Altering or Creating Temperaments
Tuning Meister comes with a short
list of temperaments you can use; these are
available
under Options | Temperament.
But this list can be tailored to your needs, and Options | Temperament Pitches & Menu launches the
dialog
for creating temperaments, or
altering or deleting ones already on your list. This
first image shows the values for the standard meantone, with 2 flats
and three sharps. The dialog allows you to
adjust the notes of the
temperament relative to C.
The pitches of the current scale are displayed in
relationship to the notes of equal temperament (up to 50 cents plus or
minus). One way you might want to do this is just to define a
scale according to the
actual sounding of the notes, for instance to define it from an
existing
tuning on a keyboard instrument. First be sure your pitch is set
accurately for your C. Start the Tuning Graph if it isn't running.
(You may launch the Pitch
& Range dialog to set A even when the Scale dialog is
active; then adjust A until the trace for C is exactly on the center
line in the fine-tuning [lower] graph). Once you are aligned on
C, adjust the
appropriate slider for each of the other notes as they are
played
[1].
The tuning graph will change as you do so; you just stop when
the pitch of the note being tested is drawn on the center line, neither
sharp nor flat. Of course you will want to expand the lower graph by
raising the splitter bar, and perhaps show it at a greater
magnification [select View | Lower
Graph Scaling], so that it can be read in finer detail.
If you want to enter specific pitch values for a
particular scale, they must be calculated in the form of cents, and
then set accordingly. You can type the cents deviation from equal
temperament into the edit boxes for the notes
[2].
Or, if you know the
values as a
decimal ratio, enter that into the left-hand box in the Cents
Convertor area below
[3],
and the cents value will be displayed for
you. For people working with just
intervals - type the numerator
and denominator into the boxes of ratio control
[4]
and the cents value
will be
calculated and displayed, and a decimal ratio shown as well
[3].
This value
will show you the offset from equal temperament. Here is an example,
illustrated below:
let us define a strict meantone temperament that uses an Ab
instead of a
G#. Now this happens to use the pure ratio 8/5 (major thirds are pure
5/4, and this is a major third below the octave C). The values 8 and 5
were entered in the ratio boxes and the Cents Convertor automatically
calculates the other values shown: 813.7 comes closest to the equal
temperament note of 800. So it is the 8th note in the list, and its
offset is 13.7 cents. By checking the Auto-adjust
Note Value
box
[5]
you can have the appropriate note adjusted automatically, after you
enter a valid decimal or integer ratio. Only values between 1 and 2
will have an effect. [But, be careful when entering subsequent integer
ratios in Auto-adjust mode - if you enter the numerator and it makes a
value between 1 and 2 with the denominator value already in its edit
box (or vice versa), a note may get changed that you did not intend.
You may need to delete one of the fields first. Or, uncheck the Auto-adjust box.]
After adjusting the note to the 8/5 ratio, we can see that "G#" has a
very different cents value
[6].
An Undo
control is provided
[7],
which will restore previous values one note at a
time.
In the image above, we can also see the effects of
changing the pitch of G#. As above, the ration 8/5 was entered
[1]. With
a tone generator playing the pitch of
the new note, when the left-to-right trace
[2]
reached about the middle
point of the
graph the note value was auto-adjusted
[3];
so the trace in the fine-tuning
graph jumped to the center line
[4]
( the averaging trace took some time to
catch up
[5]).
The upper graph is quite instructive - we can see the old
placement for G#
[6]
begin to be replaced by the new position of the Ab
[7]
[but, to clean a
little empty space, that drawing is always a bit farther ahead]; the
large jump of
40+ cents is quite visible. This illuminates also how the placement of
the lines in the upper graph exactly mirrors the pitch of the semitones
in the scale. (Equal temperament has all equally spaced lines, as the
most
obvious example). The graph of the melody is linear in pitch (logarithm
of frequency) in the vertical direction, and remains unchanged
[8]
no
matter what variations in the selected scale are projected in back of
it.
Let's continue with the controls for adjusting the
temperament. You can enter or edit the name
associated with this temperament .
OK allows tuning to
continue with any changes you have made, but no alteration is made to
the stored scale list. Those changes will be lost if the program is
closed or another scale is selected. Use Save to permanently record any
changes you made to a scale, Save As to
enter the information as a brand-new entry in the scale list, and Delete to remove the selected scale
from the list. (After Deleting a scale from the list, its values
continue to be used for tuning until you decide to select a new one.
And so in the case where you decide your deletion was a mistake, you
can restart the Scale Pitches dialog and Save the
deleted scale As a new name,
then rename it).
There are
instances where you may wish
to measure a temperament's deviation
from another than Equal, and so the
comparison
temperament can be
selected from the
drop-down list
[1]
(the
dialog always begins with Equal as the
comparison). In this case, by comparing with the
original standard meantone, we can see pitch of G# has been raised 41.2
cents (to become Ab)
[2];
all the other notes are identical. But observe, Tuning Meister can't
associate certain pitches with enharmonic note-names - the label
continues to read G#, and you should not ascribe any meaning to the
names of the notes in this box.
A name for
this new temperament, reflecting the range of
accidentals Ab - C#, has been entered in
the Temperament
Name
field at the top
[3];
consequently the Delete
button has been
grayed out
[4],
as we can delete only the originally selected scale from
the list, and the Save As...
button is activated
[5]
for creating a new
entry in the list of scales.
After building up a selection of temperaments
that fit your particular work, you may wish to reduce menu clutter by
deleting extraneous sample
scales from the original list.
The scale/temperament list is maintained on a file
which you should back up
periodically. If that file is not found or is corrupt, Tuning Meister
has a built-in Equal Temperament which it will use. Back up both files
TM Scales.dta and TM Instruments.dta together, as they are linked. If
the Scales file doesn't correspond to the arrangement of files that the
Instrument file references, you will have problems.
