User talk:FloraC: Difference between revisions

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Hey, Flora, I was messing around, and I've discovered that the 13-limit is really good for trientone (third-tone) intervals in the same way that the 11-limit is really good for quartertone intervals- seriously, the simplest combination of trientone intervals adding up to 9/8 is basically 27/26-27/26-169/162, with [[27/26]] acting as the parachromatic interval and [[169/162]] acting as the paradiatonic interval. So now, I'm looking for a name for 169/162... do you have any ideas? --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 21:53, 23 November 2020 (UTC)

: That's not how I approach just intonation. I can use three different but much simpler third tones to reach an exact whole tone: 9/8 = (27/26)*(26/25)*(25/24). Alternatively I might want to temper out 2197/2187 = (9/8)/(27/26)<sup>3</sup>, or even {325/324, 625/624}, which equates all three.

: But as I see 169/162 is the difference between 13/9 and 18/13, it can be the "tridecimal tritonic third tone". [[User:FloraC|FloraC]] ([[User talk:FloraC|talk]]) 06:40, 24 November 2020 (UTC)

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 Hey, Flora, I was messing around, and I've discovered that the 13-limit is really good for trientone (third-tone) intervals in the same way that the 11-limit is really good for quartertone intervals- seriously, the simplest combination of trientone intervals adding up to 9/8 is basically 27/26-27/26-169/162, with [[27/26]] acting as the parachromatic interval and [[169/162]] acting as the paradiatonic interval.  So now, I'm looking for a name for 169/162... do you have any ideas? --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 21:53, 23 November 2020 (UTC)
+: That's not how I approach just intonation. I can use three different but much simpler third tones to reach an exact whole tone: 9/8 = (27/26)*(26/25)*(25/24). Alternatively I might want to temper out 2197/2187 = (9/8)/(27/26)<sup>3</sup>, or even {325/324, 625/624}, which equates all three.
+: But as I see 169/162 is the difference between 13/9 and 18/13, it can be the "tridecimal tritonic third tone". [[User:FloraC|FloraC]] ([[User talk:FloraC|talk]]) 06:40, 24 November 2020 (UTC)