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Slendric: Difference between revisions

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For technical data, see [[Gamelismic clan #Slendric]].
For technical data, see [[Gamelismic clan #Slendric]].


== Interval chains ==
== Intervals ==
=== Interval chains ===
In the following tables, odd harmonics and subharmonics 1–27 are labeled in '''bold'''.  
In the following tables, odd harmonics and subharmonics 1–27 are labeled in '''bold'''.  


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<nowiki/>* In 2.3.7-subgroup [[CWE tuning]]
<nowiki/>* In 2.3.7-subgroup [[CWE tuning]]


== Chords ==
* [[Slendric pentad]]
== Scales ==
=== 5-note and 6-note (both proper) ===
The 5-note [[MOS]] of slendric is [[1L 4s|Lssss]], in which L is [[7/6]] and s is [[8/7]]; this serves as an approximation to [[5edo]]. This expands to the 6-note MOS, [[5L 1s|LLLLLs]], in which L is 8/7 and s is the characteristic small interval of slendric (sometimes known as the [[quark]]) representing both [[64/63]] and [[49/48]].
Both of these scales are somewhat lacking in harmonic resources relative to similar-sized scales of other temperaments. Even within the 2.3.7 subgroup, [[Superpyth|archy]] and [[Semaphore]] have pentatonic scales with more consonant intervals and chords; or if more accuracy is desired a 2.3.7 [[JI]] scale could be used.
Slendric really shines when used with larger scales than these. The 5-note MOS, however, has a special role in organizing the intervals of slendric because it is so close to [[5edo]] - that is, slendric is very suitable for a pentatonic framework of categorization, rather than a heptatonic/diatonic one.
=== 11-note (LsLsLsLsLss, improper) ===
The 11-note MOS, [[5L 6s|LsLsLsLsLss]], has [[9/8]] "whole tones" in alternation with ~32 cent "sixth tones", with the exception of one pair of adjacent "sixth tones".
{| class="wikitable"
|-
! Small ("minor") interval
| 31.56
| 63.13
| 265.25
| 296.81
| 498.94
| 530.50
| 732.63
| 764.19
| 966.31
| 997.88
|-
! JI intervals represented
| 49/48, 64/63
| 28/27
| 7/6
| 32/27
| 4/3
| 49/36
| 32/21, 49/32
| 14/9
| 7/4
| 16/9
|-
! Large ("major") interval
| 202.12
| 233.69
| 435.81
| 467.37
| 669.50
| 701.06
| 903.19
| 934.75
| 1136.87
| 1168.44
|-
! JI intervals represented
| 9/8
| 8/7
| 9/7
| 21/16, 64/49
| 72/49
| 3/2
| 27/16
| 12/7
| 27/14
| 63/32, 96/49
|}


=== Alternate way of organizing intervals ===
=== Alternate way of organizing intervals ===
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| 27/16
| 27/16
| 27/14
| 27/14
|}
== Chords ==
* [[Slendric pentad]]
== Scales ==
=== 5-note and 6-note (both proper) ===
The 5-note [[MOS]] of slendric is [[1L 4s|Lssss]], in which L is [[7/6]] and s is [[8/7]]; this serves as an approximation to [[5edo]]. This expands to the 6-note MOS, [[5L 1s|LLLLLs]], in which L is 8/7 and s is the characteristic small interval of slendric (sometimes known as the [[quark]]) representing both [[64/63]] and [[49/48]].
Both of these scales are somewhat lacking in harmonic resources relative to similar-sized scales of other temperaments. Even within the 2.3.7 subgroup, [[Superpyth|archy]] and [[Semaphore]] have pentatonic scales with more consonant intervals and chords; or if more accuracy is desired a 2.3.7 [[JI]] scale could be used.
Slendric really shines when used with larger scales than these. The 5-note MOS, however, has a special role in organizing the intervals of slendric because it is so close to [[5edo]] - that is, slendric is very suitable for a pentatonic framework of categorization, rather than a heptatonic/diatonic one.
=== 11-note (LsLsLsLsLss, improper) ===
The 11-note MOS, [[5L 6s|LsLsLsLsLss]], has [[9/8]] "whole tones" in alternation with ~32 cent "sixth tones", with the exception of one pair of adjacent "sixth tones".
{| class="wikitable"
|-
! Small ("minor") interval
| 31.56
| 63.13
| 265.25
| 296.81
| 498.94
| 530.50
| 732.63
| 764.19
| 966.31
| 997.88
|-
! JI intervals represented
| 49/48, 64/63
| 28/27
| 7/6
| 32/27
| 4/3
| 49/36
| 32/21, 49/32
| 14/9
| 7/4
| 16/9
|-
! Large ("major") interval
| 202.12
| 233.69
| 435.81
| 467.37
| 669.50
| 701.06
| 903.19
| 934.75
| 1136.87
| 1168.44
|-
! JI intervals represented
| 9/8
| 8/7
| 9/7
| 21/16, 64/49
| 72/49
| 3/2
| 27/16
| 12/7
| 27/14
| 63/32, 96/49
|}
|}


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