50edo: Difference between revisions

Line 7:

50edo is also quite strong in the realm of tertian harmony for a meantone system, as the errors on [[7/6]], [[6/5]], [[5/4]], and [[9/7]] are all balanced to be roughly half as flat as the fifth, meaning that this set of thirds taken as a whole is minimally out-of-tune given the damage induced by meantone. Though it fails to approximate [[11/9]] well by virtue of not having a perfect hemififth, it inherits the excellent [[16/13]] from [[10edo]] and additionally has a 1.2{{c}} flat [[13/11]], providing even more qualities of roughly just thirds alongside their more complex [[fifth complement]]s.

~~It tempers out [[126/125]], [[225/224]] and [[3136/3125]]~~ in ~~the [[7-limit]], indicating it [[support]]s septimal meantone; [[245/242]], [[385/384]] and [[540/539]] in the [[~~11~~-limit]] and [[105/104]], [[144/143]] and 196/195~~ in ~~the [[13-limit]], and can be used for even higher limits. Aside from meantone and its extension [[meanpop]], it can be used to advantage for the [[coblack]] temperament (15 &~~ 50~~), and provides the optimal patent val for 11- and 13-limit [[Meantone family #Bimeantone~~|~~bimeantone]]. It is also the unique equal temperament tempering out both 81/80 and the [[vishnuzma]], {{monzo~~| ~~23 6 -14~~ }}~~, so that in 50edo seven chromatic semitones stack to a perfect fourth. By comparison, this gives a perfect fifth in 12edo, a doubly diminished fifth in 31edo, and a diminished fourth in 19edo.~~

=== Odd harmonics ===

{{Harmonics in equal|50|intervals=odd|columns=12|start=12|collapsed=true|title=Approximation of odd harmonics in 50edo (continued)}}

=== ~~Odd harmonics~~ ===

=== As a tuning of other temperaments ===

~~{{Harmonics~~ in ~~equal|~~50|~~columns=14|prec=2}}~~

50et tempers out [[126/125]], [[225/224]] and [[3136/3125]] in the [[7-limit]], indicating it [[support]]s septimal meantone; [[245/242]], [[385/384]] and [[540/539]] in the [[11-limit]] and [[105/104]], [[144/143]] and 196/195 in the [[13-limit]], and can be used for even higher limits. Aside from meantone and its extension [[meanpop]], it can be used to advantage for the [[coblack]] temperament (15 & 50), and provides the optimal patent val for 11- and 13-limit [[Meantone family #Bimeantone|bimeantone]]. It is also the unique equal temperament tempering out both 81/80 and the [[vishnuzma]], {{monzo| 23 6 -14 }}, so that in 50edo seven chromatic semitones stack to a perfect fourth. By comparison, this gives a perfect fifth in 12edo, a doubly diminished fifth in 31edo, and a diminished fourth in 19edo.

{{~~Harmonics in equal|50|intervals=odd~~|~~columns=~~14~~|prec=2|start=15|collapsed=true|title=Approximation of odd harmonics~~ in 50edo ~~(continued)}}~~

=== Relations ===

@@ Line 7: / Line 7: @@
 edo is also quite strong in the realm of tertian harmony for a meantone system, as the errors on [[7/6]], [[6/5]], [[5/4]], and [[9/7]] are all balanced to be roughly half as flat as the fifth, meaning that this set of thirds taken as a whole is minimally out-of-tune given the damage induced by meantone. Though it fails to approximate [[11/9]] well by virtue of not having a perfect hemififth, it inherits the excellent [[16/13]] from [[10edo]] and additionally has a 1.2{{c}} flat [[13/11]], providing even more qualities of roughly just thirds alongside their more complex [[fifth complement]]s.
-It tempers out [[126/125]], [[225/224]] and [[3136/3125]] in the [[7-limit]], indicating it [[support]]s septimal meantone; [[245/242]], [[385/384]] and [[540/539]] in the [[11-limit]] and [[105/104]], [[144/143]] and 196/195 in the [[13-limit]], and can be used for even higher limits. Aside from meantone and its extension [[meanpop]], it can be used to advantage for the [[coblack]] temperament (15 &amp; 50), and provides the optimal patent val for 11- and 13-limit [[Meantone family #Bimeantone|bimeantone]]. It is also the unique equal temperament tempering out both 81/80 and the [[vishnuzma]], {{monzo| 23 6 -14 }}, so that in 50edo seven chromatic semitones stack to a perfect fourth. By comparison, this gives a perfect fifth in 12edo, a doubly diminished fifth in 31edo, and a diminished fourth in 19edo.
+=== Odd harmonics ===
+{{Harmonics in equal|50|intervals=odd|columns=11}}
+{{Harmonics in equal|50|intervals=odd|columns=12|start=12|collapsed=true|title=Approximation of odd harmonics in 50edo (continued)}}
-=== Odd harmonics ===
+=== As a tuning of other temperaments ===
-{{Harmonics in equal|50|columns=14|prec=2}}
+et tempers out [[126/125]], [[225/224]] and [[3136/3125]] in the [[7-limit]], indicating it [[support]]s septimal meantone; [[245/242]], [[385/384]] and [[540/539]] in the [[11-limit]] and [[105/104]], [[144/143]] and 196/195 in the [[13-limit]], and can be used for even higher limits. Aside from meantone and its extension [[meanpop]], it can be used to advantage for the [[coblack]] temperament (15 &amp; 50), and provides the optimal patent val for 11- and 13-limit [[Meantone family #Bimeantone|bimeantone]]. It is also the unique equal temperament tempering out both 81/80 and the [[vishnuzma]], {{monzo| 23 6 -14 }}, so that in 50edo seven chromatic semitones stack to a perfect fourth. By comparison, this gives a perfect fifth in 12edo, a doubly diminished fifth in 31edo, and a diminished fourth in 19edo.
-{{Harmonics in equal|50|intervals=odd|columns=14|prec=2|start=15|collapsed=true|title=Approximation of odd harmonics in 50edo (continued)}}
 === Relations ===