Garibaldi: Difference between revisions

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'''Garibaldi temperament''' is a 7-limit (and higher) temperament of the [[Schismatic family #Garibaldi|schismatic family]]. It is an extension of [[helmholtz]] temperament beyond the 5-limit but with the same simple chain-of-fifths structure (so that standard notation may be used). As in helmholtz temperament, [[5/4]] is mapped to the diminished fourth (e.g. A-D♭), and the new mapping specific to garibaldi is that [[7/4]] is mapped to the double diminished octave (e.g. A-~~Abb~~). This makes garibaldi a [[Marvel temperaments|marvel temperament]].

'''Garibaldi temperament''' is a 7-limit (and higher) temperament of the [[Schismatic family #Garibaldi|schismatic family]]. It is an extension of [[helmholtz]] temperament beyond the 5-limit but with the same simple chain-of-fifths structure (so that standard notation may be used). As in helmholtz temperament, [[5/4]] is mapped to the diminished fourth (e.g. C-F♭), and the new mapping specific to garibaldi is that [[7/4]] is mapped to the double diminished octave (e.g. C-Cbb). This makes garibaldi a [[Marvel temperaments|marvel temperament]].

Immediate 11-limit extensions include ''cassandra'' (41&53), mapping 11/8 to +23 fifths, ''andromeda'' (29&41), mapping 11/8 to -18 fifths, and ''helenus'' (53&65d), mapping 11/8 to -30 fifths.

Immediate 11-limit extensions include ''cassandra'' (41 & 53), mapping 11/8 to +23 fifths, ''andromeda'' (29 & 41), mapping 11/8 to -18 fifths, and ''helenus'' (53 & 65d), mapping 11/8 to -30 fifths.

== Interval chain ==

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|}

<nowiki>*</nowiki> in 7-limit POTE tuning

== Notation ==

Using garibaldi can be a challenge because it defies the tradition of tertian harmony in [[circle-of-fifths notation]]. The just major triad on C is C-Fb-G, for example. One may want to adopt an additional module of accidentals such as arrows to represent the comma step, allowing them to write the chord above as C-vE-G.

{| class="wikitable center-1 center-3"

|+Cassandra nomenclature<br>for selected intervals

! Ratio

! Nominal

! Example

|-

| 3/2

| Perfect fifth

| C-G

|-

| 5/4

| Down major third

| C-vE

|-

| 7/4

| Down minor seventh

| C-vBb

|-

| 11/8

| Double-up fourth

| C-^^F

|-

| 13/8

| Double-up minor sixth

| C-^^Ab

|}

== Tuning spectra ==

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-'''Garibaldi temperament''' is a 7-limit (and higher) temperament of the [[Schismatic family #Garibaldi|schismatic family]]. It is an extension of [[helmholtz]] temperament beyond the 5-limit but with the same simple chain-of-fifths structure (so that standard notation may be used). As in helmholtz temperament, [[5/4]] is mapped to the diminished fourth (e.g. A-D♭), and the new mapping specific to garibaldi is that [[7/4]] is mapped to the double diminished octave (e.g. A-Abb). This makes garibaldi a [[Marvel temperaments|marvel temperament]].
+'''Garibaldi temperament''' is a 7-limit (and higher) temperament of the [[Schismatic family #Garibaldi|schismatic family]]. It is an extension of [[helmholtz]] temperament beyond the 5-limit but with the same simple chain-of-fifths structure (so that standard notation may be used). As in helmholtz temperament, [[5/4]] is mapped to the diminished fourth (e.g. C-F♭), and the new mapping specific to garibaldi is that [[7/4]] is mapped to the double diminished octave (e.g. C-Cbb). This makes garibaldi a [[Marvel temperaments|marvel temperament]].
-Immediate 11-limit extensions include ''cassandra'' (41&amp;53), mapping 11/8 to +23 fifths, ''andromeda'' (29&amp;41), mapping 11/8 to -18 fifths, and ''helenus'' (53&amp;65d), mapping 11/8 to -30 fifths.
+Immediate 11-limit extensions include ''cassandra'' (41 &amp; 53), mapping 11/8 to +23 fifths, ''andromeda'' (29 &amp; 41), mapping 11/8 to -18 fifths, and ''helenus'' (53 &amp; 65d), mapping 11/8 to -30 fifths.
 == Interval chain ==
@@ Line 271: / Line 271: @@
 |}
 <nowiki>*</nowiki> in 7-limit POTE tuning
+== Notation ==
+Using garibaldi can be a challenge because it defies the tradition of tertian harmony in [[circle-of-fifths notation]]. The just major triad on C is C-Fb-G, for example. One may want to adopt an additional module of accidentals such as arrows to represent the comma step, allowing them to write the chord above as C-vE-G.
+{| class="wikitable center-1 center-3"
+|+Cassandra nomenclature<br>for selected intervals
+! Ratio
+! Nominal
+! Example
+|-
+| 3/2
+| Perfect fifth
+| C-G
+|-
+| 5/4
+| Down major third
+| C-vE
+|-
+| 7/4
+| Down minor seventh
+| C-vBb
+|-
+| 11/8
+| Double-up fourth
+| C-^^F
+|-
+| 13/8
+| Double-up minor sixth
+| C-^^Ab
+|}
 == Tuning spectra ==