Superpyth: Difference between revisions

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<nowiki/>* In 7-limit CWE tuning, octave reduced

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== Chords and harmony ==

Superpyth contains a version of the [[5L 2s|diatonic]] scale where the major third represents 9/7, and the minor third represents [[7/6]]. {{W|Tertian harmony}} can thus be used, with the major and minor triads representing [[14:18:21|1–9/7–3/2]] and [[6:7:9|1–7/6–3/2]] respectively, rather than the [[4:5:6|1–5/4–3/2]] and [[10:12:15|1–6/5–3/2]] triads in meantone. Since the fifth is sharp in archy rather than flat in [[meantone]], the large steps (major seconds) are wider, being around 212–222{{c}} depending on the tuning. The small steps (minor seconds) are thus narrower, being around 44–71{{c}}. This has the effect of large and small steps being more distinct compared to meantone diatonic, as well as stronger leading tones due to narrower small steps, though one may want to use milder tunings like [[17edo]] to avoid the small step being too narrow.

== Scales ==

; 5-note mos ([[2L 3s]], proper)

* [[Archy5]] – archy in 472edo tuning

; 7-note mos ([[5L 2s]], improper)

* [[Archy7]] – archy in 472edo tuning

* [[Supra7]] – supra in 56edo tuning

In contrast to the meantone diatonic scale, the superpyth diatonic is improper.

; 12-note mos ([[5L 7s]], borderline improper)

* [[Archy12]] – archy in 472edo tuning

* [[Supra12]] – supra in 56edo tuning

* [[12-22a]] – superpyth in 22edo tuning

The boundary of propriety is [[17edo]].

== Tunings ==

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* [[DKW theory|DKW]] (2.3.5 superpyth): ~2 = 1200.000, ~3/2 = 709.758

* DKW (2.3.7 archy): ~2 = 1200.000, ~3/2 = 712.585

~~== Scales ==~~

~~; 5-note mos ([[2L 3s]], proper)~~

* [[Archy5]] – archy in 472edo tuning

~~; 7-note mos ([[5L 2s]], improper)~~

* [[Archy7]] – archy in 472edo tuning

* [[Supra7]] – supra in 56edo tuning

~~In contrast to the meantone diatonic scale, the superpyth diatonic is improper.~~

~~; 12-note mos ([[5L 7s]], borderline improper)~~

* [[Archy12]] – archy in 472edo tuning

* [[Supra12]] – supra in 56edo tuning

* [[12-22a]] – superpyth in 22edo tuning

~~The boundary of propriety is [[17edo]].~~

== Music ==

@@ Line 135: / Line 135: @@
 <nowiki/>* In 7-limit CWE tuning, octave reduced
 </div></div>
+== Chords and harmony ==
+Superpyth contains a version of the [[5L 2s|diatonic]] scale where the major third represents 9/7, and the minor third represents [[7/6]]. {{W|Tertian harmony}} can thus be used, with the major and minor triads representing [[14:18:21|1–9/7–3/2]] and [[6:7:9|1–7/6–3/2]] respectively, rather than the [[4:5:6|1–5/4–3/2]] and [[10:12:15|1–6/5–3/2]] triads in meantone. Since the fifth is sharp in archy rather than flat in [[meantone]], the large steps (major seconds) are wider, being around 212–222{{c}} depending on the tuning. The small steps (minor seconds) are thus narrower, being around 44–71{{c}}. This has the effect of large and small steps being more distinct compared to meantone diatonic, as well as stronger leading tones due to narrower small steps, though one may want to use milder tunings like [[17edo]] to avoid the small step being too narrow.
+== Scales ==
+; 5-note mos ([[2L&nbsp;3s]], proper)
+* [[Archy5]] – archy in 472edo tuning
+; 7-note mos ([[5L&nbsp;2s]], improper)
+* [[Archy7]] – archy in 472edo tuning
+* [[Supra7]] – supra in 56edo tuning
+In contrast to the meantone diatonic scale, the superpyth diatonic is improper.
+; 12-note mos ([[5L&nbsp;7s]], borderline improper)
+* [[Archy12]] – archy in 472edo tuning
+* [[Supra12]] – supra in 56edo tuning
+* [[12-22a]] – superpyth in 22edo tuning
+The boundary of propriety is [[17edo]].
 == Tunings ==
@@ Line 370: / Line 388: @@
 * [[DKW theory|DKW]] (2.3.5 superpyth): ~2 = 1200.000, ~3/2 = 709.758
 * DKW (2.3.7 archy): ~2 = 1200.000, ~3/2 = 712.585
-== Scales ==
-; 5-note mos ([[2L&nbsp;3s]], proper)
-* [[Archy5]] – archy in 472edo tuning
-; 7-note mos ([[5L&nbsp;2s]], improper)
-* [[Archy7]] – archy in 472edo tuning
-* [[Supra7]] – supra in 56edo tuning
-In contrast to the meantone diatonic scale, the superpyth diatonic is improper.
-; 12-note mos ([[5L&nbsp;7s]], borderline improper)
-* [[Archy12]] – archy in 472edo tuning
-* [[Supra12]] – supra in 56edo tuning
-* [[12-22a]] – superpyth in 22edo tuning
-The boundary of propriety is [[17edo]].
 == Music ==