User:Arseniiv/Timbres: Difference between revisions

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Arseniiv (talk | contribs)
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=== Another timbre ===
=== Another timbre ===


Now I think ''(G2)'' has its harmonics too close. We can fix this without remorse if we treat 1 as somewhat distinct from all others and start really adding two chosen differences only from φ. In that case we can choose 1 and φ (we may just scale all of ''(G1)'' by φ, effectively skipping some harmonics that are too close to their neighbors):
Now I think ''(G1)'' has its harmonics too close. We can fix this without remorse if we treat 1 as somewhat distinct from all others and start really adding two chosen differences only from φ. In that case we can choose 1 and φ (we may just scale all of ''(G1)'' by φ, effectively skipping some harmonics that are too close to their neighbors):


: '''1''', '''φ''', φ + 1 ≡ '''φ²''', 2φ + 1 ≡ '''φ³''', 3φ + 1, 3φ + 2 ≡ '''φ⁴''', 4φ + 2, 4φ + 3, 5φ + 3 ≡ '''φ⁵''', 6φ + 3, 6φ + 4, 7φ + 4, 8φ + 4, 8φ + 5 ≡ '''φ⁶''', ...  (G2)
: '''1''', '''φ''', φ + 1 ≡ '''φ²''', 2φ + 1 ≡ '''φ³''', 3φ + 1, 3φ + 2 ≡ '''φ⁴''', 4φ + 2, 4φ + 3, 5φ + 3 ≡ '''φ⁵''', 6φ + 3, 6φ + 4, 7φ + 4, 8φ + 4, 8φ + 5 ≡ '''φ⁶''', ...  (G2)