalar
+| Scalar
 |
 |
 |
 |
 |
 |
-|mnemonic: <math>k</math>ount
+| Mnemonic: <math>k</math>ount
 |-
-! colspan="17" |held-intervals
+! colspan="17" | Held-intervals
 |-
 |
-|<math>\mathrm{H}</math>
+| <math>\mathrm{H}</math>
-|[[held-interval basis]]
+| [[Held-interval basis]]
 |
-|<math>\small 𝗽</math>
+| <math>\small 𝗽</math>
-|primes
+| Primes
 |
-|<math>\scriptsize (d, h)</math>
+| <math>\scriptsize (d, h)</math>
 |
-|matrix
+| Matrix
 |
-|[[...⟩ ...]
+| [[...⟩ ...]
 |
-|<math>\textbf{h}_i</math>
+| <math>\textbf{h}_i</math>
 |
-|<math>\mathrm{h}_{ij}</math>
+| <math>\mathrm{h}_{ij}</math>
 |
 |-
 |
-|<math>h</math>
+| <math>h</math>
-|[[held-interval count]]
+| [[Held-interval count]]
 |
 |
 |
 |
-|<math>\scriptsize (1, 1)</math>
+| <math>\scriptsize (1, 1)</math>
-|integer
+| Integer
-|scalar
+| Scalar
 |
 |
 |
 |
 |
 |
 |
 |-
-! colspan="17" |exploring temperaments
+! colspan="17" | Exploring temperaments
 |-
 |
-|<math>\mathrm{C}</math>
+| <math>\mathrm{C}</math>
-|[[comma basis]]
+| [[Comma basis]]
 |
-|<math>\small 𝗽</math>
+| <math>\small 𝗽</math>
-|primes
+| Primes
 |
-|<math>\scriptsize (d, n)</math>
+| <math>\scriptsize (d, n)</math>
-|integer
+| Integer
-|matrix
+| Matrix
 |
-|[[...⟩ ...]
+| [[...⟩ ...]
 |
-|<math>\textbf{c}_i</math>
+| <math>\textbf{c}_i</math>
 |
-|<math>\mathrm{c}_{ij}</math>
+| <math>\mathrm{c}_{ij}</math>
-|jargon name: monzo list
+| Jargon name: monzo list
 |-
 |
-|<math>\textbf{c}</math>
+| <math>\textbf{c}</math>
-|[[comma]]
+| [[Comma]]
 |
-|<math>\small 𝗽</math>
+| <math>\small 𝗽</math>
-|primes
+| Primes
 |
-|<math>\scriptsize (d, 1)</math>
+| <math>\scriptsize (d, 1)</math>
-|integer
+| Integer
-|vector
+| Vector
 |
-|[...⟩
+| [...⟩
 |
 |
 |
-|<math>\mathrm{c}_i</math>
+| <math>\mathrm{c}_i</math>
-|specific type: [[prime-count vector]] (PC-vector)
+| Specific type: vector ([[prime-count vector]] or PC-vector)
 |}
-===Units===
+=== Units ===
+We recommend using a narrow no-break space (U+202F) between quantities and their units.<ref group="note">Per https://physics.nist.gov/cuu/Units/checklist.html and https://academia.stackexchange.com/questions/54885/should-there-be-a-space-between-a-value-and-the-units-used
-We recommend using a narrow no-break space (U+202F) between quantities and their units.<ref>Per https://physics.nist.gov/cuu/Units/checklist.html and https://academia.stackexchange.com/questions/54885/should-there-be-a-space-between-a-value-and-the-units-used
 .</ref> For how to type this, see the [[#WinCompose|WinCompose]] section below.
 {| class="wikitable center-all mw-collapsible"
-|+
+|+ style="font-size: 105%;" |
-!symbol
+|-
-!name
+! Symbol
-!vectorized
+! Name
+! Vectorized
 |-
-|<math>\small 𝗴</math>
+| <math>\small 𝗴</math>
-|generators
+| Generators
-|yes
+| Yes
 |-
-|<math>\small 𝗽</math>
+| <math>\small 𝗽</math>
-|primes
+| Primes
-|yes
+| Yes
 |-
-|<math>\mathsf{¢}</math><ref>It seems there is no standard symbol for a musical cent, except the word spelled in full (see https://en.wikipedia.org/wiki/Cent_(music)). But it seems unlikely anyone will interpret the cent currency symbol "¢" following a number in a musical context as anything other than musical cents.</ref>
+| <math>\mathsf{¢}</math><ref group="note">It seems there is no standard symbol for a musical cent, except the word spelled in full (see https://en.wikipedia.org/wiki/Cent_(music)). But it seems unlikely anyone will interpret the cent currency symbol "¢" following a number in a musical context as anything other than musical cents.</ref>
-|cents
+| Cents
 |
 |-
-|<math>\mathsf{¢}\small\mathsf{(U)}</math>
+| <math>\mathsf{¢}\small\mathsf{(U)}</math>
-|unity-weighted cents
+| Unity-weighted cents
 |
 |-
-|<math>\mathsf{¢}\small\mathsf{(C)}</math>
+| <math>\mathsf{¢}\small\mathsf{(C)}</math>
-|complexity-weighted cents
+| Complexity-weighted cents
 |
 |-
-|<math>\mathsf{¢}\small\mathsf{(S)}</math>
+| <math>\mathsf{¢}\small\mathsf{(S)}</math>
-|simplicity-weighted cents
+| Simplicity-weighted cents
 |
 |-
-|<math>\small\mathsf{oct}</math>
+| <math>\small\mathsf{oct}</math>
-|octaves
+| Octaves
 |
 |-
-|<math>\small\mathsf{(C)}</math>
+| <math>\small\mathsf{(C)}</math>
-|complexity weight
+| Complexity weight
 |
 |-
-|<math>\small\mathsf{(S)}</math>
+| <math>\small\mathsf{(S)}</math>
-|simplicity weight
+| Simplicity weight
 |
 |}
-===Tuning schemes===
+=== Tuning schemes ===
+Copied from {{subpage|tuning fundamentals|uprev|s=Systematic tuning scheme names}}.
-Copied from [[Dave Keenan & Douglas Blumeyer's guide to RTT: tuning fundamentals#Systematic tuning scheme names]].
 {| class="wikitable center-all mw-collapsible"
-|+
+|+ style="font-size: 105%;" |
 |-
-|'''damage weight'''
+! Damage weight
-|'''optimization power'''
+! Optimization power
-|'''systematic name'''
+! Systematic name
 |-
-|<none>
+| <none>
-| rowspan="3" |∞
+| rowspan="3" | &infin;
-|minimax-U
+| Minimax-U
 |-
-|complexity
+| Complexity
-|minimax-C
+| Minimax-C
 |-
-|1/complexity
+| 1/Complexity
-|minimax-S
+| Minimax-S
 |-
-|<none>
+| <none>
-| rowspan="3" |2
+| rowspan="3" | 2
-|miniRMS-U
+| MiniRMS-U
 |-
-|complexity
+| Complexity
-|miniRMS-C
+| MiniRMS-C
 |-
-|1/complexity
+| 1/Complexity
-|miniRMS-S
+| MiniRMS-S
 |-
-|<none>
+| &lt;none&gt;
-| rowspan="3" |1
+| rowspan="3" | 1
-|miniaverage-U
+| Miniaverage-U
 |-
-|complexity
+| Complexity
-|miniaverage-C
+| Miniaverage-C
 |-
-|1/complexity
+| 1/Complexity
-|miniaverage-S
+| Miniaverage-S
 |}
-===Damages===
+=== Damages ===
 {| class="wikitable center-all mw-collapsible"
-|+
+|+ style="font-size: 105%;" |
-! colspan="2" |quantity
+|-
-! colspan="2" |unit
+! colspan="2" | Quantity
+! colspan="2" | Unit
 |-
-!abbreviation
+! Abbreviation
-!name
+! Name
-!symbol
+! Symbol
-!name
+! Name
 |-
-|U-damage
+| U-damage
-|unity-weight damage
+| Unity-weight damage
-|<math>\mathsf{¢}\small\mathsf{(U)}</math>
+| <math>\mathsf{¢}\small\mathsf{(U)}</math>
-|unity-weighted cents
+| Unity-weighted cents
 |-
-|C-damage
+| C-damage
-|complexity-weight damage
+| Complexity-weight damage
-|<math>\mathsf{¢}\small\mathsf{(C)}</math>
+| <math>\mathsf{¢}\small\mathsf{(C)}</math>
-|complexity-weighted cents
+| Complexity-weighted cents
 |-
-|S-damage
+| S-damage
-|simplicity-weight damage
+| Simplicity-weight damage
-|<math>\mathsf{¢}\small\mathsf{(S)}</math>
+| <math>\mathsf{¢}\small\mathsf{(S)}</math>
-|simplicity-weighted cents
+| Simplicity-weighted cents
 |}
-===Complexity and simplicity===
+=== Complexity and simplicity ===
 {| class="wikitable center-all mw-collapsible"
-|+
+|+ style="font-size: 105%;" |
-! colspan="2" |quantity
-! colspan="2" |unit
 |-
-!abbreviation
+! colspan="2" | Quantity
-!name
+! colspan="2" | Unit
-!symbol
-!name
 |-
-|C
+! Abbreviation
-|complexity
+! Name
-|<math>\small\mathsf{(C)}</math>
+! Symbol
-|complexity weight
+! Name
 |-
-|S
+| C
-|simplicity
+| Complexity
-|<math>\small\mathsf{(S)}</math>
+| <math>\small\mathsf{(C)}</math>
-|simplicity weight
+| Complexity weight
+|-
+| S
+| Simplicity
+| <math>\small\mathsf{(S)}</math>
+| Simplicity weight
 |}
-<math>
+== Intermediate ==
-% \slant{} command approximates italics to allow slanted bold characters, including digits, in MathJax.
+=== Objects ===
-\def\slant#1{\style{display:inline-block;margin:-.05em;transform:skew(-14deg)translateX(.03em)}{#1}}
-% Latex equivalents of the wiki templates llzigzag and rrzigzag for double zigzag brackets.
-\def\llzigzag{\hspace{-1.6mu}\style{display:inline-block;transform:scale(.62,1.24)translateY(.07em);font-family:sans-serif}{ꗨ\hspace{-3mu}ꗨ}\hspace{-1.6mu}}
-\def\rrzigzag{\hspace{-1.6mu}\style{display:inline-block;transform:scale(-.62,1.24)translateY(.07em);font-family:sans-serif}{ꗨ\hspace{-3mu}ꗨ}\hspace{-1.6mu}}
-</math>
-==Intermediate==
-===Objects===
 {| class="wikitable mw-collapsible mw-collapsed"
-|+
+|+ style="font-size: 105%;" |
-! rowspan="2" |equivalent expressions
-! rowspan="2" |variable
-! rowspan="2" |name
-! colspan="3" |units
-! colspan="2" |shape
-! colspan="2" |type
-! colspan="2" |EBK notation
-! colspan="4" |subobjects
-! rowspan="2" |notes
 |-
-!unreduced
+! rowspan="2" | Equivalent expressions
-!reduced
+! rowspan="2" | Variable
-!read as
+! rowspan="2" | Name
-!unreduced
+! colspan="3" | Units
-!reduced
+! colspan="2" | Shape
-!numeric
+! colspan="2" | Type
-!structural
+! colspan="2" | EBK notation
-!row-first
+! colspan="4" | Subobjects
-!col-first
+! rowspan="2" | Notes
-!row
-!col
-!diag
-!entry
 |-
-! colspan="17" |mapping
+! Unreduced
+! Reduced
+! Read as
+! Unreduced
+! Reduced
+! Numeric
+! Structural
+! Row-first
+! Col-first
+! Row
+! Col
+! Diag
+! Entry
 |-
-|
+! colspan="17" | Mapping
-|<math>\textbf{i}</math>
-|[[interval|(just) interval]]
-|
-|<math>\small 𝗽</math>
-|primes
-|
-|<math>\scriptsize (d, 1)</math>
-|integer
-|vector
-|
-|[...⟩
-|
-|
-|
-|<math>\mathrm{i}_i</math>
-|specific type: [[prime-count vector]] (PC-vector)
-jargon name: monzo
 |-
 |
-|<math>M</math>
+| <math>\textbf{i}</math>
-|[[Mapping|(temperament) mapping (matrix)]]
+| [[interval|(Just) interval]]
 |
-|<math>\small 𝗴</math>/<math>\small 𝗽</math>
+| <math>\small 𝗽</math>
-|generators per prime
+| Primes
 |
-|<math>\scriptsize (r, d)</math>
+| <math>\scriptsize (d, 1)</math>
-|integer
+| Integer
-|matrix
+| Vector
-|[⟨...] ...}
+|
-|⟨[...} ...]
+| [...⟩
-|<math>𝒎_i</math>
+|
 |
 |
-|<math>m_{ij}</math>
+| <math>\mathrm{i}_i</math>
-|jargon name: val list
+| Specific type: vector ([[prime-count vector]] or PC-vector)
+Jargon name: monzo
 |-
-|<math>M\textbf{i}</math>
+|
-|<math>\textbf{y}</math>
+| <math>M</math>
-|[[mapped interval]]
+| [[Mapping|(Temperament) mapping (matrix)]]
-|<math>\scriptsize
+|
+| <math>\small 𝗴</math>/<math>\small 𝗽</math>
+| Generators per prime
+|
+| <math>\scriptsize (r, d)</math>
+| Integer
+| Matrix
+| [⟨...] ...}
+| ⟨[...} ...]
+| <math>𝒎_i</math>
+|
+|
+| <math>m_{ij}</math>
+| Jargon name: val list
+|-
+| <math>M\textbf{i}</math>
+| <math>\textbf{y}</math>
+| [[Mapped interval]]
+| <math>\scriptsize
 \begin{array} {c} M \\[-2pt] 𝗴 \hspace{-2mu} / \hspace{-2mu} \cancel{𝗽} \end{array}
 \begin{array} {c} \\[-2pt] · \end{array}
 \begin{array} {c} \textbf{i} \\[-2pt] \cancel{𝗽} \end{array}
 </math>
-|<math>\small 𝗴</math>
+| <math>\small 𝗴</math>
-|generators
+| Generators
-|<math>\scriptsize
+| <math>\scriptsize
-\!\!
+\! \!
-\begin{array} {c} M \\[-3pt] (r, \cancel{d}) \end{array}
+\begin{array} {c} M \\[-3pt] \left(r, \cancel{d}\right) \end{array}
-\!\!
+\! \!
-\begin{array} {c} \textbf{i} \\[-3pt] (\cancel{d}, 1) \end{array}
+\begin{array} {c} \textbf{i} \\[-3pt] \left(\cancel{d}, 1\right) \end{array}
-\!\!
+\! \!
 </math>
-|<math>\scriptsize (r, 1)</math>
+| <math>\scriptsize (r, 1)</math>
-|integer
+| Integer
-|vector
+| Vector
 |
-|[...}
+| [...}
 |
 |
 |
 |
-|specific type: [[generator-count vector]] (GC-vector)
+| Specific type: [[generator-count vector]] (GC-vector)
-jargon name: tmonzo; mnemonic: <math>\textbf{y}</math>nterval
+Jargon name: tmonzo; mnemonic: <math>\textbf{y}</math>nterval
 |-
 |
-|<math>𝒎</math>
+| <math>𝒎</math>
-|[[map|(temperament) map]]
+| [[map|(Temperament) map]]
 |
-|<math>\small 𝗴</math>/<math>\small 𝗽</math>
+| <math>\small 𝗴</math>/<math>\small 𝗽</math>
-|generators per prime
+| Generators per prime
 |
-|<math>\scriptsize (1, d)</math>
+| <math>\scriptsize (1, d)</math>
-|integer
+| Integer
-|vector
+| Vector
-|⟨...]
+| ⟨...]
 |
 |
 |
 |
-|<math>m_i</math>
+| <math>m_i</math>
-|jargon name: val
+| Jargon name: val
 |-
-|<math>n + r</math>
+| <math>n + r</math>
-|<math>d</math>
+| <math>d</math>
-|[[dimensionality]]
+| [[Dimensionality]]
 |
 |
 |
 |
-|<math>\scriptsize (1, 1)</math>
+| <math>\scriptsize (1, 1)</math>
-|integer
+| Integer
-|scalar
+| Scalar
 |
 |
 |
 |
 |
 |
 |
 |-
-|<math>d - n</math>
+| <math>d - n</math>
-|<math>r</math>
+| <math>r</math>
-|[[rank]]
+| [[Rank]]
 |
 |
 |
 |
-|<math>\scriptsize (1, 1)</math>
+| <math>\scriptsize (1, 1)</math>
-|integer
+| Integer
-|scalar
+| Scalar
 |
 |
 |
 |
 |
 |
 |
 |-
-|<math>d - r</math>
+| <math>d - r</math>
-|<math>n</math>
+| <math>n</math>
-|[[nullity]]
+| [[Nullity]]
 |
 |
 |
 |
-|<math>\scriptsize (1, 1)</math>
+| <math>\scriptsize (1, 1)</math>
-|integer
+| Integer
-|scalar
+| Scalar
 |
 |
 |
 |
 |
 |
 |
 |-
-! colspan="17" |tuning
+! colspan="17" | Tuning
 |-
 |
-|<math>𝒋</math>
+| <math>{\large\textbf{𝓁}}\hspace{2mu}</math>
-|[[just tuning map|just(-prime) tuning map]]
+| [[Log-prime map]]
 |
-|<math>\mathsf{¢}</math>/<math>\small 𝗽</math>
+| <math>\small\mathsf{oct}</math>/<math>\small 𝗽</math>
-|cents per prime
+| Octaves per prime
 |
-|<math>\scriptsize (1, d)</math>
+| <math>\scriptsize (1, d)</math>
-|real
+| Real
-|vector
+| Vector
-|⟨...]
+| ⟨...]
 |
 |
 |
 |
-|<math>j_i</math>
+| <math>{\large 𝓁}\hspace{2mu}_i</math>
 |
 |-
-|
+| <math>1200×{\large\textbf{𝓁}}\hspace{2mu}</math>
-|<math>𝒈</math>
+| <math>𝒋</math>
-|[[generator tuning map]]
+| [[just tuning map|Just(-prime) tuning map]]
 |
-|<math>\mathsf{¢}</math>/<math>\small 𝗴</math>
+| <math>\mathsf{¢}</math>/<math>\small 𝗽</math>
-|cents per generator
+| Cents per prime
 |
-|<math>\scriptsize (1, r)</math>
+| <math>\scriptsize (1, d)</math>
-|real
+| Real
-|vector
+| Vector
-|{...]
+| ⟨...]
 |
 |
 |
 |
-|<math>g_i</math>
+| <math>j_i</math>
 |
+|-
+|
+| <math>𝒈</math>
+| [[Generator tuning map]]
+|
+| <math>\mathsf{¢}</math>/<math>\small 𝗴</math>
+| Cents per generator
+|
+| <math>\scriptsize (1, r)</math>
+| Real
+| Vector
+| {...]
+|
+|
+|
+|
+| <math>g_i</math>
+|
 |-
 |
-|<math>𝒕</math>
+| <math>𝒕</math>
-|[[tuning map|(tempered-prime) tuning map]]
+| [[tuning map|(Tempered-prime) tuning map]]
 |
-|<math>\mathsf{¢}</math>/<math>\small 𝗽</math>
+| <math>\mathsf{¢}</math>/<math>\small 𝗽</math>
-|cents per prime
+| Cents per prime
 |
-|<math>\scriptsize (1, d)</math>
+| <math>\scriptsize (1, d)</math>
-|real
+| Real
-|vector
+| Vector
-|⟨...]
+| ⟨...]
 |
 |
 |
 |
-|<math>t_i</math>
+| <math>t_i</math>
 |
 |-
-|<math>𝒕 - 𝒋 \\
+| <math>𝒕 - 𝒋</math><br />
-×\slant{\mathbf{1}}L(P - I)</math>
+<math>1200×\slant{\mathbf{1}}L(P - I)</math>
-|<math>𝒓</math>
+| <math>𝒓</math>
-|[[retuning map|retuning (or mistuning) map]]
+| [[retuning map|Retuning (or mistuning) map]]
 |
-|<math>\mathsf{¢}</math>/<math>\small 𝗽</math>
+| <math>\mathsf{¢}</math>/<math>\small 𝗽</math>
-|cents per prime
+| Cents per prime
 |
-|<math>\scriptsize (1, d)</math>
+| <math>\scriptsize (1, d)</math>
-|real
+| Real
-|vector
+| Vector
 | ⟨...]
 |
 |
 |
 |
-|<math>r_i</math>
+| <math>r_i</math>
-|previous name: prime error map
+| Previous name: prime error map
 |-
-|<math>𝒋\textbf{i}</math>
+| <math>𝒋\textbf{i}</math>
-|<math>\mathrm{o}</math>
+| <math>\mathrm{o}</math>
-|[[interval span|(just) (interval) size]]
+| [[interval span|(Just) (interval) size]]
-|<math>\scriptsize
+| <math>\scriptsize
 \begin{array} {c} 𝒋 \\[-2pt] {\small\mathsf{¢}} \hspace{-2mu} / \hspace{-2mu} \cancel{𝗽} \end{array}
 \begin{array} {c} \\[-2pt] · \end{array}
 \begin{array} {c} \textbf{i} \\[-2pt] \cancel{𝗽} \end{array}
 </math>
-|<math>\mathsf{¢}</math>
+| <math>\mathsf{¢}</math>
-|cents
+| Cents
-|<math>\scriptsize
+| <math>\scriptsize
-\!\!
+\! \!
-\begin{array} {c} 𝒋 \\[-3pt] (1, \cancel{d}) \end{array}
+\begin{array} {c} 𝒋 \\[-3pt] \left(1, \cancel{d}\right) \end{array}
-\!\!
+\! \!
-\begin{array} {c} \mathbf{i} \\[-3pt] (\cancel{d}, 1) \end{array}
+\begin{array} {c} \mathbf{i} \\[-3pt] \left(\cancel{d}, 1\right) \end{array}
-\!\!
+\! \!
 </math>
-|<math>\scriptsize (1, 1)</math>
+| <math>\scriptsize (1, 1)</math>
-|real
+| Real
-|scalar
+| Scalar
 |
 |
 |
 |
 |
 |
-|mnemonic: <math>\mathrm{o}</math>riginal size
+| Mnemonic: <math>\mathrm{o}</math>riginal size
 |-
-|<math>𝒈M\textbf{i} \\
+| <math>𝒈M\textbf{i}</math><br />
-𝒕\textbf{i}</math>
+<math>𝒕\textbf{i}</math>
-|<math>\mathrm{a}</math>
+| <math>\mathrm{a}</math>
-|[[Dave_Keenan_%26_Douglas_Blumeyer%27s_guide_to_RTT:_tuning_fundamentals#Example_3|tempered (interval) size]]
+| {{subpage|tuning fundamentals|uprev|s=Example 3|text=Tempered (interval) size}}
-|<math>\scriptsize
+| <math>\scriptsize
 \begin{array} {c} 𝒕 \\[-2pt] {\small\mathsf{¢}} \hspace{-2mu} / \hspace{-2mu} \cancel{𝗽} \end{array}
 \begin{array} {c} \\[-2pt] · \end{array}
 \begin{array} {c} \textbf{i} \\[-2pt] \cancel{𝗽} \end{array}
 </math>
-|<math>\mathsf{¢}</math>
+| <math>\mathsf{¢}</math>
-|cents
+| Cents
-|<math>\scriptsize
+| <math>\scriptsize
-\!\!
+\! \!
-\begin{array} {c} 𝒕 \\[-3pt] (1, \cancel{d}) \end{array}
+\begin{array} {c} 𝒕 \\[-3pt] \left(1, \cancel{d}\right) \end{array}
-\!\!
+\! \!
-\begin{array} {c} \textbf{i} \\[-3pt] (\cancel{d}, 1) \end{array}
+\begin{array} {c} \textbf{i} \\[-3pt] \left(\cancel{d}, 1\right) \end{array}
-\!\!
+\! \!
