Photosynthesis: Difference between revisions
CompactStar (talk | contribs) 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..." |
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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 | |||
|} | |} | ||
== 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]] | |||