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Superpyth: Difference between revisions

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m Undo style (temperament names aren't proper nouns). Get rid of "table notes" and unnecessary character escaping
Tag: Undo
Line 24: Line 24:
|+ style="font-size: 105%;" | Archy (2.3.7)
|+ style="font-size: 105%;" | Archy (2.3.7)
|-
|-
! # !! Cents{{asterisk}} !! Approximate Ratios
! # !! Cents* !! Approximate Ratios
|-
|-
| 0 || 0.0 || '''1/1'''
| 0 || 0.0 || '''1/1'''
Line 41: Line 41:
|-
|-
| 7 || 167.2 || 54/49
| 7 || 167.2 || 54/49
{{table notes|cols=3
| In 2.3.7-subgroup [[CTE]] tuning
}}
|}
|}
<nowiki>*</nowiki> In 2.3.7-subgroup [[CTE]] tuning
</div>
</div>


Line 51: Line 49:
|+ style="font-size: 105%;" | Supra (2.3.7.11)
|+ style="font-size: 105%;" | Supra (2.3.7.11)
|-
|-
! &#35; !! Cents{{asterisk}} !! Approximate Ratios
! # !! Cents* !! Approximate Ratios
|-
|-
| 0 || 0.0 || '''1/1'''
| 0 || 0.0 || '''1/1'''
Line 68: Line 66:
|-
|-
| 7 || 159.2 || 12/11
| 7 || 159.2 || 12/11
{{table notes|cols=3
| In 2.3.7.11-subgroup CTE tuning
}}
|}
|}
<nowiki>*</nowiki> In 2.3.7.11-subgroup CTE tuning
</div>
</div>


Line 78: Line 74:
|+ style="font-size: 105%;" | Full 7-limit superpyth
|+ style="font-size: 105%;" | Full 7-limit superpyth
|-
|-
! rowspan="3" | &#35; !! rowspan="3" | Cents{{asterisk}} !! colspan="3" | Approximate Ratios
! rowspan="3" | # !! rowspan="3" | Cents* !! colspan="3" | Approximate Ratios
|-
|-
! rowspan="2" | 7-limit !! colspan="2" | 11-limit Extension
! rowspan="2" | 7-limit !! colspan="2" | 11-limit Extension
Line 119: Line 115:
|-
|-
| 17 || 63.0 || 25/24 || 22/21, 33/32 || 45/44
| 17 || 63.0 || 25/24 || 22/21, 33/32 || 45/44
{{table notes|cols=5
| In 7-limit CTE tuning
}}
|}
|}
<nowiki>*</nowiki> In 7-limit CTE tuning
</div></div>
</div></div>


== Scales ==
== Scales ==
; 5-note MOS ([[2L 3s]], proper)
; 5-note MOS ([[2L 3s]], proper)
* [[Archy5]] &ndash; Archy in 472edo tuning
* [[Archy5]] – archy in 472edo tuning


; 7-note MOS ([[5L 2s]], improper)
; 7-note MOS ([[5L 2s]], improper)
* [[Archy7]] &ndash; Archy in 472edo tuning
* [[Archy7]] – archy in 472edo tuning
* [[Supra7]] &ndash; Supra in 56edo tuning
* [[Supra7]] – supra in 56edo tuning
In contrast to the meantone diatonic scale, the superpyth diatonic is improper.
In contrast to the meantone diatonic scale, the superpyth diatonic is improper.


; 12-note MOS ([[5L 7s]], borderline improper)
; 12-note MOS ([[5L 7s]], borderline improper)
* [[Archy12]] &ndash; Archy in 472edo tuning
* [[Archy12]] – archy in 472edo tuning
* [[Supra12]] &ndash; Supra in 56edo tuning
* [[Supra12]] – supra in 56edo tuning
* [[12-22a]] &ndash; Superpyth in 22edo tuning
* [[12-22a]] – superpyth in 22edo tuning
The boundary of propriety is [[17edo]].
The boundary of propriety is [[17edo]].