 </math>
-|<math>\scriptsize (1, 1)</math>
+| <math>\scriptsize (1, 1)</math>
-|real
+| Real
-|scalar
+| Scalar
 |
 |
 |
 |
 |
 |
-|mnemonic: <math>\mathrm{a}</math>ltered size
+| Mnemonic: <math>\mathrm{a}</math>ltered size
 |-
-|<math>𝒕\textbf{i} - 𝒋\textbf{i} \\
+| <math>𝒕\textbf{i} - 𝒋\textbf{i}</math><br />
-a - o \\
+<math>a - o</math><br />
-𝒓\textbf{i}</math>
+<math>𝒓\textbf{i}</math>
-|<math>\mathrm{e}</math>
+| <math>\mathrm{e}</math>
-|[[error|(interval) error]]
+| [[error|(Interval) error]]
-|<math>\scriptsize
+| <math>\scriptsize
 \begin{array} {c} 𝒓 \\[-2pt] {\small\mathsf{¢}} \hspace{-2mu} / \hspace{-2mu} \cancel{𝗽} \end{array}
 \begin{array} {c} \\[-2pt] · \end{array}
 \begin{array} {c} \textbf{i} \\[-2pt] \cancel{𝗽} \end{array}
 </math>
-|<math>\mathsf{¢}</math>
+| <math>\mathsf{¢}</math>
-|cents
+| Cents
-|<math>\scriptsize
+| <math>\scriptsize
-\!\!
+\! \!
-\begin{array} {c} 𝒓 \\[-3pt] (1, \cancel{d}) \end{array}
+\begin{array} {c} 𝒓 \\[-3pt] \left(1, \cancel{d}\right) \end{array}
-\!\!
+\! \!
-\begin{array} {c} \textbf{i} \\[-3pt] (\cancel{d}, 1) \end{array}
+\begin{array} {c} \textbf{i} \\[-3pt] \left(\cancel{d}, 1\right) \end{array}
-\!\!
+\! \!
 </math>
-|<math>\scriptsize (1, 1)</math>
+| <math>\scriptsize (1, 1)</math>
-|real
+| Real
-| scalar
+| Scalar
 |
 |
 |
 |
 |
 |
 |
 |-
-! colspan="17" |optimization
+! colspan="17" | Optimization
 |-
 |
-|<math>p</math>
+| <math>p</math>
-|[[optimization power]]
+| [[Optimization power]]
 |
 |
 |
 |
-|<math>\scriptsize (1, 1)</math>
+| <math>\scriptsize (1, 1)</math>
-|real
+| Real
-|scalar
+| Scalar
 |
 |
 |
 |
 |
 |
 |
 |-
 |
-|<math>⟪\,·\,⟫_p</math>
+| <math>\llangle\,·\,\rrangle_p</math>
-|[[power mean]] (<math>p</math>-mean)
+| [[Power mean]] (<math>p</math>-mean)
 |
 |
 |
 |
-|<math>\scriptsize (1, 1)</math>
+| <math>\scriptsize (1, 1)</math>
-|real
+| Real
-|scalar
+| Scalar
 |
 |
 |
 |
 |
 |
 |
 |-
-! colspan="17" |damage
+! colspan="17" | Damage
 |-
 |
-|<math>c</math>
+| <math>c</math>
-|[[Dave_Keenan_%26_Douglas_Blumeyer%27s_guide_to_RTT:_tuning_fundamentals#Complexity|complexity]]
+| {{subpage|tuning_fundamentals|uprev|s=Complexity}}
-| colspan="3" |(see complexities section of complexities and simplicities table)
+| colspan="3" | (See complexities section of complexities and simplicities table)
 |
-|<math>\scriptsize (1, 1)</math>
+| <math>\scriptsize (1, 1)</math>
-|real
+| Real
-|scalar
+| Scalar
 |
 |
 |
 |
 |
 |
 |
 |-
-|<math>\dfrac1c</math>
+| <math>\dfrac1c</math>
-|<math>s</math>
+| <math>s</math>
-|[[simplicity]]
+| [[Simplicity]]
-| colspan="3" |(see simplicities section of complexities and simplicities table)
+| colspan="3" | (See simplicities section of complexities and simplicities table)
 |
-|<math>\scriptsize (1, 1)</math>
+| <math>\scriptsize (1, 1)</math>
-|real
+| Real
-|scalar
+| Scalar
 |
 |
 |
 |
 |
 |
 |
 |-
-|<math>c</math> or <math>s</math>
+| <math>c</math> or <math>s</math>
-|<math>w</math>
+| <math>w</math>
-|[[weight]]
+| [[weight]]
-| colspan="3" |(see complexities and simplicities table)
+| colspan="3" | (See complexities and simplicities table)
 |
-|<math>\scriptsize (1, 1)</math>
+| <math>\scriptsize (1, 1)</math>
-|real
+| Real
-|scalar
+| Scalar
 |
 |
 |
 |
 |
 |
 |
 |-
-|<math>|\mathrm{e}|w</math>
+| <math>\abs{\mathrm{e}} w</math>
-|<math>\mathrm{d}</math>
+| <math>\mathrm{d}</math>
-|[[damage]]
+| [[Damage]]
-| colspan="3" |(see damages table)
+| colspan="3" | (See damages table)
 |
-|<math>\scriptsize (1, 1)</math>
+| <math>\scriptsize (1, 1)</math>
-|real
+| Real
-|scalar
+| Scalar
 |
 |
 |
 |
 |
 |
 |
 |-
-! colspan="17" |target-intervals
+! colspan="17" | Target-intervals
 |-
 |
-|<math>\mathrm{T}</math>
+| <math>\mathrm{T}</math>
-|[[target-interval list]]
+| [[Target-interval list]]
 |
-|<math>\small 𝗽</math>
+| <math>\small 𝗽</math>
-|primes
+| Primes
 |
-|<math>\scriptsize (d, k)</math>
+| <math>\scriptsize (d, k)</math>
-|integer
+| Integer
-|matrix
+| Matrix
 |
 | [[...⟩ ...]
 |
-|<math>\textbf{t}_i</math>
+| <math>\textbf{t}_i</math>
 |
-|<math>\mathrm{t}_{ij}</math>
+| <math>\mathrm{t}_{ij}</math>
 |
 |-
-|<math>M\mathrm{T}</math>
+| <math>M\mathrm{T}</math>
-|<math>\mathrm{Y}</math>
+| <math>\mathrm{Y}</math>
-|[[mapped target-interval list]]
+| [[Mapped target-interval list]]
-|<math>\scriptsize
+| <math>\scriptsize
 \begin{array} {c} M \\[-2pt] 𝗴 \hspace{-2mu} / \hspace{-2mu} \cancel{𝗽} \end{array}
 \begin{array} {c} \\[-2pt] · \end{array}
 \begin{array} {c} \mathrm{T} \\[-2pt] \cancel{𝗽} \end{array}
 </math>
-|<math>\small 𝗴</math>
+| <math>\small 𝗴</math>
-|generators
+| Generators
-|<math>\scriptsize
+| <math>\scriptsize
-\!\!
+\! \!
-\begin{array} {c} M \\[-3pt] (r, \cancel{d}) \end{array}
+\begin{array} {c} M \\[-3pt] \left(r, \cancel{d}\right) \end{array}
-\!\!
+\! \!
-\begin{array} {c} \mathrm{T} \\[-3pt] (\cancel{d}, k) \end{array}
+\begin{array} {c} \mathrm{T} \\[-3pt] \left(\cancel{d}, k\right) \end{array}
-\!\!
+\! \!
 </math>
-|<math>\scriptsize (r, k)</math>
+| <math>\scriptsize (r, k)</math>
-|integer
+| Integer
-|matrix
+| Matrix
 |
-|[[...} ...]
+| [[...} ...]
 |
-|<math>\textbf{y}_i</math>
+| <math>\textbf{y}_i</math>
 |
-|<math>\mathrm{y}_{ij}</math>
+| <math>\mathrm{y}_{ij}</math>
-|mnemonic: looks like bent-up 'T', or cross between 'M' and 'T'
+| Mnemonic: looks like bent-up 'T', or cross between 'M' and 'T'
 |-
-|<math>𝒋\mathrm{T}</math>
+| <math>𝒋\mathrm{T}</math>
-|<math>\textbf{o}</math>
+| <math>\textbf{o}</math>
-|[[Dave_Keenan_%26_Douglas_Blumeyer%27s_guide_to_RTT:_tuning_fundamentals#Primes|target-interval (just) size list]]
+| {{subpage|tuning fundamentals|uprev|s=primes|text=Target-interval (just) size list}}
-|<math>\scriptsize
+| <math>\scriptsize
 \begin{array} {c} 𝒋 \\[-2pt] {\small\mathsf{¢}} \hspace{-2mu} / \hspace{-2mu} \cancel{𝗽} \end{array}
 \begin{array} {c} \\[-2pt] · \end{array}
 \begin{array} {c} \mathrm{T} \\[-2pt] \cancel{𝗽} \end{array}
 </math>
-|<math>\mathsf{¢}</math>
+| <math>\mathsf{¢}</math>
-|cents
+| Cents
-|<math>\scriptsize
+| <math>\scriptsize
-\!\!
+\! \!
-\begin{array} {c} 𝒋 \\[-3pt] (1, \cancel{d}) \end{array}
+\begin{array} {c} 𝒋 \\[-3pt] \left(1, \cancel{d}\right) \end{array}
-\!\!
+\! \!
-\begin{array} {c} \mathrm{T} \\[-3pt] (\cancel{d}, k) \end{array}
+\begin{array} {c} \mathrm{T} \\[-3pt] \left(\cancel{d}, k\right) \end{array}
-\!\!
+\! \!
 </math>
-|<math>\scriptsize (1, k)</math>
+| <math>\scriptsize (1, k)</math>
-|real
+| Real
-|list
+| List
-|[...]
+| [...]
 |
 |
 |
 |
-|<math>\mathrm{o}_i</math>
+| <math>\mathrm{o}_i</math>
-|mnemonic: <math>\textbf{o}</math>riginal size list
+| Mnemonic: <math>\textbf{o}</math>riginal size list
 |-
-|<math>𝒕\mathrm{T}</math>
+| <math>𝒕\mathrm{T}</math>
-|<math>\textbf{a}</math>
+| <math>\textbf{a}</math>
-|[[tempered target-interval size list]]
+| [[Tempered target-interval size list]]
-|<math>\scriptsize
+| <math>\scriptsize
 \begin{array} {c} 𝒕 \\[-2pt] {\small\mathsf{¢}} \hspace{-2mu} / \hspace{-2mu} \cancel{𝗽} \end{array}
 \begin{array} {c} \\[-2pt] · \end{array}
 \begin{array} {c} \mathrm{T} \\[-2pt] \cancel{𝗽} \end{array}
 </math>
-|<math>\mathsf{¢}</math>
+| <math>\mathsf{¢}</math>
-|cents
+| Cents
-|<math>\scriptsize
+| <math>\scriptsize
-\!\!
+\! \!
-\begin{array} {c} 𝒕 \\[-3pt] (1, \cancel{d}) \end{array}
+\begin{array} {c} 𝒕 \\[-3pt] \left(1, \cancel{d}\right) \end{array}
-\!\!
+\! \!
-\begin{array} {c} \mathrm{T} \\[-3pt] (\cancel{d}, k) \end{array}
+\begin{array} {c} \mathrm{T} \\[-3pt] \left(\cancel{d}, k\right) \end{array}
-\!\!
+\! \!
 </math>
-|<math>\scriptsize (1, k)</math>
+| <math>\scriptsize (1, k)</math>
-|real
+| Real
-|list
+| List
-|[...]
+| [...]
 |
 |
 |
 |
-|<math>\mathrm{a}_i</math>
+| <math>\mathrm{a}_i</math>
-|mnemonic: <math>\textbf{a}</math>ltered size list
+| Mnemonic: <math>\textbf{a}</math>ltered size list
 |-
-|<math>𝒕\mathrm{T} - 𝒋\mathrm{T} \\
+| <math>𝒕\mathrm{T} - 𝒋\mathrm{T}</math><br />
-𝒓\mathrm{T} \\
+<math>𝒓\mathrm{T}</math><br />
-\textbf{a} - \textbf{o}</math>
+<math>\textbf{a} - \textbf{o}</math>
-|<math>\textbf{e}</math>
+| <math>\textbf{e}</math>
-|[[target-interval error list]]
+| [[Target-interval error list]]
-|<math>\scriptsize
+| <math>\scriptsize
 \begin{array} {c} 𝒓 \\[-2pt] {\small\mathsf{¢}} \hspace{-2mu} / \hspace{-2mu} \cancel{𝗽} \end{array}
 \begin{array} {c} \\[-2pt] · \end{array}
 \begin{array} {c} \mathrm{T} \\[-2pt] \cancel{𝗽} \end{array}
 </math>
-|<math>\mathsf{¢}</math>
+| <math>\mathsf{¢}</math>
-|cents
+| Cents
-|<math>\scriptsize
+| <math>\scriptsize
-\!\!
+\! \!
-\begin{array} {c} 𝒓 \\[-3pt] (1, \cancel{d}) \end{array}
+\begin{array} {c} 𝒓 \\[-3pt] \left(1, \cancel{d}\right) \end{array}
-\!\!
+\! \!
-\begin{array} {c} \mathrm{T} \\[-3pt] (\cancel{d}, k) \end{array}
+\begin{array} {c} \mathrm{T} \\[-3pt] \left(\cancel{d}, k\right) \end{array}
-\!\!
+\! \!
 </math>
-|<math>\scriptsize (1, k)</math>
+| <math>\scriptsize (1, k)</math>
-|real
+| Real
-|list
+| List
-|[...]
+| [...]
 |
 |
 |
 |
-|<math>\mathrm{e}_i</math>
+| <math>\mathrm{e}_i</math>
 |
 |-
-|<math>C</math> or <math>S</math>
+| <math>C</math> or <math>S</math>
-|<math>W</math>
+| <math>W</math>
-|[[target-interval weight matrix]]
+| [[Target-interval weight matrix]]
-| colspan="3" |(see complexities and simplicities table)
+| colspan="3" | (See complexities and simplicities table)
 |
-|<math>\scriptsize (k, k)</math>
+| <math>\scriptsize (k, k)</math>
-|real
+| Real
-|matrix
+| Matrix
 |
-|[[...] ...]
+| [[...] ...]
 |
 |
-|<math>𝒘</math>
+| <math>𝒘</math>
-|<math>w_i</math>
+| <math>w_i</math>
 |
 |-
 |
-|<math>C</math>
+| <math>C</math>
-|[[Dave_Keenan_%26_Douglas_Blumeyer%27s_guide_to_RTT:_tuning_fundamentals#Complexity-weight_damage|target-interval complexity weight matrix]]
+| {{subpage|tuning_fundamentals|uprev|s=complexity-weight damage|text=Target-interval complexity weight matrix}}
-| colspan="3" |(see complexities section of complexities and simplicities table)
+| colspan="3" | (See complexities section of complexities and simplicities table)
 |
-|<math>\scriptsize (k, k)</math>
+| <math>\scriptsize (k, k)</math>
-|real
+| Real
-|matrix
+| Matrix
 |
-|[[...] ...]
+| [[...] ...]
 |
 |
-|<math>𝒄</math>
+| <math>𝒄</math>
-|<math>c_i</math>
+| <math>c_i</math>
 |
 |-
-|<math>\dfrac1C</math>
+| <math>\dfrac1C</math>
-|<math>S</math>
+| <math>S</math>
-|[[Dave_Keenan_%26_Douglas_Blumeyer%27s_guide_to_RTT:_tuning_fundamentals#Complexity-weight_damage|target-interval simplicity weight matrix]]
+| {{subpage|tuning_fundamentals|uprev|s=complexity-weight_damage|text=Target-interval simplicity weight matrix}}
-| colspan="3" |(see simplicities section of complexities and simplicities table)
+| colspan="3" | (See simplicities section of complexities and simplicities table)
 |
-|<math>\scriptsize (k, k)</math>
+| <math>\scriptsize (k, k)</math>
-|real
+| Real
-|matrix
+| Matrix
 |
-|[[...] ...]
+| [[...] ...]
 |
 |
-|<math>𝒔</math>
+| <math>𝒔</math>
-|<math>s_i</math>
+| <math>s_i</math>
-|entrywise reciprocal of <math>C</math>
+| Entry-wise reciprocal of <math>C</math>
 |-
-|<math>|\textbf{e}|W</math>
+| <math>\abs{\textbf{e}} W</math>
-|<math>\textbf{d}</math>
+| <math>\textbf{d}</math>
-|[[target-interval damage list]]
+| [[Target-interval damage list]]
-| colspan="3" |(see damages table)
+| colspan="3" | (See damages table)
 |
-|<math>\scriptsize (1, k)</math>
+| <math>\scriptsize (1, k)</math>
-|real
+| Real
-|list
+| List
-|[...]
+| [...]
 |
 |
 |
 |
-|<math>\mathrm{d}_i</math>
+| <math>\mathrm{d}_i</math>
 |
 |-
 |
-|<math>k</math>
+| <math>k</math>
-|[[target-interval count]]
+| [[Target-interval count]]
 |
 |
 |
 |
-|<math>\scriptsize (1, 1)</math>
+| <math>\scriptsize (1, 1)</math>
-|integer
+| Integer
-|scalar
+| Scalar
 |
 |
 |
 |
 |
 |
-|mnemonic: <math>k</math>ount
+| Mnemonic: <math>k</math>ount
 |-
-! colspan="17" |held-intervals
+! colspan="17" | Held-intervals
 |-
 |
-|<math>\mathrm{H}</math>
+| <math>\mathrm{H}</math>
-|[[held-interval basis]]
+| [[Held-interval basis]]
 |
-|<math>\small 𝗽</math>
+| <math>\small 𝗽</math>
-|primes
+| Primes
 |
-|<math>\scriptsize (d, h)</math>
+| <math>\scriptsize (d, h)</math>
 |
-|matrix
+| Matrix
 |
-|[[...⟩ ...]
+| [[...⟩ ...]
 |
-|<math>\textbf{h}_i</math>
+| <math>\textbf{h}_i</math>
 |
-|<math>\mathrm{h}_{ij}</math>
+| <math>\mathrm{h}_{ij}</math>
 |
+|-
+|
+| <math>h</math>
+| [[Held-interval count]]
+|
+|
+|
+|
+| <math>\scriptsize (1, 1)</math>
+| Integer
+| Scalar
+|
+|
+|
+|
+|
+|
+|
+|-
+! colspan="17" | Exploring temperaments
+|-
+|
+| <math>\mathrm{C}</math>
+| [[Comma basis]]
+|
+| <math>\small 𝗽</math>
+| Primes
+|
+| <math>\scriptsize (d, n)</math>
+| Integer
+| Matrix
+|
+| [[...⟩ ...]
+|
+| <math>\textbf{c}_i</math>
+|
+| <math>\mathrm{c}_{ij}</math>
+| Jargon name: monzo list
 |-
 |
-|<math>h</math>
+| <math>\textbf{c}</math>
-|[[held-interval count]]
+| [[Comma]]
 |
-|
+| <math>\small 𝗽</math>
-|
+| primes
 |
-|<math>\scriptsize (1, 1)</math>
+| <math>\scriptsize (d, 1)</math>
-|integer
+| Integer
-|scalar
+| Vector
 |
-|
+| [...⟩
 |
 |
 |
-|
+| <math>\mathrm{c}_i</math>
-|
+| Specific type: vector ([[prime-count vector]] or PC-vector)
 |-
-! colspan="17" |exploring temperaments
+! colspan="17" | Computation
 |-
 |
-|<math>\mathrm{C}</math>
+| {{llzigzag}}<math>\,·\,</math>{{rrzigzag}}<math>_p</math>
-|[[comma basis]]
+| [[Power sum]] (<math>p</math>-sum)
 |
-|<math>\small 𝗽</math>
+|
-|primes
+|
 |
-|<math>\scriptsize (d, n)</math>
+| <math>\scriptsize (1, 1)</math>
-|integer
+| Real
-|matrix
+| Scalar
 |
-|[[...⟩ ...]
+|
 |
-|<math>\textbf{c}_i</math>
+|
 |
-|<math>\mathrm{c}_{ij}</math>
+|
-|jargon name: monzo list
+|
 |-
-|
+! colspan="17" | All-interval tuning schemes
-|<math>\textbf{c}</math>
-|[[comma]]
-|
-|<math>\small 𝗽</math>
-|primes
-|
-|<math>\scriptsize (d, 1)</math>
-|integer
-|vector
-|
-|[...⟩
-|
-|
-|
-|<math>\mathrm{c}_i</math>
-|specific type: [[prime-count vector]] (PC-vector)
 |-
-! colspan="17" |computation
+| <math>\mathrm{I}</math>
+| <math>\mathrm{T}_{\text{p}}</math>
+| [[Prime proxy target-interval list]]
+|
+| <math>\small 𝗽</math>
+| Primes
+|
+| <math>\scriptsize (d, d)</math>
+| Integer
+| Matrix
+|
+| ⟨[...⟩ ...]
+|
+|
+| <math>\mathbf{1}</math>
+|
+|
 |-
 |
-|<math>\llzigzag·\,\rrzigzag\!_p</math>
+| <math>X</math>
-|[[power sum]] (<math>p</math>-sum)
+| [[Complexity prescaler]]
-|
+| <math>\small\mathsf{𝟙}\scriptsize\mathsf{(C)}</math>
-|
+| <math>\small\mathsf{(C)}</math>
-|
+| Complexity weight
 |
-|<math>\scriptsize (1, 1)</math>
+| <math>\scriptsize (d, d)</math>
-|real
+| Real
-|scalar
+| Matrix
-|
+| [⟨...] ...⟩
 |
 |
 |
-|
+| <math>𝒙</math>
-|
+| <math>x_i</math>
 |
 |-
-! colspan="17" |all-interval tuning schemes
+| <math>\text{diag}({\large\textbf{𝓁}}\hspace{2mu})</math>
+| <math>L</math>
+| [[Log-prime matrix]]
+|
+| <math>\small\mathsf{oct}</math>/<math>\small 𝗽</math>
+| Octaves per prime
+|
+| <math>\scriptsize (d, d)</math>
+| Real
+| Matrix
+| [⟨...] ...⟩
+| ⟨[...⟩ ...]
+| <math>{\large\textbf{𝓁}}\hspace{2mu}_i</math>
+|
+| <math>{\large\textbf{𝓁}}\hspace{2mu}</math>
+| <math>{\large 𝓁}\hspace{2mu}_{ij}</math>
+|
 |-
-|<math>\mathrm{I}</math>
+|
-|<math>\mathrm{T}_{\text{p}}</math>
+| <math>q</math>
-|[[prime proxy target-interval list]]
+| {{subpage|all-interval_tuning_schemes|uprev|s=Dual norms|text=Interval complexity norm power}}
 |
-|<math>\small 𝗽</math>
+|
-|primes
+|
 |
-|<math>\scriptsize (d, d)</math>
+| <math>\scriptsize (1, 1)</math>
-|integer
+| Real
-|matrix
+| Scalar
 |
-|⟨[...⟩ ...]
+|
 |
 |
-|<math>\slant{\mathbf{1}}</math>
+|
 |
 |
 |-
 |
-|<math>X</math>
+| <math>\norm{·}_q</math>
-|[[complexity prescaler]]
+| [[Power norm]] (<math>p</math>-norm)
-|<math>\small\mathsf{𝟙}\scriptsize\mathsf{(C)}</math>
+|
-|<math>\small\mathsf{(C)}</math>
+|
-|complexity weight
+|
 |
-|<math>\scriptsize (d, d)</math>
+| <math>\scriptsize (1, 1)</math>
-|real
+| Real
-|matrix
+| Scalar
-|[⟨...] ...⟩
+|
 |
 |
 |
-|<math>𝒄_{\text{p}}</math>
+|
-|<math>c_{\text{p}i}</math>
+|
 |
 |-
-|
+| <math>\dfrac1{1-\frac1q}</math>
-|<math>L</math>
+| <math>\text{dual}(q)</math>
-|[[log-prime matrix]]
+| {{subpage|all-interval tuning schemes|uprev|s=Dual norms|text=Dual norm power}}
 |
-|<math>\small\mathsf{oct}</math>/<math>\small 𝗽</math>
+|
-|octaves per prime
+|
 |
-|<math>\scriptsize (d, d)</math>
+| <math>\scriptsize (1, 1)</math>
-| real
+| Real
-|matrix
+| Scalar
-|[⟨...] ...⟩
+|
-|⟨[...⟩ ...]
