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|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-Db), 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 is a 7-limit (and higher) temperament of the [[Schismatic_family#Garibaldi|schismatic family]]. It is an extension of [[Helmholtz|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-Db), 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]].


=Spectrum of Garibaldi Tunings by Eigenmonzos=
== Spectrum of garibaldi tunings by eigenmonzos ==


{| class="wikitable"
{| class="wikitable center-1 right-2"
|-
|-
! | Eigenmonzo
! Eigenmonzo
! | Fifth
! Fifth
! Comments
|-
|-
| | 16/15
| 16/15
| | 701.676
| 701.676
|
|-
|-
| | 69\118
| (69\118)
| | 701.695
| 701.695
|
|-
|-
| | 5/4
| 5/4
| | 701.711
| 701.711
|
|-
|-
| | [0 -10 17>
| {{monzo| 0 -10 17 }}
| | 701.728 (5 limit least squares)
| 701.728
| 5-odd-limit least squares
|-
|-
| | 6/5
| 6/5
| | 701.738 (5 limit minimax)
| 701.738
| 5-odd-limit minimax
|-
|-
| | 100\171
| 100\171
| | 701.754
| 701.754
|
|-
|-
| | 10/9
| 10/9
| | 701.760
| 701.760
|
|-
|-
| | 31\53
| (31\53)
| | 701.887
| 701.887
|
|-
|-
| | 15/13
| 15/13
| | 701.9355
| 701.9355
|-
|-
| | 13/10
| 13/10
| | 701.9362
| 701.9362
|
|-
|-
| | 4/3
| 4/3
| | 701.955
| 701.955
|
|-
|-
| | 16/13
| 16/13
| | 702.026
| 702.026
|
|-
|-
| | 13/12
| 13/12
| | 702.030
| 702.030
|
|-
|-
| | 18/13
| 18/13
| | 702.034
| 702.034
|
|-
|-
| | 86\147
| 86\147
| | 702.041
| 702.041
|
|-
|-
| | 11/10
| 11/10
| | 702.097
| 702.097
|
|-
|-
| | 15/11
| 15/11
| | 702.102
| 702.102
|
|-
|-
| | 14/13
| 14/13
| | 702.109 (13 and 15 limit minimax)
| 702.109
| 13- and 15-odd-limit minimax
|-
|-
| | [0 -95 -137 -129 167 143>
| {{monzo| 0 -95 -137 -129 167 143 }}
| | 702.112 (15 limit least squares)
| 702.112
| 15-odd-limit least squares
|-
|-
| | [0 -27 7 17>
| {{monzo| 0 -27 7 17 }}
| | 702.114 (9 limit least squares)
| 702.114
| 9-odd-limit least squares
|-
|-
| | 55\94
| (55\94)
| | 702.12766
| 702.12766
|
|-
|-
| | [0 -38 -80 -122 137 116>
| {{monzo| 0 -38 -80 -122 137 116 }}
| | 702.12770 (13 limit least squares)
| 702.12770
| 13-odd-limit least squares
|-
|-
| | [0 -25 11 35>
| {{monzo| 0 -25 11 35 }}
| | 702.140 (7 limit least squares)
| 702.140
| 7-odd-limit least squares
|-
|-
| | [0 17 -52 -88 134>
| {{monzo| 0 17 -52 -88 134 }}
| | 702.183 (11 limit least squares)
| 702.183
| 11-odd-limit least squares
|-
|-
| | 9/7
| 9/7
| | 702.193 (9 and 11 limit minimax)
| 702.193
| 9- and 11-odd-limit minimax
|-
|-
| | 7/6
| 7/6
| | 702.209 (7 limit minimax)
| 702.209
| 7-odd-limit minimax
|-
|-
| | 79\135
| (79\135)
| | 702.222
| 702.222
|
|-
|-
| | 8/7
| 8/7
| | 702.227
| 702.227
|
|-
|-
| | 14/11
| 14/11
| | 702.230
| 702.230
|
|-
|-
| | 11/8
| 11/8
| | 702.231
| 702.231
|
|-
|-
| | 12/11
| 12/11
| | 702.244
| 702.244
|
|-
|-
| | 11/9
| 11/9
| | 702.258
| 702.258
|
|-
|-
| | 24\41
| (24\41)
| | 702.439
| 702.439
|
|-
|-
| | 15/14
| 15/14
| | 702.778
| 702.778
|
|-
|-
| | 7/5
| 7/5
| | 702.915
| 702.915
|
|-
|-
| | 17\29
| (17\29)
| | 703.448
| 703.448
|
|-
|-
| | 13/11
| 13/11
| | 703.597
| 703.597
|
|}
|}
[[Category:7-limit]]
 
[[Category:garibaldi]]
[[Category:Temperament]]
[[Category:marvel]]
[[Category:Garibaldi| ]] <!-- main article -->
[[Category:schismatic]]
[[Category:Marvel]]
[[Category:temperament]]
[[Category:Schismatic]]

Revision as of 04:10, 28 March 2021

Garibaldi is a 7-limit (and higher) temperament of the 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-Db), 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 temperament.

Spectrum of garibaldi tunings by eigenmonzos

Eigenmonzo Fifth Comments
16/15 701.676
(69\118) 701.695
5/4 701.711
[0 -10 17⟩ 701.728 5-odd-limit least squares
6/5 701.738 5-odd-limit minimax
100\171 701.754
10/9 701.760
(31\53) 701.887
15/13 701.9355
13/10 701.9362
4/3 701.955
16/13 702.026
13/12 702.030
18/13 702.034
86\147 702.041
11/10 702.097
15/11 702.102
14/13 702.109 13- and 15-odd-limit minimax
[0 -95 -137 -129 167 143⟩ 702.112 15-odd-limit least squares
[0 -27 7 17⟩ 702.114 9-odd-limit least squares
(55\94) 702.12766
[0 -38 -80 -122 137 116⟩ 702.12770 13-odd-limit least squares
[0 -25 11 35⟩ 702.140 7-odd-limit least squares
[0 17 -52 -88 134⟩ 702.183 11-odd-limit least squares
9/7 702.193 9- and 11-odd-limit minimax
7/6 702.209 7-odd-limit minimax
(79\135) 702.222
8/7 702.227
14/11 702.230
11/8 702.231
12/11 702.244
11/9 702.258
(24\41) 702.439
15/14 702.778
7/5 702.915
(17\29) 703.448
13/11 703.597
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