Stratosphere: Difference between revisions

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'''Stratosphere''' is a 37-limit regular temperament conceived by Kaiveran that tempers out a plethora of [[~~Unnoticeable_commas|~~unnoticeable ~~commas~~]]. It gets its name from the fact that 37 pretty absurdly high to climb in the harmonic ladder. 37 is also the first [[~~Interseptimal|~~interseptimal]] interval in the harmonic series (a "hemifourth"), so this general area is a distinct new territory, or stratum if you will, of the harmonic "atmosphere".

'''Stratosphere''' is a 37-limit [[regular temperament]] conceived by [[User:Kaiveran|Kaiveran]] that tempers out a plethora of [[unnoticeable comma]]s. It gets its name from the fact that 37 pretty absurdly high to climb in the harmonic ladder. 37 is also the first [[interseptimal]] interval in the harmonic series (a "hemifourth"), so this general area is a distinct new territory, or stratum if you will, of the harmonic "atmosphere".

Aside from the psychoacoustic advantage of tempering out such small commas, a secondary concept of this temperament is that complex intervals in lower prime limits are identified with simple intervals in higher prime limits (for example, 81/64 = 19/15, 27/20 = 23/17, etc.) Since it tempers out the ragisma, it ~~could qualify~~ as a [[~~Ragismic_microtemperaments~~|ragismic microtemperament]].

Aside from the psychoacoustic advantage of tempering out such small commas, a secondary concept of this temperament is that complex intervals in lower prime limits are identified with simple intervals in higher prime limits (for example, 81/64 = 19/15, 27/20 = 23/17, etc.) Since it tempers out the ragisma, it qualifies as a [[Ragismic microtemperaments|ragismic microtemperament]], and is actually an extension of [[Ragismic microtemperaments #Quatracot|quatracot]].

~~(big ups to the temperament finder)~~

== Temperament data ==

Subgroup: 2.3.5.7.11.13.17.19.23.29.31.37

~~Commas~~: ~~4375~~/~~4374~~, ~~9801~~/~~9800~~, 625/624, ~~123201~~/~~103200~~, ~~2058~~/~~2057~~, 1216/1215, ~~460~~/~~459~~, ~~494~~/~~493, 1024/1023~~, ~~481~~/~~480~~

[[Comma list]]: 460/459, 481/480, 494/493, 625/624, 729/728, 1024/1023, 1216/1215, 1575/1573, 2058/2057, 2200/2197

~~POTE generators~~: ~~600.0000~~, ~~176.7896~~

[[Mapping]]: [{{val| 2 7 7 23 19 13 40 30 50 5 -6 11 }}, {{val| 0 -13 -8 -59 -41 -19 -108 -73 -139 16 54 -2 }}]

~~TOP generators~~: 600.~~0648~~, ~~176.8087 (~~~2 = ~~1200~~.~~130, well beyond the range of anyone caring)~~

[[POTE generator]]s: ~99/70 = 600.0000, ~21/19 = 176.7896

~~Map:~~ [~~<2 7 7 23 19 13 40 30 50 5 -6 11, <0 -13 -8 -59 -41 -19 -108 -73 -139 16 54 -2~~|]

[[TOP tuning|TOP generator]]s: 600.0648, 176.8087

~~Wedgie: ???~~

~~EDOs~~: ~~224?~~

[[Badness]]: 0.046174

~~Badness~~: ~~???~~

[[Category:Stratosphere| ]]

[[Category:Rank-2 temperaments]]

[~~http://x31eq.com/cgi-bin/rt.cgi?ets=224hl_34dgghii&limit=37 http~~:~~//x31eq.com/cgi~~-~~bin/rt.cgi?ets=224hl_34dgghii&limit=37~~]

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-'''Stratosphere''' is a 37-limit regular temperament conceived by Kaiveran that tempers out a plethora of [[Unnoticeable_commas|unnoticeable commas]]. It gets its name from the fact that 37 pretty absurdly high to climb in the harmonic ladder. 37 is also the first [[Interseptimal|interseptimal]] interval in the harmonic series (a "hemifourth"), so this general area is a distinct new territory, or stratum if you will, of the harmonic "atmosphere".
+'''Stratosphere''' is a 37-limit [[regular temperament]] conceived by [[User:Kaiveran|Kaiveran]] that tempers out a plethora of [[unnoticeable comma]]s. It gets its name from the fact that 37 pretty absurdly high to climb in the harmonic ladder. 37 is also the first [[interseptimal]] interval in the harmonic series (a "hemifourth"), so this general area is a distinct new territory, or stratum if you will, of the harmonic "atmosphere".
-Aside from the psychoacoustic advantage of tempering out such small commas, a secondary concept of this temperament is that complex intervals in lower prime limits are identified with simple intervals in higher prime limits (for example, 81/64 = 19/15, 27/20 = 23/17, etc.) Since it tempers out the ragisma, it could qualify as a [[Ragismic_microtemperaments|ragismic microtemperament]].
+Aside from the psychoacoustic advantage of tempering out such small commas, a secondary concept of this temperament is that complex intervals in lower prime limits are identified with simple intervals in higher prime limits (for example, 81/64 = 19/15, 27/20 = 23/17, etc.) Since it tempers out the ragisma, it qualifies as a [[Ragismic microtemperaments|ragismic microtemperament]], and is actually an extension of [[Ragismic microtemperaments #Quatracot|quatracot]].
-(big ups to the temperament finder)
+== Temperament data ==
+Subgroup: 2.3.5.7.11.13.17.19.23.29.31.37
-Commas: 4375/4374, 9801/9800, 625/624, 123201/103200, 2058/2057, 1216/1215, 460/459, 494/493, 1024/1023, 481/480
+[[Comma list]]: 460/459, 481/480, 494/493, 625/624, 729/728, 1024/1023, 1216/1215, 1575/1573, 2058/2057, 2200/2197
-POTE generators: 600.0000, 176.7896
+[[Mapping]]: [{{val| 2 7 7 23 19 13 40 30 50 5 -6 11 }}, {{val| 0 -13 -8 -59 -41 -19 -108 -73 -139 16 54 -2 }}]
-TOP generators: 600.0648, 176.8087 (~2 = 1200.130, well beyond the range of anyone caring)
+[[POTE generator]]s: ~99/70 = 600.0000, ~21/19 = 176.7896
-Map: [&lt;2 7 7 23 19 13 40 30 50 5 -6 11, &lt;0 -13 -8 -59 -41 -19 -108 -73 -139 16 54 -2|]
+[[TOP tuning|TOP generator]]s: 600.0648, 176.8087
-Wedgie: ???
+{{Optimal ET sequence|legend=1| 34dgghii, 190ghhiikl, 224hl }}
-EDOs: 224?
+[[Badness]]: 0.046174
-Badness: ???
+[[Category:Stratosphere| ]] <!-- main article -->
+[[Category:Rank-2 temperaments]]
-[http://x31eq.com/cgi-bin/rt.cgi?ets=224hl_34dgghii&limit=37 http://x31eq.com/cgi-bin/rt.cgi?ets=224hl_34dgghii&amp;limit=37]