* calc.texi (Logarithmic Units): Rename calc-logunits-dblevel
and calc-logunits-nplevel to calc-dblevel and calc-nplevel,
respectively.
+ (Musical Notes): New section.
+ (Customizing Calc): Mention the customizable variable
+ calc-note-threshold.
2011-03-03 Glenn Morris <rgm@gnu.org>
* 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
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
@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 + @: @: @:lupoweradd@:(a,b)}
+@r{ a b@: H l + @: @: @:lufieldadd@:(a,b)}
+@r{ a b@: l - @: @: @:lupowersub@:(a,b)}
+@r{ a b@: H l - @: @: @:lufieldsub@:(a,b)}
+@r{ a b@: l * @: @: @:lupowermul@:(a,b)}
+@r{ a b@: H l * @: @: @:lufieldmul@:(a,b)}
+@r{ a b@: l / @: @: @:lupowerdiv@:(a,b)}
+@r{ a b@: H l / @: @: @:lufielddiv@:(a,b)}
+@r{ a@: l d @: @: @:dbpowerlevel@:(a)}
+@r{ a b@: O l d @: @: @:dbpowerlevel@:(a,b)}
+@r{ a@: H l d @: @: @:dbfieldlevel@:(a)}
+@r{ a b@: O H l d @: @: @:dbfieldlevel@:(a,b)}
+@r{ a@: l n @: @: @:nppowerlevel@:(a)}
+@r{ a b@: O l n @: @: @:nppowerlevel@:(a,b)}
+@r{ a@: H l n @: @: @:npfieldlevel@:(a)}
+@r{ a b@: O H l n @: @: @:npfieldlevel@:(a,b)}
+@r{ a@: l q @: @: @:powerquant@:(a)}
+@r{ a b@: O l q @: @: @:powerquant@:(a,b)}
+@r{ a@: H l q @: @: @:fieldquant@:(a)}
+@r{ a b@: O H l q @: @: @:fieldquant@:(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@:}
* calc/calc-ext.el (calc-init-extensions):
Rename calc-logunits-dblevel and calc-logunits-nplevel to
calc-dblevel and calc-nplevel, respectively.
+ Add keybindings for calc-spn, calc-midi and calc-freq. Add
+ autoloads for calcFunc-spn, calcFunc-midi, calcFunc-freq,
+ calc-spn, calc-midi and calc-freq.
* calc/calc-units.el (calc-dblevel): Rename from
calc-logunits-dblevel.
(calc-nplevel): Rename from calc-logunits-nplevel.
+ (math-midi-round, math-freqp, math-midip, math-spnp)
+ (math-spn-to-midi, math-midi-to-spn, math-freq-to-spn)
+ (math-midi-to-freq, math-spn-to-freq, calcFunc-spn, calcFunc-midi)
+ (calcFunc-freq, calc-freq, calc-midi, calc-spn): New functions.
+ (math-notes): New variable.
+
+ * calc/calc.el (calc-note-threshold): New variable.
2011-03-06 Chong Yidong <cyd@stupidchicken.com>
(define-key calc-mode-map "l-" 'calc-logunits-sub)
(define-key calc-mode-map "l*" 'calc-logunits-mul)
(define-key calc-mode-map "l/" 'calc-logunits-divide)
+ (define-key calc-mode-map "ls" 'calc-spn)
+ (define-key calc-mode-map "lm" 'calc-midi)
+ (define-key calc-mode-map "lf" 'calc-freq)
+
(define-key calc-mode-map "l?" 'calc-l-prefix-help)
(define-key calc-mode-map "m" nil)
calcFunc-lufieldmul calcFunc-lupowermul calcFunc-lufielddiv
calcFunc-lupowerdiv calcFunc-fieldquant calcFunc-powerquant
calcFunc-dbfieldlevel calcFunc-dbpowerlevel calcFunc-npfieldlevel
-calcFunc-nppowerlevel
+calcFunc-nppowerlevel calcFunc-spn calcFunc-midi calcFunc-freq
math-build-units-table math-build-units-table-buffer
math-check-unit-name math-convert-temperature math-convert-units
math-extract-units math-remove-units math-simplify-units
calc-remove-units calc-simplify-units calc-undefine-unit
calc-view-units-table calc-logunits-quantity calc-dblevel
calc-nplevel calc-logunits-add calc-logunits-sub
-calc-logunits-mul calc-logunits-divide)
+calc-logunits-mul calc-logunits-divide calc-spn calc-midi
+calc-freq)
("calc-vec" calc-arrange-vector calc-build-vector calc-cnorm
calc-conj-transpose calc-cons calc-cross calc-kron calc-diag
(calc-binary-op "lunp" 'calcFunc-nppowerlevel arg)
(calc-unary-op "lunp" 'calcFunc-nppowerlevel arg)))))
+;;; Musical notes
+
+
+(defvar calc-note-threshold)
+
+(defun math-midi-round (num)
+ "Round NUM to an integer N if NUM is within calc-note-threshold cents of N."