+|
-|<math>\textbf{𝓁}_i</math>
+|
 |
-|<math>\textbf{𝓁}</math>
+|
-|<math>𝓁_{ij}</math>
+|
 |
 |-
 |
-|<math>q</math>
+| <math>\norm{X\mathbf{i}}_q</math>
-|[[Dave_Keenan_%26_Douglas_Blumeyer%27s_guide_to_RTT:_all-interval_tuning_schemes#Dual_norms|interval complexity norm power]]
+| [[interval complexity]]
 |
-|
+| <math>\small\mathsf{(C)}</math>
 |
 |
-|<math>\scriptsize (1, 1)</math>
+| <math>\scriptsize (1, 1)</math>
-| real
+| Real
-|scalar
+| Scalar
 |
 |
 |
 |
 |
 |
 |
 |-
 |
-|<math>‖ · ‖_q</math>
+| <math>\norm{𝒓X^{-1}}_{\text{dual}(q)}</math>
-|[[power norm]] (<math>p</math>-norm)
+| [[Retuning magnitude]]
 |
-|
+| <math>\mathsf{¢}\small\mathsf{(C^{-1})}</math>
 |
 |
-|<math>\scriptsize (1, 1)</math>
+| <math>\scriptsize (1, 1)</math>
-|real
+| Real
-|scalar
+| Scalar
 |
 |
 |
 |
 |
 |
 |
 |}
-===Units===
+=== Units ===
 Same as the basic level.
-===Tuning schemes===
+=== Tuning schemes ===
 {| class="wikitable center-all mw-collapsible mw-collapsed"
-|+
+|+ style="font-size: 105%;" |
 |-
-! colspan="3" rowspan="3" |retuning (or mistuning) magnitude
+! colspan="3" rowspan="3" | Retuning (or mistuning) magnitude
-! colspan="9" |damage
+! colspan="9" | Damage
-! rowspan="4" |target
+! rowspan="4" | Target<br />intervals
+! colspan="2" rowspan="3" | Systematic name
-intervals
+! rowspan="4" | Previously named tuning schemes that are specific types of this tuning scheme
-! colspan="2" rowspan="3" |systematic name
+! rowspan="4" | Of interest?
-! rowspan="4" |previously named tuning schemes that are specific types of this tuning scheme
-! rowspan="4" |of interest?
 |-
-! colspan="6" |weight
+! colspan="6" | Weight
-! colspan="3" rowspan="1" |optimization
+! colspan="3" rowspan="1" | Optimization
 |-
-! colspan="3" |interval complexity
+! colspan="3" | Interval complexity
-! colspan="3" rowspan="1" |slope
+! colspan="3" rowspan="1" | Slope
-! colspan="1" rowspan="2" |initial
+! colspan="1" rowspan="2" | Initial
-! colspan="1" rowspan="2" | name
+! colspan="1" rowspan="2" | Name
-! colspan="1" rowspan="2" |power
+! colspan="1" rowspan="2" | Power
 |-
-!initial
+! Initial
-!name
+! Name
-!power
+! Power
-!initial
+! Initial
-!name
+! Name
-!power
+! Power
-!initial
+! Initial
-!name
+! Name
-! multiplier
+! Multiplier
-! colspan="1" |abbreviated
+! colspan="1" | Abbreviated
-! colspan="1" |read ("____ tuning scheme")
+! colspan="1" | Read ("____ tuning scheme")
 |-
-|<n/a>
+| <n/a>
-|maximum
+| Maximum
-|∞
+| &infin;
-|(t)
+| (t)
-|taxicab
+| Taxicab
-|1
+| 1
-| rowspan="2" |S
+| rowspan="2" | ''S''
-| rowspan="2" |simplicity-weight
+| rowspan="2" | Simplicity-weight
-| rowspan="2" |1/complexity
+| rowspan="2" | 1/Complexity
-| rowspan="17" |<n/a>
+| rowspan="17" | <n/a>
-| rowspan="7" |minimax
+| rowspan="7" | Minimax
-| rowspan="7" |∞
+| rowspan="7" | ∞
-| rowspan="2" |all
+| rowspan="2" | All
-| minimax-S
+| Minimax-S
-|minimax simplicity-weight damage
+| Minimax simplicity-weight damage
-|"[[TOP]]"/"[[T1]]"/"[[TIPTOP]]"*, "[[CTOP]]", "[[POTOP]]"/"[[POTT]]"*, "[[BOP tuning|BOP]]", "[[Weil Norms, Tenney-Weil Norms, and TWp Interval and Tuning Space|Weil]]", "[[Kees]]"
+| "[[TOP]]"/"[[T1]]"/"[[TIPTOP]]"*, "[[CTOP]]", "[[POTOP]]"/"[[POTT]]"*, "[[BOP tuning|BOP]]", "[[Weil Norms, Tenney-Weil Norms, and TWp Interval and Tuning Space|Weil]]", "[[Kees]]"
-|yes
+| Yes
 |-
-|<n/a>
+| <n/a>
-|Euclidean
+| Euclidean
-|2
+| 2
-|E
+| E
-|Euclidean
+| Euclidean
-|2
+| 2
-|minimax-ES
+| Minimax-ES
-|minimax Euclideanized-simplicity-weight damage
+| Minimax Euclideanized-simplicity-weight damage
-|"[[Tenney-Euclidean tuning|TE]]"/"[[T2]]"/"[[TOP-RMS]]", "[[CTE tuning|CTE]]", "[[POTE tuning|POTE]]", "[[Frobenius]]", "[[BE]]", "[[WE]]", "[[KE]]"
+| "[[Tenney-Euclidean tuning|TE]]"/"[[T2]]"/"[[TOP-RMS]]", "[[CTE tuning|CTE]]", "[[POTE tuning|POTE]]", "[[Frobenius]]", "[[BE]]", "[[WE]]", "[[KE]]"
 |
 |-
-| colspan="3" rowspan="15" |<n/a>
+| colspan="3" rowspan="15" | <n/a>
-| colspan="3" |<n/a>
+| colspan="3" | <n/a>
-|U
+| U
-|unity-weight
+| Unity-weight
-|<none>
+| <none>
 | rowspan="15" | <set>
-|<set> minimax-U
+| <set> Minimax-U
-|<set> minimax unity-weight-damage
+| <set> Minimax unity-weight-damage
-|"[[Minimax tuning|minimax]]"
+| "[[Minimax tuning| minimax]]"
-|yes
+| yes
 |-
-|(t)
+| (t)
-|taxicab
+| taxicab
-|1
+| 1
-| rowspan="2" |S
+| rowspan="2" | S
-| rowspan="2" |simplicity-weight
+| rowspan="2" | Simplicity-weight
-| rowspan="2" |1/complexity
+| rowspan="2" | 1/Complexity
-|<set> minimax-S
+| <set> Minimax-S
-|<set> minimax simplicity-weight damage
+| <set> Minimax simplicity-weight damage
 |
-|yes
+| Yes
 |-
-|E
+| E
-|Euclidean
+| Euclidean
-|2
+| 2
-|<set> minimax-ES
+| <set> Minimax-ES
-|<set> minimax Euclideanized-simplicity-weight damage
+| <set> Minimax Euclideanized-simplicity-weight damage
 |
 |
 |-
-|(t)
+| (t)
-|taxicab
+| Taxicab
-|1
+| 1
-| rowspan="2" |C
+| rowspan="2" | C
-| rowspan="2" |complexity-weight
+| rowspan="2" | Complexity-weight
-| rowspan="2" |complexity
+| rowspan="2" | Complexity
-|<set> minimax-C
+| <set> Minimax-C
-|<set> minimax complexity-weight damage
+| <set> Minimax complexity-weight damage
 |
-|yes
+| Yes
 |-
-|E
+| E
-|Euclidean
+| Euclidean
-|2
+| 2
-|<set> minimax-EC
+| <set> Minimax-EC
-|<set> minimax Euclideanized-complexity-weight damage
+| <set> Minimax Euclideanized-complexity-weight damage
 |
 |
 |-
-| colspan="3" |<n/a>
+| colspan="3" | <n/a>
-|U
+| U
-|unity-weight
+| Unity-weight
-|<none>
+| <none>
-| rowspan="5" |miniRMS
+| rowspan="5" | MiniRMS
-| rowspan="5" |2
+| rowspan="5" | 2
-|<set> miniRMS-U
+| <set> MiniRMS-U
-|<set> miniRMS unity-weight damage
+| <set> MiniRMS unity-weight damage
-|"[[least squares]]"
+| "[[Least squares]]"
-|yes
+| Yes
 |-
-|(t)
+| (t)
-|taxicab
+| Taxicab
-|1
+| 1
-| rowspan="2" |S
+| rowspan="2" | S
-| rowspan="2" |simplicity-weight
+| rowspan="2" | Simplicity-weight
-| rowspan="2" |1/complexity
+| rowspan="2" | 1/Complexity
-|<set> miniRMS-S
+| <set> MiniRMS-S
-|<set> miniRMS simplicity-weight damage
+| <set> MiniRMS simplicity-weight damage
 |
-|yes
+| Yes
 |-
-|E
+| E
-|Euclidean
+| Euclidean
-|2
+| 2
-|<set> miniRMS-ES
+| <set> MiniRMS-ES
-|<set> miniRMS Euclideanized-simplicity-weight damage
+| <set> MiniRMS Euclideanized-simplicity-weight damage
 |
 |
 |-
-|(t)
+| (t)
-|taxicab
+| Taxicab
-|1
+| 1
-| rowspan="2" |C
+| rowspan="2" | C
-| rowspan="2" |complexity-weight
+| rowspan="2" | Complexity-weight
-| rowspan="2" |complexity
+| rowspan="2" | Complexity
-|<set> miniRMS-C
+| <set> MiniRMS-C
-|<set> miniRMS complexity-weight damage
+| <set> MiniRMS complexity-weight damage
 |
-|yes
+| Yes
 |-
-|E
+| E
-|Euclidean
+| Euclidean
-|2
+| 2
-|<set> miniRMS-EC
+| <set> MiniRMS-EC
-|<set> miniRMS Euclideanized-complexity-weight damage
+| <set> MiniRMS Euclideanized-complexity-weight damage
 |
 |
 |-
-| colspan="3" |<n/a>
+| colspan="3" | <n/a>
-|U
+| U
-|unity-weight
+| Unity-weight
-|<none>
+| <none>
-| rowspan="5" |miniaverage
+| rowspan="5" | Miniaverage
-| rowspan="5" |1
+| rowspan="5" | 1
-|<set> miniaverage-U
+| <set> Miniaverage-U
-|<set> miniaverage unity-weight damage
+| <set> Miniaverage unity-weight damage
 |
-|yes
+| Yes
 |-
-|(t)
+| (t)
-|taxicab
+| Taxicab
-|1
+| 1
-| rowspan="2" |S
+| rowspan="2" | S
-| rowspan="2" |simplicity-weight
+| rowspan="2" | Simplicity-weight
-| rowspan="2" |1/complexity
+| rowspan="2" | 1/Complexity
-|<set> miniaverage-S
+| <set> Miniaverage-S
-|<set> miniaverage simplicity-weight damage
+| <set> Miniaverage simplicity-weight damage
 |
-|yes
+| Yes
 |-
-|E
+| E
-|Euclidean
+| Euclidean
-|2
+| 2
-|<set> miniaverage-ES
+| <set> Miniaverage-ES
-|<set> miniaverage Euclideanized-simplicity-weight damage
+| <set> Miniaverage Euclideanized-simplicity-weight damage
 |
 |
 |-
-|(t)
+| (t)
-|taxicab
+| Taxicab
-|1
+| 1
-| rowspan="2" |C
+| rowspan="2" | C
-| rowspan="2" |complexity-weight
+| rowspan="2" | Complexity-weight
-| rowspan="2" |complexity
+| rowspan="2" | Complexity
-|<set> miniaverage-C
+| <set> Miniaverage-C
-|<set> miniaverage complexity-weight damage
+| <set> Miniaverage complexity-weight damage
 |
-|yes
+| Yes
 |-
 | E
-|Euclidean
+| Euclidean
-|2
+| 2
-|<set> miniaverage-EC
+| <set> Miniaverage-EC
-|<set> miniaverage Euclideanized-complexity-weight damage
+| <set> Miniaverage Euclideanized-complexity-weight damage
 |
 |
 |}
-===Damages===
+=== Damages ===
 {| class="wikitable center-all mw-collapsible mw-collapsed"
-|+
+|+ style="font-size: 105%;" |
 |-
-! colspan="2" |quantity
+! colspan="2" | Quantity
-! colspan="2" |unit
+! colspan="2" | Unit
 |-
-!abbreviation
+! Abbreviation
-!name
+! Name
-! symbol
+! Symbol
-!name
+! Name
 |-
 | U-damage
-|unity-weight damage
+| Unity-weight damage
-|<math>\mathsf{¢}\small\mathsf{(U)}</math>
+| <math>\mathsf{¢}\small\mathsf{(U)}</math>
-|unity-weighted cents
+| Unity-weighted cents
 |-
-|C-damage
+| C-damage
-|complexity-weight damage
+| Complexity-weight damage
-|<math>\mathsf{¢}\small\mathsf{(C)}</math>
+| <math>\mathsf{¢}\small\mathsf{(C)}</math>
-|complexity-weighted cents
+| Complexity-weighted cents
 |-
-|EC-damage
+| EC-damage
-|Euclideanized-complexity-weight damage
+| Euclideanized-complexity-weight damage
-|<math>\mathsf{¢}</math><math>\small\mathsf{(EC)}</math>
+| <math>\mathsf{¢}</math><math>\small\mathsf{(EC)}</math>
-|Euclideanized-complexity-weighted cents
+| Euclideanized-complexity-weighted cents
 |-
-|S-damage
+| S-damage
-|simplicity-weight damage
+| Simplicity-weight damage
-|<math>\mathsf{¢}\small\mathsf{(S)}</math>
+| <math>\mathsf{¢}\small\mathsf{(S)}</math>
-| simplicity-weighted cents
+| Simplicity-weighted cents
 |-
-|ES-damage
+| ES-damage
-|Euclideanized-simplicity-weight damage
+| Euclideanized-simplicity-weight damage
-|<math>\mathsf{¢}</math><math>\small\mathsf{(ES)}</math>
+| <math>\mathsf{¢}</math><math>\small\mathsf{(ES)}</math>
-|Euclideanized-simplicity-weighted cents
+| Euclideanized-simplicity-weighted cents
 |}
-===Complexity and simplicity===
+=== Complexity and simplicity ===
 {| class="wikitable center-all mw-collapsible mw-collapsed"
-|+
+|+ style="font-size: 105%;" |
-! colspan="2" |quantity
+|-
-! colspan="2" |unit
+! colspan="2" | Quantity
+! colspan="2" | Unit
 |-
-! abbreviation
+! Abbreviation
-!name
+! Name
-!symbol
+! Symbol
-!name
+! Name
 |-
-|C
+| C
-|complexity
+| Complexity
-|<math>\small\mathsf{(C)}</math>
+| <math>\small\mathsf{(C)}</math>
-|complexity weight
+| Complexity weight
 |-
-|EC
+| EC
-|Euclideanized complexity
+| Euclideanized complexity
-|<math>\small\mathsf{(EC)}</math>
+| <math>\small\mathsf{(EC)}</math>
-|Euclideanized-complexity weight
+| Euclideanized-complexity weight
 |-
-|S
+| S
-|simplicity
+| Simplicity
-|<math>\small\mathsf{(S)}</math>
+| <math>\small\mathsf{(S)}</math>
-|simplicity weight
+| Simplicity weight
 |-
-|ES
+| ES
-|Euclideanized simplicity
+| Euclideanized simplicity
-|<math>\small\mathsf{(ES)}</math>
+| <math>\small\mathsf{(ES)}</math>
 | Euclideanized-simplicity weight
 |}
-==Advanced==
+== Advanced ==
+=== Objects ===
-===Objects===
 {| class="wikitable mw-collapsible mw-collapsed"
-|+
+|+ style="font-size: 105%;" |
-! rowspan="2" |equivalent expressions
+|-
-! rowspan="2" |variable
+! rowspan="2" | Equivalent expressions
-! rowspan="2" |name
+! rowspan="2" | Variable
-! colspan="3" |units
+! rowspan="2" | Name
-! colspan="2" |shape
+! colspan="3" | Units
-! colspan="2" |type
+! colspan="2" | Shape
-! colspan="2" |EBK notation
+! colspan="2" | Type
-! colspan="4" |subobjects
+! colspan="2" | EBK notation
-! rowspan="2" |notes
+! colspan="4" | Subobjects
+! rowspan="2" | Notes
 |-
-!unreduced
+! Unreduced
-!reduced
+! Reduced
-!read as
+! Read as
-!unreduced
+! Unreduced
-! reduced
+! Reduced
-!numeric
+! Numeric
-!structural
+! Structural
-!row-first
+! Row-first
-!col-first
+! Col-first
-!row
+! Row
-!col
+! Column
-!diag
+! Diagonal
-!entry
+! Entry
 |-
-! colspan="17" |mapping
+! colspan="17" | Mapping
 |-
 |
-|<math>\textbf{i}</math>
+| <math>\textbf{i}</math>
-|[[interval|(just) interval]]
+| [[interval|(Just) interval]]
 |
-|<math>\small 𝗽</math>
+| <math>\small 𝗽</math>
-|primes
+| Primes
 |
-|<math>\scriptsize (d, 1)</math>
+| <math>\scriptsize (d, 1)</math>
-|integer
+| Integer
-| vector
+| Vector
 |
-|[...⟩
+| [...⟩
 |
 |
 |
-|<math>\mathrm{i}_i</math>
+| <math>\mathrm{i}_i</math>
-|specific type: [[prime-count vector]] (PC-vector)
+| Specific type: vector ([[prime-count vector]] or PC-vector)
-jargon name: monzo
+Jargon name: monzo
 |-
 |
-|<math>M</math>
+| <math>M</math>
-|[[Mapping|(temperament) mapping (matrix)]]
+| [[Mapping|(Temperament) mapping (matrix)]]
 |
-|<math>\small 𝗴</math>/<math>\small 𝗽</math>
+| <math>\small 𝗴</math>/<math>\small 𝗽</math>
-|generators per prime
+| Generators per prime
 |
-|<math>\scriptsize (r, d)</math>
+| <math>\scriptsize (r, d)</math>
-| integer
+| Integer
-|matrix
+| Matrix
-|[⟨...] ...}
+| [⟨...] ...}
-|⟨[...} ...]
+| ⟨[...} ...]
-|<math>𝒎_i</math>
+| <math>𝒎_i</math>
 |
 |
-|<math>m_{ij}</math>
+| <math>m_{ij}</math>
-|jargon name: val list
+| Jargon name: val list
 |-
-|<math>M\textbf{i}</math>
+| <math>M\textbf{i}</math>
-|<math>\textbf{y}</math>
+| <math>\textbf{y}</math>
-|[[mapped interval]]
+| [[Mapped interval]]
-|<math>\scriptsize
+| <math>\scriptsize
 \begin{array} {c} M \\[-2pt] 𝗴 \hspace{-2mu} / \hspace{-2mu} \cancel{𝗽} \end{array}
 \begin{array} {c} \\[-2pt] · \end{array}
 \begin{array} {c} \textbf{i} \\[-2pt] \cancel{𝗽} \end{array}
 </math>
-|<math>\small 𝗴</math>
+| <math>\small 𝗴</math>
 | generators
-|<math>\scriptsize
+| <math>\scriptsize
-\!\!
+\! \!
-\begin{array} {c} M \\[-3pt] (r, \cancel{d}) \end{array}
+\begin{array} {c} M \\[-3pt] \left(r, \cancel{d}\right) \end{array}
-\!\!
+\! \!
-\begin{array} {c} \textbf{i} \\[-3pt] (\cancel{d}, 1) \end{array}
+\begin{array} {c} \textbf{i} \\[-3pt] \left(\cancel{d}, 1\right) \end{array}
-\!\!
+\! \!
 </math>
-|<math>\scriptsize (r, 1)</math>
+| <math>\scriptsize (r, 1)</math>
-|integer
+| Integer
-|vector
+| Vector
 |
-|[...}
+| [...}
 |
 |
 |
 |
-|specific type: [[generator-count vector]] (GC-vector)
+| Specific type: [[generator-count vector]] (GC-vector)
-jargon name: tmonzo; mnemonic: <math>\textbf{y}</math>nterval
+Jargon name: tmonzo; mnemonic: <math>\textbf{y}</math>nterval
 |-
 |
-|<math>𝒎</math>
+| <math>𝒎</math>
-|[[map|(temperament) map]]
+| [[map|(Temperament) map]]
 |
-|<math>\small 𝗴</math>/<math>\small 𝗽</math>
+| <math>\small 𝗴</math>/<math>\small 𝗽</math>
-|generators per prime
+| Generators per prime
 |
-|<math>\scriptsize (1, d)</math>
+| <math>\scriptsize (1, d)</math>
-|integer
+| Integer
-|vector
+| Vector
-|⟨...]
+| ⟨...]
 |
 |
 |
 |
-|<math>m_i</math>
+| <math>m_i</math>
-|jargon name: val
+| Jargon name: val
 |-
-|<math>n + r</math>
+| <math>n + r</math>
-|<math>d</math>
+| <math>d</math>
-|[[dimensionality]]
+| [[Dimensionality]]
 |
 |
 |
 |
-|<math>\scriptsize (1, 1)</math>
+| <math>\scriptsize (1, 1)</math>
-|integer
+| Integer
-|scalar
+| Scalar
 |
 |
 |
 |
 |
 |
 |
 |-
-|<math>d - n</math>
+| <math>d - n</math>
-|<math>r</math>
+| <math>r</math>
-|[[rank]]
+| [[Rank]]
 |
 |
 |
 |
-|<math>\scriptsize (1, 1)</math>
+| <math>\scriptsize (1, 1)</math>
-|integer
+| Integer
-| scalar
+| Scalar
 |
 |
 |
 |
 |
 |
 |
 |-
-|<math>d - r</math>
+| <math>d - r</math>
-|<math>n</math>
+| <math>n</math>
-|[[nullity]]
+| [[Nullity]]
 |
 |
 |
 |
-|<math>\scriptsize (1, 1)</math>
+| <math>\scriptsize (1, 1)</math>
-|integer
+| Integer
-|scalar
+| Scalar
 |
 |
 |
 |
 |
 |
 |
 |-
-! colspan="17" |tuning
+! colspan="17" | Tuning
 |-
-|<math>1200×\slant{\mathbf{1}}LG_{\text{j}}M_{\text{j}} \\
+| <math>\slant{\mathbf{1}}L</math>
-×\slant{\mathbf{1}}L \\
+| <math>{\large\textbf{𝓁}}\hspace{2mu}</math>
-𝒈_{\text{j}}M_{\text{j}}</math>
+| [[Log-prime map]]
-|<math>𝒋</math>
+|
-|[[just tuning map|just(-prime) tuning map]]
+| <math>\small\mathsf{oct}</math>/<math>\small 𝗽</math>
-|<math>\scriptsize
+| Octaves per prime
+|
+| <math>\scriptsize (1, d)</math>
+| Real
+| Vector
+| ⟨...]
+|
+|
+|
+|
+| <math>{\large 𝓁}\hspace{2mu}_i</math>
+|
+|-
+| <math>1200×\slant{\mathbf{1}}LG_{\text{j}}M_{\text{j}}</math><br />
+<math>1200×\slant{\mathbf{1}}L</math><br />
+<math>𝒈_{\text{j}}M_{\text{j}}</math>
+| <math>𝒋</math>
+| [[just tuning map|Just(-prime) tuning map]]
+| <math>\scriptsize
 \begin{array} {c} 1200 \\[-2pt] {\small\mathsf{¢}} \hspace{-2mu} / \hspace{-2mu} \cancel{\mathsf{oct}} \end{array}
 \begin{array} {c} \\[-2pt] · \end{array}
@@ Line 2,268: / Line 2,359: @@
 \begin{array} {c} M_{\text{j}} \\[-2pt] \cancel{𝗴} \hspace{-2mu} / \hspace{-2mu} 𝗽 \end{array}
 </math>
-|<math>\mathsf{¢}</math>/<math>\small 𝗽</math>
+| <math>\mathsf{¢}</math>/<math>\small 𝗽</math>
-|cents per prime
+| Cents per prime
-|<math>\scriptsize
+| <math>\scriptsize
-\!\!
+\! \!
