Garibaldi: Difference between revisions

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'''Garibaldi''' 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|chain-of-fifths]] structure (so that [[chain-of-fifths notation|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]].

'''Garibaldi''' 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|chain-of-fifths]] structure (so that [[chain-of-fifths notation|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 doubly-diminished octave (e.g. C-C𝄫). 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. 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-Eb). This is sometimes known as ''garibaldi nestoria''.

Immediate 11-limit extensions include ''cassandra'' (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.

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{| class="wikitable center-1 right-2"

! rowspan="3" | #

! rowspan="3" | Cents*

! colspan="4" | Approximate Ratios

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|

|}

<nowiki>*~~</nowiki> in~~ 7-limit CTE tuning

<nowiki />* In 7-limit CTE tuning

== Notation ==

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

|+Cassandra nomenclature ~~for~~ selected intervals

|+ style="font-size: 105%; white-space: nowrap;" | Cassandra nomenclature for selected intervals

|-

! Ratio

! Nominal

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|-

| 5/4

| ~~Down major~~ third

| Downmajor third

| C-vE

|-

| 7/4

| ~~Down minor~~ seventh

| Downminor seventh

| C-vBb

|-

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{| class="wikitable center-1 center-3 mw-collapsible mw-collapsed"

|+ style=white-space:nowrap | Andromeda nomenclature for selected intervals

|+ style="font-size: 105%; white-space: nowrap;" | Andromeda nomenclature for selected intervals

|-

! Ratio

! Nominal

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|-

| 11/8

| Down diminished fifth Double-down augmented fourth

| Down-diminished fifth Double-down augmented fourth

| C-vGb C-vvF#

| C-vGb C-vvF#

|-

| 13/8

| Double ~~down major~~ sixth

| Double downmajor sixth

| C-vvA

|}

{| class="wikitable center-1 center-3 mw-collapsible mw-collapsed"

|+ style=white-space:nowrap | Helenus nomenclature for selected intervals

|+ style="font-size: 105%; white-space: nowrap;" | Helenus nomenclature for selected intervals

|-

! Ratio

! Nominal

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|-

| 11/8

| Double-down diminished fifth Triple-down augmented fourth

| Double-down diminished fifth Triple-down augmented fourth

| C-vvGb C-v3F#

| C-vvGb C-v3F#

|-

| 13/8

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==== Garibaldi ====

{| class="wikitable center-all left-4"

~~|+ style=white-space:nowrap | Tuning spectrum for garibaldi~~

! Edo Generator

|-

! [[Eigenmonzo|Eigenmonzo (Unchanged-interval)]]

! Edo Generator

! [[Eigenmonzo|Eigenmonzo (Unchanged-interval)]]

! Generator (¢)

! Comments

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|

| 700.0000

| Lower bound of 9-odd-limit, 2.3.5.7.19 subgroup 19- and 21-odd-limit diamond monotone

| Lower bound of 9-odd-limit, 2.3.5.7.19 subgroup 19- and 21-odd-limit diamond monotone

|-

|

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|

| 703.4483

| Upper bound of 9-odd-limit, 2.3.5.7.19 subgroup 19- and 21-odd-limit diamond monotone

| Upper bound of 9-odd-limit, 2.3.5.7.19 subgroup 19- and 21-odd-limit diamond monotone

|-

|

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{| class="wikitable mw-collapsible mw-collapsed center-all left-4"

~~|+ style=white-space:nowrap | Tuning spectrum for cassandra~~

! Edo Generator

|-

! [[Eigenmonzo|Eigenmonzo (Unchanged-interval)]]

! Edo Generator

! [[Eigenmonzo|Eigenmonzo (Unchanged-interval)]]

! Generator (¢)

! Comments

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|

| 701.8868

| Lower bound of 11-, 13-, 15-odd-limit, 2.3.5.7.11.13.19 subgroup 19- and 21-odd-limit diamond monotone

| Lower bound of 11-, 13-, 15-odd-limit, 2.3.5.7.11.13.19 subgroup 19- and 21-odd-limit diamond monotone

|-

|

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|

| 702.4390

| Upper bound of 11-, 13-, 15-odd-limit, 2.3.5.7.11.13.19 subgroup 19- and 21-odd-limit diamond monotone

| Upper bound of 11-, 13-, 15-odd-limit, 2.3.5.7.11.13.19 subgroup 19- and 21-odd-limit diamond monotone

|-

|

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{| class="wikitable mw-collapsible mw-collapsed center-all left-4"

~~|+ style=white-space:nowrap | Tuning spectrum for andromeda~~

! Edo Generator

|-

! Eigenmonzo (Unchanged-interval)

! Edo Generator

! Eigenmonzo (Unchanged-interval)

! Generator (¢)

