Microtemperament: Difference between revisions
m Xenwolf moved page Microtempering to Microtemperament over redirect: better this way round, for categories etc. |
redirect lemma bold, categorized |
||
| Line 1: | Line 1: | ||
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, 236, 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, 236, 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 [http://en.wikipedia.org/wiki/Schismatic_temperament schismatic temperament], which tempers out the schisma of 32805/32768, is a microtemperament when appropriately tuned. Putting 171 and 270 together, we see that [[Breedsmic_temperaments|ennealimmal temperament]], which tempers out the [http://en.wikipedia.org/wiki/Breedsma breedsma] 2401/2400 and the [http://en.wikipedia.org/wiki/Ragisma ragisma] 4375/4374 is also a microtemperament. | Putting 118 and 171 together, we see that the 5-limit [http://en.wikipedia.org/wiki/Schismatic_temperament schismatic temperament], which tempers out the schisma of 32805/32768, is a microtemperament when appropriately tuned. Putting 171 and 270 together, we see that [[Breedsmic_temperaments|ennealimmal temperament]], which tempers out the [http://en.wikipedia.org/wiki/Breedsma breedsma] 2401/2400 and the [http://en.wikipedia.org/wiki/Ragisma ragisma] 4375/4374 is also a microtemperament. | ||
[[Category:Microtemperament| ]] <!-- main article --> | |||
[[Category:Theory]] | |||
[[Category:Method]] | |||
Revision as of 17:02, 11 September 2020
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, 236, 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 temperament, which tempers out the schisma of 32805/32768, is a microtemperament when appropriately tuned. Putting 171 and 270 together, we see that ennealimmal temperament, which tempers out the breedsma 2401/2400 and the ragisma 4375/4374 is also a microtemperament.