-\begin{array} {c} 1200 \\[-3pt] (1, \cancel{1}) \end{array}
+\begin{array} {c} 1200 \\[-3pt] \left(1, \cancel{1}\right) \end{array}
-\!\!
+\! \!
-\begin{array} {c} \slant{\mathbf{1}} \\[-3pt] (\cancel{1}, \cancel{d}) \end{array}
+\begin{array} {c} \slant{\mathbf{1}} \\[-3pt] \left(\cancel{1}, \cancel{d}\right) \end{array}
-\!\!
+\! \!
-\begin{array} {c} L \\[-3pt] (\cancel{d}, \cancel{d}) \end{array}
+\begin{array} {c} L \\[-3pt] \left(\cancel{d}, \cancel{d}\right) \end{array}
 \\ \scriptsize \quad
-\!\!
+\! \!
-\begin{array} {c} G_{\text{j}} \\[-3pt] (\cancel{d}, \cancel{r}) \end{array}
+\begin{array} {c} G_{\text{j}} \\[-3pt] \left(\cancel{d}, \cancel{r}\right) \end{array}
-\!\!
+\! \!
-\begin{array} {c} M_{\text{j}} \\[-3pt] (\cancel{r}, d) \end{array}
+\begin{array} {c} M_{\text{j}} \\[-3pt] \left(\cancel{r}, d\right) \end{array}
-\!\!
+\! \!
 </math>
-|<math>\scriptsize (1, d_{\text{p}})</math>
+| <math>\scriptsize \left(1, d_{\text{p}}\right)</math>
-|real
+| Real
-|vector
+| Vector
-|⟨...]
+| ⟨...]
 |
 |
 |
 |
-|<math>j_i</math>
+| <math>j_i</math>
 |
 |-
-|<math>1200×\slant{\mathbf{1}}LG</math>
+| <math>1200×\slant{\mathbf{1}}LG</math>
-|<math>𝒈</math>
+| <math>𝒈</math>
-|[[generator tuning map]]
+| [[Generator tuning map]]
-|<math>\scriptsize
+| <math>\scriptsize
 \begin{array} {c} 1200 \\[-2pt] {\small\mathsf{¢}} \hspace{-2mu} / \hspace{-2mu} \cancel{\mathsf{oct}} \end{array}
 \begin{array} {c} \\[-2pt] · \end{array}
@@ Line 2,308: / Line 2,399: @@
 \begin{array} {c} G \\[-2pt] \cancel{𝗽} \hspace{-2mu} / \hspace{-2mu} 𝗴 \end{array}
 </math>
-|<math>\mathsf{¢}</math>/<math>\small 𝗴</math>
+| <math>\mathsf{¢}</math>/<math>\small 𝗴</math>
-|cents per generator
+| Cents per generator
-|<math>\scriptsize
+| <math>\scriptsize
-\!\!
+\! \!
 \begin{array} {c} 1200 \\[-3pt] (1, \cancel{1}) \end{array}
-\!\!
+\! \!
 \begin{array} {c} \slant{\mathbf{1}} \\[-3pt] (\cancel{1}, \cancel{d}) \end{array}
-\!\!
+\! \!
 \begin{array} {c} L \\[-3pt] (\cancel{d}, \cancel{d}) \end{array}
 \\ \scriptsize \quad
-\!\!
+\! \!
 \begin{array} {c} G \\[-3pt] (\cancel{d}, r) \end{array}
-\!\!
+\! \!
 </math>
-|<math>\scriptsize (1, r)</math>
+| <math>\scriptsize (1, r)</math>
-|real
+| Real
-|vector
+| Vector
-|{...]
+| {...]
 |
 |
 |
 |
-|<math>g_i</math>
+| <math>g_i</math>
 |
 |-
-|<math>1200×\slant{\mathbf{1}}LGM \\
+| <math>1200×\slant{\mathbf{1}}LGM</math><br />
-×\slant{\mathbf{1}}LP \\
+<math>1200×\slant{\mathbf{1}}LP</math><br />
-𝒈M</math>
+<math>𝒈M</math>
-|<math>𝒕</math>
+| <math>𝒕</math>
-|[[tuning map|(tempered-prime) tuning map]]
+| [[tuning map|(Tempered-prime) tuning map]]
-|<math>\scriptsize
+| <math>\scriptsize
 \begin{array} {c} 1200 \\[-2pt] {\small\mathsf{¢}} \hspace{-2mu} / \hspace{-2mu} \cancel{\mathsf{oct}} \end{array}
 \begin{array} {c} \\[-2pt] · \end{array}
@@ Line 2,350: / Line 2,441: @@
 \begin{array} {c} M \\[-2pt] \cancel{𝗴} \hspace{-2mu} / \hspace{-2mu} 𝗽 \end{array}
 </math>
-|<math>\mathsf{¢}</math>/<math>\small 𝗽</math>
+| <math>\mathsf{¢}</math>/<math>\small 𝗽</math>
-|cents per prime
+| Cents per prime
-|<math>\scriptsize
+| <math>\scriptsize
-\!\!
+\! \!
-\begin{array} {c} 1200 \\[-3pt] (1, \cancel{1}) \end{array}
+\begin{array} {c} 1200 \\[-3pt] \left(1, \cancel{1}\right) \end{array}
-\!\!
+\! \!
-\begin{array} {c} \slant{\mathbf{1}} \\[-3pt] (\cancel{1}, \cancel{d}) \end{array}
+\begin{array} {c} \slant{\mathbf{1}} \\[-3pt] \left(\cancel{1}, \cancel{d}\right) \end{array}
-\!\!
+\! \!
-\begin{array} {c} L \\[-3pt] (\cancel{d}, \cancel{d}) \end{array}
+\begin{array} {c} L \\[-3pt] \left(\cancel{d}, \cancel{d}\right) \end{array}
 \\ \scriptsize \quad
-\!\!
+\! \!
-\begin{array} {c} G \\[-3pt] (\cancel{d}, \cancel{r}) \end{array}
+\begin{array} {c} G \\[-3pt] \left(\cancel{d}, \cancel{r}\right) \end{array}
-\!\!
+\! \!
-\begin{array} {c} M \\[-3pt] (\cancel{r}, d) \end{array}
+\begin{array} {c} M \\[-3pt] \left(\cancel{r}, d\right) \end{array}
-\!\!
+\! \!
 </math>
-|<math>\scriptsize (1, d)</math>
+| <math>\scriptsize (1, d)</math>
-|real
+| Real
-|vector
+| Vector
-|⟨...]
+| ⟨...]
 |
 |
 |
 |
-|<math>t_i</math>
+| <math>t_i</math>
 |
 |-
-|<math>𝒕 - 𝒋 \\
+| <math>𝒕 - 𝒋</math><br />
-×\slant{\mathbf{1}}L(P - I)</math>
+<math>1200×\slant{\mathbf{1}}L(P - I)</math>
-|<math>𝒓</math>
+| <math>𝒓</math>
-|[[retuning map|retuning (or mistuning) map]]
+| [[retuning map|Retuning (or mistuning) map]]
 |
-|<math>\mathsf{¢}</math>/<math>\small 𝗽</math>
+| <math>\mathsf{¢}</math>/<math>\small 𝗽</math>
-|cents per prime
+| Cents per prime
 |
-|<math>\scriptsize (1, d)</math>
+| <math>\scriptsize (1, d)</math>
-|real
+| Real
-|vector
+| Vector
-|⟨...]
+| ⟨...]
 |
 |
 |
 |
-|<math>r_i</math>
+| <math>r_i</math>
-| previous name: prime error map
+| Previous name: prime error map
 |-
-|<math>𝒋\textbf{i}</math>
+| <math>𝒋\textbf{i}</math>
-|<math>\mathrm{o}</math>
+| <math>\mathrm{o}</math>
-|[[interval span|(just) (interval) size]]
+| [[interval span|(Just) (interval) size]]
-|<math>\scriptsize
+| <math>\scriptsize
 \begin{array} {c} 𝒋 \\[-2pt] {\small\mathsf{¢}} \hspace{-2mu} / \hspace{-2mu} \cancel{𝗽} \end{array}
 \begin{array} {c} \\[-2pt] · \end{array}
 \begin{array} {c} \textbf{i} \\[-2pt] \cancel{𝗽} \end{array}
 </math>
-|<math>\mathsf{¢}</math>
+| <math>\mathsf{¢}</math>
-|cents
+| Cents
-|<math>\scriptsize
+| <math>\scriptsize
-\!\!
+\! \!
-\begin{array} {c} 𝒋 \\[-3pt] (1, \cancel{d}) \end{array}
+\begin{array} {c} 𝒋 \\[-3pt] \left(1, \cancel{d}\right) \end{array}
-\!\!
+\! \!
-\begin{array} {c} \textbf{i} \\[-3pt] (\cancel{d}, 1) \end{array}
+\begin{array} {c} \textbf{i} \\[-3pt] \left(\cancel{d}, 1\right) \end{array}
-\!\!
+\! \!
 </math>
-|<math>\scriptsize (1, 1)</math>
+| <math>\scriptsize (1, 1)</math>
-|real
+| Real
-|scalar
+| Scalar
 |
 |
 |
 |
 |
 |
-|mnemonic: <math>\mathrm{o}</math>riginal size
+| Mnemonic: <math>\mathrm{o}</math>riginal size
 |-
-|<math>𝒈M\textbf{i} \\
+| <math>𝒈M\textbf{i}</math><br />
-𝒕\textbf{i}</math>
+<math>𝒕\textbf{i}</math>
-|<math>\mathrm{a}</math>
+| <math>\mathrm{a}</math>
-|[[Dave_Keenan_%26_Douglas_Blumeyer%27s_guide_to_RTT:_tuning_fundamentals#Example_3|tempered (interval) size]]
+| {{subpage|tuning fundamentals|uprev|s=Example 3|text=Tempered (interval) size}}
-|<math>\scriptsize
+| <math>\scriptsize
 \begin{array} {c} 𝒕 \\[-2pt] {\small\mathsf{¢}} \hspace{-2mu} / \hspace{-2mu} \cancel{𝗽} \end{array}
 \begin{array} {c} \\[-2pt] · \end{array}
 \begin{array} {c} \textbf{i} \\[-2pt] \cancel{𝗽} \end{array}
 </math>
-|<math>\mathsf{¢}</math>
+| <math>\mathsf{¢}</math>
-|cents
+| cents
-|<math>\scriptsize
+| <math>\scriptsize
-\!\!
+\! \!
-\begin{array} {c} 𝒕 \\[-3pt] (1, \cancel{d}) \end{array}
+\begin{array} {c} 𝒕 \\[-3pt] \left(1, \cancel{d}\right) \end{array}
-\!\!
+\! \!
-\begin{array} {c} \textbf{i} \\[-3pt] (\cancel{d}, 1) \end{array}
+\begin{array} {c} \textbf{i} \\[-3pt] \left(\cancel{d}, 1\right) \end{array}
-\!\!
+\! \!
 </math>
-|<math>\scriptsize (1, 1)</math>
+| <math>\scriptsize (1, 1)</math>
-| real
+| Real
-|scalar
+| Scalar
 |
 |
 |
 |
 |
 |
-|mnemonic: <math>\mathrm{a}</math>ltered size
+| Mnemonic: <math>\mathrm{a}</math>ltered size
 |-
-|<math>𝒕\textbf{i} - 𝒋\textbf{i} \\
+| <math>𝒕\textbf{i} - 𝒋\textbf{i}</math><br />
-a - o \\
+<math>a - o</math><br />
-𝒓\textbf{i}</math>
+<math>𝒓\textbf{i}</math>
-|<math>\mathrm{e}</math>
+| <math>\mathrm{e}</math>
-|[[error|(interval) error]]
+| [[error|(Interval) error]]
-|<math>\scriptsize
+| <math>\scriptsize
 \begin{array} {c} 𝒓 \\[-2pt] {\small\mathsf{¢}} \hspace{-2mu} / \hspace{-2mu} \cancel{𝗽} \end{array}
 \begin{array} {c} \\[-2pt] · \end{array}
 \begin{array} {c} \textbf{i} \\[-2pt] \cancel{𝗽} \end{array}
 </math>
-|<math>\mathsf{¢}</math>
+| <math>\mathsf{¢}</math>
-|cents
+| Cents
-|<math>\scriptsize
+| <math>\scriptsize
-\!\!
+\! \!
-\begin{array} {c} 𝒓 \\[-3pt] (1, \cancel{d}) \end{array}
+\begin{array} {c} 𝒓 \\[-3pt] \left(1, \cancel{d}\right) \end{array}
-\!\!
+\! \!
-\begin{array} {c} \textbf{i} \\[-3pt] (\cancel{d}, 1) \end{array}
+\begin{array} {c} \textbf{i} \\[-3pt] \left(\cancel{d}, 1\right) \end{array}
-\!\!
+\! \!
 </math>
-|<math>\scriptsize (1, 1)</math>
+| <math>\scriptsize (1, 1)</math>
-|real
+| Real
-|scalar
+| Scalar
 |
 |
 |
 |
 |
 |
 |
 |-
-! colspan="17" |optimization
+! colspan="17" | Optimization
 |-
 |
-|<math>p</math>
+| <math>p</math>
-|[[optimization power]]
+| [[Optimization power]]
 |
 |
 |
 |
-|<math>\scriptsize (1, 1)</math>
+| <math>\scriptsize (1, 1)</math>
-|real
+| Real
-|scalar
+| Scalar
 |
 |
 |
 |
 |
 |
 |
 |-
 |
-|<math>⟪\,·\,⟫_p</math>
+| <math>\llangle\,·\,\rrangle_p</math>
-|[[power mean]] (<math>p</math>-mean)
+| [[Power mean]] (<math>p</math>-mean)
 |
 |
 |
 |
-|<math>\scriptsize (1, 1)</math>
+| <math>\scriptsize (1, 1)</math>
-|real
+| Real
-|scalar
+| Scalar
 |
 |
 |
 |
 |
 |
 |
 |-
-! colspan="17" |damage
+! colspan="17" | Damage
 |-
 |
-|<math>c</math>
+| <math>c</math>
-|[[Dave_Keenan_%26_Douglas_Blumeyer%27s_guide_to_RTT:_tuning_fundamentals#Complexity|complexity]]
+| {{subpage|Tuning_fundamentals|prev|s=complexity}}
-| colspan="3" |(see complexities section of complexities and simplicities table)
+| colspan="3" | (See complexities section of complexities and simplicities table)
 |
-|<math>\scriptsize (1, 1)</math>
+| <math>\scriptsize (1, 1)</math>
-|real
+| Real
-|scalar
+| Scalar
 |
 |
 |
 |
 |
 |
 |
 |-
-|<math>\dfrac1c</math>
+| <math>\dfrac1c</math>
-|<math>s</math>
+| <math>s</math>
-|[[simplicity]]
+| [[Simplicity]]
-| colspan="3" |(see simplicities section of complexities and simplicities table)
+| colspan="3" | (See simplicities section of complexities and simplicities table)
 |
-|<math>\scriptsize (1, 1)</math>
+| <math>\scriptsize (1, 1)</math>
-|real
+| Real
-|scalar
+| Scalar
 |
 |
 |
 |
 |
 |
 |
 |-
-|<math>c</math> or <math>s</math>
+| <math>c</math> or <math>s</math>
-|<math>w</math>
+| <math>w</math>
-|[[weight]]
+| [[Weight]]
-| colspan="3" |(see complexities and simplicities table)
+| colspan="3" | (See complexities and simplicities table)
 |
-|<math>\scriptsize (1, 1)</math>
+| <math>\scriptsize (1, 1)</math>
-|real
+| Real
-|scalar
+| Scalar
 |
 |
 |
 |
 |
 |
 |
 |-
-|<math>|\mathrm{e}|w</math>
+| <math>\abs{\mathrm{e}} w</math>
-|<math>\mathrm{d}</math>
+| <math>\mathrm{d}</math>
-|[[damage]]
+| [[Damage]]
-| colspan="3" |(see damages table)
+| colspan="3" | (See damages table)
 |
-|<math>\scriptsize (1, 1)</math>
+| <math>\scriptsize (1, 1)</math>
-|real
+| Real
-|scalar
+| Scalar
 |
 |
 |
 |
 |
 |
 |
 |-
-! colspan="17" |target-intervals
+! colspan="17" | Target-intervals
 |-
 |
-|<math>\mathrm{T}</math>
+| <math>\mathrm{T}</math>
-|[[target-interval list]]
+| [[Target-interval list]]
 |
-|<math>\small 𝗽</math>
+| <math>\small 𝗽</math>
-|primes
+| Primes
 |
-|<math>\scriptsize (d, k)</math>
+| <math>\scriptsize (d, k)</math>
-|integer
+| Integer
-|matrix
+| Matrix
 |
 | [[...⟩ ...]
 |
-|<math>\textbf{t}_i</math>
+| <math>\textbf{t}_i</math>
 |
-|<math>\mathrm{t}_{ij}</math>
+| <math>\mathrm{t}_{ij}</math>
 |
 |-
-|<math>M\mathrm{T}</math>
+| <math>M\mathrm{T}</math>
-|<math>\mathrm{Y}</math>
+| <math>\mathrm{Y}</math>
-|[[mapped target-interval list]]
+| [[Mapped target-interval list]]
-|<math>\scriptsize
+| <math>\scriptsize
 \begin{array} {c} M \\[-2pt] 𝗴 \hspace{-2mu} / \hspace{-2mu} \cancel{𝗽} \end{array}
 \begin{array} {c} \\[-2pt] · \end{array}
 \begin{array} {c} \mathrm{T} \\[-2pt] \cancel{𝗽} \end{array}
 </math>
-|<math>\small 𝗴</math>
+| <math>\small 𝗴</math>
-|generators
+| Generators
-|<math>\scriptsize
+| <math>\scriptsize
-\!\!
+\! \!
-\begin{array} {c} M \\[-3pt] (r, \cancel{d}) \end{array}
+\begin{array} {c} M \\[-3pt] \left(r, \cancel{d}\right) \end{array}
-\!\!
+\! \!
-\begin{array} {c} \mathrm{T} \\[-3pt] (\cancel{d}, k) \end{array}
+\begin{array} {c} \mathrm{T} \\[-3pt] \left(\cancel{d}, k\right) \end{array}
-\!\!
+\! \!
 </math>
-|<math>\scriptsize (r, k)</math>
+| <math>\scriptsize (r, k)</math>
-|integer
+| Integer
-|matrix
+| Matrix
 |
-|[[...} ...]
+| [[...} ...]
 |
-|<math>\textbf{y}_i</math>
+| <math>\textbf{y}_i</math>
 |
-|<math>\mathrm{y}_{ij}</math>
+| <math>\mathrm{y}_{ij}</math>
-|mnemonic: looks like bent-up 'T', or cross between 'M' and 'T'
+| Mnemonic: looks like bent-up 'T', or cross between 'M' and 'T'
 |-
-|<math>𝒋\mathrm{T}</math>
+| <math>𝒋\mathrm{T}</math>
-|<math>\textbf{o}</math>
+| <math>\textbf{o}</math>
-|[[Dave_Keenan_%26_Douglas_Blumeyer%27s_guide_to_RTT:_tuning_fundamentals#Primes|target-interval (just) size list]]
+| {{subpage|tuning fundamentals|uprev|s=primes|text=Target-interval (just) size list}}
-|<math>\scriptsize
+| <math>\scriptsize
 \begin{array} {c} 𝒋 \\[-2pt] {\small\mathsf{¢}} \hspace{-2mu} / \hspace{-2mu} \cancel{𝗽} \end{array}
 \begin{array} {c} \\[-2pt] · \end{array}
 \begin{array} {c} \mathrm{T} \\[-2pt] \cancel{𝗽} \end{array}
 </math>
-|<math>\mathsf{¢}</math>
+| <math>\mathsf{¢}</math>
-|cents
+| Cents
-|<math>\scriptsize
+| <math>\scriptsize
-\!\!
+\! \!
-\begin{array} {c} 𝒋 \\[-3pt] (1, \cancel{d}) \end{array}
+\begin{array} {c} 𝒋 \\[-3pt] \left(1, \cancel{d}\right) \end{array}
-\!\!
+\! \!
-\begin{array} {c} \mathrm{T} \\[-3pt] (\cancel{d}, k) \end{array}
+\begin{array} {c} \mathrm{T} \\[-3pt] \left(\cancel{d}, k\right) \end{array}
-\!\!
+\! \!
 </math>
-|<math>\scriptsize (1, k)</math>
+| <math>\scriptsize (1, k)</math>
-|real
+| Real
-|list
+| List
-|[...]
+| [...]
 |
 |
 |
 |
-|<math>\mathrm{o}_i</math>
+| <math>\mathrm{o}_i</math>
-|mnemonic: <math>\textbf{o}</math>riginal size list
+| Mnemonic: <math>\textbf{o}</math>riginal size list
 |-
-|<math>𝒕\mathrm{T}</math>
+| <math>𝒕\mathrm{T}</math>
-|<math>\textbf{a}</math>
+| <math>\textbf{a}</math>
-|[[tempered target-interval size list]]
+| [[Tempered target-interval size list]]
-|<math>\scriptsize
+| <math>\scriptsize
 \begin{array} {c} 𝒕 \\[-2pt] {\small\mathsf{¢}} \hspace{-2mu} / \hspace{-2mu} \cancel{𝗽} \end{array}
 \begin{array} {c} \\[-2pt] · \end{array}
 \begin{array} {c} \mathrm{T} \\[-2pt] \cancel{𝗽} \end{array}
 </math>
-|<math>\mathsf{¢}</math>
+| <math>\mathsf{¢}</math>
-| cents
+| Cents
-|<math>\scriptsize
+| <math>\scriptsize
-\!\!
+\! \!
-\begin{array} {c} 𝒕 \\[-3pt] (1, \cancel{d}) \end{array}
+\begin{array} {c} 𝒕 \\[-3pt] \left(1, \cancel{d}\right) \end{array}
-\!\!
+\! \!
-\begin{array} {c} \mathrm{T} \\[-3pt] (\cancel{d}, k) \end{array}
+\begin{array} {c} \mathrm{T} \\[-3pt] \left(\cancel{d}, k\right) \end{array}
-\!\!
+\! \!
 </math>
-|<math>\scriptsize (1, k)</math>
+| <math>\scriptsize (1, k)</math>
-|real
+| Real
-|list
+| List
-|[...]
+| [...]
 |
 |
 |
 |
-|<math>\mathrm{a}_i</math>
+| <math>\mathrm{a}_i</math>
-|mnemonic: <math>\textbf{a}</math>ltered size list
+| Mnemonic: <math>\textbf{a}</math>ltered size list
 |-
-|<math>𝒕\mathrm{T} - 𝒋\mathrm{T} \\
+| <math>𝒕\mathrm{T} - 𝒋\mathrm{T}</math><br />
-𝒓\mathrm{T} \\
+<math>𝒓\mathrm{T}</math><br />
-\textbf{a} - \textbf{o}</math>
+<math>\textbf{a} - \textbf{o}</math>
-|<math>\textbf{e}</math>
+| <math>\textbf{e}</math>
-|[[target-interval error list]]
+| [[target-interval error list]]
-|<math>\scriptsize
+| <math>\scriptsize
 \begin{array} {c} 𝒓 \\[-2pt] {\small\mathsf{¢}} \hspace{-2mu} / \hspace{-2mu} \cancel{𝗽} \end{array}
 \begin{array} {c} \\[-2pt] · \end{array}
 \begin{array} {c} \mathrm{T} \\[-2pt] \cancel{𝗽} \end{array}
 </math>
-|<math>\mathsf{¢}</math>
+| <math>\mathsf{¢}</math>
-|cents
+| Cents
-|<math>\scriptsize
+| <math>\scriptsize
-\!\!
+\! \!
-\begin{array} {c} 𝒓 \\[-3pt] (1, \cancel{d}) \end{array}
+\begin{array} {c} 𝒕 \\[-3pt] \left(1, \cancel{d}\right) \end{array}
-\!\!
+\! \!
-\begin{array} {c} \mathrm{T} \\[-3pt] (\cancel{d}, k) \end{array}
+\begin{array} {c} \mathrm{T} \\[-3pt] \left(\cancel{d}, k\right) \end{array}
-\!\!
+\! \!
 </math>
-|<math>\scriptsize (1, k)</math>
+| <math>\scriptsize (1, k)</math>
-|real
+| Real
-|list
+| List
-|[...]