! Comments

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|

| 702.4390

| Lower bound of 13-, 15-odd-limit, 2.3.5.7.11.13.19 subgroup 19- and 21-odd-limit diamond monotone

| Lower bound of 13-, 15-odd-limit, 2.3.5.7.11.13.19 subgroup 19- and 21-odd-limit diamond monotone

|-

|

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|

| 703.4483

| Upper bound of 9-, 11-, 13-, 15-odd-limit, 2.3.5.7.11.13.19 subgroup 19- and 21-odd-limit diamond monotone

| Upper bound of 9-, 11-, 13-, 15-odd-limit, 2.3.5.7.11.13.19 subgroup 19- and 21-odd-limit diamond monotone

|-

|

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{| class="wikitable mw-collapsible mw-collapsed center-all left-4"

~~|+ style=white-space:nowrap | Tuning spectrum for helenus~~

! Edo Generator

|-

! Eigenmonzo (Unchanged-interval)

! Edo Generator

! Eigenmonzo (Unchanged-interval)

! Generator (¢)

! Comments

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|

| 701.5385

| Lower bound of 13-, 15-odd-limit, 2.3.5.7.11.13.19 subgroup 19- and 21-odd-limit diamond monotone

| Lower bound of 13-, 15-odd-limit, 2.3.5.7.11.13.19 subgroup 19- and 21-odd-limit diamond monotone

|-

|

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|

| 701.8868

| Upper bound of 11-, 13-, 15-odd-limit, 2.3.5.7.11.13.19 subgroup 19- and 21-odd-limit diamond monotone

| Upper bound of 11-, 13-, 15-odd-limit, 2.3.5.7.11.13.19 subgroup 19- and 21-odd-limit diamond monotone

|-

|

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|}

[[Category:Garibaldi| ]]

[[Category:Garibaldi| ]]

[[Category:Temperaments]]

[[Category:Schismatic family]]

