@end quotation
@end copying
-@dircategory Emacs
+@dircategory Emacs misc features
@direntry
* Calc: (calc). Advanced desk calculator and mathematical tool.
@end direntry
* Predefined Units::
* User-Defined Units::
* Logarithmic Units::
+* Musical Notes::
@end menu
@node Basic Operations on Units, The Units Table, Units, Units
is replaced by the new set. (@xref{General Mode Commands}, for a way to
tell Calc to use a different file for the Calc init file.)
-@node Logarithmic Units, , User-Defined Units, Units
+@node Logarithmic Units, Musical Notes, User-Defined Units, Units
@section Logarithmic Units
The units @code{dB} (decibels) and @code{Np} (nepers) are logarithmic
-units which are typically manipulated differently than standard units.
-Calc provides commands to work with these logarithmic units.
+units which are manipulated differently than standard units. Calc
+provides commands to work with these logarithmic units.
Decibels and nepers are used to measure power quantities as well as
-field quantities (quantities whose squares are proportional to power).
-The decibel and neper values of a quantity are relative to
-a reference quantity; for example, the decibel value of a sound
-pressure level of
-@infoline @math{60 uPa}
-@texline @math{60 \mu{\rm Pa}}
-relative to
-@infoline @math{20 uPa}
-@texline @math{20 \mu{\rm Pa}}
-(the threshhold of human hearing) is
-@infoline @math{20 log10(60 uPa/ 20 uPa) dB = 20 log10(3) dB},
-@texline @math{20 \log_{10}(60 \mu{\rm Pa}/20 \mu{\rm Pa}) {\rm dB} = 20 \log_{10}(3) {\rm dB}},
-which is about
-@infoline @math{9.54 dB}.
-@texline @math{9.54 {\rm dB}}.
-Note that in taking the ratio, the original units cancel and so these
-logarithmic units are dimensionless.
-
-@vindex calc-logunits-power-reference
-@vindex calc-logunits-field-reference
-The Calc commands for the logarithmic units assume that power quantities
-are being used unless the @kbd{H} prefix is used, in which case they assume that
-field quantities are being used. For power quantities, Calc uses
-@infoline @math{1 mW}
-@texline @math{1 {\rm mW}}
-as the default reference quantity; this default can be changed by changing
-the value of the customizable variable
-@code{calc-logunits-power-reference} (@pxref{Customizing Calc}).
-For field quantities, Calc uses
-@infoline @math{20 uPa}
-@texline @math{20 \mu{\rm Pa}}
-as the default reference quantity; this is the value used in acoustics
-which is where decibels are commonly encountered. This default can be
-changed by changing the value of the customizable variable
-@code{calc-logunits-field-reference} (@pxref{Customizing Calc}). A
-non-default reference quantity will be read from the stack if the
-capital @kbd{O} prefix is used.
+field quantities (quantities whose squares are proportional to power);
+these two types of quantities are handled slightly different from each
+other. By default the Calc commands work as if power quantities are
+being used; with the @kbd{H} prefix the Calc commands work as if field
+quantities are being used.
The decibel level of a power
@infoline @math{P1},
is defined as
@infoline @math{20 log10(F1/F0) dB}.
@texline @math{20 \log_{10}(F_{1}/F_{0}) {\rm dB}}.
+For example, the decibel value of a sound pressure level of
+@infoline @math{60 uPa}
+@texline @math{60 \mu{\rm Pa}}
+relative to
+@infoline @math{20 uPa}
+@texline @math{20 \mu{\rm Pa}}
+(the threshhold of human hearing) is
+@infoline @math{20 log10(60 uPa/ 20 uPa) dB = 20 log10(3) dB},
+@texline @math{20 \log_{10}(60 \mu{\rm Pa}/20 \mu{\rm Pa}) {\rm dB} = 20 \log_{10}(3) {\rm dB}},
+which is about
+@infoline @math{9.54 dB}.
+@texline @math{9.54 {\rm dB}}.