+| [...]
 |
 |
 |
 |
-|<math>\mathrm{e}_i</math>
+| <math>\mathrm{e}_i</math>
 |
 |-
-|<math>C</math> or <math>S</math>
+| <math>C</math> or <math>S</math>
-|<math>W</math>
+| <math>W</math>
-|[[target-interval weight matrix]]
+| [[Target-interval weight matrix]]
-| colspan="3" |(see complexities and simplicities table)
+| colspan="3" | (See complexities and simplicities table)
 |
-|<math>\scriptsize (k, k)</math>
+| <math>\scriptsize (k, k)</math>
-|real
+| Real
-|matrix
+| Matrix
 |
-|[[...] ...]
+| [[...] ...]
 |
 |
-|<math>𝒘</math>
+| <math>𝒘</math>
-|<math>w_i</math> or [math]w_{ij}[/math]
+| <math>w_i</math> or <math>w_{ij}</math>
 |
 |-
 |
-|<math>C</math>
+| <math>C</math>
-|[[Dave_Keenan_%26_Douglas_Blumeyer%27s_guide_to_RTT:_tuning_fundamentals#Complexity-weight_damage|target-interval complexity weight matrix]]
+| {{subpage|tuning fundamentals|uprev|s=complexity-weight damage|text=Target-interval complexity weight matrix}}
-| colspan="3" |(see complexities section of complexities and simplicities table)
+| colspan="3" | (See complexities section of complexities and simplicities table)
 |
-|<math>\scriptsize (k, k)</math>
+| <math>\scriptsize (k, k)</math>
-|real
+| Real
-|matrix
+| Matrix
 |
-|[[...] ...]
+| [[...] ...]
 |
 |
-|<math>𝒄</math>
+| <math>𝒄</math>
-|<math>c_i</math>
+| <math>c_i</math>
 |
 |-
-|<math>\dfrac1C</math>
+| <math>\dfrac1C</math>
-|<math>S</math>
+| <math>S</math>
-|[[Dave_Keenan_%26_Douglas_Blumeyer%27s_guide_to_RTT:_tuning_fundamentals#Complexity-weight_damage|target-interval simplicity weight matrix]]
+| {{subpage|tuning fundamentals|uprev|s=complexity-weight_damage|text=Target-interval simplicity weight matrix}}
-| colspan="3" |(see simplicities section of complexities and simplicities table)
+| colspan="3" | (See simplicities section of complexities and simplicities table)
 |
-|<math>\scriptsize (k, k)</math>
+| <math>\scriptsize (k, k)</math>
-|real
+| Real
-|matrix
+| Matrix
 |
-|[[...] ...]
+| [[...] ...]
 |
 |
-|<math>𝒔</math>
+| <math>𝒔</math>
-|<math>s_i</math>
+| <math>s_i</math>
-|entrywise reciprocal of <math>C</math>
+| Entry-wise reciprocal of <math>C</math>
 |-
-|<math>|\textbf{e}|W \\
+| <math>\abs{\textbf{e}} W</math><br />
-×\slant{\mathbf{1}}L|P - I|\mathrm{T}W</math>
+<math>1200×\slant{\mathbf{1}}L\abs{P - I} \mathrm{T}W</math>
-|<math>\textbf{d}</math>
+| <math>\textbf{d}</math>
-|[[target-interval damage list]]
+| [[Target-interval damage list]]
-| colspan="3" |(see damages table)
+| colspan="3" | (See damages table)
 |
-|<math>\scriptsize (1, k)</math>
+| <math>\scriptsize (1, k)</math>
-|real
+| Real
-|list
+| List
-|[...]
+| [...]
 |
 |
 |
 |
-|<math>\mathrm{d}_i</math>
+| <math>\mathrm{d}_i</math>
 |
 |-
 |
-|<math>k</math>
+| <math>k</math>
-|[[target-interval count]]
+| [[Target-interval count]]
 |
 |
 |
 |
-|<math>\scriptsize (1, 1)</math>
+| <math>\scriptsize (1, 1)</math>
-|integer
+| Integer
-|scalar
+| Scalar
 |
 |
 |
 |
 |
 |
-|mnemonic: <math>k</math>ount
+| Mnemonic: <math>k</math>ount
 |-
-! colspan="17" |held-intervals
+! colspan="17" | Held-intervals
 |-
 |
-|<math>\mathrm{H}</math>
+| <math>\mathrm{H}</math>
-|[[held-interval basis]]
+| [[Held-interval basis]]
 |
-|<math>\small 𝗽</math>
+| <math>\small 𝗽</math>
-|primes
+| Primes
 |
-|<math>\scriptsize (d, h)</math>
+| <math>\scriptsize (d, h)</math>
 |
-|matrix
+| Matrix
 |
-|[[...⟩ ...]
+| [[...⟩ ...]
 |
-|<math>\textbf{h}_i</math>
+| <math>\textbf{h}_i</math>
 |
-|<math>\mathrm{h}_{ij}</math>
+| <math>\mathrm{h}_{ij}</math>
 |
 |-
 |
-|<math>h</math>
+| <math>h</math>
-|[[held-interval count]]
+| [[Held-interval count]]
 |
 |
 |
 |
-|<math>\scriptsize (1, 1)</math>
+| <math>\scriptsize (1, 1)</math>
-|integer
+| Integer
-|scalar
+| Scalar
 |
 |
 |
 |
 |
 |
 |
 |-
-! colspan="17" |exploring temperaments
+! colspan="17" | Exploring temperaments
 |-
 |
-|<math>\mathrm{C}</math>
+| <math>\mathrm{C}</math>
-|[[comma basis]]
+| [[Comma basis]]
 |
-|<math>\small 𝗽</math>
+| <math>\small 𝗽</math>
-|primes
+| Primes
 |
-|<math>\scriptsize (d, n)</math>
+| <math>\scriptsize (d, n)</math>
-|integer
+| Integer
-| matrix
+| Matrix
 |
-|[[...⟩ ...]
+| [[...⟩ ...]
 |
-|<math>\textbf{c}_i</math>
+| <math>\textbf{c}_i</math>
 |
-|<math>\mathrm{c}_{ij}</math>
+| <math>\mathrm{c}_{ij}</math>
-|jargon name: monzo list
+| Jargon name: monzo list
 |-
 |
-|<math>\textbf{c}</math>
+| <math>\textbf{c}</math>
-|[[comma]]
+| [[Comma]]
 |
-|<math>\small 𝗽</math>
+| <math>\small 𝗽</math>
-|primes
+| Primes
 |
-|<math>\scriptsize (d, 1)</math>
+| <math>\scriptsize (d, 1)</math>
-|integer
+| Integer
-|vector
+| Vector
 |
-|[...⟩
+| [...⟩
 |
 |
 |
-|<math>\mathrm{c}_i</math>
+| <math>\mathrm{c}_i</math>
-|specific type: [[prime-count vector]] (PC-vector)
+| Specific type: vector ([[prime-count vector]] or PC-vector)
 |-
-! colspan="17" |computation
+! colspan="17" | Computation
 |-
 |
-|<math>\llzigzag·\,\rrzigzag\!_p</math>
+| {{llzigzag}}<math>\,·\,</math>{{rrzigzag}}<math>_p</math>
-|[[power sum]] (<math>p</math>-sum)
+| [[Power sum]] (<math>p</math>-sum)
 |
 |
 |
 |
-|<math>\scriptsize (1, 1)</math>
+| <math>\scriptsize (1, 1)</math>
-|real
+| Real
-|scalar
+| Scalar
 |
 |
 |
 |
 |
 |
 |
 |-
-! colspan="17" | all-interval tuning schemes
+! colspan="17" | All-interval tuning schemes
 |-
-|<math>\mathrm{I}</math>
+| <math>\mathrm{I}</math>
-|<math>\mathrm{T}_{\text{p}}</math>
+| <math>\mathrm{T}_{\text{p}}</math>
-|[[prime proxy target-interval list]]
+| [[Prime proxy target-interval list]]
 |
-|<math>\small 𝗽</math>
+| <math>\small 𝗽</math>
-|primes
+| Primes
 |
-|<math>\scriptsize (d, d)</math>
+| <math>\scriptsize (d, d)</math>
-|integer
+| Integer
-|matrix
+| Matrix
 |
 | ⟨[...⟩ ...]
 |
 |
-|<math>\slant{\mathbf{1}}</math>
+| <math>\slant{\mathbf{1}}</math>
 |
 |
 |-
 |
-|<math>X</math>
+| <math>X</math>
-|[[Dave_Keenan_%26_Douglas_Blumeyer%27s_guide_to_RTT:_alternative_complexities#Prescaling_vs_pretransforming|complexity pretransformer]]
+| {{subpage|alternative complexities|uprev|s=Prescaling_vs._pretransforming|text=Complexity pretransformer}}
-|<math>\small\mathsf{𝟙}\scriptsize\mathsf{(C)}</math> or <math>\small\mathsf{𝟙}\scriptsize\mathsf{(}</math><alt>-<math>\scriptsize\mathsf{C)}</math><ref>In these tables, "alternative" means any complexity other than the default of log-product complexity, and "alt" stands for its abbreviation.</ref>
+| <math>\small\mathsf{𝟙}\scriptsize\mathsf{(C)}</math> or <math>\small\mathsf{𝟙}\scriptsize\mathsf{(}</math><alt>-<math>\scriptsize\mathsf{C)}</math><ref group="note">In these tables, "alternative" means any complexity other than the default of log-product complexity, and "alt" stands for its abbreviation.</ref>
-|<math>\small\mathsf{(C)}</math> or <math>\small\mathsf{(}</math><alt>-<math>\small\mathsf{C)}</math>
+| <math>\small\mathsf{(C)}</math> or <math>\small\mathsf{(}</math><alt>-<math>\small\mathsf{C)}</math>
-|complexity weight or <alternative>-complexity weight
+| Complexity weight or <alternative>-complexity weight
 |
-|<math>\scriptsize (d, d)</math> or <math>\scriptsize (d+1, d+1)</math>
+| <math>\scriptsize (d, d)</math> or <math>\scriptsize (d+1, d+1)</math>
-|real
+| Real
-|matrix
+| Matrix
 | [⟨...] ...⟩
 |
-|<math>𝒄_{\text{p}_i}</math>
+| <math>𝒙_i</math>
 |
-|<math>𝒄_{\text{p}}</math>
+| <math>𝒙</math>
-|<math>c_{\text{p}i}</math> or [math]c_{\text{p}ij}[/math]
+| <math>x_i</math> or <math>x_{ij}</math>
 |
 |-
-|<math>\text{diag}(\log_2(\textbf{p}))</math>
+| <math>\text{diag}({\large\textbf{𝓁}}\hspace{2mu})</math>
-|<math>L</math>
+| <math>L</math>
-|[[log-prime matrix]]
+| [[Log-prime matrix]]
 |
-|<math>\small\mathsf{oct}</math>/<math>\small 𝗽</math>
+| <math>\small\mathsf{oct}</math>/<math>\small 𝗽</math>
-|octaves per prime
+| Octaves per prime
 |
-|<math>\scriptsize (d, d)</math>
+| <math>\scriptsize (d, d)</math>
-|real
+| Real
-|matrix
+| Matrix
-|[⟨...] ...⟩
+| [⟨...] ...⟩
-|⟨[...⟩ ...]
+| ⟨[...⟩ ...]
-|<math>\textbf{𝓁}_i</math>
+| <math>{\large\textbf{𝓁}}\hspace{2mu}_i</math>
 |
-|<math>\textbf{𝓁}</math>
+| <math>{\large\textbf{𝓁}}\hspace{2mu}</math>
-|<math>𝓁_{ij}</math>
+| <math>{\large 𝓁}\hspace{2mu}_{ij}</math>
 |
 |-
 |
-|<math>q</math>
+| <math>q</math>
-|[[Dave_Keenan_%26_Douglas_Blumeyer%27s_guide_to_RTT:_all-interval_tuning_schemes#Dual_norms|interval complexity norm power]]
+| {{subpage|all-interval_tuning_schemes|uprev|s=dual_norms|text=Interval complexity norm power}}
 |
 |
 |
 |
-|<math>\scriptsize (1, 1)</math>
+| <math>\scriptsize (1, 1)</math>
-|real
+| Real
-|scalar
+| Scalar
 |
 |
 |
 |
 |
 |
 |
 |-
 |
-|<math>‖ · ‖_q</math>
+| <math>\norm{·}_q</math>
-|[[power norm]] (<math>p</math>-norm)
+| [[Power norm]] (<math>p</math>-norm)
 |
 |
 |
 |
-|<math>\scriptsize (1, 1)</math>
+| <math>\scriptsize (1, 1)</math>
-|real
+| Real
-|scalar
+| Scalar
 |
 |
 |
 |
 |
 |
 |
 |-
-! colspan="17" |alternative complexities
+| <math>\dfrac1{1-\frac1q}</math>
+| <math>\text{dual}(q)</math>
+| {{subpage|all-interval tuning schemes|uprev|s=dual_norms|text=Dual norm power}}
+|
+|
+|
+|
+| <math>\scriptsize (1, 1)</math>
+| Real
+| Scalar
+|
+|
+|
+|
+|
+|
+|
 |-
 |
-|<math>𝒑</math>
+| <math>\norm{X\mathbf{i}}_q</math>
-|[[Dave_Keenan_%26_Douglas_Blumeyer%27s_guide_to_RTT:_alternative_complexities#Formulas|prime list]]<ref>May be used for a prime-limit or for any prime-only list.</ref>
+| [[Interval complexity]]
 |
-|
+| <math>\small\mathsf{(C)}</math> or <math>\small\mathsf{(}</math><alt>-<math>\small\mathsf{C)}</math>
 |
 |
-|<math>\scriptsize (1, d)</math>
+| <math>\scriptsize (1, 1)</math>
-|integer
+| Real
-|list
+| Scalar
-|[...]
+|
 |
 |
 |
 |
-|<math>p_i</math>
+|
 |
 |-
 |
-|<math>\slant{\mathbf{1}}</math>
+| <math>\norm{𝒓X^{-1}}_{\text{dual}(q)}</math>
-|[[Dave_Keenan_%26_Douglas_Blumeyer%27s_guide_to_RTT:_alternative_complexities#Proportionality_to_size|summation map]]
+| [[Retuning magnitude]]
 |
-|
+| <math>\mathsf{¢}\small\mathsf{(C^{-1})}</math> or <math>\mathsf{¢}\small\mathsf{(}</math><alt>-<math>\small\mathsf{C^{-1})}</math>
 |
 |
-|<math>\scriptsize (1, d)</math>
+| <math>\scriptsize (1, 1)</math>
-|integer
+| Real
-|vector
+| Scalar
-|⟨...]
+|
 |
 |
 |
 |
-|<math>1</math>
+|
 |
 |-
-|
+! colspan="17" | Alternative complexities
-|<math>1200</math>
-|[[Dave_Keenan_%26_Douglas_Blumeyer%27s_guide_to_RTT:_alternative_complexities#Proportionality_to_size|octaves-to-cents conversion]]
-|
-|¢/oct
-|cents per octave
-|
-|<math>\scriptsize (1, 1)</math>
-|integer
-|scalar
-|
-|
-|
-|
-|
-|
-|
 |-
 |
-|<math>Z</math>
+| <math>𝒑</math>
-|[[Dave_Keenan_%26_Douglas_Blumeyer%27s_guide_to_RTT:_alternative_complexities#Normifying:_size-sensitizing_matrix|size-sensitizing matrix]]
+| {{subpage|alternative complexities|uprev|s=formulas|text=Prime list}}<ref group="note">May be used for a prime-limit or for any prime-only list.</ref>
 |
 |
 |
 |
-|<math>\scriptsize (d+1, d)</math>
+| <math>\scriptsize (1, d)</math>
-|real
+| Integer
-|matrix
+| List
-|[⟨…]...]
+| [...]
 |
-|<math>𝒛_i</math>
+|
 |
 |
-|<math>z_{ij}</math>
+| <math>p_i</math>
 |
 |-
-! colspan="17" |non-standard domain bases
+|
+| <math>\slant{\mathbf{1}}</math>
+| {{subpage|alternative complexities|uprev|s=proportionality to size|text=Summation map}}
+|
+|
+|
+|
+| <math>\scriptsize (1, d)</math>
+| Integer
+| Vector
+| ⟨...]
+|
+|
+|
+|
+| <math>1</math>
+|
 |-
-| rowspan="2" |
+|
-|<math>B_s</math>
+| <math>1200</math>
-| rowspan="2" |[[Domain_basis#Basis_matrix_conversion|(domain) basis (change) matrix]]
+| {{subpage|alternative complexities|uprev|s=Proportionality to size|text=Octaves-to-cents conversion}}
-| rowspan="2" |
+|
-|<math>\small 𝗽</math>/<math>\small 𝗯</math>
+| ¢/oct
-|primes per nonprime basis elements
+| Cents per octave
-| rowspan="2" |
+|
-|<math>\scriptsize (d_p, d_b)</math>
+| <math>\scriptsize (1, 1)</math>
-| rowspan="2" |integer
+| Integer
-| rowspan="2" |matrix
+| Scalar
-| rowspan="2" |[[...] ...]
+|
-| rowspan="2" |[[...] ...]
+|
-| rowspan="2" |
+|
-| rowspan="2" |<math>b_i</math>
+|
-| rowspan="2" |
+|
-| rowspan="2" |<math>b_{ij}</math>
+|
-| rowspan="2" |
+|
 |-
-|<math>B_{Ls}</math>
+|
-|<math>\small 𝗕</math>/<math>\small 𝗯</math>
+| <math>Z</math>
-|superspace basis elements per (subspace) basis elements
+| {{subpage|alternative complexities|uprev|s=Normifying: size-sensitizing matrix|text=Size-sensitizing matrix}}
-|<math>\scriptsize (d_L, d_s)</math>
+|
+|
+|
+|
+| <math>\scriptsize (d+1, d)</math>
+| Real
+| Matrix
+| [⟨…]...]
+|
+| <math>𝒛_i</math>
+|
+|
+| <math>z_{ij}</math>
+|
 |-
-! colspan="17" |embedding and projection
+! colspan="17" | Non-standard domain bases
 |-
-|
+| rowspan="2" |
-|<math>G</math>
+| <math>B_s</math>
-|[[generator embedding matrix|generator embedding (matrix)]]
+| rowspan="2" | [[Domain_basis#Basis_matrix_conversion|(Domain) basis (change) matrix]]
-|
+| rowspan="2" |
-|<math>\small 𝗽</math>/<math>\small 𝗴</math>
+| <math>\small 𝗽</math>/<math>\small 𝗯</math>
-|primes per generator
+| Primes per nonprime basis elements
-|
+| rowspan="2" |
-|<math>\scriptsize (d, r)</math>
+| <math>\scriptsize (d_p, d_b)</math>
-|real
+| rowspan="2" | Integer
-|matrix
+| rowspan="2" | Matrix
-|[{...] ...⟩
+| rowspan="2" | [[...] ...]
-|{[...⟩ ...]
+| rowspan="2" | [[...] ...]
-|<math>𝒈_i</math>
+| rowspan="2" |
-|
+| rowspan="2" | <math>b_i</math>
-|
+| rowspan="2" |
-|<math>g_{ij}</math>
+| rowspan="2" | <math>b_{ij}</math>
-|
+| rowspan="2" |
 |-
-|<math>G_cF^{-1}FM_c \\
+| <math>B_{Ls}</math>
-\mathrm{V}\textit{Λ}\mathrm{V}^{-1}</math>
+| <math>\small 𝗕</math>/<math>\small 𝗯</math>
-|<math>P</math>
+| Superspace basis elements per (subspace) basis elements
-|[[Projection matrix|projection (matrix)]]
+| <math>\scriptsize (d_L, d_s)</math>
-|<math>\scriptsize
+|-
+! colspan="17" | Embedding and projection
+|-
+|
+| <math>G</math>
+| [[generator embedding matrix|Generator embedding (matrix)]]
+|
+| <math>\small 𝗽</math>/<math>\small 𝗴</math>
+| Primes per generator
+|
+| <math>\scriptsize (d, r)</math>
+| Real
+| Matrix
+| [{...] ...⟩
+| {[...⟩ ...]
+| <math>𝒈_i</math>
+|
+|
+| <math>g_{ij}</math>
+|
+|-
+| <math>G_cF^{-1}FM_c</math><br />
+<math>\mathrm{V}\textit{Λ}\mathrm{V}^{-1}</math>
+| <math>P</math>
+| [[Projection matrix|Projection (matrix)]]
+| <math>\scriptsize
 \begin{array} {c} G \\[-2pt] 𝗽 \hspace{-2mu} / \hspace{-2mu} \cancel{𝗴} \end{array}
 \begin{array} {c} \\[-2pt] · \end{array}
 \begin{array} {c} M \\[-2pt] \cancel{𝗴} \hspace{-2mu} / \hspace{-2mu} 𝗽 \end{array}
 </math>
-|<math>\small 𝗽</math>/<math>\small 𝗽</math>
+| <math>\small 𝗽</math>/<math>\small 𝗽</math>
-|primes per prime
+| Primes per prime
-|<math>\scriptsize
+| <math>\scriptsize
-\!\!
+\! \!
-\begin{array} {c} G \\[-3pt] (d, \cancel{r}) \end{array}
+\begin{array} {c} G \\[-3pt] \left(d, \cancel{r}\right) \end{array}
-\!\!
+\! \!
-\begin{array} {c} M \\[-3pt] (\cancel{r}, d) \end{array}
+\begin{array} {c} M \\[-3pt] \left(\cancel{r}, d\right) \end{array}
-\!\!
+\! \!
 </math>
-|<math>\scriptsize (d, d)</math>
+| <math>\scriptsize (d, d)</math>
-|real
+| Real
-|matrix
+| Matrix
-|[⟨...] ...⟩
+| [⟨...] ...⟩
-|⟨[...⟩ ...]
+| ⟨[...⟩ ...]
-|<math>𝒑_i</math>
+| <math>𝒑_i</math>
 |
 |
-|<math>p_i</math>
+| <math>p_i</math>
 |
 |-
-|<math>GM\textbf{i}</math>
+| <math>GM\textbf{i}</math>
-|<math>P\textbf{i}</math>
+| <math>P\textbf{i}</math>
-|[[projected interval]]
+| [[Projected interval]]
-|<math>\scriptsize
+| <math>\scriptsize
 \begin{array} {c} G \\[-2pt] 𝗽 \hspace{-2mu} / \hspace{-2mu} \cancel{𝗴} \end{array}
 \begin{array} {c} \\[-2pt] · \end{array}
@@ Line 3,150: / Line 3,295: @@
 \begin{array} {c} \textbf{i} \\[-2pt] \cancel{𝗽} \end{array}
 </math>
-|<math>\small 𝗽</math>
+| <math>\small 𝗽</math>
-|primes
+| Primes
-|<math>\scriptsize
+| <math>\scriptsize
-\!\!
+\! \!
-\begin{array} {c} G \\[-3pt] (d, \cancel{r}) \end{array}
+\begin{array} {c} G \\[-3pt] \left(d, \cancel{r}\right) \end{array}
-\!\!
+\! \!
-\begin{array} {c} M \\[-3pt] (\cancel{r}, \cancel{d}) \end{array}
+\begin{array} {c} M \\[-3pt] \left(\cancel{r}, \cancel{d}\right) \end{array}
-\!\!
+\! \!
-\begin{array} {c} \textbf{i} \\[-3pt] (\cancel{d}, 1) \end{array}
+\begin{array} {c} \textbf{i} \\[-3pt] \left(\cancel{d}, 1\right) \end{array}
-\!\!
+\! \!
 </math>
-|<math>\scriptsize (d, 1)</math>
+| <math>\scriptsize (d, 1)</math>
-|real
+| Real
-|vector
+| Vector
 |
-|[...⟩
+| [...⟩
 |
 |
 |
 |
-|specific type: [[prime-count vector]] (PC-vector)
+| Specific type: vector ([[prime-count vector]] or PC-vector)
 |-
 |
-|<math>\mathrm{U}</math>
+| <math>\mathrm{U}</math>
-|[[unchanged-interval basis]]
+| [[Unchanged-interval basis]]
 |
-|<math>\small 𝗽</math>
+| <math>\small 𝗽</math>
-|primes
+| Primes
 |
-|<math>\scriptsize (d, r)</math>
+| <math>\scriptsize (d, r)</math>
 |
-|matrix
+| Matrix
 |
-|[[...⟩ ...]