@@ Line 1: / Line 1: @@
-'''Garibaldi''' 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|chain-of-fifths]] structure (so that [[chain-of-fifths notation|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]].
+'''Garibaldi''' 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|chain-of-fifths]] structure (so that [[chain-of-fifths notation|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 doubly-diminished octave (e.g. C-C&#x1D12B;). 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. 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-Eb). This is sometimes known as ''garibaldi nestoria''.
+Immediate 11-limit extensions include ''cassandra'' (41 &amp; 53), mapping 11/8 to +23 fifths, ''andromeda'' {{nowrap|(29 &amp; 41)}}, mapping 11/8 to &minus;18 fifths, and ''helenus'' {{nowrap|(53 &amp; 65d)}}, mapping 11/8 to &minus;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.
@@ Line 9: / Line 9: @@
 {| class="wikitable center-1 right-2"
-! rowspan="3" | #
+! rowspan="3" | &#35;
 ! rowspan="3" | Cents*
 ! colspan="4" | Approximate Ratios
@@ Line 314: / Line 314: @@
 |
 |}
-<nowiki>*</nowiki> in 7-limit CTE tuning
+<nowiki />* In 7-limit CTE tuning
 == Notation ==
@@ Line 320: / Line 320: @@
 {| class="wikitable center-1 center-3"
-|+Cassandra nomenclature<br>for selected intervals
+|+ style="font-size: 105%; white-space: nowrap;" | Cassandra nomenclature for<br />selected intervals
+|-
 ! Ratio
 ! Nominal
@@ Line 330: / Line 331: @@
 |-
 | 5/4
-| Down major third
+| Downmajor third
 | C-vE
 |-
 | 7/4
-| Down minor seventh
+| Downminor seventh
 | C-vBb
 |-
@@ Line 351: / Line 352: @@
 {| class="wikitable center-1 center-3 mw-collapsible mw-collapsed"
-|+ style=white-space:nowrap | Andromeda nomenclature for selected intervals
+|+ style="font-size: 105%; white-space: nowrap;" | Andromeda nomenclature for selected intervals
+|-
 ! Ratio
 ! Nominal
@@ Line 357: / Line 359: @@
 |-
 | 11/8
-| Down diminished fifth<br>Double-down augmented fourth
+| Down-diminished fifth<br />Double-down augmented fourth
-| C-vGb<br>C-vvF#
+| C-vGb<br />C-vvF#
 |-
 | 13/8
-| Double down major sixth
+| Double downmajor sixth
 | C-vvA
 |}
 {| class="wikitable center-1 center-3 mw-collapsible mw-collapsed"
-|+ style=white-space:nowrap | Helenus nomenclature for selected intervals
+|+ style="font-size: 105%; white-space: nowrap;" | Helenus nomenclature for selected intervals
+|-
 ! Ratio
 ! Nominal
@@ Line 372: / Line 375: @@
 |-
 | 11/8
-| Double-down diminished fifth<br>Triple-down augmented fourth
+| Double-down diminished fifth<br />Triple-down augmented fourth
-| C-vvGb<br>C-v<sup>3</sup>F#
+| C-vvGb<br />C-v<sup>3</sup>F#
 |-
 | 13/8
@@ Line 406: / Line 409: @@
 ==== Garibaldi ====
 {| class="wikitable center-all left-4"
-|+ style=white-space:nowrap | Tuning spectrum for garibaldi
+! Edo<br />Generator
-|-
+! [[Eigenmonzo|Eigenmonzo<br />(Unchanged-interval)]]
-! Edo<br>Generator
-! [[Eigenmonzo|Eigenmonzo<br>(Unchanged-interval)]]
 ! Generator (¢)
 ! Comments
@@ Line 416: / Line 417: @@
 |
 | 700.0000
-| Lower bound of 9-odd-limit, <br>2.3.5.7.19 subgroup 19- and 21-odd-limit diamond monotone
+| Lower bound of 9-odd-limit, <br />2.3.5.7.19 subgroup 19- and 21-odd-limit diamond monotone
 |-
 |
@@ Line 551: / Line 552: @@
 |
 | 703.4483
-| Upper bound of 9-odd-limit, <br>2.3.5.7.19 subgroup 19- and 21-odd-limit diamond monotone
+| Upper bound of 9-odd-limit, <br />2.3.5.7.19 subgroup 19- and 21-odd-limit diamond monotone
 |-
 |
@@ Line 565: / Line 566: @@
 {| class="wikitable mw-collapsible mw-collapsed center-all left-4"
-|+ style=white-space:nowrap | Tuning spectrum for cassandra
+! Edo<br />Generator
-|-
+! [[Eigenmonzo|Eigenmonzo<br />(Unchanged-interval)]]
-! Edo<br>Generator
-! [[Eigenmonzo|Eigenmonzo<br>(Unchanged-interval)]]
 ! Generator (¢)
 ! Comments
@@ Line 635: / Line 634: @@
 |
 | 701.8868
-| Lower bound of 11-, 13-, 15-odd-limit, <br>2.3.5.7.11.13.19 subgroup 19- and 21-odd-limit diamond monotone
+| Lower bound of 11-, 13-, 15-odd-limit, <br />2.3.5.7.11.13.19 subgroup 19- and 21-odd-limit diamond monotone
 |-
 |
@@ Line 790: / Line 789: @@
 |
 | 702.4390
-| Upper bound of 11-, 13-, 15-odd-limit, <br>2.3.5.7.11.13.19 subgroup 19- and 21-odd-limit diamond monotone
+| Upper bound of 11-, 13-, 15-odd-limit, <br />2.3.5.7.11.13.19 subgroup 19- and 21-odd-limit diamond monotone
 |-
 |
@@ Line 834: / Line 833: @@
 {| class="wikitable mw-collapsible mw-collapsed center-all left-4"
-|+ style=white-space:nowrap | Tuning spectrum for andromeda
+! Edo<br />Generator
-|-
+! Eigenmonzo<br />(Unchanged-interval)
-! Edo<br>Generator
-! Eigenmonzo<br>(Unchanged-interval)
 ! Generator (¢)
 ! Comments
@@ Line 944: / Line 941: @@
 |
 | 702.4390
-| Lower bound of 13-, 15-odd-limit, <br>2.3.5.7.11.13.19 subgroup 19- and 21-odd-limit diamond monotone
+| Lower bound of 13-, 15-odd-limit, <br />2.3.5.7.11.13.19 subgroup 19- and 21-odd-limit diamond monotone
 |-
 |
@@ Line 1,024: / Line 1,021: @@
 |
 | 703.4483
-| Upper bound of 9-, 11-, 13-, 15-odd-limit, <br>2.3.5.7.11.13.19 subgroup 19- and 21-odd-limit diamond monotone
+| Upper bound of 9-, 11-, 13-, 15-odd-limit, <br />2.3.5.7.11.13.19 subgroup 19- and 21-odd-limit diamond monotone
 |-
 |
@@ Line 1,073: / Line 1,070: @@
 {| class="wikitable mw-collapsible mw-collapsed center-all left-4"
-|+ style=white-space:nowrap | Tuning spectrum for helenus
+! Edo<br />Generator
-|-
+! Eigenmonzo<br />(Unchanged-interval)
-! Edo<br>Generator
-! Eigenmonzo<br>(Unchanged-interval)
 ! Generator (¢)
 ! Comments
@@ Line 1,118: / Line 1,113: @@
 |
 | 701.5385
-| Lower bound of 13-, 15-odd-limit, <br>2.3.5.7.11.13.19 subgroup 19- and 21-odd-limit diamond monotone
+| Lower bound of 13-, 15-odd-limit, <br />2.3.5.7.11.13.19 subgroup 19- and 21-odd-limit diamond monotone
 |-
 |
@@ Line 1,208: / Line 1,203: @@
 |
 | 701.8868
-| Upper bound of 11-, 13-, 15-odd-limit, <br>2.3.5.7.11.13.19 subgroup 19- and 21-odd-limit diamond monotone
+| Upper bound of 11-, 13-, 15-odd-limit, <br />2.3.5.7.11.13.19 subgroup 19- and 21-odd-limit diamond monotone
 |-
 |
@@ Line 1,306: / Line 1,301: @@
 |}
-[[Category:Garibaldi| ]] <!-- main article -->
+[[Category:Garibaldi| ]] <!-- Main article -->
 [[Category:Temperaments]]
 [[Category:Schismatic family]]

Garibaldi: Difference between revisions

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