1619edo: Difference between revisions

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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.

~~=== The Vidarines ===~~

1619edo supports a very precise rank two temperament, 19 & 1619, which uses [[6/5]] as a generator and has a comma basis 4375/4374, 91125/91091, 196625/196608, and 54925000/54908469.

1619edo supports [[~~vidar~~]], which has ~~the~~ comma basis 4225/4224, 4375/4374, ~~and~~ 6656/6655. ~~In addition, it contains a wealth of rank-two 13-limit temperaments that are produced by adding one comma on top of~~ the ~~vidar comma basis, such as decigrave,~~ keenanose, ~~moulin~~, ~~etc~~. ~~Eliora proposes the name ''The Vidarines'' for~~ this ~~collection~~ of ~~temperaments~~.

1619edo supports the keenanose temperament, which has comma basis 4225/4224, 4375/4374, 6656/6655, and 151263/151250. Keenanisma is the 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.

~~One such~~ temperament is ~~the keenanose temperament~~, which has comma basis 4225/4224, 4375/4374, 6656/6655, ~~and 151263/151250~~. ~~Keenanisma~~ is ~~the 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~~.

Another temperament which highlights the interval relationships in 1619edo is 45 & 1619, called ''decigrave'', since 10 steps make a 7/6, which is referred to as the grave minor third sometimes. It has a comma basis 4225/4224, 4375/4374, 6656/6655, {{monzo|23 5 13 -23 1 0}} in the 13-limit. Its generator is 36 steps, which represents 65/64 and 66/65 tempered together, and 2 of them make 33/32. 5 of them make [[27/25]], and 10 of them make 7/6.

~~Another temperament which highlights~~ the ~~interval relationships in 1619edo (and is also a member of The Vidarines collection) is 45~~ & 1619~~, and if it had a name, it would be~~ called ~~''decigrave'', since 10 steps make a 7/6~~, ~~which is referred to as~~ the ~~grave minor third sometimes. It has a~~ comma basis 4225/4224, 4375/4374, 6656/6655, ~~{{monzo|23 5 13 -23 1 0}} in the 13-limit. Its generator is 36 steps, which represents 65/64 and 66/65 tempered together, and 2 of them make 33/32. 5 of them make [[27/25]], and 10 of them make 7~~/6.

1619edo supports the 494 & 1619 temperament called moulin, with the comma basis of 4225/4224, 4375/4374, 6656/6655, 91125/91091.

1619edo supports the ~~494 & 1619 temperament called moulin~~, ~~which is also a member of The Vidarines collection~~. In ~~this case~~, ~~91125/91091 has to be added to the three commas to produce~~ a rank-~~2 temperament~~.

=== The Vidarines ===

1619edo supports [[vidar]], which has the comma basis 4225/4224, 4375/4374, and 6656/6655. In addition, it contains a wealth of rank-two 13-limit temperaments that are produced by adding one comma on top of the vidar comma basis;. Temperaments described above such as decigrave, keenanose, moulin, are members of this collection. Eliora proposes the name ''The Vidarines'' for this collection of temperaments.

A quick summary is shown below.

@@ Line 9: / Line 9: @@
 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.
-=== The Vidarines ===
+edo supports a very precise rank two temperament, 19 & 1619, which uses [[6/5]] as a generator and has a comma basis 4375/4374, 91125/91091, 196625/196608, and 54925000/54908469.
-edo supports [[vidar]], which has the comma basis 4225/4224, 4375/4374, and 6656/6655. In addition, it contains a wealth of rank-two 13-limit temperaments that are produced by adding one comma on top of the vidar comma basis, such as decigrave, keenanose, moulin, etc. Eliora proposes the name ''The Vidarines'' for this collection of temperaments.
+edo supports the keenanose temperament, which has comma basis 4225/4224, 4375/4374, 6656/6655, and 151263/151250. Keenanisma is the 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.
-One such temperament is the keenanose temperament, which has comma basis 4225/4224, 4375/4374, 6656/6655, and 151263/151250. Keenanisma is the 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.
+Another temperament which highlights the interval relationships in 1619edo is 45 & 1619, called ''decigrave'', since 10 steps make a 7/6, which is referred to as the grave minor third sometimes. It has a comma basis 4225/4224, 4375/4374, 6656/6655, {{monzo|23  5 13 -23  1 0}} in the 13-limit. Its generator is 36 steps, which represents 65/64 and 66/65 tempered together, and 2 of them make 33/32. 5 of them make [[27/25]], and 10 of them make 7/6.
-Another temperament which highlights the interval relationships in 1619edo (and is also a member of The Vidarines collection) is 45 & 1619, and if it had a name, it would be called ''decigrave'', since 10 steps make a 7/6, which is referred to as the grave minor third sometimes. It has a comma basis 4225/4224, 4375/4374, 6656/6655, {{monzo|23  5 13 -23  1 0}} in the 13-limit. Its generator is 36 steps, which represents 65/64 and 66/65 tempered together, and 2 of them make 33/32. 5 of them make [[27/25]], and 10 of them make 7/6.
+edo supports the 494 & 1619 temperament called moulin, with the comma basis of 4225/4224, 4375/4374, 6656/6655, 91125/91091.
-edo supports the 494 & 1619 temperament called moulin, which is also a member of The Vidarines collection. In this case, 91125/91091 has to be added to the three commas to produce a rank-2 temperament.
+=== The Vidarines ===
+edo supports [[vidar]], which has the comma basis 4225/4224, 4375/4374, and 6656/6655. In addition, it contains a wealth of rank-two 13-limit temperaments that are produced by adding one comma on top of the vidar comma basis;. Temperaments described above such as decigrave, keenanose, moulin, are members of this collection. Eliora proposes the name ''The Vidarines'' for this collection of temperaments.
 A quick summary is shown below.