TLA CTS-5-CA, Manual

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3.4 The "cent"-values of the historical temperaments
See table at the end of this manual.
3.4.1 The "cent"- relation function
All temperament tables in the Tuning Set (including the self stored one) are calculated so that
the cent deviation of the tone "a" is zero. We may say that "a" is the "cent relation tone".
Sometimes other cent relation tones will be required. If you use a cent relation tone other than
"a" on the Tuning Set, every cent deviation value in the current temperament table will be
increased or decreased by the same value, so that the cent relation tone will have the cent
deviation value zero.
Example:
The current temperament is "Kirnberger III", the selected cent relation tone is "a" (i.e. cent
relation function is not active):
a bb b c c# d d# e f f# g g#
0 +6.5 -1.5 +10.5 +0.5 +3.5 +4.5 -3.5 +8.5 +0.5 +7.0 +2.5
By using cent relation tone = "c" all cent values will be lowered by 10.5 cent.
a bb b c c# d d# e f f# g g#
-10.5 -4.0 -12.0 0 -10.0 -7.0 -6.0 -14.0 -2.0 -10.0 -3.5 -8.0
3.4.2 The transposer
With the transposer you may transpose the selected temperament into any key. For example, if
you need to transpose from key "a" to key "c", all cent deviation values of the temperament
table have to be rotated three semi-tones to the right.
Example: transposition "a" to "c" (cent relation tone = "a"),
temperament "Kirnberger III"
Cent deviation table of "Kirnberger III"
a bb b c c# d d# e f f# g g#
0 +6.5 -1.5 +10.5 +0.5 +3.5 +4.5 -3.5 +8.5 +0.5 +7.0 +2.5
first, the table will be rotated by 3 semi-tone steps to the right
a bb b c c# d d# e f f# g g#
0.5 +7.0 +2.5 0 +6.5 -1.5 +10.5 +0.5 +3.5 +4.5 -3.5 +8.5
The cent relation function then sets the cent relation tone (in this example tone "a") to 0,
lowering every cent value by 0.5 cent.
a bb b c c# d d# e f f# g g#
0 +6.5 +2.0 -0.5 +6.0 -2.0 +10.0 0 +3.0 +4.0 -4.0 +8.0
The instruction of how to use the transposer is found in chapter 3.4.3.