Constrained tuning: Difference between revisions

Line 350:

Anyone who performs tuning optimization has [[octave reduction]] to unlearn. It is tempting to optimize for close-voiced chords such as 1-5/4-3/2 without much consideration, since textbooks often present harmony in this way. The close-voiced chord, 1-5/4-3/2, is an octave-reduced version of 1-3-5, with the latter being the simplest voicing possible in the [[chord of nature]] and nontrivially being the simplest such chord containing the fundamental (the 1st harmonic/true root). It is thus important to recognize that all octave-reductions are but simplifications for our cognitive processes.

Music making, that is when we are not abstractly naming the chords, is ~~all~~ about various open voicings. The archaic {{w|Alberti bass}} is one of the few examples of close voicing, used as a bassline to accompany other materials. It should be noted that 13/1, dismissed as too wide in the section above, is still within the range of a full choir, not to mention a {{w|rock band}}, {{w|concert band}} or {{w|orchestra}}. {{w|Ludwig van Beethoven|Beethoven}}'s {{w|Symphony No. 3 (Beethoven)|''Symphony No. 3''}} opens with 1-2-5/2-4-5-6-8-10-12-16. Such a chord will be much overtempered, its tuning profile unreasonably squeezed and strained, if we set 1-5/4-3/2 as our target.

Music making, that is when we are not abstractly naming the chords, is often about various open voicings. The archaic {{w|Alberti bass}} is one of the few examples of close voicing, used as a bassline to accompany other materials. It should be noted that 13/1, dismissed as too wide in the section above, is still within the range of a full choir, not to mention a {{w|rock band}}, {{w|concert band}} or {{w|orchestra}}. {{w|Ludwig van Beethoven|Beethoven}}'s {{w|Symphony No. 3 (Beethoven)|''Symphony No. 3''}} opens with 1-2-5/2-4-5-6-8-10-12-16. Such a chord will be much overtempered, its tuning profile unreasonably squeezed and strained, if we set 1-5/4-3/2 as our target.

CTE blackwood does not try to approximate a delta-rational 1-5/4-3/2, and not even a delta-rational 1-3-5. This is also justifiable: since prime 5 is never involved in the comma that is tempered out, it only makes sense that it is tuned pure; any new prime added to the temperament is automatically tuned pure, as in JI. The dent in prime 3 does not spread to what it does not have to, unlike the schemes introduced below.

@@ Line 350: / Line 350: @@
 Anyone who performs tuning optimization has [[octave reduction]] to unlearn. It is tempting to optimize for close-voiced chords such as 1-5/4-3/2 without much consideration, since textbooks often present harmony in this way. The close-voiced chord, 1-5/4-3/2, is an octave-reduced version of 1-3-5, with the latter being the simplest voicing possible in the [[chord of nature]] and nontrivially being the simplest such chord containing the fundamental (the 1st harmonic/true root). It is thus important to recognize that all octave-reductions are but simplifications for our cognitive processes.
-Music making, that is when we are not abstractly naming the chords, is all about various open voicings. The archaic {{w|Alberti bass}} is one of the few examples of close voicing, used as a bassline to accompany other materials. It should be noted that 13/1, dismissed as too wide in the section above, is still within the range of a full choir, not to mention a {{w|rock band}}, {{w|concert band}} or {{w|orchestra}}. {{w|Ludwig van Beethoven|Beethoven}}'s {{w|Symphony No. 3 (Beethoven)|''Symphony No. 3''}} opens with 1-2-5/2-4-5-6-8-10-12-16. Such a chord will be much overtempered, its tuning profile unreasonably squeezed and strained, if we set 1-5/4-3/2 as our target.
+Music making, that is when we are not abstractly naming the chords, is often about various open voicings. The archaic {{w|Alberti bass}} is one of the few examples of close voicing, used as a bassline to accompany other materials. It should be noted that 13/1, dismissed as too wide in the section above, is still within the range of a full choir, not to mention a {{w|rock band}}, {{w|concert band}} or {{w|orchestra}}. {{w|Ludwig van Beethoven|Beethoven}}'s {{w|Symphony No. 3 (Beethoven)|''Symphony No. 3''}} opens with 1-2-5/2-4-5-6-8-10-12-16. Such a chord will be much overtempered, its tuning profile unreasonably squeezed and strained, if we set 1-5/4-3/2 as our target.
 CTE blackwood does not try to approximate a delta-rational 1-5/4-3/2, and not even a delta-rational 1-3-5. This is also justifiable: since prime 5 is never involved in the comma that is tempered out, it only makes sense that it is tuned pure; any new prime added to the temperament is automatically tuned pure, as in JI. The dent in prime 3 does not spread to what it does not have to, unlike the schemes introduced below.