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| [[File:Garibaldi-cassandra 12et Detempering.png|thumb|Garibaldi/cassandra as a 53-tone 12et detempering]] | | [[File:Garibaldi-cassandra 12et Detempering.png|thumb|Garibaldi/cassandra as a 53-tone 12et detempering]] |
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| Garibaldi is very naturally considered as a [[detemperament]] of the [[12edo|12 equal temperament]]. The table below shows a 53-tone detempered scale, with a generator range of -26 to +26. Each interval category of the 12 equal temperament is further divided into "double-sub", "sub", "plain", "super" and "double-super" qualities, separated by an [[diesis (scale theory)|enharmonic diesis]], which represents the syntonic~septimal comma; the "plain" type here consists of a [[5L 7s]] scale in 6|5 mode. Combining this division with the minor and major qualities of the 12 equal temperament, and calling the "double-sub major" and "double-super minor" qualities ''artoneutral'' and ''tendoneutral'', respectively, garibaldi gives us at least ''eight'' qualities for each diatonic category: subminor, minor, supraminor, artoneutral, tendoneutral, submajor, major, and supermajor. | | Garibaldi is very naturally considered as a [[detemperament]] of the [[12edo|12 equal temperament]]. The diagram on the right shows a 53-tone detempered scale, with a generator range of -26 to +26. 53 is the largest number of tones for a mos where intervals in the 12 categories do not overlap. Each interval category of the 12 equal temperament is further divided into four or five qualities, separated by an [[diesis (scale theory)|enharmonic diesis]], which represents the syntonic~septimal comma. Combining this division with the minor and major diatonic qualities of the 12 equal temperament, garibaldi gives us at least ''eight'' qualities for each diatonic category: subminor, minor, supraminor, artoneutral, tendoneutral, submajor, major, and supermajor. |
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| Notice also the little comma between artoneutral and tendoneutral. This interval spans 41 generator steps. 41edo tempers it out so that it merges artoneutral and tendoneutral into one neutral interval whereas 53edo exaggerates it to the size of the syntonic~septimal comma. 94edo tunes it to one half the size of the syntonic~septimal comma, which can be seen as a good compromise. | | Notice also the little interval between artoneutral and tendoneutral. This interval spans 41 generator steps. 41edo tempers it out so that it merges artoneutral and tendoneutral into one neutral interval whereas 53edo exaggerates it to the size of the syntonic~septimal comma. 94edo tunes it to one half the size of the syntonic~septimal comma, which can be seen as a good compromise. |
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| {| class="wikitable center-all mw-collapsible mw-collapsed"
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| ! rowspan="2" | #
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| ! rowspan="2" | Interval<br>category
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| ! colspan="3" style="border-left: double;" | "Double-Sub"
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| ! colspan="3" style="border-left: double;" | "Sub"
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| ! colspan="3" style="border-left: double;" | "Plain"
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| ! colspan="3" style="border-left: double;" | "Super"
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| ! colspan="3" style="border-left: double;" | "Double-super"
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| |-
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| ! style="border-left: double;" | Gen. || Cents* || Ratios
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| ! style="border-left: double;" | Gen. || Cents* || Ratios
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| ! style="border-left: double;" | Gen. || Cents* || Ratios
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| ! style="border-left: double;" | Gen. || Cents* || Ratios
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| ! style="border-left: double;" | Gen. || Cents* || Ratios
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| |-
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| | 0
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| | P1
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| | style="border-left: double;" | || ||
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| | style="border-left: double;" | || ||
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| | style="border-left: double;" | 0 || 0.0 || 1/1
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| | style="border-left: double;" | 12 || 25.2 || 64/63~81/80
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| | style="border-left: double;" | 24 || 50.5 || 33/32~36/35
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| |-
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| | 1
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| | m2
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| | style="border-left: double;" | || ||
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| | style="border-left: double;" | −17 || 64.2 || 27/26~28/27
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| | style="border-left: double;" | −5 || 89.5 || 20/19~21/20
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| | style="border-left: double;" | 7 || 114.7 || 15/14~16/15
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| | style="border-left: double;" | 19 || 140.0 || 13/12
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| |-
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| | 2
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| | M2
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| | style="border-left: double;" | −22 || 153.7 || 12/11
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| | style="border-left: double;" | −10 || 178.9 || 10/9
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| | style="border-left: double;" | 2 || 204.2 || 9/8
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| | style="border-left: double;" | 14 || 229.5 || 8/7
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| | style="border-left: double;" | 26 || 254.7 || 22/19
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| |-
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| | 3
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| | m3
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| | style="border-left: double;" | || ||
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| | style="border-left: double;" | −15 || 268.4 || 7/6
