Orgone: Difference between revisions

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<nowiki/>* in 2.7.11-subgroup [[CWE]] tuning, octave reduced
<nowiki/>* in 2.7.11-subgroup [[CWE]] tuning, octave reduced
== List of patent vals ==
{| class="wikitable sortable"
!Edo!!Generator!!7/4 tuning!!11/8 tuning
|-
|4||300.000||900.000||600.000
|-
|19||315.789||947.368||568.421
|-
|34||317.647||952.941||564.706
|-
|15||320.000||960.000||560.000
|-
|86||320.930||962.791||558.140
|-
|71||321.127||963.380||557.746
|-
|56||321.429||964.286||557.143
|-
|97||321.649||964.948||556.701
|-
|41||321.951||965.854||556.098
|-
|108||322.222||966.667||555.556
|-
|67||322.388||967.164||555.224
|-
|160||322.500||967.500||555.000
|-
|93||322.581||967.742||554.839
|-
|119||322.689||968.067||554.622
|-
|145||322.759||968.276||554.483
|-
|171||322.807||968.421||554.386
|-
|197||322.843||968.528||554.315
|-
|26||323.077||969.231||553.846
|-
|271||323.247||969.742||553.506
|-
|245||323.265||969.796||553.469
|-
|219||323.288||969.863||553.425
|-
|193||323.316||969.948||553.368
|-
|167||323.353||970.060||553.293
|-
|308||323.377||970.130||553.247
|-
|141||323.404||970.213||553.191
|-
|256||323.438||970.312||553.125
|-
|115||323.478||970.435||553.043
|-
|319||323.511||970.533||552.978
|-
|204||323.529||970.588||552.941
|-
|293||323.549||970.648||552.901
|-
|89||323.596||970.787||552.809
|-
|241||323.651||970.954||552.697
|-
|152||323.684||971.053||552.632
|-
|215||323.721||971.163||552.558
|-
|63||323.810||971.429||552.381
|-
|163||323.926||971.779||552.147
|-
|100||324.000||972.000||552.000
|-
|137||324.088||972.263||551.825
|-
|37||324.324||972.973||551.351
|-
|85||324.706||974.118||550.588
|-
|48||325.000||975.000||550.000
|-
|59||325.424||976.271||549.153
|-
|70||325.714||977.143||548.571
|-
|11||327.273||981.818||545.455
|-
|18||333.333||1000.000||533.333
|-
|7||342.857||1028.571||514.286
|}
{{navbox regtemp}}
{{navbox regtemp}}
{{cat|temperaments}}
{{cat|temperaments}}

Revision as of 15:00, 14 March 2026

Orgone
Subgroups 2.7.11
Reduced mapping ⟨1; 3 -2]
ET join 11 & 15
Generators (CWE) ~77/64 = 323.3¢
MOS scales 4L 3s, 4L 7s, 11L 4s
Ploidacot trimech
Comma basis 65536/65219 (2.7.11)
Minimax error -odd-limit: ¢
Target scale size -odd-limit: notes

Orgone, 11 & 15, is a highly efficient temperament of the 2.7.11 subgroup, tempering out 65536/65219, such that three intervals of 11/8 reach the same point as two intervals of 8/7; the generator is therefore (11/8)/(8/7) = 77/64, two of which stack to 16/11 and three of which stack to 7/4.

26edo is a good tuning of Orgone; 41edo is on the flatter end of the generator spectrum and 37edo is on the sharper end.

Interval chain

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

# 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

* in 2.7.11-subgroup CWE tuning, octave reduced

List of patent vals

Edo Generator 7/4 tuning 11/8 tuning
4 300.000 900.000 600.000
19 315.789 947.368 568.421
34 317.647 952.941 564.706
15 320.000 960.000 560.000
86 320.930 962.791 558.140
71 321.127 963.380 557.746
56 321.429 964.286 557.143
97 321.649 964.948 556.701
41 321.951 965.854 556.098
108 322.222 966.667 555.556
67 322.388 967.164 555.224
160 322.500 967.500 555.000
93 322.581 967.742 554.839
119 322.689 968.067 554.622
145 322.759 968.276 554.483
171 322.807 968.421 554.386
197 322.843 968.528 554.315
26 323.077 969.231 553.846
271 323.247 969.742 553.506
245 323.265 969.796 553.469
219 323.288 969.863 553.425
193 323.316 969.948 553.368
167 323.353 970.060 553.293
308 323.377 970.130 553.247
141 323.404 970.213 553.191
256 323.438 970.312 553.125
115 323.478 970.435 553.043
319 323.511 970.533 552.978
204 323.529 970.588 552.941
293 323.549 970.648 552.901
89 323.596 970.787 552.809
241 323.651 970.954 552.697
152 323.684 971.053 552.632
215 323.721 971.163 552.558
63 323.810 971.429 552.381
163 323.926 971.779 552.147
100 324.000 972.000 552.000
137 324.088 972.263 551.825
37 324.324 972.973 551.351
85 324.706 974.118 550.588
48 325.000 975.000 550.000
59 325.424 976.271 549.153
70 325.714 977.143 548.571
11 327.273 981.818 545.455
18 333.333 1000.000 533.333
7 342.857 1028.571 514.286


View • Talk • EditRegular temperaments
Rank-2
Acot Blackwood (1/5-octave) • Whitewood (1/7-octave) • Compton (1/12-octave)
Monocot Meantone • Schismic • Leapday • Archy
Complexity 2 Diaschismic (diploid monocot) • Pajara (diploid monocot) • Injera (diploid monocot) • Rastmatic (dicot) • Mohajira (dicot) • Intertridecimal (dicot) • Interseptimal (alpha-dicot)
Complexity 3 Augmented (triploid) • Misty (triploid) • Slendric (tricot) • Porcupine (omega-tricot)
Complexity 4 Diminished (tetraploid) • Tetracot (tetracot) • Buzzard (alpha-tetracot) • Squares (beta-tetracot) • Negri (omega-tetracot)
Complexity 5-6 Magic (alpha-pentacot) • Amity (gamma-pentacot) • Kleismic (alpha-hexacot) • Miracle (hexacot)
Higher complexity Orwell (alpha-heptacot) • Sensi (beta-heptacot) • Octacot (octacot) • Wurschmidt (beta-octacot) • Valentine (enneacot) • Ammonite (epsilon-enneacot) • Myna (beta-decacot) • Ennealimmal (enneaploid dicot)
Straddle-3 A-Team (alter-tricot) • Machine (alter-monocot)
No-3 Trismegistus (alpha-triseph) • Orgone (trimech) • Didacus (diseph)
No-octaves Sensamagic (monogem)
Exotemperament Dicot • Mavila • Father
Higher-rank
Rank-3 Hemifamity • Marvel • Parapyth
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