1619edo: Difference between revisions

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1619edo tunes [[keenanisma]] very finely, to 6 steps, and can use it as a microchroma. In addition, it can use the keenanisma as a generator in the keenanose temperament, 270 & 1619, in which it highlights the relationship between 270 keenanismas and the octave. It also achieves this since 270 * 6 = 1620, and 1619 is 1 short of that and also excellent in the 13-limit. 1619edo has 7/6 on 360th step, a highly divisible number, 27/25 on 180th, and 33/32 on 72nd as a consequence of tempering out the commas. This means that 72ed33/32 is virtually equivalent to 1619edo. When it comes to using 33/32 as the generator, 1619edo supports the [[ravine]] temperament, which tempers out 196625/196608, 200000/199927, 2912000/2910897, and 3764768/3764475.

Since 33/32 is close to 1\45, 7\6 is close to 1\9, and 385/384 is close to 1\270, 1619edo can be thought of as [[1620edo]] where one step was extracted and all others were moved into a more harmonically just position.

Since 33/32 is close to 1\45, 7\6 is close to 1\9, and 385/384 is close to 1\270, 1619edo can be thought of as [[1620edo]] where one step was extracted and all others were moved into a more harmonically just position. It achieves this because 1620edo is contorted 270edo in the 11-limit, and its 13/8 is on the flat side coming from 324edo, and thus when it is octave stretched, steps sharpen enough to arrive at 1619edo's 13-limit excellence.

=== Prime harmonics ===

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 edo tunes [[keenanisma]] very finely, to 6 steps, and can use it as a microchroma. In addition, it can use the keenanisma as a generator in the keenanose temperament, 270 & 1619, in which it highlights the relationship between 270 keenanismas and the octave. It also achieves this since 270 * 6 = 1620, and 1619 is 1 short of that and also excellent in the 13-limit. 1619edo has 7/6 on 360th step, a highly divisible number, 27/25 on 180th, and 33/32 on 72nd as a consequence of tempering out the commas. This means that 72ed33/32 is virtually equivalent to 1619edo. When it comes to using 33/32 as the generator, 1619edo supports the [[ravine]] temperament, which tempers out 196625/196608, 200000/199927, 2912000/2910897, and 3764768/3764475.
-Since 33/32 is close to 1\45, 7\6 is close to 1\9, and 385/384 is close to 1\270, 1619edo can be thought of as [[1620edo]] where one step was extracted and all others were moved into a more harmonically just position.
+Since 33/32 is close to 1\45, 7\6 is close to 1\9, and 385/384 is close to 1\270, 1619edo can be thought of as [[1620edo]] where one step was extracted and all others were moved into a more harmonically just position. It achieves this because 1620edo is contorted 270edo in the 11-limit, and its 13/8 is on the flat side coming from 324edo, and thus when it is octave stretched, steps sharpen enough to arrive at 1619edo's 13-limit excellence.
 === Prime harmonics ===