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| | style="border-left: double;" | −3 || 293.6 || 13/11~19/16
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| | style="border-left: double;" | 9 || 318.9 || 6/5
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| | style="border-left: double;" | 21 || 344.2 || 11/9
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| |-
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| | 4
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| | M3
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| | style="border-left: double;" | −20 || 357.9 || 16/13
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| | style="border-left: double;" | −8 || 383.2 || 5/4
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| | style="border-left: double;" | 4 || 408.4 || 19/15~24/19
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| | style="border-left: double;" | 16 || 433.7 || 9/7
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| | style="border-left: double;" | || ||
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| |-
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| | 5
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| | P4
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| | style="border-left: double;" | −25 || 447.4 || 35/27
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| | style="border-left: double;" | −13 || 472.6 || 21/16
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| | style="border-left: double;" | −1 || 497.9 || 4/3
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| | style="border-left: double;" | 11 || 523.2 || 19/14
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| | style="border-left: double;" | 23 || 548.4 || 11/8
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| | 6
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| | A4, d5
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| | style="border-left: double;" | −18 || 562.1 || 18/13
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| | style="border-left: double;" | −6 || 587.4 || 7/5
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| | style="border-left: double;" | 6 || 612.6 || 10/7
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| | style="border-left: double;" | 18 || 637.9 || 13/9
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| | style="border-left: double;" | || ||
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| | 7
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| | P5
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| | style="border-left: double;" | −23 || 651.6 || 16/11
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| | style="border-left: double;" | −11 || 676.8 || 28/19
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| | style="border-left: double;" | 1 || 702.1 || 3/2
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| | style="border-left: double;" | 13 || 727.4 || 32/21
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| | style="border-left: double;" | 25 || 752.6 || 54/35
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| |-
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| | 8
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| | m6
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| | style="border-left: double;" | || ||
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| | style="border-left: double;" | −16 || 766.3 || 14/9
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| | style="border-left: double;" | −4 || 791.6 || 19/12~30/19
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| | style="border-left: double;" | 8 || 816.8 || 8/5
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| | style="border-left: double;" | 20 || 842.1 || 13/8
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| |-
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| | 9
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| | M6
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| | style="border-left: double;" | −21 || 855.8 || 18/11
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| | style="border-left: double;" | −9 || 881.1 || 5/3
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| | style="border-left: double;" | 3 || 906.3 || 22/13~27/16
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| | style="border-left: double;" | 15 || 931.6 || 12/7
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| | style="border-left: double;" | || ||
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| | 10
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| | m7
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| | style="border-left: double;" | −26 || 945.3 || 19/11
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| | style="border-left: double;" | −14 || 970.5 || 7/4
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| | style="border-left: double;" | −2 || 995.8 || 16/9
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| | style="border-left: double;" | 10 || 1021.1 || 9/5
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| | style="border-left: double;" | 22 || 1046.3 || 11/6
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| |-
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| | 11
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| | M7
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| | style="border-left: double;" | −19 || 1060.0 || 24/13
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| | style="border-left: double;" | −7 || 1085.3 || 15/8~28/15
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| | style="border-left: double;" | 5 || 1110.5 || 19/10~40/21
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| | style="border-left: double;" | 17 || 1135.8 || 27/14~52/27
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| | style="border-left: double;" | || ||
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| |-
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| | 12
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| | P8
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| | style="border-left: double;" | −24 || 1149.5 || 35/18~64/33
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| | style="border-left: double;" | −12 || 1174.7 || 63/32~65/33
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| | style="border-left: double;" | 0 || 1200.0 || 2/1
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| | style="border-left: double;" | || ||
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| | style="border-left: double;" | || ||
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| |}
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| See the diagrams on the right for isomorphic versions.
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| == Notation == | | == Notation == |