+ (let* ((n (math-round num))
+ (diff (math-abs
+ (math-sub num n))))
+ (if (< (math-compare diff (math-read-expr calc-note-threshold)) 0)
+ n
+ num)))
+
+(defconst math-notes
+ '(((var C var-C) . 0)
+ ((var Csharp var-Csharp) . 1)
+; ((var C♯ var-C♯) . 1)
+ ((var Dflat var-Dflat) . 1)
+; ((var D♭ var-D♭) . 1)
+ ((var D var-D) . 2)
+ ((var Dsharp var-Dsharp) . 3)
+; ((var D♯ var-D♯) . 3)
+ ((var E var-E) . 4)
+ ((var F var-F) . 5)
+ ((var Fsharp var-Fsharp) . 6)
+; ((var F♯ var-F♯) . 6)
+ ((var Gflat var-Gflat) . 6)
+; ((var G♭ var-G♭) . 6)
+ ((var G var-G) . 7)
+ ((var Gsharp var-Gsharp) . 8)
+; ((var G♯ var-G♯) . 8)
+ ((var A var-A) . 9)
+ ((var Asharp var-Asharp) . 10)
+; ((var A♯ var-A♯) . 10)
+ ((var Bflat var-Bflat) . 10)
+; ((var B♭ var-B♭) . 10)
+ ((var B var-B) . 11))
+ "An alist of notes with their number of semitones above C.")
+
+(defun math-freqp (freq)
+ "Non-nil if FREQ is a positive number times the unit Hz.
+If non-nil, return the coefficient of Hz."
+ (let ((freqcoef (math-simplify-units
+ (math-div freq '(var Hz var-Hz)))))
+ (if (Math-posp freqcoef) freqcoef)))
+
+(defun math-midip (num)
+ "Non-nil if NUM is a possible MIDI note number.
+If non-nil, return NUM."
+ (if (Math-numberp num) num))
+
+(defun math-spnp (spn)
+ "Non-nil if NUM is a scientific pitch note (note + cents).
+If non-nil, return a list consisting of the note and the cents coefficient."
+ (let (note cents rnote rcents)
+ (if (eq (car-safe spn) '+)
+ (setq note (nth 1 spn)
+ cents (nth 2 spn))
+ (setq note spn
+ cents nil))
+ (cond
+ ((and ;; NOTE is a note, CENTS is nil or cents.
+ (eq (car-safe note) 'calcFunc-subscr)
+ (assoc (nth 1 note) math-notes)
+ (integerp (nth 2 note))
+ (setq rnote note)
+ (or
+ (not cents)
+ (Math-numberp (setq rcents
+ (math-simplify
+ (math-div cents '(var cents var-cents)))))))
+ (list rnote rcents))
+ ((and ;; CENTS is a note, NOTE is cents.
+ (eq (car-safe cents) 'calcFunc-subscr)
+ (assoc (nth 1 cents) math-notes)
+ (integerp (nth 2 cents))
+ (setq rnote cents)
+ (or
+ (not note)
+ (Math-numberp (setq rcents
+ (math-simplify
+ (math-div note '(var cents var-cents)))))))
+ (list rnote rcents)))))
+
+(defun math-freq-to-midi (freq)
+ "Return the midi note number corresponding to FREQ Hz."
+ (let ((midi (math-add
+ 69
+ (math-mul
+ 12
+ (calcFunc-log
+ (math-div freq 440)
+ 2)))))
+ (math-midi-round midi)))
+
+(defun math-spn-to-midi (spn)
+ "Return the MIDI number corresponding to SPN."