+| [[...⟩ ...]
 |
-|<math>\textbf{u}_i</math>
+| <math>\textbf{u}_i</math>
 |
-|<math>\mathrm{u}_{ij}</math>
+| <math>\mathrm{u}_{ij}</math>
-|jargon name: eigenmonzo list
+| Jargon name: eigenmonzo list
 |-
 |
-|<math>\textit{Λ}</math>
+| <math>\textit{Λ}</math>
-|[[scaling factor matrix|scaling factor (eigenvalue) matrix]]
+| [[scaling factor matrix|Scaling factor (eigenvalue) matrix]]
 |
 |
 |
 |
-|<math>\scriptsize (d, d)</math>
+| <math>\scriptsize (d, d)</math>
 |
-|matrix
+| Matrix
-|[⟨…] …⟩
+| [⟨…] …⟩
-|⟨[…⟩ …]
+| ⟨[…⟩ …]
 |
 |
-|<math>𝝀</math>
+| <math>𝝀</math>
-|<math>λ_i</math>
+| <math>λ_i</math>
-|mnemonic: <math>\mathrm{V}</math> is mirrored of <math>\textit{Λ}</math> which it combines with to create the projection matrix; previous name: eigenvalue matrix
+| Mnemonic: <math>\mathrm{V}</math> is mirrored of <math>\textit{Λ}</math> which it combines with to create the projection matrix; previous name: eigenvalue matrix
 |-
 |
-|<math>\mathrm{V}</math>
+| <math>\mathrm{V}</math>
-|[[unrotated vector list|unrotated vector (eigenvector) list]]
+| [[unrotated vector list|Unrotated vector (eigenvector) list]]
 |
-|<math>\small 𝗽</math>
+| <math>\small 𝗽</math>
-|primes
+| Primes
 |
-|<math>\scriptsize (d, d)</math>
+| <math>\scriptsize (d, d)</math>
 |
-|matrix
+| Matrix
 |
-|⟨[...⟩ ...]
+| ⟨[...⟩ ...]
 |
-|<math>\textbf{v}_i</math>
+| <math>\textbf{v}_i</math>
 |
-|<math>\mathrm{v}_{ij}</math>
+| <math>\mathrm{v}_{ij}</math>
-|mnemonic: <math>\mathrm{V}</math> is mirrored of <math>\textit{Λ}</math> which it combines with to create the projection matrix; jargon name: eigenmonzo and comma list
+| Mnemonic: <math>\mathrm{V}</math> is mirrored of <math>\textit{Λ}</math> which it combines with to create the projection matrix; jargon name: eigenmonzo and comma list
 |-
 |
-|<math>F</math>
+| <math>F</math>
-|[[generator form matrix]]
+| [[Generator form matrix]]
 |
 |
 |
 |
-|<math>\scriptsize (r, r)</math>
+| <math>\scriptsize (r, r)</math>
 |
-|matrix
+| Matrix
-|[{...] …}
+| [{...] …}
 |
 |
-|<math>𝒇_i</math>
+| <math>𝒇_i</math>
 |
-|<math>f_{ij}</math>
+| <math>f_{ij}</math>
 |
 |-
-|<math>I</math>
+| <math>I</math>
-|<math>M_{\text{j}}</math>
+| <math>M_{\text{j}}</math>
-|[[Generator_embedding_optimization#Algebraic_setup|JI mapping (matrix)]]
+| [[Generator_embedding_optimization#Algebraic_setup|JI mapping (matrix)]]
 |
-|<math>\small 𝗴</math>/<math>\small 𝗽</math>
+| <math>\small 𝗴</math>/<math>\small 𝗽</math>
-|generators per prime
+| Generators per prime
 |
-|<math>\scriptsize (d, d)</math>
+| <math>\scriptsize (d, d)</math>
-|integer
+| Integer
-|matrix
+| Matrix
-|[⟨...] ...}
+| [⟨...] ...}
-|⟨[...} ...]
+| ⟨[...} ...]
 |
 |
-|<math>\slant{\mathbf{1}}</math>
+| <math>\slant{\mathbf{1}}</math>
 |
 |
 |-
-|<math>I</math>
+| <math>I</math>
-|<math>G_{\text{j}}</math>
+| <math>G_{\text{j}}</math>
-|[[Generator_embedding_optimization#Algebraic_setup|JI generator embedding (matrix)]]
+| [[Generator_embedding_optimization#Algebraic_setup|JI generator embedding (matrix)]]
 |
-|<math>\small 𝗽</math>/<math>\small 𝗴</math>
+| <math>\small 𝗽</math>/<math>\small 𝗴</math>
-|primes per generator
+| Primes per generator
 |
-|<math>\scriptsize (d, d)</math>
+| <math>\scriptsize (d, d)</math>
-|integer
+| Integer
-|matrix
+| Matrix
-|[{...] ...⟩
+| [{...] ...⟩
-|{[...⟩ ...]
+| {[...⟩ ...]
 |
 |
-|<math>\slant{\mathbf{1}}</math>
+| <math>\slant{\mathbf{1}}</math>
 |
 |
 |-
 |
-|<math>K</math>
+| <math>K</math>
-|[[Generator_embedding_optimization#How_to_build_constraint_matrices|constraint (matrix)]]
+| [[Generator_embedding_optimization#How_to_build_constraint_matrices|Constraint (matrix)]]
 |
 |
 |
 |
-|<math>\scriptsize (k, r)</math>
+| <math>\scriptsize (k, r)</math>
-|<math>\scriptsize \{0, +1, -1\}</math>
+| <math>\scriptsize \{0, +1, -1\}</math>
-| matrix
+| Matrix
-|[[...] ...]
+| [[...] ...]
 |
-|<math>𝒌_i</math>
+| <math>𝒌_i</math>
 |
 |
-|<math>k_{ij}</math>
+| <math>k_{ij}</math>
-|mnemonic: <math>K</math>onstraint
+| Mnemonic: <math>K</math>onstraint
 |-
 |
-|<math>𝒃</math>
+| <math>𝒃</math>
-|[[Generator embedding optimization#Generalizing to higher dimensions: the blend map|(generator tuning map) blend map]]
+| [[Generator embedding optimization#Generalizing to higher dimensions: The blend map|(Generator tuning map) blend map]]
 |
 |
 |
 |
-|<math>\scriptsize (1, τ-1)</math>
+| <math>\scriptsize (1, τ-1)</math>
-|real
+| Real
-|vector
+| Vector
-|[...]
+| [...]
 |
 |
 |
 |
-|<math>b_i</math>
+| <math>b_i</math>
 |
 |-
 |
-|<math>B</math>
+| <math>B</math>
-|[[Generator embedding optimization#How to identify tunings|(generator tuning map) blend matrix]]
+| [[Generator embedding optimization#How to identify tunings|(Generator tuning map) blend matrix]]
 |
 |
 |
 |
-|<math>\scriptsize (d, τ-1)</math>
+| <math>\scriptsize (d, τ-1)</math>
-|real
+| Real
-|matrix
+| Matrix
-|[[...⟩...]
+| [[...⟩...]
 |
 |
-|<math>𝒃_{i}</math>
+| <math>𝒃_{i}</math>
 |
-|<math>b_{ij}</math>
+| <math>b_{ij}</math>
 |
 |-
 |
-|<math>D</math>
+| <math>D</math>
-|[[Generator embedding optimization#The deltas matrix|(generator tuning map) deltas matrix]]
+| [[Generator embedding optimization#The deltas matrix|(Generator tuning map) deltas matrix]]
 |
-|<math>\mathsf{¢}</math>/<math>\small 𝗴</math>
+| <math>\mathsf{¢}</math>/<math>\small 𝗴</math>
-|cents per generator
+| Cents per generator
 |
-|<math>\scriptsize (τ-1,r)</math>
+| <math>\scriptsize (τ-1,r)</math>
-|real
+| Real
-|matrix
+| Matrix
-|[{...] ...]
+| [{...] ...]
 |
-|<math>𝜹_i</math>
+| <math>𝜹_i</math>
 |
 |
-|<math>𝛿_{ij}</math>
+| <math>𝛿_{ij}</math>
 |
 |-
 |
-|<math>τ</math>
+| <math>τ</math>
-|[[Generator embedding optimization#The deltas matrix|tied basic minimax tuning count]]
+| [[Generator embedding optimization#The deltas matrix|Tied basic minimax tuning count]]
 |
 |
 |
 |
 |
-|integer
+| Integer
-|scalar
+| Scalar
 |
 |
 |
 |
 |
 |
 |
 |-
-! colspan="17" |exterior algebra
+! colspan="17" | Exterior algebra
 |-
 |
-|<math>𝕞</math>
+| <math>𝕞</math>
-|[[multimap]]
+| [[Multimap]]
 |
-|<math>\small 𝗴</math>/<math>\small 𝗽</math>
+| <math>\small 𝗴</math>/<math>\small 𝗽</math>
-|generators per prime
+| Generators per prime
 |
-|<math>\scriptsize (1, d)</math>
+| <math>\scriptsize (1, d)</math>
-|integer
+| Integer
-|multivector
+| Multivector
-|⟨...] or ⟨⟨...]] or ⟨⟨⟨...]]] ...
+| ⟨...] or ⟨⟨...]] or ⟨⟨⟨...]]] ...
 |
 |
 |
 |
-|<math>𝕞_i</math>
+| <math>𝕞_i</math>
 |
 |-
 |
-|<math>𝕔</math>
+| <math>𝕔</math>
-|[[multicomma]]
+| [[Multicomma]]
 |
-|<math>\small 𝗽</math>
+| <math>\small 𝗽</math>
-|primes
+| Primes
 |
-|<math>\scriptsize (1, n)</math>
+| <math>\scriptsize (1, n)</math>
-|integer
+| Integer
-|multivector
+| Multivector
 |
-|[...⟩ or [[...⟩⟩ or [[[...⟩⟩⟩ ...
+| [...⟩ or [[...⟩⟩ or [[[...⟩⟩⟩ ...
 |
 |
 |
-|<math>𝕔_i</math>
+| <math>𝕔_i</math>
 |
 |-
 |
-|<math>𝕧</math>
+| <math>𝕧</math>
-|(generic temperament multivector)
+| (Generic temperament multivector)
 |
 |
 |
 |
-|<math>\scriptsize (1, {{d}\choose{r}})</math> or <math>\scriptsize (1, {{d}\choose{n}})</math>
+| <math>\scriptsize (1, {{d}\choose{r}})</math> or <math>\scriptsize (1, {{d}\choose{n}})</math>
-|integer
+| Integer
-|multivector
+| Multivector
-|⟨...] or ⟨⟨...]] or ⟨⟨⟨...]]] ...
+| ⟨...] or ⟨⟨...]] or ⟨⟨⟨...]]] ...
-|[...⟩ or [[...⟩⟩ or [[[...⟩⟩⟩ ...
+| [...⟩ or [[...⟩⟩ or [[[...⟩⟩⟩ ...
 |
 |
 |
-|<math>𝕧_i</math>
+| <math>𝕧_i</math>
 |
 |-
 |
-|<math>A</math>
+| <math>A</math>
-|(generic temperament matrix)
+| (Generic temperament matrix)
 |
 |
 |
 |
-|<math>\scriptsize (g, d)</math> or <math>\scriptsize (d, g)</math>
+| <math>\scriptsize (g, d)</math> or <math>\scriptsize (d, g)</math>
-|integer
+| Integer
-|matrix
+| Matrix
-|[⟨...] ...}
+| [⟨...] ...}
-|⟨[...} ...] or [[...⟩ ...]
+| ⟨[...} ...] or [[...⟩ ...]
-|<math>𝒂_i</math>
+| <math>𝒂_i</math>
-|<math>𝒂_i</math>
+| <math>𝒂_i</math>
-|<math>𝒂</math>
+| <math>𝒂</math>
-|<math>a_{ij}</math>
+| <math>a_{ij}</math>
 |
 |-
 |
-|<math>v</math>
+| <math>v</math>
-|[[variance]]
+| [[Variance]]
 |
 |
 |
 |
 |
 |
 |
 |
 |
 |
 |
 |
 |
 |
 |-
 |
-|<math>g</math>
+| <math>g</math>
-|[[grade]]
+| [[Grade]]
 |
 |
 |
 |
-|<math>\scriptsize (1, 1)</math>
+| <math>\scriptsize (1, 1)</math>
-|integer
+| Integer
-|scalar
+| Scalar
 |
 |
 |
 |
 |
 |
 |
 |-
-! colspan="17" |temperament addition
+! colspan="17" | Temperament addition
 |-
-|<math>\min(r, n)</math>
+| <math>\min(r, n)</math>
-|<math>g_\text{min}</math>
+| <math>g_\text{min}</math>
-|[[Temperament_addition#Introductory_examples|min-grade]]
+| [[Temperament_addition#Introductory_examples|Min-grade]]
 |
 |
 |
 |
-|<math>\scriptsize (1, 1)</math>
+| <math>\scriptsize (1, 1)</math>
-|integer
+| Integer
-|scalar
+| Scalar
 |
 |
 |
 |
 |
 |
 |
 |-
-|<math>\max(r, n)</math>
+| <math>\max(r, n)</math>
-|<math>g_\text{max}</math>
+| <math>g_\text{max}</math>
-|[[Temperament_addition#Introductory_examples|max-grade]]
+| [[Temperament_addition#Introductory_examples|Max-grade]]
 |
 |
 |
 |
-|<math>\scriptsize (1, 1)</math>
+| <math>\scriptsize (1, 1)</math>
-|integer
+| Integer
-|scalar
+| Scalar
 |
 |
 |
 |
 |
 |
 |
 |-
 |
-|<math>L_\text{dep}</math>
+| <math>L_\text{dep}</math>
-|[[Temperament_addition#1._Find_the_.5Bmath.5DL_.7B.5Ctext.7Bdep.7D.7D.5B.2Fmath.5D|linear-dependence basis]]
+| [[Temperament_addition#1._Find_the_.5Bmath.5DL_.7B.5Ctext.7Bdep.7D.7D.5B.2Fmath.5D|Linear-dependence basis]]
 |
 |
 |
 |
-|<math>\scriptsize (l_\text{dep}, d)</math> or <math>\scriptsize (d, l_\text{dep})</math>
+| <math>\scriptsize \left(l_\text{dep}, d\right)</math> or <math>\scriptsize \left(d, l_\text{dep}\right)</math>
-|integer
+| Integer
-|matrix
+| Matrix
-|[⟨...]] or [[...] ...⟩
+| [⟨...]] or [[...] ...⟩
-|⟨[...]] or [[...⟩ ...]
+| ⟨[...]] or [[...⟩ ...]
-|<math>\textbf{𝓁}_{\text{dep}i}</math>
+| <math>{\large\textbf{𝓁}}\hspace{2mu}_{\text{dep}i}</math>
-|<math>\textbf{𝓁}_{\text{dep}i}</math>
+| <math>{\large\textbf{𝓁}}\hspace{2mu}_{\text{dep}i}</math>
-|<math>\textbf{𝓁}_\text{dep}</math>
+| <math>{\large\textbf{𝓁}}\hspace{2mu}_\text{dep}</math>
-|<math>𝓁_{\text{dep}ij}</math>
+| <math>{\large 𝓁}\hspace{2mu}_{\text{dep}ij}</math>
 |
 |-
 |
-|<math>L_\text{ind}</math>
+| <math>L_\text{ind}</math>
-|[[Temperament_addition#Glossary|linear-independence basis]]
+| [[Temperament_addition#Glossary|Linear-independence basis]]
 |
 |
 |
 |
-|<math>\scriptsize (l_\text{ind}, d)</math> or <math>\scriptsize (d, l_\text{ind})</math>
+| <math>\scriptsize \left(l_\text{ind}, d\right)</math> or <math>\scriptsize \left(d, l_\text{ind}\right)</math>
-|integer
+| Integer
-|matrix
+| Matrix
-|[⟨...]] or [[...] ...⟩
+| [⟨...]] or [[...] ...⟩
-|⟨[...]] or [[...⟩ ...]
+| ⟨[...]] or [[...⟩ ...]
-|<math>\textbf{𝓁}_{\text{ind}i}</math>
+| <math>{\large\textbf{𝓁}}\hspace{2mu}_{\text{ind}i}</math>
-|<math>\textbf{𝓁}_{\text{ind}i}</math>
+| <math>{\large\textbf{𝓁}}\hspace{2mu}_{\text{ind}i}</math>
-|<math>\textbf{𝓁}_\text{ind}</math>
+| <math>{\large\textbf{𝓁}}\hspace{2mu}_\text{ind}</math>
-|<math>𝓁_{\text{ind}ij}</math>
+| <math>{\large 𝓁}\hspace{2mu}_{\text{ind}ij}</math>
 |
 |-
-|<math>\dim(L_\text{dep})</math>
+| <math>\dim(L_\text{dep})</math>
-|<math>l_\text{dep}</math>
+| <math>l_\text{dep}</math>
-|[[Temperament_addition#3._Linear_independence_between_temperaments|linear-dependence]]
+| [[Temperament_addition#3._Linear_independence_between_temperaments|Linear-dependence]]
 |
 |
 |
 |
-|<math>\scriptsize (1, 1)</math>
+| <math>\scriptsize (1, 1)</math>
-|integer
+| Integer
-|scalar
+| Scalar
 |
 |
 |
 |
 |
 |
 |
 |-
-|<math>\dim(L_\text{ind})</math>
+| <math>\dim(L_\text{ind})</math>
-|<math>l_\text{ind}</math>
+| <math>l_\text{ind}</math>
-|[[Temperament_addition#3._Linear_independence_between_temperaments|linear-independence]]
+| [[Temperament_addition#3._Linear_independence_between_temperaments|Linear-independence]]
 |
 |
 |
 |
-|<math>\scriptsize (1, 1)</math>
+| <math>\scriptsize (1, 1)</math>
-|integer
+| Integer
-|scalar
+| Scalar
 |
 |
 |
 |
 |
 |
 |
 |}
-===Units===
+=== Units ===
 {| class="wikitable center-all mw-collapsible mw-collapsed"
-|+
+|+ style="font-size: 105%;" |
-!symbol
-!name
-!vectorized
 |-
-|<math>\small 𝗴</math>
+! Symbol
-|generators
+! Name
-| yes
+! Vectorized
+|-
+| <math>\small 𝗴</math>
+| Generators
+| Yes
 |-
-|<math>\small 𝗽</math>
+| <math>\small 𝗽</math>
-|primes
+| Primes
-|yes
+| Yes
 |-
-|<math>\small 𝗯</math>
+| <math>\small 𝗯</math>
-|(subspace) basis elements
+| (Subspace) basis elements
-|yes
+| Yes
 |-
-|<math>\small 𝗕</math>
+| <math>\small 𝗕</math>
-|superspace basis elements
+| Superspace basis elements
-|yes
+| Yes
 |-
-|<math>\mathsf{¢}</math>
+| <math>\mathsf{¢}</math>
-|cents
+| Cents
 |
 |-
-|<math>\mathsf{¢}\small{(}</math><weight><math>\small\mathsf{)}</math>
+| <math>\mathsf{¢}\small{(}</math><weight><math>\small\mathsf{)}</math>
-|weighted cents
+| Weighted cents
 |
 |-
-|<math>\small\mathsf{oct}</math>
+| <math>\small\mathsf{oct}</math>
-|octaves
+| Octaves
 |
 |}
-===Tuning schemes===
+=== Tuning schemes ===
 {| class="wikitable center-all mw-collapsible mw-collapsed"
-|+
+|+ style="font-size: 105%;" |
-! colspan="6" rowspan="3" |retuning (or mistuning) magnitude
-! colspan="12" rowspan="1" |damage
-! rowspan="5" |target
-intervals
-! colspan="2" rowspan="4" |systematic name
-! rowspan="5" | previously named tuning schemes that are specific types of this tuning scheme
-! rowspan="5" |of interest?
 |-
-! colspan="9" rowspan="1" |weight
+! colspan="6" rowspan="3" | Retuning (or mistuning) magnitude
-! colspan="3" rowspan="1" |optimization
+! colspan="12" rowspan="1" | Damage
+! rowspan="5" | Target<br />intervals
+! colspan="2" rowspan="4" | Systematic name
+! rowspan="5" | Previously named tuning schemes that are specific types of this tuning scheme
+! rowspan="5" | Of interest?