+Note that in taking the ratio, the original units cancel and so these
+logarithmic units are dimensionless.
Nepers (named after John Napier, who is credited with inventing the
logarithm) are similar to bels except they use natural logarithms instead
@infoline @math{ln(F1/F0) Np}.
@texline @math{\ln(F_1/F_0) {\rm Np}}.
+@vindex calc-lu-power-reference
+@vindex calc-lu-field-reference
+For power quantities, Calc uses
+@infoline @math{1 mW}
+@texline @math{1 {\rm mW}}
+as the default reference quantity; this default can be changed by changing
+the value of the customizable variable
+@code{calc-lu-power-reference} (@pxref{Customizing Calc}).
+For field quantities, Calc uses
+@infoline @math{20 uPa}
+@texline @math{20 \mu{\rm Pa}}
+as the default reference quantity; this is the value used in acoustics
+which is where decibels are commonly encountered. This default can be
+changed by changing the value of the customizable variable
+@code{calc-lu-field-reference} (@pxref{Customizing Calc}). A
+non-default reference quantity will be read from the stack if the
+capital @kbd{O} prefix is used.
+
@kindex l q
-@pindex calc-logunits-quantity
-@tindex powerquant
-@tindex fieldquant
-The @kbd{l q} (@code{calc-logunits-quantity}) [@code{powerquant}]
+@pindex calc-lu-quant
+@tindex lupquant
+@tindex lufquant
+The @kbd{l q} (@code{calc-lu-quant}) [@code{lupquant}]
command computes the power quantity corresponding to a given number of
logarithmic units. With the capital @kbd{O} prefix, @kbd{O l q}, the
reference level will be read from the top of the stack. (In an
-algebraic formula, @code{powerquant} can be given an optional second
+algebraic formula, @code{lupquant} can be given an optional second
argument which will be used for the reference level.) For example,
@code{20 dB @key{RET} l q} will return @code{100 mW};
@code{20 dB @key{RET} 4 W @key{RET} O l q} will return @code{400 W}.
-The @kbd{H l q} [@code{fieldquant}] command behaves like @kbd{l q} but
+The @kbd{H l q} [@code{lufquant}] command behaves like @kbd{l q} but
computes field quantities instead of power quantities.
@kindex l d
-@pindex calc-logunits-dblevel
-@tindex dbpowerlevel
-@tindex dbfieldlevel
+@pindex calc-db
+@tindex dbpower
+@tindex dbfield
@kindex l n
-@pindex calc-logunits-nplevel
-@tindex nppowerlevel
-@tindex npfieldlevel
-The @kbd{l d} (@code{calc-logunits-dblevel}) [@code{dbpowerlevel}]
-command will compute the decibel level of a power quantity using the
-default reference level; @kbd{H l d} [@code{dbfieldlevel}] will
-compute the decibel level of a field quantity. The commands @kbd{l n}
-(@code{calc-logunits-nplevel}) [@code{nppowerlevel}] and @kbd{H l n}
-[@code{npfieldlevel}] will similarly compute neper levels. With the
-capital @kbd{O} prefix these commands will read a reference level
-from the stack; in an algebraic formula the reference level can be
-given as an optional second argument.
+@pindex calc-np
+@tindex nppower
+@tindex npfield
+The @kbd{l d} (@code{calc-db}) [@code{dbpower}] command will compute
+the decibel level of a power quantity using the default reference
+level; @kbd{H l d} [@code{dbfield}] will compute the decibel level of
+a field quantity. The commands @kbd{l n} (@code{calc-np})
+[@code{nppower}] and @kbd{H l n} [@code{npfield}] will similarly
+compute neper levels. With the capital @kbd{O} prefix these commands
+will read a reference level from the stack; in an algebraic formula
+the reference level can be given as an optional second argument.
