Orgone: Difference between revisions

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{{About|the regular temperament|the scale structure sometimes associated with it|4L 3s}}

'''Orgone''' is the 2.7.11 [[subgroup temperament]] generated by a minor or supraminor third which can be identified by a tempered [[77/64]] such that two of them make a tempered [[16/11]] and three of them make a tempered [[7/4]]. While it is easy enough to equate the generator with [[6/5]] by tempering out [[385/384]], extending it to include [[3/2|perfect fifths]] is not so easy. If using a flatter generator, there is a fifth at the relatively high [[complexity]] of 9 generators down (see also [[superkleismic]]). Closer to optimal tuning for orgone, but even more complex at 17 generators up, there is [[hyperkleismic]].

'''Orgone''' is the 2.7.11 [[subgroup temperament]] generated by a minor or supraminor third which can be identified by a tempered [[77/64]] such that two of them make a tempered [[16/11]] and three of them make a tempered [[7/4]]. While it is easy enough to equate the generator with [[6/5]] by tempering out [[385/384]], extending it to include [[3/2|perfect fifths]] is not so easy. If using a flatter generator, there is a fifth at the relatively high [[complexity]] of 9 generators down (see also [[superkleismic]]). Closer to optimal tuning for orgone, but even more complex at 17 generators up, there is [[hyperkleismic]]. These two merge at [[26edo]]. Extremely accurate, but more complex still is [[Ragismic_microtemperaments#Senator|senator]].

A related temperament is [[No-threes subgroup temperaments#Ultrakleismic|ultrakleismic]] in the 2.7.17 subgroup, in which the generator is instead identified with the simpler [[17/14]], by tempering out [[4913/4802]]. [[Orgonia#Ork|Ork]] temperament merges these two. These favor sharper generators so can be viewed even more as no-fifth systems.

For technical data, see [[Orgonia #Orgone]].

== Interval chain ==

In the following table, odd harmonics and subharmonics 1–11 are in '''bold'''.

{| class="wikitable right-1 right-2"

|-

! #

! Cents*

! Approximate ratios

|-

| 0

| 0.0

| '''1/1'''

|-

| 1

| 323.3

| 77/64

|-

| 2

| 646.7

| '''16/11'''

|-

| 3

| 970.0

| '''7/4'''

|-

| 4

| 93.4

| 128/121

|-

| 5

| 416.7

| 14/11

|-

| 6

| 740.1

| 49/32

|-

| 7

| 1063.4

| 224/121

|}

<nowiki/>* in 2.7.11-subgroup [[CWE]] tuning, octave reduced

== Gallery ==

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[[Category:Orgone| ]]

[[Category:~~Temperaments~~]]

[[Category:Rank-2 temperaments]]

[[Category:Subgroup temperaments]]

@@ Line 1: / Line 1: @@
 {{About|the regular temperament|the scale structure sometimes associated with it|4L 3s}}
-'''Orgone''' is the 2.7.11 [[subgroup temperament]] generated by a minor or supraminor third which can be identified by a tempered [[77/64]] such that two of them make a tempered [[16/11]] and three of them make a tempered [[7/4]]. While it is easy enough to equate the generator with [[6/5]] by tempering out [[385/384]], extending it to include [[3/2|perfect fifths]] is not so easy. If using a flatter generator, there is a fifth at the relatively high [[complexity]] of 9 generators down (see also [[superkleismic]]). Closer to optimal tuning for orgone, but even more complex at 17 generators up, there is [[hyperkleismic]].
+'''Orgone''' is the 2.7.11 [[subgroup temperament]] generated by a minor or supraminor third which can be identified by a tempered [[77/64]] such that two of them make a tempered [[16/11]] and three of them make a tempered [[7/4]]. While it is easy enough to equate the generator with [[6/5]] by tempering out [[385/384]], extending it to include [[3/2|perfect fifths]] is not so easy. If using a flatter generator, there is a fifth at the relatively high [[complexity]] of 9 generators down (see also [[superkleismic]]). Closer to optimal tuning for orgone, but even more complex at 17 generators up, there is [[hyperkleismic]]. These two merge at [[26edo]]. Extremely accurate, but more complex still is [[Ragismic_microtemperaments#Senator|senator]].
 A related temperament is [[No-threes subgroup temperaments#Ultrakleismic|ultrakleismic]] in the 2.7.17 subgroup, in which the generator is instead identified with the simpler [[17/14]], by tempering out [[4913/4802]]. [[Orgonia#Ork|Ork]] temperament merges these two. These favor sharper generators so can be viewed even more as no-fifth systems.
 For technical data, see [[Orgonia #Orgone]].
+== Interval chain ==
+In the following table, odd harmonics and subharmonics 1–11 are in '''bold'''.
+{| class="wikitable right-1 right-2"
+|-
+! #
+! Cents*
+! Approximate ratios
+|-
+| 0
+| 0.0
+| '''1/1'''
+|-
+| 1
+| 323.3
+| 77/64
+|-
+| 2
+| 646.7
+| '''16/11'''
+|-
+| 3
+| 970.0
+| '''7/4'''
+|-
+| 4
+| 93.4
+| 128/121
+|-
+| 5
+| 416.7
+| 14/11
+|-
+| 6
+| 740.1
+| 49/32
+|-
+| 7
+| 1063.4
+| 224/121
+|}
+<nowiki/>* in 2.7.11-subgroup [[CWE]] tuning, octave reduced
 == Gallery ==
@@ Line 33: / Line 75: @@
 {{Todo| expand }}
 [[Category:Orgone| ]] <!-- main article -->
-[[Category:Temperaments]]
+[[Category:Rank-2 temperaments]]
+[[Category:Subgroup temperaments]]