Decimal: Difference between revisions
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For technical data, see [[Dicot family #Decimal]]. | For technical data, see [[Dicot family #Decimal]]. | ||
== Interval chain == | == Interval chain == | ||
In the following table, odd harmonics and | In the following table, odd harmonics 1–9 and their inverses are in '''bold'''. | ||
{| class="wikitable center-1 | {| class="wikitable center-1 right-2 right-4" | ||
! rowspan="2" | # | ! rowspan="2" | # | ||
! colspan=" | ! colspan="2" | Period 0 | ||
! colspan=" | ! colspan="2" | Period 1 | ||
|- | |- | ||
! Cents* | |||
! Approx. ratios | ! Approx. ratios | ||
! Cents* | |||
! Approx. ratios | ! Approx. ratios | ||
|- | |- | ||
| 0 | | 0 | ||
| 0.0 | |||
| '''1/1''' | | '''1/1''' | ||
| 600.0 | |||
| 7/5, 10/7 | | 7/5, 10/7 | ||
|- | |- | ||
| 1 | | 1 | ||
| ''' | | 351.0 | ||
| ''' | | '''5/4''', 6/5 | ||
| 951.0 | |||
| '''7/4''', 12/7 | |||
|- | |- | ||
| 2 | | 2 | ||
| '''4/ | | 701.9 | ||
| 28/ | | '''3/2''' | ||
| 101.9 | |||
| 15/14, 21/20 | |||
|- | |||
| 3 | |||
| 1052.9 | |||
| 9/5, 15/8 | |||
| 452.9 | |||
| 9/7, 21/16 | |||
|- | |||
| 4 | |||
| 203.8 | |||
| '''9/8''' | |||
| 803.8 | |||
| 45/28, 54/35 | |||
|- | |||
| 5 | |||
| 554.8 | |||
| 27/20, 45/32 | |||
| 1154.8 | |||
| 27/14, 63/32 | |||
|} | |} | ||
<nowiki/>* In 7-limit CWE tuning, octave reduced | |||
One can see that the 10-note mos of the decimal temperament contains the 7-odd-limit [[tonality diamond]]. | One can see that the 10-note mos of the decimal temperament contains the 7-odd-limit [[tonality diamond]]. | ||
== Tunings == | |||
{| class="wikitable mw-collapsible mw-collapsed" | |||
|+ style="font-size: 105%; white-space: nowrap;" | 7-limit prime-optimized tunings | |||
|- | |||
! rowspan="2" | | |||
! colspan="3" | Euclidean | |||
|- | |||
! Constrained | |||
! Constrained & skewed | |||
! Destretched | |||
|- | |||
! Tenney | |||
| CTE: ~7/4 = 955.608{{c}} | |||
| CWE: ~7/4 = 950.957{{c}} | |||
| POTE: ~7/4 = 948.443{{c}} | |||
|} | |||
[[Category:Decimal| ]] <!-- main article --> | [[Category:Decimal| ]] <!-- main article --> | ||