@kindex l +
-@pindex calc-logunits-add
-@tindex lupoweradd
-@tindex lufieldadd
+@pindex calc-lu-plus
+@tindex lupadd
+@tindex lufadd
@kindex l -
-@pindex calc-logunits-sub
-@tindex lupowersub
-@tindex lufieldsub
+@pindex calc-lu-minus
+@tindex lupsub
+@tindex lufsub
@kindex l *
-@pindex calc-logunits-mul
-@tindex lupowermul
-@tindex lufieldmul
+@pindex calc-lu-times
+@tindex lupmul
+@tindex lufmul
@kindex l /
-@pindex calc-logunits-div
-@tindex lupowerdiv
-@tindex lufielddiv
+@pindex calc-lu-divide
+@tindex lupdiv
+@tindex lufdiv
The sum of two power or field quantities doesn't correspond to the sum
of the corresponding decibel or neper levels. If the powers
corresponding to decibel levels
@end tex
@noindent
-When field quantities are combined, it often means the
-corresponding powers are added and so the above formula might be used.
-In acoustics, for example, the decibel sound pressure level is defined
-using the field formula but the sound pressure levels are combined
-as the sound power levels, and so the above formula should be used. If
-two field quantities themselves are added, the new decibel level will be
-
+When field quantities are combined, it often means the corresponding
+powers are added and so the above formula might be used. In
+acoustics, for example, the sound pressure level is a field quantity
+and so the decibels are often defined using the field formula, but the
+sound pressure levels are combined as the sound power levels, and so
+the above formula should be used. If two field quantities themselves
+are added, the new decibel level will be
@ifnottex
@example
@end tex
@noindent
-There are similar formulas for combining nepers.
-The @kbd{l +} (@code{calc-logunits-add}) [@code{lupoweradd}] command
-will ``add'' two logarithmic unit power levels this way; with the
-@kbd{H} prefix, @kbd{H l +} [@code{lufieldadd}] will add logarithmic
-unit field levels. Similarly, logarithmic units can be
-``subtracted'' with @kbd{l -} (@code{calc-logunits-sub})
-[@code{lupowersub}] or @kbd{H l -} [@code{lufieldsub}].
-The @kbd{l *} (@code{calc-logunits-mul}) [@code{lupowermul}]
-and @kbd{H l *} [@code{lufieldmul}] commands will ``multiply''
-a logarithmic unit by a number; the @kbd{l /}
-(@code{calc-logunits-divide}) [@code{lupowerdiv}] and
-@kbd{H l /} [@code{lufielddiv}] commands will ``divide'' a
-logarithmic unit by a number. Note that the reference quantities don't
-play a role in this arithmetic.
+There are similar formulas for combining nepers. The @kbd{l +}
+(@code{calc-lu-plus}) [@code{lupadd}] command will ``add'' two
+logarithmic unit power levels this way; with the @kbd{H} prefix,
+@kbd{H l +} [@code{lufadd}] will add logarithmic unit field levels.
+Similarly, logarithmic units can be ``subtracted'' with @kbd{l -}
+(@code{calc-lu-minus}) [@code{lupsub}] or @kbd{H l -} [@code{lufsub}].
+The @kbd{l *} (@code{calc-lu-times}) [@code{lupmul}] and @kbd{H l *}
+[@code{lufmul}] commands will ``multiply'' a logarithmic unit by a
+number; the @kbd{l /} (@code{calc-lu-divide}) [@code{lupdiv}] and
+@kbd{H l /} [@code{lufdiv}] commands will ``divide'' a logarithmic
+unit by a number. Note that the reference quantities don't play a role
+in this arithmetic.
+
+@node Musical Notes, , Logarithmic Units, Units
+@section Musical Notes
+
+Calc can convert between musical notes and their associated
+frequencies. Notes can be given using either scientific pitch
+notation or midi numbers. Since these note systems are basically
+logarithmic scales, Calc uses the @kbd{l} prefix for functions
+operating on notes.
