Flattone: Difference between revisions
The article already starts with "flattone is an alternative extension to 5-limit meantone", so I can't see how this thing helps. Whatever its relation to meantone is, we're documenting this temp as a coherent 7-limit structure Tag: Undo |
m Adjust the section title. Formatting |
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<nowiki/> | <nowiki>*</nowiki> In 13-limit CTE tuning, octave reduced | ||
=== As a detemperament of 7et === | |||
Flattone is best analyzed as a 7-form system. It is melodically intuitive compared to standard meantone, in that 7-limit intervals are found as augmented and diminished versions of the category they "should" belong to (that is, the quartertone represents both 25/24 and 64/63). | |||
{| class="wikitable right-2 right-4 right-6 right-8 right-10" | |||
! rowspan="2" | Interval category | |||
! colspan="2" | -2 quartertones | |||
! colspan="2" | -1 quartertone | |||
! colspan="2" | 0 quartertones | |||
! colspan="2" | 1 quartertone | |||
! colspan="2" | 2 quartertones | |||
|- | |||
! Cents* | |||
! Approx. ratios | |||
! Cents* | |||
! Approx. ratios | |||
! Cents* | |||
! Approx. ratios | |||
! Cents* | |||
! Approx. ratios | |||
! Cents* | |||
! Approx. ratios | |||
|- | |||
| Unison | |||
| 1098 | |||
| 28/15 | |||
| 1149 | |||
| 48/25, 52/27, 64/33, 35/18, 98/55, 63/32 | |||
| 0 | |||
| 1/1 | |||
| 51 | |||
| 25/24, 27/26, 33/32, 36/35, 55/54, 64/63 | |||
| 102 | |||
| 15/14 | |||
|- | |||
| Second | |||
| 84 | |||
| 28/27, 21/20 | |||
| 135 | |||
| 16/15, 12/11, 13/12, 14/13 | |||
| 186 | |||
| 9/8, 10/9, 11/10 | |||
| 237 | |||
| 8/7, 15/13 | |||
| 288 | |||
| | |||
|- | |||
| Third | |||
| 219 | |||
| | |||
| 270 | |||
| 7/6 | |||
| 321 | |||
| 6/5 | |||
| 372 | |||
| 5/4, 16/13, 26/21 | |||
| 423 | |||
| 9/7 | |||
|- | |||
| Fourth | |||
| 405 | |||
| | |||
| 456 | |||
| 13/10, 21/16 | |||
| 507 | |||
| 4/3 | |||
| 558 | |||
| 11/8, 18/13 | |||
| 609 | |||
| 10/7 | |||
|- | |||
| Fifth | |||
| 591 | |||
| 7/5 | |||
| 642 | |||
| 16/11, 13/9 | |||
| 693 | |||
| 3/2 | |||
| 744 | |||
| 20/13, 32/21 | |||
| 795 | |||
| | |||
|- | |||
| Sixth | |||
| 777 | |||
| 14/9 | |||
| 828 | |||
| 8/5, 13/8, 21/13 | |||
| 879 | |||
| 5/3 | |||
| 930 | |||
| 12/7 | |||
| 981 | |||
| | |||
|- | |||
| Seventh | |||
| 912 | |||
| | |||
| 963 | |||
| 7/4, 26/15 | |||
| 1014 | |||
| 9/5, 16/9 | |||
| 1065 | |||
| 15/8, 11/6, 13/7, 24/13 | |||
| 1116 | |||
| 40/21, 27/14 | |||
|} | |||
== Scales == | == Scales == | ||
| Line 80: | Line 187: | ||
{| class="wikitable center-all left-4" | {| class="wikitable center-all left-4" | ||
! Edo<br>generator | ! Edo<br>generator | ||
! [[Eigenmonzo|Eigenmonzo<br>( | ! [[Eigenmonzo|Eigenmonzo<br>(unchanged-interval)]]* | ||
! Generator<br>(¢) | ! Generator<br>(¢) | ||
! Comments | ! Comments | ||
| Line 272: | Line 379: | ||
[[Category:Flattone| ]] <!-- Main article --> | [[Category:Flattone| ]] <!-- Main article --> | ||
[[Category:Rank-2 temperaments]] | [[Category:Rank-2 temperaments]] | ||
[[Category:Meantone family]] | [[Category:Meantone family]] | ||
[[Category:Avicennmic temperaments]] | [[Category:Avicennmic temperaments]] | ||
[[Category:Keemic temperaments]] | [[Category:Keemic temperaments]] | ||