 |-
-! colspan="6" rowspan="1" |interval complexity
+! colspan="9" rowspan="1" | Weight
-! colspan="3" rowspan="1" |slope
+! colspan="3" rowspan="1" | Optimization
-! colspan="1" rowspan="3" |initial
-! colspan="1" rowspan="3" |name
-! colspan="1" rowspan="3" |power
 |-
-! colspan="3" rowspan="1" |norm pretransformer
+! colspan="6" rowspan="1" | Interval complexity
-! colspan="3" rowspan="1" |norm power
+! colspan="3" rowspan="1" | Slope
-! colspan="3" rowspan="1" |norm pretransformer
+! colspan="1" rowspan="3" | Initial
-! colspan="3" rowspan="1" |norm power
+! colspan="1" rowspan="3" | Name
-! colspan="1" rowspan="2" |initial
+! colspan="1" rowspan="3" | Power
-! colspan="1" rowspan="2" |name
-! colspan="1" rowspan="2" |multiplier
 |-
-!initial
+! colspan="3" rowspan="1" | Norm pretransformer
-!name
+! colspan="3" rowspan="1" | Norm power
-!multiplier
+! colspan="3" rowspan="1" | Norm pretransformer
-!initial
+! colspan="3" rowspan="1" | Norm power
-!name
+! colspan="1" rowspan="2" | Initial
-! power
+! colspan="1" rowspan="2" | Name
-!initial
+! colspan="1" rowspan="2" | Multiplier
-!name
-!multiplier
-!initial
-!name
-!power
-! colspan="1" |abbreviated
-! colspan="1" |read ("____ tuning scheme")
 |-
-| colspan="3" |<none>
+! Initial
-| rowspan="4" |<n/a>
+! Name
-| rowspan="2" |maximum
+! Multiplier
-| rowspan="2" |∞
+! Initial
-| colspan="3" |<none>
+! Name
-| rowspan="2" |(t)
+! Power
-| rowspan="2" |taxicab
+! Initial
-| rowspan="2" |1
+! Name
-| rowspan="4" |S
+! Multiplier
-| rowspan="4" |simplicity-weight
+! Initial
-| rowspan="4" |1/complexity
+! Name
-| rowspan="31" |<n/a>
+! Power
-| rowspan="13" |minimax
+! colspan="1" | Abbreviated
-| rowspan="13" |∞
+! colspan="1" | Read ("____ tuning scheme")
-| rowspan="4" |all
-|minimax-S
-| minimax simplicity-weight damage
-|"[[TOP]]"/"[[T1]]"/"[[TIPTOP]]"*, "[[CTOP]]", "[[POTOP]]"/"[[POTT]]"*
-|yes
 |-
-| colspan="3" |<various>
+| colspan="3" | <none>
-| colspan="3" |<various>
+| rowspan="4" | <n/a>
-|minimax-<alt>-S
+| rowspan="2" | Maximum
-|minimax <alternative>-simplicity-weight damage
+| rowspan="2" | &infin;
-|"[[BOP tuning|BOP]]", "[[Weil Norms, Tenney-Weil Norms, and TWp Interval and Tuning Space|Weil]]", "[[Kees]]"
+| colspan="3" | <none>
-|yes
+| rowspan="2" | (t)
+| rowspan="2" | Taxicab
+| rowspan="2" | 1
+| rowspan="4" | S
+| rowspan="4" | Simplicity-weight
+| rowspan="4" | 1/Complexity
+| rowspan="31" | <n/a>
+| rowspan="13" | Minimax
+| rowspan="13" | &infin;
+| rowspan="4" | All
+| Minimax-S
+| Minimax simplicity-weight damage
+| "[[TOP]]"/"[[T1]]"/"[[TIPTOP]]"*, "[[CTOP]]", "[[POTOP]]"/"[[POTT]]"*
+| yes
 |-
-| colspan="3" |<none>
+| colspan="3" | <various>
-| rowspan="2" |Euclidean
+| colspan="3" | <various>
-| rowspan="2" |2
+| Minimax-<alt>-S
-| colspan="3" |<none>
+| Minimax <alternative>-simplicity-weight damage
-| rowspan="2" |E
+| "[[BOP tuning|BOP]]", "[[Weil Norms, Tenney-Weil Norms, and TWp Interval and Tuning Space|Weil]]", "[[Kees]]"
-| rowspan="2" |Euclidean
+| yes
-| rowspan="2" |2
-|minimax-ES
-|minimax Euclideanized-simplicity-weight damage
-|"[[Tenney-Euclidean tuning|TE]]"/"[[T2]]"/"[[TOP-RMS]]", "[[CTE tuning|CTE]]", "[[POTE tuning|POTE]]"
-|yes
 |-
-| colspan="3" |<various>
+| colspan="3" | <none>
-| colspan="3" |<various>
+| rowspan="2" | Euclidean
-|minimax-E-<alt>-S
+| rowspan="2" | 2
-|minimax Euclideanized-<alternative>-simplicity-weight damage
+| colspan="3" | <none>
-|"[[Frobenius]]", "[[BE]]", "[[WE]]", "[[KE]]"
+| rowspan="2" | E
-|yes
+| rowspan="2" | Euclidean
+| rowspan="2" | 2
+| Minimax-ES
+| Minimax Euclideanized-simplicity-weight damage
+| "[[Tenney-Euclidean tuning|TE]]"/"[[T2]]"/"[[TOP-RMS]]", "[[CTE tuning|CTE]]", "[[POTE tuning|POTE]]"
+| yes
 |-
-| colspan="6" rowspan="27" |<n/a>
+| colspan="3" | <various>
-| colspan="6" |<n/a>
+| colspan="3" | <various>
-|U
+| Minimax-E-<alt>-S
-|unity-weight
+| Minimax Euclideanized-<alternative>-simplicity-weight damage
-|<none>
+| "[[Frobenius]]", "[[BE]]", "[[WE]]", "[[KE]]"
+| Yes
+|-
+| colspan="6" rowspan="27" | <n/a>
+| colspan="6" | <n/a>
+| U
+| Unity-weight
+| <none>
 | rowspan="27" | <set>
-|<set> minimax-U
+| <set> Minimax-U
-|<set> minimax unity-weight damage
+| <set> Minimax unity-weight damage
-|"[[Minimax tuning|minimax]]"
+| "[[Minimax tuning|Minimax]]"
-|yes
+| yes
 |-
-| colspan="3" |<none>
+| colspan="3" | <none>
-| rowspan="2" |(t)
+| rowspan="2" | (t)
-| rowspan="2" |taxicab
+| rowspan="2" | Taxicab
-| rowspan="2" |1
+| rowspan="2" | 1
-| rowspan="4" |S
+| rowspan="4" | S
-| rowspan="4" |simplicity-weight
+| rowspan="4" | Simplicity-weight
-| rowspan="4" |1/complexity
+| rowspan="4" | 1/Complexity
-|<set> minimax-S
+| <set> Minimax-S
-|<set> minimax simplicity-weight damage
+| <set> Minimax simplicity-weight damage
 |
-|yes
+| Yes
 |-
-| colspan="3" |<various>
+| colspan="3" | <various>
-|<set> minimax-<alt>-S
+| <set> Minimax-<alt>-S
-|<set> minimax <alternative>-simplicity-weight damage
+| <set> Minimax <alternative>-simplicity-weight damage
 |
 |
 |-
-| colspan="3" |<none>
+| colspan="3" | <none>
-| rowspan="2" |E
+| rowspan="2" | E
-| rowspan="2" |Euclidean
+| rowspan="2" | Euclidean
-| rowspan="2" |2
+| rowspan="2" | 2
-|<set> minimax-ES
+| <set> Minimax-ES
-|<set> minimax Euclideanized-simplicity-weight damage
+| <set> Minimax Euclideanized-simplicity-weight damage
 |
 |
 |-
-| colspan="3" |<various>
+| colspan="3" | <various>
-|<set> minimax-E-<alt>-S
+| <set> Minimax-E-<alt>-S
-|<set> minimax Euclideanized-<alternative>-simplicity-weight damage
+| <set> Minimax Euclideanized-<alternative>-simplicity-weight damage
 |
 |
 |-
-| colspan="3" |<none>
+| colspan="3" | <none>
-| rowspan="2" |(t)
+| rowspan="2" | (t)
-| rowspan="2" |taxicab
+| rowspan="2" | Taxicab
-| rowspan="2" |1
+| rowspan="2" | 1
-| rowspan="4" |C
+| rowspan="4" | C
-| rowspan="4" |complexity-weight
+| rowspan="4" | Complexity-weight
-| rowspan="4" |complexity
+| rowspan="4" | Complexity
-|<set> minimax-C
+| <set> Cinimax-C
-|<set> minimax complexity-weight damage
+| <set> Cinimax complexity-weight damage
 |
-|yes
+| Yes
 |-
-| colspan="3" |<various>
+| colspan="3" | <various>
-|<set> minimax-<alt>-C
+| <set> Minimax-<alt>-C
-|<set> minimax <alternative>-complexity-weight damage
+| <set> Minimax <alternative>-complexity-weight damage
 |
 |
 |-
-| colspan="3" |<none>
+| colspan="3" | <none>
-| rowspan="2" |E
+| rowspan="2" | E
-| rowspan="2" |Euclidean
+| rowspan="2" | Euclidean
-| rowspan="2" |2
+| rowspan="2" | 2
-|<set> minimax-EC
+| <set> Minimax-EC
-|<set> minimax Euclideanized-complexity-weight damage
+| <set> Minimax Euclideanized-complexity-weight damage
 |
 |
 |-
-| colspan="3" |<various>
+| colspan="3" | <various>
-|<set> minimax-E-<alt>-C
+| <set> Minimax-E-<alt>-C
-|<set> minimax Euclideanized-<alternative>-complexity-weight damage
+| <set> Minimax Euclideanized-<alternative>-complexity-weight damage
 |
 |
 |-
-| colspan="6" |<n/a>
+| colspan="6" | <n/a>
-|U
+| U
-|unity-weight
+| Unity-weight
 | <none>
-| rowspan="9" |miniRMS
+| rowspan="9" | MiniRMS
-| rowspan="9" |2
+| rowspan="9" | 2
-| <set> miniRMS-U
+| <set> MiniRMS-U
-|<set> miniRMS unity-weight damage
+| <set> MiniRMS unity-weight damage
-|"[[least squares]]"
+| "[[Least squares]]"
-|yes
+| yes
 |-
-| colspan="3" |<none>
+| colspan="3" | <none>
 | rowspan="2" | (t)
-| rowspan="2" |taxicab
+| rowspan="2" | Taxicab
 | rowspan="2" | 1
-| rowspan="4" |S
+| rowspan="4" | S
-| rowspan="4" |simplicity-weight
+| rowspan="4" | Simplicity-weight
-| rowspan="4" |1/complexity
+| rowspan="4" | 1/Complexity
-|<set> miniRMS-S
+| <set> MiniRMS-S
-|<set> miniRMS simplicity-weight damage
+| <set> MiniRMS simplicity-weight damage
 |
-|yes
+| Yes
 |-
-| colspan="3" |<various>
+| colspan="3" | <various>
-|<set> miniRMS-<alt>-S
+| <set> MiniRMS-<alt>-S
-|<set> miniRMS <alternative>-simplicity-weight damage
+| <set> MiniRMS <alternative>-simplicity-weight damage
 |
 |
 |-
-| colspan="3" |<none>
+| colspan="3" | <none>
-| rowspan="2" |E
+| rowspan="2" | E
-| rowspan="2" |Euclidean
+| rowspan="2" | Euclidean
-| rowspan="2" |2
+| rowspan="2" | 2
-| <set> miniRMS-ES
+| <set> MiniRMS-ES
-|<set> miniRMS Euclideanized-simplicity-weight damage
+| <set> MiniRMS Euclideanized-simplicity-weight damage
 |
 |
 |-
-| colspan="3" |<various>
+| colspan="3" | <various>
-|<set> miniRMS-E-<alt>-S
+| <set> MiniRMS-E-<alt>-S
-|<set> miniRMS Euclideanized-<alternative>-simplicity-weight damage
+| <set> MiniRMS Euclideanized-<alternative>-simplicity-weight damage
 |
 |
 |-
-| colspan="3" |<none>
+| colspan="3" | <none>
-| rowspan="2" |(t)
+| rowspan="2" | (t)
-| rowspan="2" |taxicab
+| rowspan="2" | Taxicab
-| rowspan="2" |1
+| rowspan="2" | 1
-| rowspan="4" |C
+| rowspan="4" | C
-| rowspan="4" |complexity-weight
+| rowspan="4" | Complexity-weight
-| rowspan="4" |complexity
+| rowspan="4" | Complexity
-|<set> miniRMS-C
+| <set> MiniRMS-C
-|<set> miniRMS complexity-weight damage
+| <set> MiniRMS complexity-weight damage
 |
-|yes
+| yes
 |-
-| colspan="3" |<various>
+| colspan="3" | <various>
-|<set> miniRMS-<alt>-C
+| <set> MiniRMS-<alt>-C
-|<set> miniRMS <alternative>-complexity-weight damage
+| <set> MiniRMS <alternative>-complexity-weight damage
 |
 |
 |-
-| colspan="3" |<none>
+| colspan="3" | <none>
-| rowspan="2" |E
+| rowspan="2" | E
-| rowspan="2" |Euclidean
+| rowspan="2" | Euclidean
-| rowspan="2" |2
+| rowspan="2" | 2
-|<set> miniRMS-EC
+| <set> MiniRMS-EC
-|<set> miniRMS Euclideanized-complexity-weight damage
+| <set> MiniRMS Euclideanized-complexity-weight damage
 |
 |
 |-
 | colspan="3" | <various>
-|<set> miniRMS-E-<alt>-C
+| <set> MiniRMS-E-<alt>-C
-|<set> miniRMS Euclideanized-<alternative>-complexity-weight damage
+| <set> MiniRMS Euclideanized-<alternative>-complexity-weight damage
 |
 |
 |-
-| colspan="6" |<n/a>
+| colspan="6" | <n/a>
-|U
+| U
-|unity-weight
+| Unity-weight
-|<none>
+| <none>
-| rowspan="9" |miniaverage
+| rowspan="9" | Miniaverage
-| rowspan="9" |1
+| rowspan="9" | 1
-| <set> miniaverage-U
+| <set> Miniaverage-U
-|<set> miniaverage unity-weight damage
+| <set> Miniaverage unity-weight damage
 |
-|yes
+| yes
 |-
-| colspan="3" |<none>
+| colspan="3" | <none>
 | rowspan="2" | (t)
-| rowspan="2" |taxicab
+| rowspan="2" | Taxicab
 | rowspan="2" | 1
-| rowspan="4" |S
+| rowspan="4" | S
-| rowspan="4" |simplicity-weight
+| rowspan="4" | Simplicity-weight
-| rowspan="4" | 1/complexity
+| rowspan="4" | 1/Complexity
-|<set> miniaverage-S
+| <set> Miniaverage-S
-|<set> miniaverage simplicity-weight damage
+| <set> Miniaverage simplicity-weight damage
 |
-|yes
+| Yes
 |-
-| colspan="3" |<various>
+| colspan="3" | <various>
-|<set> miniaverage-<alt>-S
+| <set> Miniaverage-<alt>-S
-|<set> miniaverage <alternative>-simplicity-weight damage
+| <set> Miniaverage <alternative>-simplicity-weight damage
 |
 |
 |-
-| colspan="3" |<none>
+| colspan="3" | <none>
-| rowspan="2" |E
+| rowspan="2" | E
-| rowspan="2" |Euclidean
+| rowspan="2" | Euclidean
-| rowspan="2" |2
+| rowspan="2" | 2
-|<set> miniaverage-ES
+| <set> Miniaverage-ES
-|<set> miniaverage Euclideanized-simplicity-weight damage
+| <set> Miniaverage Euclideanized-simplicity-weight damage
 |
 |
 |-
-| colspan="3" |<various>
+| colspan="3" | <various>
-|<set> miniaverage-E-<alt>-S
+| <set> Miniaverage-E-<alt>-S
-|<set> miniaverage Euclideanized-<alternative>-simplicity-weight damage
+| <set> Miniaverage Euclideanized-<alternative>-simplicity-weight damage
 |
 |
 |-
-| colspan="3" |<none>
+| colspan="3" | <none>
-| rowspan="2" |(t)
+| rowspan="2" | (t)
-| rowspan="2" |taxicab
+| rowspan="2" | Taxicab
-| rowspan="2" |1
+| rowspan="2" | 1
-| rowspan="4" |C
+| rowspan="4" | C
-| rowspan="4" |complexity-weight
+| rowspan="4" | Complexity-weight
-| rowspan="4" |complexity
+| rowspan="4" | Complexity
-|<set> miniaverage-C
+| <set> Miniaverage-C
-|<set> miniaverage complexity-weight damage
+| <set> Miniaverage complexity-weight damage
 |
-|yes
+| Yes
 |-
-| colspan="3" |<various>
+| colspan="3" | <various>
-|<set> miniaverage-<alt>-C
+| <set> Miniaverage-<alt>-C
-|<set> miniaverage <alternative>-complexity-weight damage
+| <set> Miniaverage <alternative>-complexity-weight damage
 |
 |
 |-
-| colspan="3" |<none>
+| colspan="3" | <none>
-| rowspan="2" |E
+| rowspan="2" | E
-| rowspan="2" |Euclidean
+| rowspan="2" | Euclidean
-| rowspan="2" |2
+| rowspan="2" | 2
-|<set> miniaverage-EC
+| <set> Miniaverage-EC
-| <set> miniaverage Euclideanized-complexity-weight damage
+| <set> Miniaverage Euclideanized-complexity-weight damage
 |
 |
 |-
-| colspan="3" |<various>
+| colspan="3" | <various>
-|<set> miniaverage-E-<alt>-C
+| <set> Miniaverage-E-<alt>-C
-|<set> miniaverage Euclideanized-<alternative>-complexity-weight damage
+| <set> Miniaverage Euclideanized-<alternative>-complexity-weight damage
 |
 |
 |}
-===Damages===
+=== Damages ===
 {| class="wikitable center-all mw-collapsible mw-collapsed"
-|+
+|+ style="font-size: 105%;" |
-! colspan="2" |quantity
-! colspan="2" |unit
 |-
-!abbreviation
+! colspan="2" | Quantity
-!name
+! colspan="2" | Unit
-!symbol
-!name
 |-
-|U-damage
+! Abbreviation
-|unity-weight damage
+! Name
-|<math>\mathsf{¢}\small\mathsf{(U)}</math>
+! Symbol
-|unity-weighted cents
+! Name
 |-
-|C-damage
+| U-damage
-|complexity-weight damage
+| Unity-weight damage
-|<math>\mathsf{¢}\small\mathsf{(C)}</math>
+| <math>\mathsf{¢}\small\mathsf{(U)}</math>
-|complexity-weighted cents
+| Unity-weighted cents
 |-
-|<alt>-C-damage
+| C-damage
-|<alternative>-complexity-weight damage
+| Complexity-weight damage
-|<math>\mathsf{¢}</math><math>\small\mathsf{(}</math><alt>-<math>\small\mathsf{C)}</math>
+| <math>\mathsf{¢}\small\mathsf{(C)}</math>
-|<alternative>-complexity-weighted cents
+| Complexity-weighted cents
+|-
+| <alt>-C-damage
+| <alternative>-complexity-weight damage
+| <math>\mathsf{¢}</math><math>\small\mathsf{(}</math><alt>-<math>\small\mathsf{C)}</math>
+| <alternative>-complexity-weighted cents
 |-
 | EC-damage
-|Euclideanized-complexity-weight damage
+| Euclideanized-complexity-weight damage
-|<math>\mathsf{¢}</math><math>\small\mathsf{(EC)}</math>
+| <math>\mathsf{¢}</math><math>\small\mathsf{(EC)}</math>
-|Euclideanized-complexity-weighted cents
+| Euclideanized-complexity-weighted cents
 |-
-|E-<alt>-C-damage
+| E-<alt>-C-damage
-|Euclideanized-<alternative>-complexity-weight damage
+| Euclideanized-<alternative>-complexity-weight damage
-|<math>\mathsf{¢}</math><math>\small\mathsf{(E}</math>-<alt>-<math>\small\mathsf{C)}</math>
+| <math>\mathsf{¢}</math><math>\small\mathsf{(E}</math>-<alt>-<math>\small\mathsf{C)}</math>
-|Euclideanized-<alternative>-complexity-weighted cents
+| Euclideanized-<alternative>-complexity-weighted cents
 |-
-|S-damage
+| S-damage
-|simplicity-weight damage
+| Simplicity-weight damage
-|<math>\mathsf{¢}\small\mathsf{(S)}</math>
+| <math>\mathsf{¢}\small\mathsf{(S)}</math>
-|simplicity-weighted cents
+| Simplicity-weighted cents
 |-
-|<alt>-S-damage
+| <alt>-S-damage
-|<alternative>-simplicity-weight damage
+| <alternative>-simplicity-weight damage
-|<math>\mathsf{¢}</math><math>\small\mathsf{(}</math><alt>-<math>\small\mathsf{S)}</math>
+| <math>\mathsf{¢}</math><math>\small\mathsf{(}</math><alt>-<math>\small\mathsf{S)}</math>
-|<alternative>-simplicity-weighted cents
+| <alternative>-simplicity-weighted cents
 |-
-|ES-damage
+| ES-damage
-|Euclideanized-simplicity-weight damage
+| Euclideanized-simplicity-weight damage
-|<math>\mathsf{¢}</math><math>\small\mathsf{(ES)}</math>
+| <math>\mathsf{¢}</math><math>\small\mathsf{(ES)}</math>
-|Euclideanized-simplicity-weighted cents
+| Euclideanized-simplicity-weighted cents
 |-
-|E-<alt>-S-damage
+| E-<alt>-S-damage
-|Euclideanized-<alternative>-simplicity-weight damage
+| Euclideanized-<alternative>-simplicity-weight damage
-|<math>\mathsf{¢}</math><math>\small\mathsf{(E}</math>-<alt>-<math>\small\mathsf{S)}</math>
+| <math>\mathsf{¢}</math><math>\small\mathsf{(E}</math>-<alt>-<math>\small\mathsf{S)}</math>
-|Euclideanized-<alternative>-simplicity-weighted cents
+| Euclideanized-<alternative>-simplicity-weighted cents
 |}
-===Complexity and simplicity===
+=== Complexity and simplicity ===
 {| class="wikitable center-all mw-collapsible mw-collapsed"
-|+
+|+ style="font-size: 105%;" |
-! colspan="2" |quantity
+|-
-! colspan="2" |unit
+! colspan="2" | Quantity
+! colspan="2" | Unit
 |-
-!abbreviation
+! Abbreviation
-!name
+! Name
-!unit
+! Unit
-!name
+! Name
 |-
-|C
+| C
-|complexity
+| Complexity
-|<math>\small\mathsf{𝟙}\scriptsize\mathsf{(C)}</math> = <math>\small\mathsf{(C)}</math>
+| <math>\small\mathsf{𝟙}\scriptsize\mathsf{(C)}</math> = <math>\small\mathsf{(C)}</math>
-|complexity weight
+| Complexity weight
 |-
-|<alt>-C
+| <alt>-C
-|<alternative> complexity
+| <alternative> complexity
-|<math>\small\mathsf{𝟙}\scriptsize\mathsf{(}</math><alt>-<math>\scriptsize\mathsf{C)}</math> = <math>\small\mathsf{(}</math><alt>-<math>\small\mathsf{C)}</math>
+| <math>\small\mathsf{𝟙}\scriptsize\mathsf{(}</math><alt>-<math>\scriptsize\mathsf{C)}</math> = <math>\small\mathsf{(}</math><alt>-<math>\small\mathsf{C)}</math>
-|<alternative>-complexity weight
+| <alternative>-complexity weight
 |-
-|EC
+| EC
-|Euclideanized complexity
+| Euclideanized complexity
-|<math>\small\mathsf{𝟙}\scriptsize\mathsf{(EC)}</math> = <math>\small\mathsf{(EC)}</math>
+| <math>\small\mathsf{𝟙}\scriptsize\mathsf{(EC)}</math> = <math>\small\mathsf{(EC)}</math>
-|Euclideanized-complexity weight
+| Euclideanized-complexity weight
 |-
-|E-<alt>-C
+| E-<alt>-C
-|Euclideanized-<alternative> complexity
+| Euclideanized-<alternative> complexity
-|<math>\small\mathsf{𝟙}\scriptsize\mathsf{(E}</math>-<alt>-<math>\scriptsize\mathsf{C)}</math> = <math>\small\mathsf{(E}</math>-<alt>-<math>\small\mathsf{C)}</math>
+| <math>\small\mathsf{𝟙}\scriptsize\mathsf{(E}</math>-<alt>-<math>\scriptsize\mathsf{C)}</math> = <math>\small\mathsf{(E}</math>-<alt>-<math>\small\mathsf{C)}</math>
-|Euclideanized-<alternative>-complexity weight
+| Euclideanized-<alternative>-complexity weight
 |-
-|S
+| S
-|simplicity
+| Simplicity
-|<math>\small\mathsf{𝟙}\scriptsize\mathsf{(S)}</math> = <math>\small\mathsf{(S)}</math>
+| <math>\small\mathsf{𝟙}\scriptsize\mathsf{(S)}</math> = <math>\small\mathsf{(S)}</math>
-|simplicity weight
+| Simplicity weight
 |-
-|<alt>-S
+| <alt>-S
-|<alternative> simplicity
+| <alternative> simplicity
-|<math>\small\mathsf{𝟙}\scriptsize\mathsf{(}</math><alt>-<math>\scriptsize\mathsf{S)}</math> = <math>\small\mathsf{(}</math><alt>-<math>\small\mathsf{S)}</math>
+| <math>\small\mathsf{𝟙}\scriptsize\mathsf{(}</math><alt>-<math>\scriptsize\mathsf{S)}</math> = <math>\small\mathsf{(}</math><alt>-<math>\small\mathsf{S)}</math>
-|<alternative>-simplicity weight
+| <alternative>-simplicity weight
 |-
-|ES
+| ES
-|Euclideanized simplicity
+| Euclideanized simplicity
-|<math>\small\mathsf{𝟙}\scriptsize\mathsf{(ES)}</math> = <math>\small\mathsf{(ES)}</math>
+| <math>\small\mathsf{𝟙}\scriptsize\mathsf{(ES)}</math> = <math>\small\mathsf{(ES)}</math>
-|Euclideanized-simplicity weight
+| Euclideanized-simplicity weight
 |-
-|E-<alt>-S
+| E-<alt>-S
-|Euclideanized-<alternative> simplicity
+| Euclideanized-<alternative> simplicity
-|<math>\small\mathsf{𝟙}\scriptsize\mathsf{(E}</math>-<alt>-<math>\scriptsize\mathsf{S)}</math> = <math>\small\mathsf{(E}</math>-<alt>-<math>\small\mathsf{S)}</math>
+| <math>\small\mathsf{𝟙}\scriptsize\mathsf{(E}</math>-<alt>-<math>\scriptsize\mathsf{S)}</math> = <math>\small\mathsf{(E}</math>-<alt>-<math>\small\mathsf{S)}</math>
-|Euclideanized-<alternative>-simplicity weight
+| Euclideanized-<alternative>-simplicity weight
 |}
-==WinCompose==
+== WinCompose ==
+Are you tired of every time web-searching for and copy-pasting special characters that you use over and over in RTT discussions, or would like to use if only it were easy, such as ♯, ♭, ¢, √, °, ₂, ×, {{inv}}, ⟩, ∞, and ϕ? Well, try [http://wincompose.info/ WinCompose]! This tool lets you communicate about these ideas without disrupting your train of thought, by typing these characters with simple and memorable key sequences. These sequences always begin with your chosen Compose-key, which defaults to being your right Alt key. When describing these sequences we represent this key with the symbol ⎄. So for example, you type {{nowrap|♯ as <code>⎄##</code>|♭ as <code>⎄bb</code>|¢ as <code>⎄c/</code>|√ as <code>⎄v/</code>|° as <code>⎄00</code>|₂ as <code>⎄-2</code>|× as <code>⎄xx</code>|{{inv}} as <code>⎄11</code>|⟩ as <code>⎄&gt;&gt;</code>|∞ as <code>⎄88</code>|and ϕ as <code>⎄8f</code>}}.