+
+Scientific pitch notation refers to a note by giving a letter
+A through G, possibly followed by a flat or sharp) with a subscript
+indicating an octave number. Each octave starts with C and ends with
+B and
+@c increasing each note by a semitone will result
+@c in the sequence @expr{C}, @expr{C} sharp, @expr{D}, @expr{E} flat, @expr{E},
+@c @expr{F}, @expr{F} sharp, @expr{G}, @expr{A} flat, @expr{A}, @expr{B}
+@c flat and @expr{B}.
+the octave numbered 0 was chosen to correspond to the lowest
+audible frequency. Using this system, middle C (about 261.625 Hz)
+corresponds to the note @expr{C} in octave 4 and is denoted
+@expr{C_4}. Any frequency can be described by giving a note plus an
+offset in cents (where a cent is a ratio of frequencies so that a
+semitone consists of 100 cents).
+
+The midi note number system assigns numbers to notes so that
+@expr{C_(-1)} corresponds to the midi note number 0 and @expr{G_9}
+corresponds to the midi note number 127. A midi controller can have
+up to 128 keys and each midi note number from 0 to 127 corresponds to
+a possible key.
+
+@kindex l s
+@pindex calc-spn
+@tindex spn
+The @kbd{l s} (@code{calc-spn}) [@code{spn}] command converts either
+a frequency or a midi number to scientific pitch notation. For
+example, @code{500 Hz} gets converted to
+@code{B_4 + 21.3094853649 cents} and @code{84} to @code{C_6}.
+
+
+@kindex l m
+@pindex calc-midi
+@tindex midi
+The @kbd{l m} (@code{calc-midi}) [@code{midi}] command converts either
+a frequency or a note given in scientific pitch notation to the
+corresponding midi number. For example, @code{C_6} gets converted to 84
+and @code{440 Hz} to 69.
+
+@kindex l f
+@pindex calc-freq
+@tindex freq
+The @kbd{l f} (@code{calc-freq}) [@code{freq}] command converts either
+either a midi number or a note given in scientific pitch notation to
+the corresponding frequency. For example, @code{Asharp_2 + 30 cents}
+gets converted to @code{118.578040134 Hz} and @code{55} to
+@code{195.99771799 Hz}.
+
+Since the frequencies of notes are not usually given exactly (and are
+typically irrational), the customizable variable
+@code{calc-note-threshold} determines how close (in cents) a frequency
+needs to be to a note to be recognized as that note
+(@pxref{Customizing Calc}). This variable has a default value of
+@code{1}. For example, middle @var{C} is approximately
+@expr{261.625565302 Hz}; this frequency is often shortened to
+@expr{261.625 Hz}. Without @code{calc-note-threshold} (or a value of
+@expr{0}), Calc would convert @code{261.625 Hz} to scientific pitch
+notation @code{B_3 + 99.9962592773 cents}; with the default value of
+@code{1}, Calc converts @code{261.625 Hz} to @code{C_4}.
+
+
@node Store and Recall, Graphics, Units, Top
@chapter Storing and Recalling
and @code{calc-embedded-open-close-plain-alist}.
@end defvar
-@defvar calc-logunits-power-reference
-@defvarx calc-logunits-field-reference
+@defvar calc-lu-power-reference
+@defvarx calc-lu-field-reference
See @ref{Logarithmic Units}.@*
-The variables @code{calc-logunits-power-reference} and
-@code{calc-logunits-field-reference} are unit expressions (written as
+The variables @code{calc-lu-power-reference} and
+@code{calc-lu-field-reference} are unit expressions (written as
strings) which Calc will use as reference quantities for logarithmic
units.
-The default value of @code{calc-logunits-power-reference} is @code{"mW"}
-and the default value of @code{calc-logunits-field-reference} is
+The default value of @code{calc-lu-power-reference} is @code{"mW"}
+and the default value of @code{calc-lu-field-reference} is
@code{"20 uPa"}.
@end defvar
+@defvar calc-note-threshold
+See @ref{Musical Notes}.@*
+The variable @code{calc-note-threshold} is a number (written as a
+string) which determines how close (in cents) a frequency needs to be
+to a note to be recognized as that note.