Line 153: Line 147:
| Weil || CWE: ~3/2 = 709.3901¢
| Weil || CWE: ~3/2 = 709.3901¢
|-
|-
| Equilateral || CEE: ~3/2 = 712.8606¢<br />[[Eigenmonzo basis]] ([[unchanged-interval basis]]): 2.49/3 (2/5-comma tuning)
| Equilateral || CEE: ~3/2 = 712.8606¢<br>[[Eigenmonzo basis]] ([[unchanged-interval basis]]): 2.49/3 (2/5-comma tuning)
|-
|-
| Skewed-equilateral || CSEE: ~3/2 = 711.9997¢<br />Eigenmonzo basis (unchanged-interval basis): 2.823543/243 (7/19-comma tuning)
| Skewed-equilateral || CSEE: ~3/2 = 711.9997¢<br>Eigenmonzo basis (unchanged-interval basis): 2.823543/243 (7/19-comma tuning)
|-
|-
| Benedetti/Wilson || CBE: ~3/2 = 707.7286¢<br />Eigenmonzo basis (unchanged-interval basis): 2.{{monzo| 0 -49 0 18 }} (18/85-comma tuning)
| Benedetti/Wilson || CBE: ~3/2 = 707.7286¢<br>Eigenmonzo basis (unchanged-interval basis): 2.{{monzo| 0 -49 0 18 }} (18/85-comma tuning)
|-
|-
| Skewed-Benedetti/Wilson || CSBE: ~3/2 = 707.9869¢<br />Eigenmonzo basis (unchanged-interval basis): 2.{{monzo| 0 -63 25 }} (25/113-comma tuning)
| Skewed-Benedetti/Wilson || CSBE: ~3/2 = 707.9869¢<br>Eigenmonzo basis (unchanged-interval basis): 2.{{monzo| 0 -63 25 }} (25/113-comma tuning)
|}
|}


Line 171: Line 165:
| Weil || CWE: ~3/2 = 710.1193¢
| Weil || CWE: ~3/2 = 710.1193¢
|-
|-
| Equilateral || CEE: ~3/2 = 709.7805¢<br />Eigenmonzo basis (unchanged-interval basis): 2.5859375/49
| Equilateral || CEE: ~3/2 = 709.7805¢<br>Eigenmonzo basis (unchanged-interval basis): 2.5859375/49
|-
|-
| Skewed-equilateral || CSEE: ~3/2 = 710.2428¢<br />Eigenmonzo basis (unchanged-interval basis): 2.{{monzo| 0 3 -37 18 }}
| Skewed-equilateral || CSEE: ~3/2 = 710.2428¢<br>Eigenmonzo basis (unchanged-interval basis): 2.{{monzo| 0 3 -37 18 }}
|-
|-
| Benedetti/Wilson || CBE: ~3/2 = 709.4859¢<br />Eigenmonzo basis (unchanged-interval basis): 2.{{monzo| 0 -1225 -3969 450 }}
| Benedetti/Wilson || CBE: ~3/2 = 709.4859¢<br>Eigenmonzo basis (unchanged-interval basis): 2.{{monzo| 0 -1225 -3969 450 }}
|-
|-
| Skewed-Benedetti/Wilson || CSBE: ~3/2 = 710.0321¢<br />Eigenmonzo basis (unchanged-interval basis): 2.{{monzo| 0 665 -15771 5160 }}
| Skewed-Benedetti/Wilson || CSBE: ~3/2 = 710.0321¢<br>Eigenmonzo basis (unchanged-interval basis): 2.{{monzo| 0 665 -15771 5160 }}
|}
|}


=== Tuning spectrum ===
=== Tuning spectrum ===
{| class="wikitable center-all left-4"
{| class="wikitable center-all left-4"
! Edo<br />Generator
! Edo<br>Generator
! [[Eigenmonzo|Eigenmonzo<br />(Unchanged-interval)]]
! [[Eigenmonzo|Eigenmonzo<br>(Unchanged-interval)]]
! Generator<br />(¢)
! Generator<br>(¢)
! Comments
! Comments
|-
|-
Retrieved from "https://en.xen.wiki/w/Superpyth"