-Are you tired of every time web-searching for and copy-pasting special characters that you use over and over in RTT discussions, or would like to use if only it were easy, such as ♯, ♭, ¢, √, °, ₂, ×, ⁻¹, ⟩, ∞, and ϕ? Well, try [http://wincompose.info/ WinCompose]! This tool lets you communicate about these ideas without disrupting your train of thought, by typing these characters with simple and memorable key sequences. These sequences always begin with your chosen Compose-key, which defaults to being your right Alt key. When describing these sequences we represent this key with the symbol ⎄. So for example, you type ♯ as ⎄##, ♭ as ⎄bb, ¢ as ⎄c/, √ as ⎄v/, ° as ⎄00, ₂ as ⎄-2, × as ⎄xx, ⁻¹ as ⎄11, ⟩ as ⎄>>, ∞ as ⎄88, and ϕ as ⎄8f.
-For Windows users, install WinCompose then copy-paste the contents of this file: https://dkeenan.com/XCompose.txt into your user sequences (Show sequences → User-defined sequences → Edit). Then save and reload. You can always choose to override or add alternatives to our sequences if you find others to be more intuitive.
+For Windows users, install WinCompose then copy-paste the contents of this file: https://dkeenan.com/XCompose.txt into your user sequences (Show sequences &rarr; User-defined sequences &rarr; Edit). Then save and reload. You can always choose to override or add alternatives to our sequences if you find others to be more intuitive.
-For Mac users, we refer you to these instructions (from the author of WinCompose) for how to set up Compose-key sequences in Mac OS: http://sam.hocevar.net/blog/category/osx/
+For Mac users, we refer you to this repo, which gives tools and instructions for setting up key bindings as compose rules in Mac OS, and even comes pre-packaged with our rules: https://github.com/cmloegcmluin/compose2keybindings
-===Table of noteworthy sequences===
+=== Table of noteworthy sequences ===
 {| class="wikitable mw-collapsible mw-collapsed"
-|+
+|+ style="font-size: 105%; white-space: nowrap;" | Dave Keenan & Douglas Blumeyer's compose-key sequences
-! scope="col" width="130px" |Compose-key sequence
+|- style="white-space: nowrap;"
-! scope="col" width="75px" |resulting text
+! scope="col" style="width: 130px;" | Compose-key sequence
-!description
+! scope="col" style="width: 75px;" | Resulting text
+! Description
+|- style="white-space: nowrap;"
+! colspan="3" | Keyboard key symbols
 |-
-! colspan="3" rowspan="1" |Keyboard key symbols
+| ⎄⎄⎄
+| ⎄
+| Compose key symbol (the right alt key by default)
 |-
-|⎄⎄⎄
+| ⎄\␣
-|⎄
+| ␣
-|compose key symbol (the right alt key by default)
+| Spacebar symbol
 |-
-|⎄\␣
+| ⎄\▶︎ etc.
-|␣
+| ▶︎ etc.
-|spacebar symbol
+| Right etc. arrow key symbols
 |-
-|⎄\▶︎ etc.
+| ⎄\A or ⎄\O
-|▶︎ etc.
+| ⌥
-|right etc. arrow key symbols
+| Alt or option key symbol
 |-
-|⎄\A or ⎄\O
+| ⎄\B
-|⌥
+| ⌫
-|alt or option key symbol
+| Backspace key symbol
 |-
-|⎄\B
+| ⎄\C
-|⌫
+| ✲
-|backspace key symbol
+| Control key symbol
 |-
-|⎄\C
+| ⎄\D
-|✲
+| ⌦
-|control key symbol
+| Delete key symbol
 |-
-|⎄\D
+| ⎄\E
-|⌦
+| ⎋
-|delete key symbol
+| Escape key symbol
 |-
-|⎄\E
+| ⎄\L
-|⎋
+| ⇪
-|escape key symbol
+| Caps lock key symbol
 |-
-|⎄\L
+| ⎄\R or ⎄\.E
-|⇪
+| ⏎
-|caps lock key symbol
+| Return or enter key symbol
 |-
-|⎄\R or ⎄\.E or ⎄\\
+| ⎄\S
-|⏎
+| ⇧
-|return or enter key symbol
+| Shift key symbol
 |-
-|⎄\S
+| ⎄\T
-|⇧
+| ⭾
-|shift key symbol
+| Tab key symbol
 |-
-|⎄\T
+| ⎄()
-|⭾
+| ◌
-|tab key symbol
+| Dotted circle, represents any character (such as the character preceding a combining mark)
 |-
-|⎄()
+! colspan="3" style="white-space: nowrap;" | Double key sequences
-|◌
-|dotted circle, represents any character (such as the character preceding a combining mark)
 |-
-! colspan="3" rowspan="1" |Double key sequences
+| ⎄␣␣
+|
+| Narrow no-break space (used between quantities and their units)
 |-
-|⎄␣␣
+| ⎄..
-|
+| ·
-|narrow no-break space (used between quantities and their units)
+| Middle dot (used to multiply units when juxtaposition is ambiguous)
 |-
-|⎄..
+| ⎄::
-|·
+| ÷
-|middle dot (used to multiply units when juxtaposition is ambiguous)
+| Divide sign
 |-
-|⎄::
+| ⎄;;
-|÷
+| ◌̲̅
-|divide sign
+| Combining overline and low line (undirected value)
 |-
-|⎄;;
+| ⎄{{pipe}} {{pipe}}
-|◌̲̅
+| ‖
-|combining overline and low line (undirected value)
+| Power norm bracket
 |-
-|<nowiki>⎄||</nowiki>
+| ⎄<<
-|‖
+| ⟨
-|power norm bracket
+| Left angle bracket
 |-
-|⎄\\
+| ⎄>>
-|⏎
+| ⟩
-|return or enter key symbol
+| Right angle bracket
 |-
-|⎄<<
+| ⎄~~
-|⟨
+| ≈
-|left angle bracket
+| Approximately equal
 |-
-|⎄>>
+| ⎄**
-|⟩
+| ★
-|right angle bracket
+| Black star
 |-
-|⎄~~
+| ⎄&#39;&#39;
-|≈
+| ′
-|approximately equal
+| prime mark
 |-
-|⎄**
+| ⎄11
-|★
+| ⁻¹
-|black star
+| Power of &minus;1 or inverse
 |-
-|⎄<nowiki>''</nowiki>
+| ⎄22 through ⎄77
-|′
+| ² ³ ⁴ ⁵ ⁶ ⁷
-|prime mark
+| Squared, cubed, fourth through seventh power
 |-
-|⎄11
+| ⎄88
-|⁻¹
+| ∞
-|power of -1 or inverse
+| Infinity
 |-
-|⎄22 through ⎄77
+| ⎄00
-|² ³ ⁴ ⁵ ⁶ ⁷
+| °
-|squared, cubed, fourth through seventh power
+| Degree sign
 |-
-|⎄88
+| ⎄nn
-|∞
+| ⁿ
-|infinity
+| Superscript small n
 |-
-|⎄00
+| ⎄--
-|°
+| ₋
-|degree sign
+| Subscript minus sign
 |-
-|⎄nn
+| ⎄__
-|ⁿ
+| ◌̲
-|superscript small n
+| Combining low line (underline)
 |-
-|⎄--
+| ⎄==
-|₋
+| ≡
-|subscript minus sign
+| Modular congruence
 |-
-|⎄__
+| ⎄//
-|◌̲
+| ⁄
-|combining low line (underline)
+| Fraction slash (use with super and subscripts to create fractions)
 |-
-|⎄==
+| ⎄##
-|≡
+| ♯
-|modular congruence
+| Musical sharp
 |-
-|⎄//
+| ⎄bb
-|⁄
+| ♭
-|fraction slash (use with super and subscripts to create fractions)
+| Musical flat
 |-
-|⎄##
+| ⎄dd
-|♯
+| ∂
-|musical sharp
+| Partial derivative
 |-
-|⎄bb
+| ⎄ff
-|♭
+| ϕ
-|musical flat
+| Small phi symbol
 |-
-|⎄dd
+| ⎄gg
-|∂
+| ɡ
-|partial derivative
+| Single-storey (opentail) small g
 |-
-|⎄ff
+| ⎄ll
-|ϕ
-|small phi symbol
-|-
-|⎄gg
-|ɡ
-|single-storey (opentail) small g
-|-
-|⎄ll
 | ℓ
-|script small L
+| Script small L
 |-
-|⎄uu
+| ⎄uu
-|µ
+| µ
-|micro sign
+| Micro sign
 |-
-|⎄xx
+| ⎄xx
-|×
+| ×
-|multiplication sign
+| Multiplication sign
 |-
-|⎄DD
+| ⎄DD
-|∆
+| ∆
-|delta (small difference) operator
+| Delta (small difference) operator
 |-
-|⎄FF
+| ⎄FF
-|Φ
+| Φ
-|Greek capital phi
+| Greek capital phi
 |-
-|⎄QQ
+| ⎄QQ
-|Ϙ
+| Ϙ
-|Greek capital letter archaic qoppa (small quotient operator)
+| Greek capital letter archaic qoppa (small quotient operator)
 |-
-|⎄TT
+| ⎄TT
 | ᵀ
-|superscript capital T (matrix transpose)
+| Superscript capital T (matrix transpose)
 |-
-|⎄++
+| ⎄++
-|⁺
+| ⁺
-|superscript plus sign (matrix pseudoinverse)
+| Superscript plus sign (matrix pseudoinverse)
 |-
-|⎄▶︎▶︎ etc.
+| ⎄▶︎▶︎ etc.
-|→ etc.
+| → etc.
-|right etc. arrows
+| Right etc. arrows
 |-
-! colspan="3" rowspan="1" |Multiplication operators
+! colspan="3" style="white-space: nowrap;" | Multiplication operators
 |-
 | ⎄xx
-|×
+| ×
-|multiplication sign
+| Multiplication sign
 |-
-|⎄Xx or ⎄xX
+| ⎄Xx or ⎄xX
-|⨯
+| ⨯
-|vector or cross product (barely distinguishable from multiplication sign)
+| Vector or cross product (barely distinguishable from multiplication sign)
 |-
 | ⎄XX
-|✕
+| ✕
-|large multiplication sign (a better symbol for cross product)
+| Large multiplication sign (a better symbol for cross product)
 |-
-|⎄x*
+| ⎄x*
 | ⋆
-| star operator (prefix: tensor complement, Hodge)
+| Star operator (prefix: tensor complement, Hodge)
 |-
-|⎄X*
+| ⎄X*
-|∗
+| ∗
-|asterisk operator (infix: scalar product, Dorst)
+| Asterisk operator (infix: scalar product, Dorst)
 |-
 | ⎄x.
-|⋅
+| ⋅
-|dot (product) operator
+| Dot (product) operator
 |-
-|⎄X.
+| ⎄X.
-|•
+| •
-|bullet (infix: fat dot product, Dorst)
+| Bullet (infix: fat dot product, Dorst)
 |-
-! colspan="3" rowspan="1" |Other operators
+! colspan="3" style="white-space: nowrap;" | Other operators
 |-
-|⎄v/
+| ⎄v/
-|√
+| √
-| square root sign
+| Square root sign
 |-
-|⎄3v/
+| ⎄3v/
 | ∛
-|cube root sign
+| Cube root sign
 |-
-|⎄4v/
+| ⎄4v/
-|∜
+| ∜
-|fourth root sign
+| Fourth root sign
 |-
 | ⎄-+
-|₊
+| ₊
-|subscript plus sign
+| Subscript plus sign
 |-
-|⎄--
+| ⎄--
-|₋
+| ₋
-|subscript minus sign
+| Subscript minus sign
 |-
-|⎄-=
+| ⎄-=
-|₌
+| ₌
-|subscript equals sign
+| Subscript equals sign
 |-
-|⎄++
+| ⎄++
 | ⁺
-| superscript plus sign (matrix pseudoinverse)
+| Superscript plus sign (matrix pseudoinverse)
 |-
-|⎄+- or ⎄+=
+| ⎄+- or ⎄+=
-|±
+| ±
-|plus or minus sign
+| Plus or minus sign
 |-
-|⎄=+
+| ⎄=+
-|∓
+| ∓
-|minus or plus sign
+| Minus or plus sign
 |-
-|⎄=-
+| ⎄=-
-|−
+| −
-| minus sign
+| Minus sign
 |-
-|⎄==
+| ⎄==
-|≡
+| ≡
-|modular congruence
+| Modular congruence
 |-
-|⎄/\
+| ⎄/\
-|∧
+| ∧
-|logical AND, wedge product, progressive product
+| Logical AND, wedge product, progressive product
 |-
-|⎄\/
+| ⎄\/
-|∨
+| ∨
-| logical OR, vee product, regressive product
+| Logical OR, vee product, regressive product
 |-
-|⎄⎄/\
+| ⎄⎄/\
-|⋀
+| ⋀
-| larger logical AND, wedge product, progressive product
+| Larger logical AND, wedge product, progressive product
 |-
-|⎄⎄\/
+| ⎄⎄\/
-|⋁
+| ⋁
-|larger logical OR, vee product, regressive product
+| Larger logical OR, vee product, regressive product
 |-
-|<nowiki>⎄|_</nowiki>
+| <nowiki>⎄| _</nowiki>
-|⌊
+| ⌊
-|left floor (infix: right contraction, Dorst)
+| Left floor (infix: right contraction, Dorst)
 |-
-|<nowiki>⎄_|</nowiki>
+| <nowiki>⎄_| </nowiki>
-|⌋
+| ⌋
-|right floor (infix: left contraction, Dorst)
+| Right floor (infix: left contraction, Dorst)
 |-
-|<nowiki>⎄|^</nowiki>
+| <nowiki>⎄| ^</nowiki>
-|⌈
+| ⌈
-|left ceiling
+| Left ceiling
 |-
-|<nowiki>⎄^|</nowiki>
+| <nowiki>⎄^| </nowiki>
-|⌉
+| ⌉
-|right ceiling
+| Right ceiling
 |-
-|⎄'-
+| ⎄'-
-|⨽
+| ⨽
-|righthand interior product
+| Righthand interior product
 |-
-|⎄-'
+| ⎄-'
-|⨼
+| ⨼
-|(lefthand) interior product
+| (Left-hand) interior product
 |-
-|⎄-,
+| ⎄-,
-|¬
+| ¬
-|not sign (prefix: multivector complement)
+| Not sign (prefix: multivector complement)
 |-
-|⎄⎄<>
+| ⎄⎄<>
-|⋄
+| ⋄
-|diamond operator (prefix: multivector dual)
+| Diamond operator (prefix: multivector dual)
 |-
-|⎄(.)
+| ⎄(.)
-|⨀
+| ⨀
-| entrywise vector multiplication operator
+| Entry-wise vector multiplication operator
 |-
-|⎄(..)
+| ⎄(..)
-|⊙
+| ⊙
-|alternative entrywise vector multiplication operator
+| Alternative entry-wise vector multiplication operator
 |-
-|⎄(/)
+| ⎄(/)
-|⊘
+| ⊘
-|entrywise vector division operator
+| Entry-wise vector division operator
 |-
-! colspan="3" |Mathematical letter and digit prefixes
+! colspan="3" | Mathematical letter and digit prefixes
 |-
-|⎄3◌
+| ⎄3◌
-|я
+| я
-| cyrillic, ⎄3q is ya (example)
+| Cyrillic, ⎄3q is ya (example)
 |-
-|⎄4◌
+| ⎄4◌
-|ℵ
+| ℵ
-|hebrew, ⎄4a is aleph (only a b g d)
+| Hebrew, ⎄4a is aleph (example)
 |-
-|⎄5◌
+| ⎄5◌
-|𝔞
+| 𝔞
-|fraktur, ⎄5a
+| Fraktur, ⎄5a
 |-
-|⎄6◌
+| ⎄6◌
-|ᵃ ¹  ᪲  ⁸
+| ᵃ ¹  ᪲  ⁸
-|superscripts, ⎄6a ⎄61 ⎄688 ⎄68␣ (not all letters, some only approximate) (same key as ^ but without shift)
+| Superscripts, ⎄6a ⎄61 ⎄688 ⎄68␣ (not all letters, some only approximate) (same key as ^ but without shift)
 |-
-|⎄68◌
+| ⎄68◌
-|ᵝ
+| ᵝ
-|superscript greek, ⎄68b is superscript beta (only a few)
+| Superscript greek, ⎄68b is superscript beta (only a few)
 |-
-|⎄7◌
+| ⎄7◌
 | 𝒶
-|script, ⎄7a
+| Script, ⎄7a
 |-
-|⎄8◌
+| ⎄8◌
-|α
+| α
-|greek, ⎄8a is alpha (by sound where possible otherwise letter-shape)
+| Greek, ⎄8a is alpha (by sound where possible otherwise letter-shape)
 |-
-|⎄8.◌
+| ⎄8.◌
-|ς
+| ς
-|greek variants, ⎄8.s is final sigma
+| Greek variants, ⎄8.s is final sigma
 |-
-|⎄9◌
+| ⎄9◌
 | 𝐚 𝟏 𝟓 𝟕 𝟖 𝟎
-|bold, ⎄9a ⎄91 ⎄95␣ ⎄97␣ ⎄98␣ ⎄90␣
+| Bold, ⎄9a ⎄91 ⎄95␣ ⎄97␣ ⎄98␣ ⎄90␣
 |-
-|⎄95◌
+| ⎄95◌
-|𝖆
+| 𝖆
-|bold fraktur, ⎄95a
+| Bold fraktur, ⎄95a
 |-
-|⎄97◌
+| ⎄97◌
-|𝓪
+| 𝓪
-|bold script, ⎄97a
+| Bold script, ⎄97a
 |-
-|⎄98◌
+| ⎄98◌
-|𝛂
+| 𝛂
-|bold greek, ⎄98a is bold alpha
+| Bold greek, ⎄98a is bold alpha
 |-
-|⎄90◌
+| ⎄90◌
-|𝒂
+| 𝒂
-| bold italic, ⎄90a
+| Bold italic, ⎄90a
 |-
-|⎄908◌
+| ⎄908◌
-|𝜶
+| 𝜶
-|bold italic greek, ⎄908a is bold italic alpha
+| Bold italic greek, ⎄908a is bold italic alpha
 |-
-|⎄0◌
+| ⎄0◌
-|𝑎
+| 𝑎
-|italic, ⎄0a
+| Italic, ⎄0a
 |-
 | ⎄08◌
-|𝛼
+| 𝛼
-|italic greek, ⎄08a is italic alpha
+| Italic greek, ⎄08a is italic alpha
 |-
-|⎄-◌
+| ⎄-◌
-|ₐ ᴀ   ͚ ₈
+| ₐ ᴀ   ͚ ₈
-|subscripts and small caps, ⎄-a ⎄-A ⎄-88 ⎄-8␣ (not all letters, some only approximate) (same key as _ but without shift)
+| Subscripts and small caps, ⎄-a ⎄-A ⎄-88 ⎄-8␣ (not all letters, some only approximate) (same key as _ but without shift)
 |-
-|⎄-8◌
+| ⎄-8◌
-|ᵦ
+| ᵦ
-|subscript greek, ⎄-8b is subscript beta (only a few)
+| Subscript greek, ⎄-8b is subscript beta (only a few)
 |-
-|⎄{◌
+| ⎄{◌
-|𝖺 𝟣 𝟫
+| 𝖺 𝟣 𝟫
-|sans-serif, ⎄{a ⎄{1 ⎄{9␣
+| Sans-serif, ⎄{a ⎄{1 ⎄{9␣
 |-
-|⎄{9◌
+| ⎄{9◌
-|𝗮 𝟭
+| 𝗮 𝟭
-|sans-serif bold, ⎄{9a ⎄{91
+| Sans-serif bold, ⎄{9a ⎄{91
 |-
-|⎄}◌
+| ⎄}◌
-|𝚊 𝟷
+| 𝚊 𝟷
-|monospace, ⎄}a ⎄}1
+| Monospace, ⎄}a ⎄}1
 |-
-|<nowiki>⎄|◌</nowiki>
+| ⎄{{pipe}} ◌
 | 𝕒 𝟙 𝟠 𝟘
-|<nowiki>double-struck, ⎄|a ⎄|1 ⎄|8␣ ⎄|0␣</nowiki>
+| Double-struck, ⎄{{pipe}} a ⎄{{pipe}} 1 ⎄{{pipe}} 8␣ ⎄{{pipe}} 0␣
 |-
-|<nowiki>⎄|8◌</nowiki>
+| ⎄{{pipe}} 8◌
-|ℼ
+| ℼ
-|<nowiki>double-struck greek, ⎄|8p (only a few)</nowiki>
+| Double-struck greek, ⎄{{pipe}} 8p (only a few)
 |-
-|<nowiki>⎄|0◌</nowiki>
+| ⎄{{pipe}} 0◌
 | ⅇ ⅈ
-|<nowiki>double-struck italic, ⎄|0e ⎄|i (only a few)</nowiki>
+| Double-struck italic, ⎄{{pipe}} 0e ⎄{{pipe}} i (only a few)
 |-
-! colspan="3" rowspan="1" |Power statistics brackets
+! colspan="3" style="white-space: nowrap;" | Power statistics brackets
 |-
-|<nowiki>⎄⎄|| or ⎄||</nowiki>
+| ⎄{{pipe}} {{pipe}}
-|‖
+| ‖
-|power-norm bracket
+| Power-norm bracket
 |-
-|<nowiki>⎄|-1</nowiki>
+| ⎄{{pipe}}-1
-|‖₁
+| ‖₁
-|1-norm right bracket
+| 1-Norm right bracket
 |-
-|<nowiki>⎄|-2</nowiki>
+| ⎄{{pipe}}-2
-|‖₂
+| ‖₂
-|2-norm right bracket
+| 2-Norm right bracket
 |-
-|<nowiki>⎄|-8</nowiki>
+| ⎄{{pipe}}-8
-|‖ ͚
+| ‖ ͚
-|∞-norm right bracket
+| ∞-Norm right bracket
 |-
-|⎄⎄<<
+| ⎄⎄<<
-|⟪
+| ⟪
-| left power-mean bracket
+| Left power-mean bracket
 |-
-|⎄⎄>>
+| ⎄⎄>>
-|⟫
+| ⟫
-|right power-mean bracket
+| Right power-mean bracket
 |-
-|<nowiki>⎄⎄{{</nowiki>
+| ⎄⎄{{((}}
-|⧛
+| ⧛
-|left power-sum bracket (substitute for {{llzigzag}} when HTML is not available)
+| Left power-sum bracket (substitute for {{llzz}} when HTML is not available)
 |-
-|<nowiki>⎄⎄}}</nowiki>
+| ⎄⎄{{))}}
 | ⧚
-|right power-sum bracket (substitute for {{rrzigzag}} when HTML is not available)
+| Right power-sum bracket (substitute for {{rrzz}} when HTML is not available)
 |-
-! colspan="3" rowspan="1" |Combining marks
+! colspan="3" style="white-space: nowrap;" | Combining marks
 |-
-|⎄\-
+| ⎄\-
 | ◌̶
-|combining strike-thru
+| Combining strike-thru
 |-
-|⎄^_
+| ⎄^_
-|◌̅
+| ◌̅
-|combining overline
+| Combining overline
 |-
-|⎄__
+| ⎄__
-|◌̲
+| ◌̲
-|combining low line
+| Combining low line
 |-
-|⎄-_ or ⎄_- or ⎄_^
+| ⎄;; or ⎄-_ or ⎄_^
-|◌̲̅
+| ◌̲̅
-|combining overline and low line (undirected value)
+| Combining overline and low line (undirected value)
-|}
-===Keyboard map===
-{| class="wikitable mw-collapsible mw-collapsed"
-|+
-|[[File:WinCompose keyboard map.png|1000px]]
 |}
-== Footnotes==
+=== Keyboard map ===
+[[File:WinCompose keyboard map.png|1000px]]
-<references />
+== Footnotes ==
+<references group="note" />
-[[Category:Regular temperament theory]]
+[[Category:Dave Keenan & Douglas Blumeyer's guide to RTT]]
 [[Category:Tuning]]

Dave Keenan & Douglas Blumeyer's guide to RTT/Conventions for names, variables, units, and notations: Difference between revisions

Latest revision as of 01:44, 7 August 2025

Basic

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