+ (let* ((note (cdr (assoc (nth 1 (car spn)) math-notes)))
+ (octave (math-add (nth 2 (car spn)) 1))
+ (cents (nth 1 spn))
+ (midi (math-add
+ (math-mul 12 octave)
+ note)))
+ (if cents
+ (math-add midi (math-div cents 100))
+ midi)))
+
+(defun math-midi-to-spn (midi)
+ "Return the scientific pitch notation corresponding to midi number MIDI."
+ (let (midin cents)
+ (if (math-integerp midi)
+ (setq midin midi
+ cents nil)
+ (setq midin (math-floor midi)
+ cents (math-mul 100 (math-sub midi midin))))
+ (let* ((nr ;; This should be (math-idivmod midin 12), but with
+ ;; better behavior for negative midin.
+ (if (Math-negp midin)
+ (let ((dm (math-idivmod (math-neg midin) 12)))
+ (if (= (cdr dm) 0)
+ (cons (math-neg (car dm)) 0)
+ (cons
+ (math-sub (math-neg (car dm)) 1)
+ (math-sub 12 (cdr dm)))))
+ (math-idivmod midin 12)))
+ (n (math-sub (car nr) 1))
+ (note (car (rassoc (cdr nr) math-notes))))
+ (if cents
+ (list '+ (list 'calcFunc-subscr note n)
+ (list '* cents '(var cents var-cents)))
+ (list 'calcFunc-subscr note n)))))
+
+(defun math-freq-to-spn (freq)
+ "Return the scientific pitch notation corresponding to FREQ Hz."
+ (math-with-extra-prec 3
+ (math-midi-to-spn (math-freq-to-midi freq))))
+
+(defun math-midi-to-freq (midi)
+ "Return the frequency of the note with midi number MIDI."
+ (list '*
+ (math-mul
+ 440
+ (math-pow
+ 2
+ (math-div
+ (math-sub
+ midi
+ 69)
+ 12)))
+ '(var Hz var-Hz)))
+
+(defun math-spn-to-freq (spn)
+ "Return the frequency of the note with scientific pitch notation SPN."
+ (math-midi-to-freq (math-spn-to-midi spn)))
+
+(defun calcFunc-spn (expr)
+ "Return EXPR written as scientific pitch notation + cents."
+ ;; Get the coeffecient of Hz
+ (let (note)
+ (cond
+ ((setq note (math-freqp expr))
+ (math-freq-to-spn note))
+ ((setq note (math-midip expr))
+ (math-midi-to-spn note))
+ ((math-spnp expr)
+ expr)
+ (t
+ (math-reject-arg expr "*Improper expression")))))
+
+(defun calcFunc-midi (expr)
+ "Return EXPR written as a MIDI number."
+ (let (note)
+ (cond
+ ((setq note (math-freqp expr))
+ (math-freq-to-midi note))
+ ((setq note (math-spnp expr))
+ (math-spn-to-midi note))
+ ((math-midip expr)
+ expr)
+ (t
+ (math-reject-arg expr "*Improper expression")))))
+
+(defun calcFunc-freq (expr)
+ "Return the frequency corresponding to EXPR."
+ (let (note)
+ (cond
+ ((setq note (math-midip expr))
+ (math-midi-to-freq note))
+ ((setq note (math-spnp expr))
+ (math-spn-to-freq note))
+ ((math-freqp expr)
+ expr)
+ (t
+ (math-reject-arg expr "*Improper expression")))))
+
+(defun calc-freq (arg)
+ "Return the frequency corresponding to the expression on the stack."
+ (interactive "P")
+ (calc-slow-wrapper
+ (calc-unary-op "freq" 'calcFunc-freq arg)))
+
+(defun calc-midi (arg)
+ "Return the MIDI number corresponding to the expression on the stack."
+ (interactive "P")
+ (calc-slow-wrapper
+ (calc-unary-op "midi" 'calcFunc-midi arg)))
+
+(defun calc-spn (arg)
+ "Return the scientific pitch notation corresponding to the expression on the stack."
+ (interactive "P")
+ (calc-slow-wrapper
+ (calc-unary-op "spn" 'calcFunc-spn arg)))
+
+
(provide 'calc-units)
;; Local variables:
:group 'calc
:type '(string))
+(defcustom calc-note-threshold "1"
+ "The number of cents that a frequency should be near a note
+to be identified as that note."
+ :type 'string
+ :group 'calc)
(defface calc-nonselected-face
'((t :inherit shadow
HCoop / bpt / emacs.git / commitdiff