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m →As a detemperament of 12et: I don't know about linking "MOS" as MOSDiagrams. Also generally lowercase is preferred.
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| Odd limit 2 = 2.3.5.7.19 21 | Mistuning 2 = 4.65 | Complexity 2 = 17
| Odd limit 2 = 2.3.5.7.19 21 | Mistuning 2 = 4.65 | Complexity 2 = 17
}}
}}
'''Garibaldi''' is a [[7-limit]] (and higher) [[regular temperament|temperament]] of the [[schismatic family #Garibaldi|schismatic family]]. It is an [[extension]] of [[helmholtz (temperament)|helmholtz]] temperament beyond the 5-limit but with the same simple [[chain of fifths|chain-of-fifths]] structure (so that [[chain-of-fifths notation|standard notation]] may be used). The garibaldi temperament tempers together the Pythagorean, syntonic, and archytas commas into a jack-of-all-trades "generic comma", which can be used to reach intervals of 3, 5, and 7. As in helmholtz temperament, [[5/4]] is mapped to the diminished fourth (e.g. C–F♭; a comma-flat major third), and the new mapping specific to garibaldi is that [[7/4]] is mapped to the double-diminished octave (e.g. C–C𝄫; a comma-flat minor seventh). This makes garibaldi a [[marvel temperaments|marvel]] and [[hemifamity temperaments|hemifamity]] temperament. Tuning the fifth a fraction of a cent sharp gives the best tunings.  
'''Garibaldi''' is a [[7-limit]] (and higher) [[regular temperament|temperament]] of the [[schismatic family #Garibaldi|schismatic family]]. It is an [[extension]] of [[helmholtz (temperament)|helmholtz]] temperament beyond the 5-limit but with the same simple [[chain of fifths|chain-of-fifths]] structure (so that [[chain-of-fifths notation|standard notation]] may be used). Garibaldi tempers together the Pythagorean, syntonic, and archytas commas into a jack-of-all-trades "generic comma", which can be used to reach intervals of 3, 5, and 7. As in helmholtz temperament, [[5/4]] is mapped to the diminished fourth (e.g. C–F♭; a comma-flat major third), and as a [[septischismic]] temperament, [[7/4]] is mapped to the double-diminished octave (e.g. C–C𝄫; a comma-flat minor seventh). This makes garibaldi the unique intersection of [[marvel]] and [[aberschismic]]. Tuning the fifth a fraction of a cent sharp gives the best tunings.  


Immediate 11-limit extensions include '''cassandra''' ({{nowrap| 41 & 53 }}), mapping 11/8 to +23 fifths, '''andromeda''' ({{nowrap| 29 & 41 }}), mapping 11/8 to −18 fifths, and '''helenus''' ({{nowrap| 53 & 65d }}), mapping 11/8 to −30 fifths. Garibaldi is most naturally a 2.3.5.7.19-[[subgroup]] temperament due to its immediate availability of [[19/16]] at the minor third (C–E♭). This is sometimes known as ''garibaldi nestoria.''  
Immediate 11-limit extensions include '''cassandra''' ({{nowrap| 41 & 53 }}), mapping 11/8 to +23 fifths, '''andromeda''' ({{nowrap| 29 & 41 }}), mapping 11/8 to −18 fifths, and '''helenus''' ({{nowrap| 53 & 65d }}), mapping 11/8 to −30 fifths. Garibaldi is most naturally a 2.3.5.7.19-[[subgroup]] temperament due to its immediate availability of [[19/16]] at the minor third (C–E♭). This is sometimes known as ''garibaldi nestoria.''  


Garibaldi was named in honor of [[Eduardo Sábat-Garibaldi]], who developed the [[dinarra]], a 53-tone [[microtonal guitar]] in the 1/9-schisma tuning.
Garibaldi was named in honor of [[Eduardo Sábat-Garibaldi]] ('''not''' Giuseppe Garibaldi), who developed the [[dinarra]], a 53-tone [[microtonal guitar]] in the 1/9-schisma tuning.


See [[Schismatic family #Garibaldi]] for technical data.
See [[Schismatic family #Garibaldi]] for technical data.
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* '''~[[19/16]] (minor)'''
* '''~[[19/16]] (minor)'''
* ~[[6/5]] (superminor)
* ~[[6/5]] (superminor)
* ~[[11/9]] (artoneutral)
* ~[[11/9]] (hyperminor)
* ~[[27/22]] (tendoneutral)
* ~[[27/22]] (hypomajor)
* ~[[5/4]] (submajor)
* ~[[5/4]] (submajor)
* '''~[[19/15]] (major)'''
* '''~[[19/15]] (major)'''
* ~[[9/7]] (supermajor)
* ~[[9/7]] (supermajor)


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.
The choice of nomenclature is due to the fact that cassandra is a relabeling of the 3-limit – it doesn't split primes in half, so it has no ''neutral'' intervals. Notice also the little interval between hyperminor and hypomajor, ~[[243/242]]. This interval spans 41 generator steps. 41edo tempers it out so that it merges hyperminor and hypominor into a true neutral [[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 neutraloid 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 ==
== 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.  
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
| 3/2
| Perfect fifth
| colspan="3" | C–G (perfect fifth)
| C–G
|-
|-
| 5/4
| 5/4
| Downmajor third
| colspan="3" | C–↓E (submajor third)
| C–vE
|-
|-
| 7/4
| 7/4
| Downminor seventh
| colspan="3" | C–↓Bb (subminor seventh)
| C–vBb
|-
|-
| 11/8
| 11/8
| Double-up fourth
| C–↑↑F (hyperfourth)
| C–^^F
| C–↓↓F#* (hypotritone)
| C–3↓F#* (3-subtritone)
|-
|-
| 13/8
| 13/8
| Double-up minor sixth
| C–↑↑Ab (hyperminor sixth)
| C–^^Ab
| C–↓↓A (hypomajor sixth)
| C–3↓A (3-submajor sixth)
|-
|-
| 19/16
| 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 ==
== Chords and harmony ==
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* 1–19/16–3/2 (C–Eb–G)
* 1–19/16–3/2 (C–Eb–G)


Note that the major third also represents [[24/19]], and the minor third, [[13/11]]. These chords are typically associated with a sort of coldness and metalness, like those in [[12edo]] if not more so.  
Note that the major third also represents [[24/19]], and the minor third, [[13/11]]. These chords are typically associated with a sort of coldness and metalness, like those in [[12edo]] if not more so, due to the [[hard]]<nowiki/>er fifths.  


If a warm, sweet, laid-back sound is desired, the thirds can be inflected inwards by a comma to yield
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
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 ==
== Scales ==
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[[Category:Marvel temperaments]]
[[Category:Marvel temperaments]]
[[Category:Gariboh clan]]
[[Category:Gariboh clan]]
[[Category:Hemifamity temperaments]]
[[Category:Aberschismic temperaments]]
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