+
+The default value of @code{calc-note-threshold} is 1.
+@end defvar
+
@defvar calc-highlight-selections-with-faces
@defvarx calc-selected-face
@defvarx calc-nonselected-face
@r{ v x@: I k T @: @: @:ltpt@:(x,v)}
@c
-@r{ a b@: l + @: @: 2 @:lupoweradd@:(a,b)}
-@r{ a b@: H l + @: @: 2 @:lufieldadd@:(a,b)}
-@r{ a b@: l - @: @: 2 @:lupowersub@:(a,b)}
-@r{ a b@: H l - @: @: 2 @:lufieldsub@:(a,b)}
-@r{ a b@: l * @: @: 2 @:lupowermul@:(a,b)}
-@r{ a b@: H l * @: @: 2 @:lufieldmul@:(a,b)}
-@r{ a b@: l / @: @: 2 @:lupowerdiv@:(a,b)}
-@r{ a b@: H l / @: @: 2 @:lufielddiv@:(a,b)}
-@r{ a@: l d @: @: 1 @:dbpowerlevel@:(a)}
-@r{ a b@: O l d @: @: 2 @:dbpowerlevel@:(a,b)}
-@r{ a@: H l d @: @: 1 @:dbfieldlevel@:(a)}
-@r{ a b@: O H l d @: @: 2 @:dbfieldlevel@:(a,b)}
-@r{ a@: l n @: @: 1 @:nppowerlevel@:(a)}
-@r{ a b@: O l n @: @: 2 @:nppowerlevel@:(a,b)}
-@r{ a@: H l n @: @: 1 @:npfieldlevel@:(a)}
-@r{ a b@: O H l n @: @: 2 @:npfieldlevel@:(a,b)}
-@r{ a@: l q @: @: 1 @:powerquant@:(a)}
-@r{ a b@: O l q @: @: 2 @:powerquant@:(a,b)}
-@r{ a@: H l q @: @: 1 @:fieldquant@:(a)}
-@r{ a b@: O H l q @: @: 2 @:fieldquant@:(a,b)}
+@r{ a b@: l + @: @: @:lupadd@:(a,b)}
+@r{ a b@: H l + @: @: @:lufadd@:(a,b)}
+@r{ a b@: l - @: @: @:lupsub@:(a,b)}
+@r{ a b@: H l - @: @: @:lufsub@:(a,b)}
+@r{ a b@: l * @: @: @:lupmul@:(a,b)}
+@r{ a b@: H l * @: @: @:lufmul@:(a,b)}
+@r{ a b@: l / @: @: @:lupdiv@:(a,b)}
+@r{ a b@: H l / @: @: @:lufdiv@:(a,b)}
+@r{ a@: l d @: @: @:dbpower@:(a)}
+@r{ a b@: O l d @: @: @:dbpower@:(a,b)}
+@r{ a@: H l d @: @: @:dbfield@:(a)}
+@r{ a b@: O H l d @: @: @:dbfield@:(a,b)}
+@r{ a@: l n @: @: @:nppower@:(a)}
+@r{ a b@: O l n @: @: @:nppower@:(a,b)}
+@r{ a@: H l n @: @: @:npfield@:(a)}
+@r{ a b@: O H l n @: @: @:npfield@:(a,b)}
+@r{ a@: l q @: @: @:lupquant@:(a)}
+@r{ a b@: O l q @: @: @:lupquant@:(a,b)}
+@r{ a@: H l q @: @: @:lufquant@:(a)}
+@r{ a b@: O H l q @: @: @:lufquant@:(a,b)}
+@r{ a@: l s @: @: @:spn@:(a)}
+@r{ a@: l m @: @: @:midi@:(a)}
+@r{ a@: l f @: @: @:freq@:(a)}
@c
@r{ @: m a @: @: 12,13 @:calc-algebraic-mode@:}
HCoop / bpt / emacs.git / blobdiff