User:VIxen/Temperament proposals: Difference between revisions

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In the 33/19.2.3.5.7.11.13.17 basis of the full 19-limit subgroup, it is q23 & q82 & q282 (with equave 2/1, it is 29g & 103h & 354), and a Fokker block of 23 notes per equave is available, corresponding to the [[29edo|29g]] val, although it is complex - perhaps the simplest of the highly available intervals is 7/5 - with a preference for open harmonies, and just about enough to contain the chord of prime harmonics (1:2:3:5:7:11:13:17:19) on one root per equave.

Extensions to higher limits, perhaps 31-limit at least, seem possible but will require using blocks of 82 notes corresponding to the ~~103p~~ val.

Extensions to higher limits, perhaps 31-limit at least, seem possible but will require using blocks of 82 notes corresponding to the 103h val.

Data for equave 2/1 is provided below for compatibility. The TE error is small enough - 0.~~012~~ cents/octave - but the complexity of most intervals involving powers of 2 is high like in ennealimmal, which makes the badness high.

Data for equave 2/1 is provided below for compatibility. The TE error is small enough - 0.011 cents/octave - but the complexity of most intervals involving powers of 2 is high like in ennealimmal, which makes the badness high.

Subgroup: 2.3.5.7.11.13.17.19

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Mapping generators: ~2, ~3, ~266/165

{{~~Val list~~|legend=1| 29g, 74g, 103h, 132degh, 222cdeefgh, 251eh, 354, 486g, 737, 840 }}

{{Optimal ET sequence|legend=1| 29g, 74g, 103h, 132degh, 222cdeefgh, 251eh, 354, 486g, 737, 840 }}

[[Badness]]: 1.78 × 10<sup>-3</sup>

@@ Line 8: / Line 8: @@
 In the 33/19.2.3.5.7.11.13.17 basis of the full 19-limit subgroup, it is q23 & q82 & q282 (with equave 2/1, it is 29g & 103h & 354), and a Fokker block of 23 notes per equave is available, corresponding to the [[29edo|29g]] val, although it is complex - perhaps the simplest of the highly available intervals is 7/5 - with a preference for open harmonies, and just about enough to contain the chord of prime harmonics (1:2:3:5:7:11:13:17:19) on one root per equave.
-Extensions to higher limits, perhaps 31-limit at least, seem possible but will require using blocks of 82 notes corresponding to the 103p val.
+Extensions to higher limits, perhaps 31-limit at least, seem possible but will require using blocks of 82 notes corresponding to the 103h val.
-Data for equave 2/1 is provided below for compatibility. The TE error is small enough - 0.012 cents/octave - but the complexity of most intervals involving powers of 2 is high like in ennealimmal, which makes the badness high.
+Data for equave 2/1 is provided below for compatibility. The TE error is small enough - 0.011 cents/octave - but the complexity of most intervals involving powers of 2 is high like in ennealimmal, which makes the badness high.
 Subgroup: 2.3.5.7.11.13.17.19
@@ Line 20: / Line 20: @@
 Mapping generators: ~2, ~3, ~266/165
-{{Val list|legend=1| 29g, 74g, 103h, 132degh, 222cdeefgh, 251eh, 354, 486g, 737, 840 }}
+{{Optimal ET sequence|legend=1| 29g, 74g, 103h, 132degh, 222cdeefgh, 251eh, 354, 486g, 737, 840 }}
 [[Badness]]: 1.78 × 10<sup>-3</sup>