Altering or Creating Temperaments

Scale Dialog image  
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.

Scale Dialog and Trace - Ab Meantone

    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).

Scale Ab relative    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.

Next (Showing Enharmonic Notes - Extended Temperaments)

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