User:Dummy index

• 2-dimensional tuning spectrum
• 3rd-tritave temperaments
• About harmonics
• Bimetallic MOS
• Chromatic pairs and how we define haplotonic
• Heuristics for picking a nonstandard basis of JI subgroup
• Just odd intonation
• Layouts
• MOS tree with continued fraction
• No-1s odd-limit consistency
• Random lists of temperaments by generator size
• Related to 1729/1728
• SandBox
• Semitritave

memo

12ET-complementary comma pairs (e.g. syntonic-schismatic relation)

M3 or d4	A: 4*P5=M3+2*P8	B: 8*P5+d4=5*P8	Remarks
32/27	2187/2048=[-11 7⟩	256/243=[8 -5⟩	A/B=[-19 12⟩, A: (7edo), B: (5edo)
6/5	135/128=[-7 3 1⟩	(64/63)^2*(245/243)=[12 -9 1⟩	A/B=[-19 12⟩, A: Mavila, B: Superpyth
11/9	729/704=[-6 6 0 0 -1⟩	(64/63)^2/(99/98)=[13 -6 0 0 -1⟩	A/B=[-19 12⟩, A: Meanenneadecal?, B: Supra
8192/6561	531441/524288=[-19 12⟩	1/1	A: (12edo)
5/4	81/80=[-4 4 -1⟩	32805/32768=[-15 8 1⟩	A*B=[-19 12⟩, A: Meantone, B: Schismatic
81/64	1/1	531441/524288=[-19 12⟩	B: (12edo)
9/7	64/63=[6 -2 0 -1⟩	59049/57344=[-13 10 0 -1⟩	B/A=[-19 12⟩, A: Archytas clan, B: Septimal meantone
4/3	256/243=[8 -5⟩	2187/2048=[-11 7⟩	B/A=[-19 12⟩, A: (5edo), B: (7edo)

Q: Mavila must have the fifth flatter than 7edo's, why be placed between 7edo and 5edo?

A: I wrote the 32/27 in this table as a monzo-ish value. 32/27 constructed of P5 & P8 will much sharper when flatter P5 situation.

(3/2)^(1/2)	2187/2048=[-11 7⟩	17-comma=[27 -17⟩	A/B=[-38 24⟩, A: (7edo), B: (17edo)
(3/2)^(4/7)	531441/524288=[-19 12⟩	531441/524288=[-19 12⟩	A*B=[-38 24⟩, A: (12edo), B: (12edo)
(3/2)^(2/3)	256/243=[8 -5⟩	[-41 26⟩	B/A=[-49 31⟩, A: (5edo), B: (26edo)

temperaments with septimal tritones

Fifthspan	-8	-6	4	6	Remarks
Septimal meantone	32/25	10/7	5/4	7/5	Good 4:5:7 in 10 fifthspan
Garibaldi	5/4	7/5	80/63	10/7	4:5:6:7 in 15 fifthspan
Hemififths		7/5		10/7