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'''Garibaldi''' is a [[7-limit]] (and higher) [[regular temperament|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]].  
'''Garibaldi''' is a [[7-limit]] (and higher) [[regular temperament|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'' {{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]], 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"
{| class="wikitable center-1 right-2"
|-
! rowspan="3" | #
! rowspan="3" | #
! rowspan="3" | Cents*
! rowspan="3" | Cents*
Line 333: Line 334:
! colspan="3" style="border-left: double;" | "Super"
! colspan="3" style="border-left: double;" | "Super"
! colspan="3" style="border-left: double;" | "Double-super"
! colspan="3" style="border-left: double;" | "Double-super"
|-
|- style="border-left: double;"
! style="border-left: double;" | Gen. || Cents* || Ratios
! Gen. || Cents* || Ratios
! style="border-left: double;" | Gen. || Cents* || Ratios
! Gen. || Cents* || Ratios
! style="border-left: double;" | Gen. || Cents* || Ratios
! Gen. || Cents* || Ratios
! style="border-left: double;" | Gen. || Cents* || Ratios
! Gen. || Cents* || Ratios
! style="border-left: double;" | Gen. || Cents* || Ratios
! Gen. || Cents* || Ratios
|-
|- style="border-left: double;"
| 0
| 0
| P1
| P1
| style="border-left: double;" |  || ||  
| || ||  
| style="border-left: double;" |  || ||  
| || ||  
| style="border-left: double;" | 0 || 0.0 || 1/1
| 0 || 0.0 || 1/1
| style="border-left: double;" | 12 || 25.2 || 64/63~81/80
| 12 || 25.2 || 64/63~81/80
| style="border-left: double;" | 24 || 50.5 || 33/32~36/35
| 24 || 50.5 || 33/32~36/35
|-
|- style="border-left: double;"
| 1
| 1
| m2
| m2
| style="border-left: double;" | ||  ||  
| || ||  
| style="border-left: double;" | -17 || 64.2 || 27/26~28/27
| -17 || 64.2 || 27/26~28/27
| style="border-left: double;" | -5 || 89.5 || 20/19~21/20
| -5 || 89.5 || 20/19~21/20
| style="border-left: double;" | 7 || 114.7 || 15/14~16/15
| 7 || 114.7 || 15/14~16/15
| style="border-left: double;" | 19 || 140.0 || 13/12
| 19 || 140.0 || 13/12
|-
|-
| 2
| 2
| M2
| M2
| style="border-left: double;" | -22 || 153.7 || 12/11
| -22 || 153.7 || 12/11
| style="border-left: double;" | -10 || 178.9 || 10/9
| -10 || 178.9 || 10/9
| style="border-left: double;" | 2 || 204.2 || 9/8
| 2 || 204.2 || 9/8
| style="border-left: double;" | 14 || 229.5 || 8/7
| 14 || 229.5 || 8/7
| style="border-left: double;" | 26 || 254.7 || 22/19
| 26 || 254.7 || 22/19
|-
|-
| 3
| 3
| m3
| m3
| style="border-left: double;" |  || ||  
| || ||  
| style="border-left: double;" | -15 || 268.4 || 7/6
| -15 || 268.4 || 7/6
| style="border-left: double;" | -3 || 293.6 || 13/11~19/16
| -3 || 293.6 || 13/11~19/16
| style="border-left: double;" | 9 || 318.9 || 6/5
| 9 || 318.9 || 6/5
| style="border-left: double;" | 21 || 344.2 || 11/9
| 21 || 344.2 || 11/9
|-
|- style="border-left: double;"
| 4
| 4
| M3
| M3
| style="border-left: double;" | -20 || 357.9 || 16/13
| -20 || 357.9 || 16/13
| style="border-left: double;" | -8 || 383.2 || 5/4
| -8 || 383.2 || 5/4
| style="border-left: double;" | 4 || 408.4 || 19/15~24/19
| 4 || 408.4 || 19/15~24/19
| style="border-left: double;" | 16 || 433.7 || 9/7
| 16 || 433.7 || 9/7
| style="border-left: double;" |  ||  ||
| || ||
|-
|- style="border-left: double;"
| 5
| 5
| P4
| P4
| style="border-left: double;" | -25 || 447.4 || 35/27
| -25 || 447.4 || 35/27
| style="border-left: double;" | -13 || 472.6 || 21/16
