Miracle: Difference between revisions
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Miracle is an exceptionally efficient linear temperament which is a member of both the marvel temperaments (→ [[Marvel temperaments #Miracle]]) and the [[gamelismic clan]]. It is quite accurate, with [[TOP]] error only 0.63 [[cent]]s/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: | Miracle is an exceptionally efficient linear temperament which is a member of both the marvel temperaments (→ [[Marvel temperaments #Miracle]]) and the [[gamelismic clan]]. It is quite accurate, with [[TOP]] error only 0.63 [[cent]]s/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: | ||
{| class="wikitable" | {| class="wikitable center-1 right-2" | ||
|- | |- | ||
! number of <br>secors | ! number of <br>secors | ||
| Line 144: | Line 144: | ||
Miracle can also be thought of as a [[cluster temperament]] with 10 clusters of notes in an octave. The small chroma interval between adjacent notes in each cluster is very versatile, representing [[45/44]] ~ [[49/48]] ~ [[50/49]] ~ [[55/54]] ~ [[56/55]] ~ [[64/63]] all [[tempered]] together. | Miracle can also be thought of as a [[cluster temperament]] with 10 clusters of notes in an octave. The small chroma interval between adjacent notes in each cluster is very versatile, representing [[45/44]] ~ [[49/48]] ~ [[50/49]] ~ [[55/54]] ~ [[56/55]] ~ [[64/63]] all [[tempered]] together. | ||
=Spectrum of | == Spectrum of miracle tunings by eigenmonzos == | ||
{| class="wikitable" | {| class="wikitable center-1 right-2" | ||
|- | |- | ||
! Eigenmonzo | ! Eigenmonzo | ||
! Secor | ! Secor | ||
! Comments | |||
|- | |- | ||
| 8/7 | | 8/7 | ||
| 115.587 | | 115.587 | ||
| | |||
|- | |- | ||
| 11/9 | | 11/9 | ||
| 115.803 | | 115.803 | ||
| | |||
|- | |- | ||
| 5/4 | | 5/4 | ||
| 116.241 | | 116.241 | ||
| | |||
|- | |- | ||
| 7/5 | | 7/5 | ||
| 116.502 | | 116.502 | ||
| | |||
|- | |- | ||
| |0 -27 25 5 | | {{monzo| 0 -27 25 5 }} | ||
| 116.573 | | 116.573 | ||
| 7-odd-limit least squares | |||
|- | |- | ||
| |0 -19 20 | | {{monzo| 0 -19 20 }} | ||
| 116.578 | | 116.578 | ||
| 5-odd-limit least squares | |||
|- | |- | ||
| 6/5 | | 6/5 | ||
| 116.588 | | 116.588 | ||
| 5- and 7-odd-limit minimax | |||
|- | |- | ||
| 11/10 | | 11/10 | ||
| 116.591 | | 116.591 | ||
| | |||
|- | |- | ||
| 12/11 | | 12/11 | ||
| 116.596 | | 116.596 | ||
| | |||
|- | |- | ||
| 14/11 | | 14/11 | ||
| 116.617 | | 116.617 | ||
| | |||
|- | |- | ||
| 7/6 | | 7/6 | ||
| 116.641 | | 116.641 | ||
| | |||
|- | |- | ||
| |0 17 -11 -6 11 | | {{monzo| 0 17 -11 -6 11 }} | ||
| 116.672 | | 116.672 | ||
| 11-odd-limit least squares | |||
|- | |- | ||
| 10/9 | | 10/9 | ||
| 116.716 | | 116.716 | ||
| 9- and 11-odd-limit minimax, <br>Secor's definition of secor | |||
|- | |- | ||
| |0 117 -44 -19 | | {{monzo| 0 117 -44 -19 }} | ||
| 116.721 | | 116.721 | ||
| 9-odd-limit least squares | |||
|- | |- | ||
| 11/8 | | 11/8 | ||
| 116.755 | | 116.755 | ||
| | |||
|- | |- | ||
| 9/7 | | 9/7 | ||
| 116.792 | | 116.792 | ||
| | |||
|- | |- | ||
| 4/3 | | 4/3 | ||
| 116.993 | | 116.993 | ||
| | |||
|} | |} | ||
[[Category:Miracle]] | [[Category:Miracle| ]] <!-- main article --> | ||
[[Category:Temperament]] | [[Category:Temperament]] | ||