19edo: Difference between revisions

Standard 12edo notation can be used, whether it is staff notation (with five lines), letter notation (with standard accidentals), solfege, or sargam.  Note that D# and Eb are two different notes.

! Degree

! Cents

! Ratios*

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| unison

| D

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| aug 1sn, dim 2nd

| D#, Ebb

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| minor 2nd

| Eb

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| major 2nd

| E

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| aug 2nd, dim 3rd

| E#, Fb

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| minor 3rd

| F

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| major 3rd

| F#

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| aug 3rd, dim 4th

| Fx, Gb

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| perfect 4th

| G

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| aug 4th

| G#

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| dim 5th

| Ab

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| perfect 5th

| A

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| aug 5th, dim 6th

| A#, Bbb

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| minor 6th

| Bb

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| major 6th

| B

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| aug 6th, dim 7th

| B#, Cb

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| minor 7th

| C

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| major 7th

| C#

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| aug 7th, dim 8ve

| Cx, Db

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| perfect 8ve

| D

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<nowiki>*</nowiki> based on treating 19-EDO as a 2.3.5.7.13 subgroup temperament; other approaches are possible.

Using [[Kite's_color_notation|color notation]], qualities can be loosely associated with colors:

! quality

! color

! examples

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All 19edo chords can be named using conventional methods, expanded to include augmented and diminished 2nd, 3rds, 6ths and 7ths. Here are the zo, gu, yo and ru triads:

! [[Kite's color notation|color of the 3rd]]

! JI chord

! spoken name

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=== Best direct mapping, even if inconsistent ===

! Interval, complement

! Error (abs., in [[cent|cents]])

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! Interval, complement

! Error (abs., in [[cent|cents]])

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[[:File:19ed2-001.svg|19ed2-001.svg]]

19 EDO [[tempering out|tempers out]] the following [[Comma|comma]]s. (Note: This assumes the [[val]] &lt; 19 30 44 53 66 70 |.)

! [[Ratio]]

! [[Monzos|Monzo]]

! Name(s)

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| {{Monzo| -14 3 4 }}

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| {{Monzo| -10 -1 5 }}

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| {{Monzo| -4 4 -1 }}

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| {{Monzo| 2 9 -7 }}

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| {{Monzo| -6 -5 6 }}

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| {{Monzo| 8 14 -13 }}

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| {{Monzo| -14 -19 19 }}

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| {{Monzo| -3 1 -3 3 }}

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| {{Monzo| -9 1 2 1 }}

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| {{Monzo| -4 -1 0 2 }}

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| {{Monzo| 1 -3 -2 3 }}

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| {{Monzo| -5 -3 3 1 }}

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| {{Monzo| 0 -5 1 2 }}

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| {{Monzo| 1 2 -3 1 }}

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| {{Monzo| -5 2 2 -1 }}

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| {{Monzo| -4 9 -2 -2 }}

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| {{Monzo| 5 -7 -1 3 }}

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| {{Monzo| 6 0 -5 2 }}

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| {{Monzo| -11 2 7 -3 }}

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| {{Monzo| -1 -7 4 1 }}

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| {{Monzo| 2 -2 2 0 -1 }}

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| {{Monzo| 7 -4 0 1 -1 }}

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| {{Monzo| 16 0 0 -2 -3 }}

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| {{Monzo| -7 -1 1 1 1 }}

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| {{Monzo| 2 3 1 -2 -1 }}

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| {{Monzo| -1 -2 -1 1 0 1 }}

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| {{Monzo| 2 -3 -2 0 0 2 }}

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Since 19 is prime, all rank two temperaments in 19edo have one period per octave (i.e. are linear). Therefore you can make a correspondence between intervals and the linear temperaments they generate.

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! Degree

! Generator for

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