back to list

Amity[21] and Hemisixths[11]

🔗Gene Ward Smith <gwsmith@svpal.org>

3/22/2003 8:25:49 PM

It should be noted when examining these that these are accurate
temperaments. Hemisixths has an rms error of 1.575 cents, and amity,
with an error of 0.383 cents, might be considered in the
microtemperament range, though not to the extent of the nameless[89]
system presented previously, which is 0.003 cents.

Amity[21]

1600000/1594323
[1, 81/80, 800/729, 10/9, 9/8, 6/5, 243/200, 100/81, 4/3, 27/20,
1000/729, 729/500, 40/27, 3/2, 81/50, 400/243, 5/3, 16/9, 9/5,
729/400, 160/81]
[9/8, 1000/729, 5/3, 81/80, 100/81, 3/2, 729/400, 10/9, 27/20,
400/243, 1, 243/200, 40/27, 9/5, 800/729, 4/3, 81/50, 160/81, 6/5,
729/500, 16/9]

Generator = 243/200
[1, 6/5, 36/25]
[1, 6/5, 36/25]
[1, 6/5, 36/25]
[1, 6/5, 36/25]
[1, 6/5, 36/25]
[1, 6/5, 3/2]
[1, 6/5, 3/2]
[1, 6/5, 3/2]
[1, 6/5, 3/2]
[1, 6/5, 3/2]
[1, 6/5, 3/2]
[1, 6/5, 3/2]
[1, 6/5, 3/2]
[1, 5/4, 3/2]
[1, 5/4, 3/2]
[1, 5/4, 3/2]
[1, 5/4, 3/2]
[1, 5/4, 3/2]
[1, 5/4, 3/2]
[1, 5/4, 3/2]
[1, 5/4, 3/2]

Hemisixths[11]

78732/78125
[1, 27/25, 10/9, 6/5, 162/125, 25/18, 36/25, 125/81, 5/3, 9/5, 50/27]
[10/9, 36/25, 50/27, 6/5, 125/81, 1, 162/125, 5/3, 27/25, 25/18, 9/5]

Generator = 162/125
[1, 5/4, 3/2]
[1, 5/4, 3/2]
[1, 6/5, 3/2]
[1, 6/5, 3/2]
[1, 6/5, 36/25]
[1, 6/5, 36/25]
[1, 6/5, 36/25]
[1, 6/5, 36/25]
[1, 6/5, 36/25]
[1, 6/5, 36/25]
[1, 6/5, 36/25]