Garibaldi: Difference between revisions

← Older edit Newer edit →

VisualWikitext

@@ Line 359: / Line 359: @@
 Notice also the little interval between artoneutral and tendoneutral, ~[[243/242]]. This interval spans 41 generator steps. 41edo tempers it out so that it merges artoneutral and tendoneutral into a [[Sqrt(3/2)|hemififth]] whereas 53edo exaggerates it to the size of the generic comma. 94edo tunes it to one half the size of the general comma, which can be seen as a good compromise.
-On another note, excluding 41edo, the two neutral intervals also have natural 13-limit interpretations in cassandra: 11/9~[[39/32]] and 27/22~[[16/13]], tempering out [[352/351]].
+On another note, excluding 41edo, the two neutral intervals also have natural 13-limit interpretations in cassandra: 11/9~[[39/32]] and 27/22~[[16/13]], tempering out [[352/351]]. This also means the minor third is ~[[13/11]].
 == Notation ==
 Like in [[schismic]], it is recommended to adopt an additional module of accidentals such as arrows to represent the comma step. Garibaldi further benefits from this as the arrow also stands in for the septimal comma, so that the same inflection can be used to reach classical and septimal intervals alike.
-The following tables show how to notate 11- and 13-limit intervals in each extension of garibaldi.
+The following table shows how to notate 2.3.5.7.11.13.19 intervals in each extension of garibaldi.
-{| class="wikitable center-1 center-3"
+{| class="wikitable" style="text-align:center; vertical-align:middle;"
-|+ style="font-size: 105%; white-space: nowrap;" | Cassandra nomenclature for<br>selected intervals
+|+Nomenclature of selected intervals
-|-
+|- style="font-weight:bold;"
-! Ratio
+! rowspan="2" | Ratio
-! Nominal
+! colspan="3" | Example
-! Example
+|- style="font-weight:bold;"
+| Cassandra
+| Andromeda
+| Helenus
 |-
 | 3/2
-| Perfect fifth
+| colspan="3" | C–G (perfect fifth)
-| C–G
 |-
 | 5/4
-| Downmajor third
+| colspan="3" | C–↓E (downmajor third)
-| C–vE
 |-
 | 7/4
-| Downminor seventh
+| colspan="3" | C–↓Bb (downminor seventh)
-| C–vBb
 |-
 | 11/8
-| Double-up fourth
+| C–↑↑F (dupfourth)
-| C–^^F
+| C–↓↓F#* (dudtritone)
+| C–↓3F#* (trudtritone)
 |-
 | 13/8
-| Double-up minor sixth
+| C–↑↑Ab (dupminor sixth)
-| C–^^Ab
+| C–↓↓A (dudmajor sixth)
+| C–↓3A (trudmajor sixth)
 |-
 | 19/16
-| Minor third
+| colspan="3" | C–Eb (minor third)
-| C–Eb
-|}
-{| class="wikitable center-1 center-3 mw-collapsible mw-collapsed"
-|+ style="font-size: 105%; white-space: nowrap;" | Andromeda nomenclature for selected intervals
-|-
-! Ratio
-! Nominal
-! Example
-|-
-| 11/8
-| Down diminished fifth<br>Double-down augmented fourth
-| C–vGb<br>C–vvF#
-|-
-| 13/8
-| Double downmajor sixth
-| C–vvA
 |}
-{| class="wikitable center-1 center-3 mw-collapsible mw-collapsed"
+<nowiki/>*Can also be spelt ↓Gb and ↓↓Gb respectively, since F# = ↑Gb.
-|+ style="font-size: 105%; white-space: nowrap;" | Helenus nomenclature for selected intervals
-|-
-! Ratio
-! Nominal
-! Example
-|-
-| 11/8
-| Double-down diminished fifth<br>Triple-down augmented fourth
-| C–vvGb<br>C–v<sup>3</sup>F#
-|-
-| 13/8
-| Triple-down major sixth
-| C–v<sup>3</sup>A
-|}
 == Chords and harmony ==
@@ Line 438: / Line 409: @@
 If a warm, sweet, laid-back sound is desired, the thirds can be inflected inwards by a comma to yield
-* 1–5/4–3/2 (C–vE–G)
+* 1–5/4–3/2 (C–↓E–G)
-* 1–6/5–3/2 (C–^Eb–G)
+* 1–6/5–3/2 (C–↑Eb–G)
 Contrarily, for a more sour and active sound, they can be inflected outwards by a comma to yield
-* 1–9/7–3/2 (C–^E-G)
+* 1–9/7–3/2 (C–↑E-G)
-* 1–7/6–3/2 (C–vEb-G)
+* 1–7/6–3/2 (C–↓Eb-G)
 == Scales ==