| -13 || 472.6 || 21/16
| style="border-left: double;" | -1 || 497.9 || 4/3
| -1 || 497.9 || 4/3
| style="border-left: double;" | 11 || 523.2 || 19/14
| 11 || 523.2 || 19/14
| style="border-left: double;" | 23 || 548.4 || 11/8
| 23 || 548.4 || 11/8
|-
|- style="border-left: double;"
| 6
| 6
| A4, d5
| A4, d5
| style="border-left: double;" | -18 || 562.1 || 18/13
| -18 || 562.1 || 18/13
| style="border-left: double;" | -6 || 587.4 || 7/5
| -6 || 587.4 || 7/5
| style="border-left: double;" | 6 || 612.6 || 10/7
| 6 || 612.6 || 10/7
| style="border-left: double;" | 18 || 637.9 || 13/9
| 18 || 637.9 || 13/9
| style="border-left: double;" |  ||  ||
| || ||
|-
|- style="border-left: double;"
| 7
| 7
| P5
| P5
| style="border-left: double;" | -23 || 651.6 || 16/11
| -23 || 651.6 || 16/11
| style="border-left: double;" | -11 || 676.8 || 28/19
| -11 || 676.8 || 28/19
| style="border-left: double;" | 1 || 702.1 || 3/2
| 1 || 702.1 || 3/2
| style="border-left: double;" | 13 || 727.4 || 32/21
| 13 || 727.4 || 32/21
| style="border-left: double;" | 25 || 752.6 || 54/35
| 25 || 752.6 || 54/35
|-
|- style="border-left: double;"
| 8
| 8
| m6
| m6
| style="border-left: double;" |  || ||  
| || ||  
| style="border-left: double;" | -16 || 766.3 || 14/9
| -16 || 766.3 || 14/9
| style="border-left: double;" | -4 || 791.6 || 19/12~30/19
| -4 || 791.6 || 19/12~30/19
| style="border-left: double;" | 8 || 816.8 || 8/5
| 8 || 816.8 || 8/5
| style="border-left: double;" | 20 || 842.1 || 13/8
| 20 || 842.1 || 13/8
|-
|- style="border-left: double;"
| 9
| 9
| M6
| M6
| style="border-left: double;" | -21 || 855.8 || 18/11
| -21 || 855.8 || 18/11
| style="border-left: double;" | -9 || 881.1 || 5/3
| -9 || 881.1 || 5/3
| style="border-left: double;" | 3 || 906.3 || 22/13~27/16
| 3 || 906.3 || 22/13~27/16
| style="border-left: double;" | 15 || 931.6 || 12/7
| 15 || 931.6 || 12/7
| style="border-left: double;" |  ||  ||
| || ||
|-
|- style="border-left: double;"
| 10
| 10
| m7
| m7
| style="border-left: double;" | -26 || 945.3 || 19/11
| -26 || 945.3 || 19/11
| style="border-left: double;" | -14 || 970.5 || 7/4
| -14 || 970.5 || 7/4
| style="border-left: double;" | -2 || 995.8 || 16/9
| -2 || 995.8 || 16/9
| style="border-left: double;" | 10 || 1021.1 || 9/5
| 10 || 1021.1 || 9/5
| style="border-left: double;" | 22 || 1046.3 || 11/6
| 22 || 1046.3 || 11/6
|-
|- style="border-left: double;"
| 11
| 11
| M7
| M7
| style="border-left: double;" | -19 || 1060.0 || 24/13
| -19 || 1060.0 || 24/13
| style="border-left: double;" | -7 || 1085.3 || 15/8~28/15
| -7 || 1085.3 || 15/8~28/15
| style="border-left: double;" | 5 || 1110.5 || 19/10~40/21
| 5 || 1110.5 || 19/10~40/21
| style="border-left: double;" | 17 || 1135.8 || 27/14~52/27
| 17 || 1135.8 || 27/14~52/27
| style="border-left: double;" |  ||  ||
| || ||
|-
|- style="border-left: double;"
| 12
| 12
| P8
| P8
| style="border-left: double;" | -24 || 1149.5 || 35/18~64/33
| -24 || 1149.5 || 35/18~64/33
| style="border-left: double;" | -12 || 1174.7 || 63/32~65/33
| -12 || 1174.7 || 63/32~65/33
| style="border-left: double;" | 0 || 1200.0 || 2/1
| 0 || 1200.0 || 2/1
| style="border-left: double;" | ||  ||  
| || ||  
| style="border-left: double;" |  || ||  
| || ||  
|}
|}


Line 1,419: Line 1,420:
|  
|  
|}
|}
<nowiki>*</nowiki> Besides the octave
<nowiki />* Besides the octave


[[Category:Garibaldi| ]] <!-- Main article -->
[[Category:Garibaldi| ]] <!-- Main article -->
Retrieved from "https://en.xen.wiki/w/Garibaldi"