Photosynthesis: Difference between revisions

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Created page with "'''Photosynthesis''' is the nonoctave temperament tempering out the comma 243/(5 ϕ^8) in the ϕ.3.5 fractional subgroup, equating 5 3/1 with 5/1. It has a..."
 
m Collect non-octave temperaments in one category
 
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'''Photosynthesis''' is the [[nonoctave]] [[temperament]] tempering out the comma 243/(5 ϕ^8) in the ϕ.3.5 fractional [[subgroup]], equating 5 [[3/1]] with [[5/1]]. It has a period of [[acoustic phi]] and a generator of a major second just flat of 3/(ϕ^2), the "phi-reduced 3rd harmonic".
'''Photosynthesis''' is the [[nonoctave]] [[temperament]] tempering out the comma 243/(5 ϕ^8) in the ϕ.3.5 fractional [[subgroup]], equating 5 [[3/1]] with [[5/1]]. It has a period of [[acoustic phi]] and a generator of a major second just flat of 3/(ϕ^2), the "phi-reduced 3rd harmonic". It possesses MOS scales of the families 3L 1s<ϕ>, 4L 3s<ϕ>, 4L 7s<ϕ>, and 11L 4s<ϕ>.
== Interval chain (CTE tuning) ==
== Interval chain (CTE tuning) ==
{|class="wikitable"
{|class="wikitable"
|-
|-
!Generators up
! Generators up
!Cents
! Cents
!Generators down
! Generators down
!Cents
! Cents
|-
|-
|0
| 0
|0.00
| 0.00
|0
| 0
|0.00
| 0.00
|-
|-
|1
| 1
|224.90
| 224.90
|1
| 1
|608.19
| 608.19
|-
| 2
| 449.80
| 2
| 383.29
|-
| 3
| 674.70
| 3
| 158.39
|-
| 4
| 66.51
| 4
| 766.58
|-
| 5
| 291.41
| 5
| 541.68
|-
| 6
| 516.31
| 6
| 316.78
|}
|}
WIP
== Temperament data ==
Note: This data is not 100% exact, it was calculated using a very close JI approximation of acoustic phi rather than acoustic phi itself
 
[[Subgroup]]: ϕ.3.5
 
[[Comma list]]: 243/(5 ϕ^8)
 
[[Mapping]]: [{{val|1 1 -3}}, {{val|0 1 5}}]]
 
[[CTE tuning|CTE generator]]: ~3/ϕ = 1057.989
 
[[Edφ|Edϕ]]s: 11, 15, 7[+5], 19[-5], 26, 5[--5], 18[+5], 23[-3, -5], 34[-3, -5], 37, 41[-3], 27[-3, -5], 49[-3, -5], 31[-3, --5]
 
[[Category:Photosynthesis| ]] <!-- main article -->
[[Category:Rank-2 temperaments]]
[[Category:Non-octave temperaments]]
[[Category:Golden ratio]]