Orgone: Difference between revisions

From Xenharmonic Reference
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| MOS scales = [[4L 3s]], [[4L 7s]], [[11L 4s]]
| MOS scales = [[4L 3s]], [[4L 7s]], [[11L 4s]]
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'''Orgone''' 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 11/6 and three of which stack to 7/4.
'''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 11/6 and three of which stack to 7/4.


== Interval chain ==
== Interval chain ==

Revision as of 03:19, 9 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 11/6 and three of which stack to 7/4.

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