Miracle: Difference between revisions

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'''Miracle temperament''' is a regular temperament discovered by [[George Secor]] in 1974 which has as a generator an interval, called '''secor''', that serves as both [[15/14]] and [[16/15]] semitones.

'''Miracle temperament''' is a regular temperament discovered by [[George Secor]] in 1974 which has as a generator an interval, called '''secor''', that serves as both [[15/14]] and [[16/15]] semitones. In terms of 13-limit extensions, it is discussed in [[Miracle extensions|miraculous, benediction, and manna]].

Miracle is an exceptionally efficient linear temperament which is a member of both the [[Marvel_temperaments|marvel temperaments]] and the [[Gamelismic_clan|gamelismic clan]]. It is quite accurate, with TOP error only 0.63 cents/octave, meaning intervals of the 11-limit tonality diamond are represented with only one or two cents of error. Yet it is also very "low complexity" (efficient), as evidenced by the high density of 11-odd-limit ratios (in bold) in the following table:

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| | 7/5

| | 116.502

|-

| | |0 -27 25 5>

| | 116.573 (7 limit least squares)

|-

| | |0 -19 20>

| | 116.578 (5 limit least squares)

|-

| | 6/5

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| | 7/6

| | 116.641

|-

| | |0 17 -11 -6 11>

| | 116.672 (11 limit least squares)

|-

| | 10/9

| | 116.716 (9 and 11 limit minimax, <br>Secor's definition of secor)

|-

| | |0 117 -44 -19>

| | 116.721 (9 limit least squares)

|-

| | 11/8

@@ Line 1: / Line 1: @@
-'''Miracle temperament''' is a regular temperament discovered by [[George Secor]] in 1974 which has as a generator an interval, called '''secor''', that serves as both [[15/14]] and [[16/15]] semitones.
+'''Miracle temperament''' is a regular temperament discovered by [[George Secor]] in 1974 which has as a generator an interval, called '''secor''', that serves as both [[15/14]] and [[16/15]] semitones. In terms of 13-limit extensions, it is discussed in [[Miracle extensions|miraculous, benediction, and manna]].
 Miracle is an exceptionally efficient linear temperament which is a member of both the [[Marvel_temperaments|marvel temperaments]] and the [[Gamelismic_clan|gamelismic clan]]. It is quite accurate, with TOP error only 0.63 cents/octave, meaning intervals of the 11-limit tonality diamond are represented with only one or two cents of error. Yet it is also very "low complexity" (efficient), as evidenced by the high density of 11-odd-limit ratios (in bold) in the following table:
@@ Line 161: / Line 161: @@
 | | 7/5
 | | 116.502
+|-
+| | |0 -27 25 5&gt;
+| | 116.573 (7 limit least squares)
+|-
+| | |0 -19 20&gt;
+| | 116.578 (5 limit least squares)
 |-
 | | 6/5
@@ Line 176: / Line 182: @@
 | | 7/6
 | | 116.641
+|-
+| | |0 17 -11 -6 11&gt;
+| | 116.672 (11 limit least squares)
 |-
 | | 10/9
 | | 116.716 (9 and 11 limit minimax, <br>Secor's definition of secor)
+|-
+| | |0 117 -44 -19&gt;
+| | 116.721 (9 limit least squares)
 |-
 | | 11/8