Photosynthesis: Difference between revisions
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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" | ||
Revision as of 03:39, 6 April 2023
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)
| Generators up | Cents | Generators down | Cents |
|---|---|---|---|
| 0 | 0.00 | 0 | 0.00 |
| 1 | 224.90 | 1 | 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: [⟨1 1 -3], ⟨0 1 5]]]
CTE generator: ~3/ϕ = 1057.989
Edϕs: 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]