Stratosphere: Difference between revisions
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'''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". | '''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 qualifies as a [[ | 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]]. | ||
== Temperament data == | == Temperament data == | ||
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[[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 }}] | [[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 }}] | ||
[[POTE generator]]s: ~99/70 = 600.0000, 176.7896 | [[POTE generator]]s: ~99/70 = 600.0000, ~21/19 = 176.7896 | ||
[[TOP tuning|TOP generator]]s: 600.0648, 176.8087 | [[TOP tuning|TOP generator]]s: 600.0648, 176.8087 | ||
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{{Val list|legend=1| 34dgghii, 190ghhiikl, 224hl }} | {{Val list|legend=1| 34dgghii, 190ghhiikl, 224hl }} | ||
[[Badness]]: 0. | [[Badness]]: 0.046174 | ||
{{IoT}} | {{IoT}} | ||
Revision as of 13:26, 18 October 2021
Stratosphere is a 37-limit regular temperament conceived by Kaiveran that tempers out a plethora of 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 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 qualifies as a ragismic microtemperament, and is actually an extension of quatracot.
Temperament data
Subgroup: 2.3.5.7.11.13.17.19.23.29.31.37
Comma list: 460/459, 481/480, 494/493, 625/624, 729/728, 1024/1023, 1216/1215, 1575/1573, 2058/2057, 2200/2197
Mapping: [⟨2 7 7 23 19 13 40 30 50 5 -6 11], ⟨0 -13 -8 -59 -41 -19 -108 -73 -139 16 54 -2]]
POTE generators: ~99/70 = 600.0000, ~21/19 = 176.7896
TOP generators: 600.0648, 176.8087
Badness: 0.046174