Microtemperament: Difference between revisions

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Any system of temperament in which all of the intervals considered to be consonances of the system are so closely approximated as to be effectively just is a '''microtemperament'''. There is no agreed on value for the threshold to '''microtempering''', and here we will use less than a cent in error as our line of demarcation, which some people would call a ''nanotemperament''. Using this definition and the tonality diamond as our consonance set, we find that the equal temperaments 118, 171, 270 … are 5-limit microtmeperaments; that 171, 270, 441, 612, 643 … are 7-limit microtemperaments; 764, 836, 1084, 1106 … are 11-limit microtemperaments, and that 1171, 1178, 1186 … are 13-limit microtemperaments.

Any system of [[temperament]] in which all of the intervals considered to be consonances of the system are so closely approximated as to be effectively just is a '''microtemperament'''. There is no agreed on value for the threshold to '''microtempering''', and here we will use less than a cent in error as our line of demarcation, which some people would call a ''nanotemperament''. Using this definition and the tonality diamond as our consonance set, we find that the equal temperaments 118, 171, 270 … are 5-limit microtmeperaments; that 171, 270, 441, 612, 643 … are 7-limit microtemperaments; 764, 836, 1084, 1106 … are 11-limit microtemperaments, and that 1171, 1178, 1186 … are 13-limit microtemperaments.

Putting 118 and 171 together, we see that the 5-limit [[Schismatic|schismatic temperament]], which tempers out the [[schisma]] of 32805/32768, is a microtemperament when appropriately tuned. Putting 171 and 270 together, we see that [[Ennealimmal|ennealimmal temperament]], which tempers out the [[2401/2400|breedsma]] 2401/2400 and [[4375/4374|ragisma]] 4375/4374, is also a microtemperament.

The opposite of a microtemperament is an [[exotemperament]].

Tuning microtemperaments can be challenging due to the sheer number of pitch materials, but one may take advantage of MIDI channels. See [[Tuning per channel]].

[[Category:Microtemperament| ]]

[[Category:Regular temperament theory]]

[[Category:Method]]

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-Any system of temperament in which all of the intervals considered to be consonances of the system are so closely approximated as to be effectively just is a '''microtemperament'''. There is no agreed on value for the threshold to '''microtempering''', and here we will use less than a cent in error as our line of demarcation, which some people would call a ''nanotemperament''. Using this definition and the tonality diamond as our consonance set, we find that the equal temperaments 118, 171, 270 … are 5-limit microtmeperaments; that 171, 270, 441, 612, 643 … are 7-limit microtemperaments; 764, 836, 1084, 1106 … are 11-limit microtemperaments, and that 1171, 1178, 1186 … are 13-limit microtemperaments.
+Any system of [[temperament]] in which all of the intervals considered to be consonances of the system are so closely approximated as to be effectively just is a '''microtemperament'''. There is no agreed on value for the threshold to '''microtempering''', and here we will use less than a cent in error as our line of demarcation, which some people would call a ''nanotemperament''. Using this definition and the tonality diamond as our consonance set, we find that the equal temperaments 118, 171, 270 … are 5-limit microtmeperaments; that 171, 270, 441, 612, 643 … are 7-limit microtemperaments; 764, 836, 1084, 1106 … are 11-limit microtemperaments, and that 1171, 1178, 1186 … are 13-limit microtemperaments.
 Putting 118 and 171 together, we see that the 5-limit [[Schismatic|schismatic temperament]], which tempers out the [[schisma]] of 32805/32768, is a microtemperament when appropriately tuned. Putting 171 and 270 together, we see that [[Ennealimmal|ennealimmal temperament]], which tempers out the [[2401/2400|breedsma]] 2401/2400 and [[4375/4374|ragisma]] 4375/4374, is also a microtemperament.
 The opposite of a microtemperament is an [[exotemperament]].
+Tuning microtemperaments can be challenging due to the sheer number of pitch materials, but one may take advantage of MIDI channels. See [[Tuning per channel]].
 [[Category:Microtemperament| ]] <!-- main article -->
 [[Category:Regular temperament theory]]
 [[Category:Method]]