-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}.
+
+
HCoop / bpt / emacs.git / blobdiff