Major-minthmic chords: Difference between revisions

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'''Major minthmic chords''' are [[~~Dyadic chord|~~essentially tempered dyadic ~~chords~~]] in the [[13-limit]] rank-5 temperament, and in addition the rank-3 2.3.11.13 [[subgroup]] temperament, tempered by the major minthma, [[352/351]].

'''Major-minthmic chords''' are [[essentially tempered dyadic chord]]s in the [[13-limit]] rank-5 temperament, and in addition the rank-3 2.3.11.13-[[subgroup]] temperament, tempered by the major minthma, [[352/351]].

There are 8 triads, 27 tetrads, 28 pentads, 12 hexads and 2 heptads as 2.3.11.13 subgroup [[13-odd-limit]] essentially tempered chords.

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Finally, there is a pair of heptads in inverse relationship:

* 1–9/8–16/13–4/3–3/2–18/11–24/13 with steps of 9/8, 12/11, 13/12, 9/8, 12/11, 9/8, 13/12 (→[[minthmic7a]]), and its inverse

* 1–9/8–16/13–4/3–3/2–18/11–24/13 with steps of 9/8, 12/11, 13/12, 9/8, 12/11, 9/8, 13/12 (→ [[minthmic7a]]), and its inverse

* 1–9/8–11/9–4/3–3/2–13/8–11/6 with steps of 9/8, 13/12, 12/11, 9/8, 13/12, 9/8, 12/11 (→[[minthmic7b]]).

* 1–9/8–11/9–4/3–3/2–13/8–11/6 with steps of 9/8, 13/12, 12/11, 9/8, 13/12, 9/8, 12/11 (→ [[minthmic7b]]).

~~Mintha was a nymph turned into a mint plant by a goddess whom she got in the way of~~

Equal temperaments with major minthmic chords include {{Optimal ET sequence| 22, 29, 46, 53, 80, 87, 111, 121, 140, 198 and 205 }}.

<ref>''[https://www.perseus.tufts.edu/hopper/text?doc=Perseus%3Atext%3A1999.04.0104%3Aalphabetic+letter%3DM%3Aentry+group%3D26%3Aentry%3Dmintha-bio-1 Dictionary of Greek and Roman Biography and Mythology]'' - William Smith (1849)</ref>

~~<ref>''[https://web.archive.org/web/20221230130135/http://mythandreligion.upatras.gr/english/__trashed/ Dictionary of Classical Mythology]'' - M.R. Wright (2012)</ref>~~

~~<ref>''[https://www.greekboston.com/culture/mythology/minthe All About Minthe – Myth of Greek Mythology]'' - Greek Boston (2024)</ref>~~

~~, and major minthmic tempering has the slightly sharp, minty-fresh fifths some people appreciate ([[Margo Schulter]] has expressed great fondness for this comma, for example).~~ Equal temperaments with major minthmic chords include {{Optimal ET sequence| 22, 29, 46, 53, 80, 87, 111, 121, 140, 198 and 205 }}.

~~== Notes ==~~

[[Category:13-odd-limit chords]]

@@ Line 1: / Line 1: @@
-'''Major minthmic chords''' are [[Dyadic chord|essentially tempered dyadic chords]] in the [[13-limit]] rank-5 temperament, and in addition the rank-3 2.3.11.13 [[subgroup]] temperament, tempered by the major minthma, [[352/351]].
+'''Major-minthmic chords''' are [[essentially tempered dyadic chord]]s in the [[13-limit]] rank-5 temperament, and in addition the rank-3 2.3.11.13-[[subgroup]] temperament, tempered by the major minthma, [[352/351]].
 There are 8 triads, 27 tetrads, 28 pentads, 12 hexads and 2 heptads as 2.3.11.13 subgroup [[13-odd-limit]] essentially tempered chords.
@@ Line 91: / Line 91: @@
 Finally, there is a pair of heptads in inverse relationship:
-* 1–9/8–16/13–4/3–3/2–18/11–24/13 with steps of 9/8, 12/11, 13/12, 9/8, 12/11, 9/8, 13/12 (→[[minthmic7a]]), and its inverse
+* 1–9/8–16/13–4/3–3/2–18/11–24/13 with steps of 9/8, 12/11, 13/12, 9/8, 12/11, 9/8, 13/12 (→ [[minthmic7a]]), and its inverse
-* 1–9/8–11/9–4/3–3/2–13/8–11/6 with steps of 9/8, 13/12, 12/11, 9/8, 13/12, 9/8, 12/11 (→[[minthmic7b]]).
+* 1–9/8–11/9–4/3–3/2–13/8–11/6 with steps of 9/8, 13/12, 12/11, 9/8, 13/12, 9/8, 12/11 (→ [[minthmic7b]]).
-Mintha was a nymph turned into a mint plant by a goddess whom she got in the way of
+Equal temperaments with major minthmic chords include {{Optimal ET sequence| 22, 29, 46, 53, 80, 87, 111, 121, 140, 198 and 205 }}.
-<ref>''[https://www.perseus.tufts.edu/hopper/text?doc=Perseus%3Atext%3A1999.04.0104%3Aalphabetic+letter%3DM%3Aentry+group%3D26%3Aentry%3Dmintha-bio-1  Dictionary of Greek and Roman Biography and Mythology]'' - William Smith (1849)</ref>
-<ref>''[https://web.archive.org/web/20221230130135/http://mythandreligion.upatras.gr/english/__trashed/ Dictionary of Classical Mythology]'' - M.R. Wright (2012)</ref>
-<ref>''[https://www.greekboston.com/culture/mythology/minthe All About Minthe – Myth of Greek Mythology]'' - Greek Boston (2024)</ref>
-, and major minthmic tempering has the slightly sharp, minty-fresh fifths some people appreciate ([[Margo Schulter]] has expressed great fondness for this comma, for example). Equal temperaments with major minthmic chords include {{Optimal ET sequence| 22, 29, 46, 53, 80, 87, 111, 121, 140, 198 and 205 }}.
-== Notes ==
 [[Category:13-odd-limit chords]]