2.3.7 subgroup: Difference between revisions

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== Chords and harmony ==

There are a number of ways to approach harmony in this subgroup, most of which are discussed in [[Superpyth #Chords and harmony]]. The basic forms of chords include the triad [[6:7:9]], the tetrad [[6:7:8:9]], and their utonal inverses. ~~Similarly, the~~ fourth-spanning triads [[6:7:8]] and [[21:24:28]] can be used, as well as their wide voicing 4:7:12 and 7:12:21. ~~Examples of extensions~~ of these chords are [[12:14:18:21]] and [[14:18:21:24]]. Like in [[5-limit]] [[JI]], one quickly runs into [[wolf interval]]s without care, but the 2.3.7 wolf being [[21/16]] or [[32/21]] may be considered less discordant, and useful in its own ways.

There are a number of ways to approach harmony in this subgroup, most of which are discussed in [[Superpyth #Chords and harmony]]. The basic forms of chords include the {{w|tertian harmony|tertian}} triad [[6:7:9]], the tetrad [[6:7:8:9]], and their utonal inverses. The fourth-spanning triads [[6:7:8]] and [[21:24:28]] can also be used, as well as their wide voicing 4:7:12 and 7:12:21. Extensions of these chords include but are not limited to the [[9-odd-limit]] [[anomalous saturated suspension|saturated suspensions]], [[12:14:18:21]] and [[14:18:21:24]].

Like in [[5-limit]] [[JI]], one quickly runs into [[wolf interval]]s without care, but the 2.3.7 wolf being [[21/16]] or [[32/21]] may be considered less discordant, and useful in its own ways. For example, 1–9/8–21/16–3/2 and 1–8/7–4/3–3/2 may be considered [[21-odd-limit]] concords. They are conflated in superpyth as the sus2-4 chord, but subtlely contrast each other in JI.

== Properties ==

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==== Misc ====

* [[Diasem]]/Tas[9] ([[chirality|left-handed]]): 1/1 9/8 7/6 21/16 4/3 3/2 14/9 7/4 16/9 2/1

* Archytas Diatonic: 8/7, 32/27, 4/3, 3/2, 12/7, 16/9, 2/1

* Safi al-Din Septimal: 8/7, 9/7, 4/3, 32/21, 12/7, 16/9, 2/1

== Regular temperaments ==

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== Music ==

; [[Domin]]

* [https://www.youtube.com/watch?v=0CoFmqptcGU ''Pnong (2.3.7 JI)''] (2024)

* [https://www.youtube.com/watch?v=JU_e2AK3cQ0 ''Ngaat (2.3.7 JI non octave)''] (2024)

* [https://www.youtube.com/watch?v=_UFNfu7angg ''Xiticix (2.3.7 JI)''] (2024)

* [https://www.youtube.com/watch?v=uFwJzgj49bU ''Traudn (2.3.7 JI)''] (2024)

; [[Michael Harrison]]

* From Ancient Worlds (for harmonic piano), 1992

@@ Line 10: / Line 10: @@
 == Chords and harmony ==
-There are a number of ways to approach harmony in this subgroup, most of which are discussed in [[Superpyth #Chords and harmony]]. The basic forms of chords include the triad [[6:7:9]], the tetrad [[6:7:8:9]], and their utonal inverses. Similarly, the fourth-spanning triads [[6:7:8]] and [[21:24:28]] can be used, as well as their wide voicing 4:7:12 and 7:12:21. Examples of extensions of these chords are [[12:14:18:21]] and [[14:18:21:24]]. Like in [[5-limit]] [[JI]], one quickly runs into [[wolf interval]]s without care, but the 2.3.7 wolf being [[21/16]] or [[32/21]] may be considered less discordant, and useful in its own ways.
+There are a number of ways to approach harmony in this subgroup, most of which are discussed in [[Superpyth #Chords and harmony]]. The basic forms of chords include the {{w|tertian harmony|tertian}} triad [[6:7:9]], the tetrad [[6:7:8:9]], and their utonal inverses. The fourth-spanning triads [[6:7:8]] and [[21:24:28]] can also be used, as well as their wide voicing 4:7:12 and 7:12:21. Extensions of these chords include but are not limited to the [[9-odd-limit]] [[anomalous saturated suspension|saturated suspensions]], [[12:14:18:21]] and [[14:18:21:24]].
+Like in [[5-limit]] [[JI]], one quickly runs into [[wolf interval]]s without care, but the 2.3.7 wolf being [[21/16]] or [[32/21]] may be considered less discordant, and useful in its own ways. For example, 1–9/8–21/16–3/2 and 1–8/7–4/3–3/2 may be considered [[21-odd-limit]] concords. They are conflated in superpyth as the sus2-4 chord, but subtlely contrast each other in JI.
 == Properties ==
@@ Line 33: / Line 35: @@
 ==== Misc ====
 * [[Diasem]]/Tas[9] ([[chirality|left-handed]]): 1/1 9/8 7/6 21/16 4/3 3/2 14/9 7/4 16/9 2/1
+* Archytas Diatonic: 8/7, 32/27, 4/3, 3/2, 12/7, 16/9, 2/1
+* Safi al-Din Septimal: 8/7, 9/7, 4/3, 32/21, 12/7, 16/9, 2/1
 == Regular temperaments ==
@@ Line 204: / Line 208: @@
 == Music ==
+; [[Domin]]
+* [https://www.youtube.com/watch?v=0CoFmqptcGU ''Pnong (2.3.7 JI)''] (2024)
+* [https://www.youtube.com/watch?v=JU_e2AK3cQ0 ''Ngaat (2.3.7 JI non octave)''] (2024)
+* [https://www.youtube.com/watch?v=_UFNfu7angg ''Xiticix (2.3.7 JI)''] (2024)
+* [https://www.youtube.com/watch?v=uFwJzgj49bU ''Traudn (2.3.7 JI)''] (2024)
 ; [[Michael Harrison]]
 * From Ancient Worlds (for harmonic piano), 1992