%%splittune
%%textfont Helvetica 14
%%scale .9


%%begintext obeylines
=================
temperamentlinear
=================
%%endtext
%%begintext justify
Microtone accidentals can be used along with temperamentlinear. 

In that case, the accidental ratio is based on the new chromatic semitone size,
defined as 7 fifths minus 4 octaves. (Run abc2midi with the verbose
option (-v) to see the temperament values.)

As an exception, the microtonal deviation in cents can be represented
by using denominator=100 in the accidentals. Example:
%%endtext

X:1
T:\%\%MIDI temperamentlinear - microtone accidentals in cents
%%postscript /ft5475{M -3 3 RM 6 -6 RL 2 SLW stroke}def
%%postscript /ft35939{2 copy ft0 M -7.5 -3 RM 12 F3 (7) show}def
M:none
K:C
%%scale 1.3
V:1
%%MIDI program 17
%%MIDI temperamentlinear 1200 702 %% Pythagorian tunings
%%MIDI makechordchannels 3
"^Pure;major;chord"\
[C_22/100EG]8 y |\
"^Pythagorian;major;chord"\
[CEG]8 y ||\
"^Pure;4:5:6:7;chord"\
[C_22/100EG_141/100B]8 y |\
"^Pythagorean;7-chord"\
[CEG_B]8 y ||

%%newpage

%%begintext obeylines
================
temperamentequal
================
%%endtext
%%begintext justify
New command.

\%\%MIDI temperamentequal <ndiv> [octave_cents] [fifth_steps] [sharp_steps]

This commans sets a tempered scale defined by 'ndiv' equal divisions
of 'octave_cents' (default is the octave = 1200 cents).

The optional parameter 'fifth_steps', if provided, is an integer that 
defines the size of the fifth in steps of the temperament.
This sets where is the note G in the temperament.

When 'fifth_steps' is omited or 0 (zero), the program computes it
as an approximation of the frequency ratio 3/1, minus the
(possibly tempered) octave.

The optional 'sharp_steps' defines the meaning of the accidentals.
'sharp_steps' is the number of steps between a natural note and
a sharpened note (e.g. between =C and ^C).

By default, the size of a sharp/flat deviation is based on the
size of the chromatic semitone in the specified temperament: 7 fifths minus
4 octaves. The values in use in the temperament can be viewed
by running abc2midi with the command-line option -v (verbose).

With temperamentequal (as with temperamentlinear), microtone accidentals
are interpreted as fractions of the sharp size in the
specified temperament, except if they use denominator=100, which
defines microtonal deviations in cents.

The conventional temperament can be reset with the command temperamentnormal.


See also: temperamentlinear, temperamentnormal, makechordchannels


Example:
%%endtext

X:2
T:\%\%MIDI temperamentequal
%%stretchlast 1
M:none
L:1/2
K:C
V:1
%%MIDI program 44
%%MIDI makechordchannels 3
%
%%text \%\%MIDI temperamentequal 7 1200 4 \% N.B.: fifth = 4 steps
%%MIDI temperamentequal 7 1200 4 % N.B.: fifth = 4 steps
"^Octave divided in 7 equal parts"\
c d e f g a b c' & [I:MIDI=program 44] C8 | [CEGc]2 z |
%
%%text \%\%MIDI temperamentequal 17
%%MIDI temperamentequal 17
"^Octave divided in 17 equal parts"\
=c ^/c ^c =d _/d _d =c & C7 | [CEGc]2 z |
%
%%text \%\%MIDI temperamentequal 22 \% N.B.: 1/3-sharps
%%postscript /sh2{M 0 -5 RM 14 F3 (/) show}bind def
%%postscript /sh258{2 copy M -7.5 -5 RM 14 F3 (\\) show sh0}bind def
%%postscript /ft2{M 0 -5 RM 14 F3 (\\) show}bind def
%%postscript /ft258{2 copy M -7.5 -5 RM 14 F3 (/) show ft0}bind def
%%MIDI temperamentequal 22 % N.B.: 1/3-sharps
"^Octave divided in 22 equal parts"\
=c ^1/3c ^2/3c ^c =d _1/3d _2/3d _d =c & C8-C | [C_1/3EGc]2 z |
%
%%text \%\%MIDI temperamentequal 31
%%MIDI temperamentequal 31
"^Octave divided in 31 equal parts"\
=c ^/c ^c ^3/c ^^c =d _/d _d _3/d __d =c2 & C12 | [CEGc]2 z |
%
%%text \%\%MIDI temperamentequal 19
%%MIDI temperamentequal 19
"^Octave divided in 19 equal parts"\
=c ^c ^^c =d _d __d =c & C7 | [CEGc]2 z |
%
%%text \%\%MIDI temperamentequal 19 1205
%%MIDI temperamentequal 19 1205
"^Streched octave (1205 cents) divided in 19 equal parts"\
=c ^c ^^c =d _d __d =c & C7 | [CEGc]2 z |
%
%%text \%\%MIDI temperamentequal 11 1200 7 1
%%MIDI temperamentequal 11 1200 7 1
"^Octave divided in 11 equal parts"\
c __d _d =d ^d ^^d =e =g ^g ^^g =a =c' & C12 |
%
%%tex \%\%MIDI temperamentnormal
%%MIDI temperamentnormal
"^Conventional temperament: octave divided in 12 equal parts"\
c _d =d ^d =e =f ^f =g ^g =a _b =b =c'2 & C14 |