Formal comma: Difference between revisions
Formal commas are notation-specific |
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A JI notation will typically have for each prime ''p'' a pair of [[inflections and alterations|inflections]] that raise/lower a note by ''p'''s formal comma. Thus 5/4 from C is notated as an inflected E, 7/4 as an inflected B♭, etc. Ratios like [[35/32]] and [[49/48]] are inflected twice, and the commas accumulate, so complex ratios may be quite distant from the uninflected 3-limit note. | A JI notation will typically have for each prime ''p'' a pair of [[inflections and alterations|inflections]] that raise/lower a note by ''p'''s formal comma. Thus 5/4 from C is notated as an inflected E, 7/4 as an inflected B♭, etc. Ratios like [[35/32]] and [[49/48]] are inflected twice, and the commas accumulate, so complex ratios may be quite distant from the uninflected 3-limit note. | ||
Each JI notation assumes certain formal commas. The notations largely agree but do diverge for certain primes, because the exact method for choosing the best formal commas is disputed. Ideally, both the 3-count and the size in cents is minimized, and there are other considerations as well. The choice for neutral-sounding primes like 11 (P4 vs. A4) and 13 (m6 vs. M6) is particularly tricky. Certain choices map the ratio [[13/11]] = 289{{c}} to either M2 or M3. | Each JI notation assumes certain formal commas. The notations largely agree but do diverge for certain primes, because the exact method for choosing the best formal commas is disputed. Ideally, both the 3-count and the size in cents is minimized, and there are other considerations as well. The choice for neutral-sounding primes like 11 (P4 vs. A4) and 13 (m6 vs. M6) is particularly tricky. Certain choices map the ratio [[13/11]] = 289{{c}} to either M2 or M3. Some notation systems allow one to replace the formal comma for such a prime with its [[chromatic]] and/or [[enharmonic]] counterparts. | ||
{| class="wikitable center-all" | |||
{| class="wikitable" | |||
|+Formal commas used by various JI notations | |+Formal commas used by various JI notations | ||
! | ! | ||
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! 17 | ! 17 | ||
! 19 | ! 19 | ||
! 23 | |||
|- | |- | ||
! [[Color notation]] | ! [[Color notation]] | ||
| M3 | | [[81/80|80/81]] (M3) | ||
| m7 | | [[64/63|63/64]] (m7) | ||
| P4/A4 | | [[33/32]] (P4)<br>[[729/704|704/729]] (A4) | ||
| m6/M6 | | [[1053/1024]] (m6)<br> [[27/26|26/27]] (M6) | ||
| m2 | | [[4131/4096]] (m2) | ||
| m3 | | [[513/512]] (m3) | ||
| [[16767/16384]] (d5) | |||
|- | |- | ||
! [[Functional Just System]] | ! [[Functional Just System]] | ||
| M3 | | 80/81 (M3) | ||
| m7 | | 63/64 (m7) | ||
| P4 | | 33/32 (P4) | ||
| m6 | | 1053/1024 (m6) | ||
| m2 | | 4131/4096 (m2) | ||
| m3 | | 513/512 (m3) | ||
| [[736/729]] (A4) | |||
|- | |- | ||
! [[Helmholtz–Ellis notation]] | ! [[Helmholtz–Ellis notation]] | ||
| M3 | | 80/81 (M3) | ||
| m7 | | 63/64 (m7) | ||
| P4 | | 33/32 (P4) | ||
| M6 | | 26/27 (M6) | ||
| A1 | | [[2187/2176]] (A1) | ||
| m3 | | 513/512 (m3) | ||
| 736/729 (A4) | |||
|- | |- | ||
! Prime-factor [[Sagittal notation|Sagittal]] | ! Prime-factor [[Sagittal notation|Sagittal]] | ||
| M3 | | 80/81 (M3) | ||
| m7 | | 63/64 (m7) | ||
| P4 | | 33/32 (P4) | ||
| M6 | | 26/27 (M6) | ||
| m2 | | 4131/4096 (m2) | ||
| m3 | | 513/512 (m3) | ||
| 736/729 (A4) | |||
|} | |} | ||