Superpyth: Difference between revisions

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Another approach is also possible. In the 5-limit, the major triad can be constructed by octave-reducing odd harmonics 1, 3, and 5, giving us 4:5:6, with the minor triad being its utonal inversion. A similar construction of septimal chords gives us [[6:7:8]] and its inversion [[21:24:28]], which are built with the intervals [[7/6]] and [[8/7]]. These intervals contrast by [[49/48]], similarly to how 5-limit thirds contrast by [[25/24]]. There are some issues, however. For example, the 6:7:8 chord has the root on the top rather than the bottom, and the notes may clash from being too close to each other. However, the wide voicing of these chords, those being 4:7:12 and 7:12:21, solve both of these issues. These triads span a twelfth. In terms of the [[chain of fifths]], these chords are simpler in superpyth than the 5-limit triads in meantone.

Since the intervals of the 2.3.7-subgroup cluster around [[5edo]], a [[pentatonic]] system of interval classification may be preferred over the [[heptatonic]] one, with 7/6 becoming a major interval and 8/7~9/8 becoming a minor one, and 49/48~[[28/27]] becoming a chroma.

== Scales ==

; 5-note mos ([[2L 3s]], proper)

~~{{Todo|inline=1|expand}}~~

In contrast to the meantone pentic scale, the superpyth pentic is proper and mellow in quality, which is related to the fact that the intervals of the 2.3.7 subgroup cluster around [[5edo]]. As such, this system may be preferred over diatonic for interval classification, with 7/6 becoming a major interval and 8/7~9/8 becoming a minor one, and 49/48~[[28/27]] becoming a chroma.

; 7-note mos ([[5L 2s]], improper)

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

In contrast to the meantone diatonic scale, the superpyth diatonic is improper. Since the fifth is sharp 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 bend the leading tone down by a small step to avoid it being too close to the tonic.

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~~.

; 12-note mos ([[5L 7s]], improper)

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

The superpyth chromatic scale is also improper (the boundary of propriety is [[17edo]]).

=== Scala files ===

@@ Line 154: / Line 154: @@
 Another approach is also possible. In the 5-limit, the major triad can be constructed by octave-reducing odd harmonics 1, 3, and 5, giving us 4:5:6, with the minor triad being its utonal inversion. A similar construction of septimal chords gives us [[6:7:8]] and its inversion [[21:24:28]], which are built with the intervals [[7/6]] and [[8/7]]. These intervals contrast by [[49/48]], similarly to how 5-limit thirds contrast by [[25/24]]. There are some issues, however. For example, the 6:7:8 chord has the root on the top rather than the bottom, and the notes may clash from being too close to each other. However, the wide voicing of these chords, those being 4:7:12 and 7:12:21, solve both of these issues. These triads span a twelfth. In terms of the [[chain of fifths]], these chords are simpler in superpyth than the 5-limit triads in meantone.
-Since the intervals of the 2.3.7-subgroup cluster around [[5edo]], a [[pentatonic]] system of interval classification may be preferred over the [[heptatonic]] one, with 7/6 becoming a major interval and 8/7~9/8 becoming a minor one, and 49/48~[[28/27]] becoming a chroma.
 == Scales ==
 ; 5-note mos ([[2L&nbsp;3s]], proper)
-{{Todo|inline=1|expand}}
+In contrast to the meantone pentic scale, the superpyth pentic is proper and mellow in quality, which is related to the fact that the intervals of the 2.3.7 subgroup cluster around [[5edo]]. As such, this system may be preferred over diatonic for interval classification, with 7/6 becoming a major interval and 8/7~9/8 becoming a minor one, and 49/48~[[28/27]] becoming a chroma.
 ; 7-note mos ([[5L&nbsp;2s]], improper)
-In contrast to the meantone diatonic scale, the superpyth diatonic is improper.
+In contrast to the meantone diatonic scale, the superpyth diatonic is improper. Since the fifth is sharp 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 bend the leading tone down by a small step to avoid it being too close to the tonic.
-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.
 ; 12-note mos ([[5L&nbsp;7s]], improper)
-The boundary of propriety is [[17edo]].
+The superpyth chromatic scale is also improper (the boundary of propriety is [[17edo]]).
 === Scala files ===

Superpyth: Difference between revisions

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