Search found 1000 matches

by Dave Keenan
Tue Mar 23, 2021 4:00 pm
Forum: Linear Temperament notations
Topic: 5-limit misty (12p&51p) notation
Replies: 9
Views: 279

Re: 5-limit misty (12p&51p) notation

But for an octave-repeating notation, we only care about the number of periods modulo the number per octave, so the mapping we care about is just the octave-equivalent mapping: 3 5 <0 -1] 400c <1 -4] 703c So we have 3 chains of fifths. We can notate one chain of up to 35 notes in the conventional ma...
by Dave Keenan
Tue Mar 23, 2021 3:37 pm
Forum: Linear Temperament notations
Topic: 5-limit misty (12p&51p) notation
Replies: 9
Views: 279

Re: 5-limit misty (12p&51p) notation

[⟨3 0 26], ⟨0 1 -4]⟩ and [ ⟨ 3 5 6 ] ⟨ 0 -1 4 ] ⟩ are equivalent -- the wedge product for both is <<3 -12 -26]] -- but [<3 -3 14|, <0 1 -4|] has a wedge product of <<3 -12 -2]] so there must be some mistake. I'd leave the mapping and correct the generator size to 1903 cents. You've just shown the u...
by Dave Keenan
Tue Mar 23, 2021 11:45 am
Forum: Linear Temperament notations
Topic: 5-limit misty (12p&51p) notation
Replies: 9
Views: 279

Re: 5-limit misty (12p&51p) notation

OK. I see that the Wiki entry is simply wrong. The given mapping does not match the given generator. Both mappings agree that the period is approx 1/3-octave (approx 400 cents). If prime 3 is 1 gen and 0 periods then the generator must be 1903 cents, not 703 cents. Or if the gen is 703 cents, the ma...
by Dave Keenan
Tue Mar 23, 2021 11:15 am
Forum: Linear Temperament notations
Topic: 5-limit misty (12p&51p) notation
Replies: 9
Views: 279

Re: 5-limit misty (12p&51p) notation

I see that Misty is not in Middle Path . And the mapping given in the Xen Wiki https://en.xen.wiki/w/Misty_family is the far more complex: [⟨3 0 26], ⟨0 1 -4]⟩ Comma: 67108864/66430125 = [26 -12 -3⟩ POTE generator: ~3/2 = 703.111 Map: [<3 0 26|, <0 1 -4|] EDOs: 12, 51, 63, 75, 87, 99, 285, 384 So th...
by Dave Keenan
Mon Mar 22, 2021 12:53 pm
Forum: Linear Temperament notations
Topic: Schisma accents in regular temperament notation
Replies: 1
Views: 60

Re: Schisma accents in regular temperament notation

That's a great result! Thanks for doing that survey, Herman.
by Dave Keenan
Sun Mar 21, 2021 10:42 pm
Forum: Linear Temperament notations
Topic: 5-limit ripple (12p&23p) notation
Replies: 3
Views: 93

Re: 5-limit ripple (12p&23p) notation

Oh yes. That's beautiful. So G:#: = A:b::/|: and G:#::E:b: can be spelled A:b::/|::E:b: and everything obeys the rule that it's a properly -tempered 2:3 if it's spelled anti-alphabetically, or if it's spelled alphabetically and is narrowed by a 5-comma symbol. Same for tempered 4:5s. This seems to v...
by Dave Keenan
Sat Mar 20, 2021 1:38 pm
Forum: Linear Temperament notations
Topic: 5-limit ripple (12p&23p) notation
Replies: 3
Views: 93

Re: 5-limit ripple (12p&23p) notation

Ooh yeah. That's a tricky one. Another approach would be to use 12 pseudo-nominals, so a 12-note chain of the approximately 101 cent generators would be notated the same as 12edo.: A Bb B C C# D Eb E F F# G G# Then we only need a sagittal for 12 generators, to represent an approximate 12 cent sharpe...
by Dave Keenan
Sat Mar 20, 2021 3:16 am
Forum: Linear Temperament notations
Topic: general methods for linear temperament notation
Replies: 31
Views: 691

Re: general methods for linear temperament notation

Perhaps if I started over going through my 1/1 journals (beginning in 1985) but this time keeping my eyes peeled for prime exponent vectors, I might not find any. You might, if there's an article by Joe Monzo. But he may have used a different term. Their use seems to be a key historical development...
by Dave Keenan
Sat Mar 20, 2021 2:21 am
Forum: Linear Temperament notations
Topic: general methods for linear temperament notation
Replies: 31
Views: 691

Re: general methods for linear temperament notation

I also ended up on your (Dave) page , and it says you're the "one of the developers of the regular mapping paradigm". That links out to the same page I commented about on Facebook yesterday , that came up in relation to the "bent tuning forks". I certainly am one of the develope...
by Dave Keenan
Fri Mar 19, 2021 2:07 pm
Forum: Comparison with other notation systems
Topic: paper by Sabat and Nicholson
Replies: 2
Views: 105

Re: paper by Sabat and Nicholson

Jeez. They have one Sagittal symbol in the whole paper. It's for the single most important comma. And they got it wrong! Figure 10 on page 16.