Pentacircle comma: Difference between revisions

| Ratio = 896/891

| Name = pentacircle comma, undecimal semicomma

| Color name = s1uz2, Saluzo comma

The '''pentacircle comma''' or '''undecimal semicomma''', '''896/891''' (9.68796 [[cent]]s), is an [[11-limit]] [[comma]] with monzo {{monzo|7 -4 0 1 -1}}. It is similar to the Didymus or syntonic comma, [[81/80]], in that it makes a stack of four fifths equal a major third (octave equivalent). In the case of 81/80, however, the major third is [[5/4]], while with the pentacircle comma, the major third is [[14/11]].

 

Pentacircle is tempered out by the following edos, using their patent vals: {{EDOs|5, 12, 17, 19, 22, 24, 27, 29, 36, 41, 44, 46, 51, 58, 60, 63, 65, 68, 80, 82, 85, 87, 90, 92, 104, 109, 114, 121, 123, 126, 128, 131, 133, 136, 138, 145, 150, 155, 167, 169, 172, 174, 177, 184, 189, 191, 196, 201, 208, 213, 218, 230, 232, 237, 242, 254, 259, 271, 278, 283, and 295}}.

 

Pentacircle can be factored into two [[13-limit]] [[superparticular]] commas, [[364/363]] (which is {{monzo| 2 -1 0 1 -2 1 }}) and [[352/351]] (which is {{monzo| 5 -3 0 0 1 -1 }}).

 

364/363 is the gentle comma, which is the difference between (14/11 × 13/11) and 3/2. If both pentacircle and 364/363 are tempered out (which implies that 352/351 is also tempered out, of course), a 14/11 major third and a 13/11 minor third together add up to a perfect fifth. (This isn't necessary for traditional minor and major thirds, because 5/4 × 6/5 = 3/2.)

 

352/351 is the minthma: see the article on [[minthmic chords]].

 

 

Example scales: [[Cantonpenta]] is a scale that tempers out the pentacircle comma. Also, the MOSes with an octave period and 17\29 as a generator temper out the pentacircle comma.

 

In the [[Sagittal]] system, the downward version of this comma (possibly tempered) is represented by the sagittal {{sagittal | )!( }} and is called the '''11/7 kleisma''', or '''11/7k''' for short, because the simplest interval it notates is 11/7, as for example in A-F{{nbhsp}}{{sagittal | )!( }}. The upward version is called '''7/11k''' or '''11/7k up''' and is represented by {{sagittal| )|( }}.