Flattone: Difference between revisions
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<nowiki>*</nowiki> In 13-limit CTE tuning, octave reduced | <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). | 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" | |||
! rowspan="2" |Interval category | {| class="wikitable right-2 right-4 right-6 right-8 right-10" | ||
! colspan="2" |-2 quartertones | ! rowspan="2" | Interval category | ||
! colspan="2" |-1 quartertone | ! colspan="2" | -2 quartertones | ||
! colspan="2" |0 quartertones | ! colspan="2" | -1 quartertone | ||
! colspan="2" |1 quartertone | ! colspan="2" | 0 quartertones | ||
! colspan="2" |2 quartertones | ! colspan="2" | 1 quartertone | ||
! colspan="2" | 2 quartertones | |||
|- | |- | ||
!Cents* | ! Cents* | ||
! | ! Approx. ratios | ||
!Cents* | ! Cents* | ||
! | ! Approx. ratios | ||
!Cents* | ! Cents* | ||
! | ! Approx. ratios | ||
!Cents* | ! Cents* | ||
! | ! Approx. ratios | ||
!Cents* | ! Cents* | ||
! | ! Approx. ratios | ||
|- | |- | ||
|Unison | | Unison | ||
|1098 | | 1098 | ||
|28/15 | | 28/15 | ||
|1149 | | 1149 | ||
|48/25, 52/27, 64/33, 35/18, 98/55, 63/32 | | 48/25, 52/27, 64/33, 35/18, 98/55, 63/32 | ||
|0 | | 0 | ||
|1/1 | | 1/1 | ||
|51 | | 51 | ||
|25/24, 27/26, 33/32, 36/35, 55/54, 64/63 | | 25/24, 27/26, 33/32, 36/35, 55/54, 64/63 | ||
|102 | | 102 | ||
|15/14 | | 15/14 | ||
|- | |- | ||
|Second | | Second | ||
|84 | | 84 | ||
|28/27, 21/20 | | 28/27, 21/20 | ||
|135 | | 135 | ||
|16/15, 12/11, 13/12, 14/13 | | 16/15, 12/11, 13/12, 14/13 | ||
|186 | | 186 | ||
|9/8, 10/9, 11/10 | | 9/8, 10/9, 11/10 | ||
|237 | | 237 | ||
|8/7, 15/13 | | 8/7, 15/13 | ||
|288 | | 288 | ||
| | | | ||
|- | |- | ||
|Third | | Third | ||
|219 | | 219 | ||
| | | | ||
|270 | | 270 | ||
|7/6 | | 7/6 | ||
|321 | | 321 | ||
|6/5 | | 6/5 | ||
|372 | | 372 | ||
|5/4, 16/13, 26/21 | | 5/4, 16/13, 26/21 | ||
|423 | | 423 | ||
|9/7 | | 9/7 | ||
|- | |- | ||
|Fourth | | Fourth | ||
|405 | | 405 | ||
| | | | ||
|456 | | 456 | ||
|13/10, 21/16 | | 13/10, 21/16 | ||
|507 | | 507 | ||
|4/3 | | 4/3 | ||
|558 | | 558 | ||
|11/8, 18/13 | | 11/8, 18/13 | ||
|609 | | 609 | ||
|10/7 | | 10/7 | ||
|- | |- | ||
|Fifth | | Fifth | ||
|591 | | 591 | ||
|7/5 | | 7/5 | ||
|642 | | 642 | ||
|16/11, 13/9 | | 16/11, 13/9 | ||
|693 | | 693 | ||
|3/2 | | 3/2 | ||
|744 | | 744 | ||
|20/13, 32/21 | | 20/13, 32/21 | ||
|795 | | 795 | ||
| | | | ||
|- | |- | ||
|Sixth | | Sixth | ||
|777 | | 777 | ||
|14/9 | | 14/9 | ||
|828 | | 828 | ||
|8/5, 13/8, 21/13 | | 8/5, 13/8, 21/13 | ||
|879 | | 879 | ||
|5/3 | | 5/3 | ||
|930 | | 930 | ||
|12/7 | | 12/7 | ||
|981 | | 981 | ||
| | | | ||
|- | |- | ||
|Seventh | | Seventh | ||
|912 | | 912 | ||
| | | | ||
|963 | | 963 | ||
|7/4, 26/15 | | 7/4, 26/15 | ||
|1014 | | 1014 | ||
|9/5, 16/9 | | 9/5, 16/9 | ||
|1065 | | 1065 | ||
|15/8, 11/6, 13/7, 24/13 | | 15/8, 11/6, 13/7, 24/13 | ||
|1116 | | 1116 | ||
|40/21, 27/14 | | 40/21, 27/14 | ||
|} | |} | ||
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{| 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 | ||