58edo: Difference between revisions

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The '''58 equal temperament''', often abbreviated 58-tET, 58-EDO, or 58-ET, is the scale derived by dividing the [[octave]] into 58 equally-sized steps. Each step represents a frequency ratio of 20.69 cents.

== Theory ==

The ''58 equal temperament'', often abbreviated 58-tET, 58-EDO, or 58-ET, is the scale derived by dividing the [[octave]] into 58 equally-sized steps. Each step represents a frequency ratio of 20.69 cents. It tempers out 2048/2025, 126/125, 1728/1715, 144/143, 176/175, 896/891, 243/242, 5120/5103, 351/350, 364/363, 441/440, and 540/539, and is a strong system in the [[11-limit|11]], [[13-limit|13]] and [[17-limit|17-limits]]. It is the smallest [[EDO|equal temperament]] which is [[consistent]] through the 17-limit, and is also the first et to map the entire 11-limit [[tonality diamond]] to distinct scale steps, and hence the first et which can define a version of the famous 43-note [[Harry_Partch_related_scales|Genesis scale]] of [[Harry Partch]]. It supports [[hemififths]], [[myna]], [[diaschismic]], [[harry]], [[Hemifamity_temperaments#Mystery|mystery]], [[Hemifamity_temperaments#Buzzard|buzzard]] and [[Starling_temperaments#Thuja|thuja]] [[Regular_Temperaments|temperament]]s, and supplies the [[Optimal_patent_val|optimal patent val]] for 7-, 11- and 13-limit diaschismic, 11- and 13-limit hemififths, 11- and 13-limit thuja, and 13-limit myna. It also supplies the optimal patent val for the 13-limit rank three temperaments [[Starling_family#Thrush|thrush]], [[Starling_family#Thrush-Bluebird|bluebird]], [[Starling_family#Aplonis|aplonis]] and [[Breed_family#Jove, aka Wonder-Jofur|jofur]].

58edo tempers out 2048/2025, 126/125, 1728/1715, 144/143, 176/175, 896/891, 243/242, 5120/5103, 351/350, 364/363, 441/440, and 540/539, and is a strong system in the [[11-limit|11]], [[13-limit|13]] and [[17-limit|17-limits]]. It is the smallest [[EDO|equal temperament]] which is [[consistent]] through the 17-limit, and is also the first et to map the entire 11-limit [[tonality diamond]] to distinct scale steps, and hence the first et which can define a version of the famous 43-note [[Harry_Partch_related_scales|Genesis scale]] of [[Harry Partch]]. It supports [[hemififths]], [[myna]], [[diaschismic]], [[harry]], [[Hemifamity_temperaments#Mystery|mystery]], [[Hemifamity_temperaments#Buzzard|buzzard]] and [[Starling_temperaments#Thuja|thuja]] [[Regular_Temperaments|temperament]]s, and supplies the [[Optimal_patent_val|optimal patent val]] for 7-, 11- and 13-limit diaschismic, 11- and 13-limit hemififths, 11- and 13-limit thuja, and 13-limit myna. It also supplies the optimal patent val for the 13-limit rank three temperaments [[Starling_family#Thrush|thrush]], [[Starling_family#Thrush-Bluebird|bluebird]], [[Starling_family#Aplonis|aplonis]] and [[Breed_family#Jove, aka Wonder-Jofur|jofur]].

While the 17th harmonic is a cent and a half flat, the harmonics below it are all a little sharp, giving it the sound of a sharp system. 58 = 2*29, and 58 shares the same excellent fifth with [[29edo]].

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+The '''58 equal temperament''', often abbreviated 58-tET, 58-EDO, or 58-ET, is the scale derived by dividing the [[octave]] into 58 equally-sized steps. Each step represents a frequency ratio of 20.69 cents.
 == Theory ==
-The ''58 equal temperament'', often abbreviated 58-tET, 58-EDO, or 58-ET, is the scale derived by dividing the [[octave]] into 58 equally-sized steps. Each step represents a frequency ratio of 20.69 cents. It tempers out 2048/2025, 126/125, 1728/1715, 144/143, 176/175, 896/891, 243/242, 5120/5103, 351/350, 364/363, 441/440, and 540/539, and is a strong system in the [[11-limit|11]], [[13-limit|13]] and [[17-limit|17-limits]]. It is the smallest [[EDO|equal temperament]] which is [[consistent]] through the 17-limit, and is also the first et to map the entire 11-limit [[tonality diamond]] to distinct scale steps, and hence the first et which can define a version of the famous 43-note [[Harry_Partch_related_scales|Genesis scale]] of [[Harry Partch]]. It supports [[hemififths]], [[myna]], [[diaschismic]], [[harry]], [[Hemifamity_temperaments#Mystery|mystery]], [[Hemifamity_temperaments#Buzzard|buzzard]] and [[Starling_temperaments#Thuja|thuja]] [[Regular_Temperaments|temperament]]s, and supplies the [[Optimal_patent_val|optimal patent val]] for 7-, 11- and 13-limit diaschismic, 11- and 13-limit hemififths, 11- and 13-limit thuja, and 13-limit myna. It also supplies the optimal patent val for the 13-limit rank three temperaments [[Starling_family#Thrush|thrush]], [[Starling_family#Thrush-Bluebird|bluebird]], [[Starling_family#Aplonis|aplonis]] and [[Breed_family#Jove, aka Wonder-Jofur|jofur]].
+edo tempers out 2048/2025, 126/125, 1728/1715, 144/143, 176/175, 896/891, 243/242, 5120/5103, 351/350, 364/363, 441/440, and 540/539, and is a strong system in the [[11-limit|11]], [[13-limit|13]] and [[17-limit|17-limits]]. It is the smallest [[EDO|equal temperament]] which is [[consistent]] through the 17-limit, and is also the first et to map the entire 11-limit [[tonality diamond]] to distinct scale steps, and hence the first et which can define a version of the famous 43-note [[Harry_Partch_related_scales|Genesis scale]] of [[Harry Partch]]. It supports [[hemififths]], [[myna]], [[diaschismic]], [[harry]], [[Hemifamity_temperaments#Mystery|mystery]], [[Hemifamity_temperaments#Buzzard|buzzard]] and [[Starling_temperaments#Thuja|thuja]] [[Regular_Temperaments|temperament]]s, and supplies the [[Optimal_patent_val|optimal patent val]] for 7-, 11- and 13-limit diaschismic, 11- and 13-limit hemififths, 11- and 13-limit thuja, and 13-limit myna. It also supplies the optimal patent val for the 13-limit rank three temperaments [[Starling_family#Thrush|thrush]], [[Starling_family#Thrush-Bluebird|bluebird]], [[Starling_family#Aplonis|aplonis]] and [[Breed_family#Jove, aka Wonder-Jofur|jofur]].
 While the 17th harmonic is a cent and a half flat, the harmonics below it are all a little sharp, giving it the sound of a sharp system. 58 = 2*29, and 58 shares the same excellent fifth with [[29edo]].