No-fives subgroup temperaments: Difference between revisions

=== Ultraflat ===

Ultraflat is a diatonic-based [[exotemperament]] that makes [[27/26]] vanish, so [[13/8]] is a major sixth.  

[[Comma list]]: 27/26

{{Mapping|legend=2| 1 0 -1 | 0 1 3 }}

[[Optimal tuning]]s:

* [[WE]]: ~2 = 1201.6561{{c}}, ~3/2 = 686.9485{{c}}

: [[error map]]: {{val| +1.656 -13.350 +23.630 }}

* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 687.1143{{c}}

: error map: {{val| 0.000 -14.841 +20.815 }}

{{Optimal ET sequence|legend=1| 2, 5, 7 }}

[[Badness]] (Sintel): 0.200

=== Superflat ===

Superflat is a less inaccurate cousin of ultraflat, with less flat fifths. It tempers out [[1053/1024]], so [[13/8]] is a minor sixth, and [[16/13]] is a major third. Superflat and ultraflat intersect in [[7edo]], where major sixths and minor sixths are not distinguished.  

The more accurate tunings for this temperament are generated by a fifth at least as flat as those of [[flattone]], although often even flatter (such as [[40edo]]'s fifth). Superflat can be viewed as a 2.3.13 subgroup analogue of [[meantone]] and [[archy]]. Superflat diatonic scales have a character somewhere between neutral third scales (or [[3L 4s|mosh]]) and meantone diatonic scales.  

[[Comma list]]: 1053/1024

{{Mapping|legend=2| 1 0 10 | 0 1 -4 }}

[[Optimal tuning]]s:

* [[WE]]: ~2 = 1203.1291{{c}} ~3/2 = 695.6489{{c}}

* [[CWE]]: ~2 = 1200.0000{{c}} ~3/2 = 693.6081{{c}}

: error map: {{val| 0.000 -8.347 +14.960 }}

{{Optimal ET sequence|legend=1| 5f, 7, 12, 19, 45f, 64f, 147bfff }}

[[Badness]] (Sintel): 0.610

{{Optimal ET sequence|legend=1| 11bff, 13f, 15, 17, 36, 53, 70, 123, 193, 316, 755f }}