User:Moremajorthanmajor/30wtn: Difference between revisions
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A '''30 tone well tempered nonet''' (30WTN) is related to well temperaments of [[25edo]] and [[26edo]], but with a nonet rather than the 2/1 being constant. Its patent tunings optimally alternate [[EDF|division of the just perfect fifth]] into 15 equal parts (15EDF) with sequences of fifteen equal steps of 40 to 53.333 cents each. This will create fifteen equally-spaced intervals between an interval between 600 and 800 cents and the just perfect fifth. | A '''30 tone well tempered nonet''' (30WTN) is related to well temperaments of [[25edo]] and [[26edo]], but with a nonet rather than the 2/1 being constant. Its patent tunings optimally alternate [[EDF|division of the just perfect fifth]] into 15 equal parts (15EDF) with sequences of fifteen equal steps of 40 to 53.333 cents each. This will create fifteen equally-spaced intervals between an interval between 600 and 800 cents and the just perfect fifth. | ||
== | == Patent Intervals == | ||
{| class="wikitable" | {| class="wikitable" | ||
|+ | |+ | ||
| Line 7: | Line 7: | ||
!Target a | !Target a | ||
!Target b | !Target b | ||
!Alternating [[edo]] and *ed(9/8) a | |||
!Alternating edo and *ed(9/8) b | |||
|- | |- | ||
!1 | !1 | ||
! colspan="2" |46.797 | ! colspan="2" |46.797 | ||
|48 | |||
|46.154 | |||
|- | |- | ||
!2 | !2 | ||
! colspan="2" |93.594 | ! colspan="2" |93.594 | ||
|96 | |||
|92.308 | |||
|- | |- | ||
!3 | !3 | ||
! colspan="2" |140.391 | ! colspan="2" |140.391 | ||
|144 | |||
|138.4615 | |||
|- | |- | ||
!4 | !4 | ||
! colspan="2" |187.188 | ! colspan="2" |187.188 | ||
|192 | |||
|184.615 | |||
|- | |- | ||
!5 | !5 | ||
! colspan="2" |233.985 | ! colspan="2" |233.985 | ||
|240 | |||
|230.769 | |||
|- | |- | ||
!6 | !6 | ||
! colspan="2" |280.782 | ! colspan="2" |280.782 | ||
|288 | |||
|276.923 | |||
|- | |- | ||
!7 | !7 | ||
! colspan="2" |327.579 | ! colspan="2" |327.579 | ||
|336 | |||
|323.077 | |||
|- | |- | ||
!8 | !8 | ||
! colspan="2" |374.376 | ! colspan="2" |374.376 | ||
|384 | |||
|369.231 | |||
|- | |- | ||
!9 | !9 | ||
! colspan="2" |421.173 | ! colspan="2" |421.173 | ||
|432 | |||
|415.385 | |||
|- | |- | ||
!10 | !10 | ||
! colspan="2" |467.97 | ! colspan="2" |467.97 | ||
|480 | |||
|461.5385 | |||
|- | |- | ||
!11 | !11 | ||
! colspan="2" |514.767 | ! colspan="2" |514.767 | ||
|528 | |||
|507.692 | |||
|- | |- | ||
!12 | !12 | ||
! colspan="2" |561.564 | ! colspan="2" |561.564 | ||
|576 | |||
|553.846 | |||
|- | |- | ||
!13 | !13 | ||
! colspan="2" |608.361 | ! colspan="2" |608.361 | ||
|624 | |||
|600.00 | |||
|- | |- | ||
!14 | !14 | ||
! colspan="2" |655.158 | ! colspan="2" |655.158 | ||
|672 | |||
|646.154 | |||
|- | |- | ||
!15 | !15 | ||
! colspan="2" |701.955 | ! colspan="2" |701.955 | ||
|720 | |||
|692.308 | |||
|- | |- | ||
|16 | |16 | ||
|751.7595 | |751.7595 | ||
|747.232 | |747.232 | ||
|768 | |||
|738.4615 | |||
|- | |- | ||
|17 | |17 | ||
|801.564 | |801.564 | ||
|792.509 | |792.509 | ||
|816 | |||
|784.615 | |||
|- | |- | ||
|18 | |18 | ||
|851.3685 | |851.3685 | ||
|837.7855 | |837.7855 | ||
|864 | |||
|830.769 | |||
|- | |- | ||
|19 | |19 | ||
|901.173 | |901.173 | ||
|883.062 | |883.062 | ||
|912 | |||
|876.923 | |||
|- | |- | ||
|20 | |20 | ||
|950.9775 | |950.9775 | ||
|928.339 | |928.339 | ||
|960 | |||
|923.077 | |||
|- | |- | ||
|21 | |21 | ||
|1000.782 | |1000.782 | ||
|973.616 | |973.616 | ||
|1008 | |||
|969.231 | |||
|- | |- | ||
|22 | |22 | ||
|1050.6865 | |1050.6865 | ||
|1018.938 | |1018.938 | ||
|1056 | |||
|1015.385 | |||
|- | |- | ||
|23 | |23 | ||
|1100.391 | |1100.391 | ||
|1064.1695 | |1064.1695 | ||
|1104 | |||
|1061.5385 | |||
|- | |- | ||
|24 | |24 | ||
|1150.1955 | |1150.1955 | ||
|1109.446 | |1109.446 | ||
|1152 | |||
|1107.692 | |||
|- | |- | ||
|25 | |25 | ||
|1200 | |1200 | ||
|1154.723 | |1154.723 | ||
|1200 | |||
|1153.846 | |||
|- | |- | ||
|26 | |26 | ||
|1249.8045 | |1249.8045 | ||
|1200 | |||
|1240.782 | |||
|1200 | |1200 | ||
|- | |- | ||
| Line 100: | Line 154: | ||
|1299.609 | |1299.609 | ||
|1245.277 | |1245.277 | ||
|1281.564 | |||
|1250.9775 | |||
|- | |- | ||
|28 | |28 | ||
|1349.4135 | |1349.4135 | ||
|1290.554 | |1290.554 | ||
|1322.346 | |||
|1301.955 | |||
|- | |- | ||
|29 | |29 | ||
|1399.218 | |1399.218 | ||
|1335.8305 | |1335.8305 | ||
|1363.128 | |||
|1352.9325 | |||
|- | |- | ||
|30 | |30 | ||
|1449.0225 | |1449.0225 | ||
|1381.107 | |1381.107 | ||
! colspan="2" |1403.91 | |||
|} | |} | ||