Valentine/Chords: Difference between revisions

Below are listed the [[dyadic chord]]s of 11-limit [[Valentine|valentine temperament]]. Typing the chords requires consideration of the fact that valentine conflates 12/11 and 11/10 and so also 11/6 and 20/11. If a transversal can be found which shows the chord to be essentially just, that transversal is listed along with a typing as otonal, utonal, or ambitonal. If the chord is essentially tempered, it is analyzed in terms of the transversal which employs 11/10 and 20/11.

If only [[126/125]] needs to be tempered out, the chord is labeled starling, if [[121/120]], biyatismic, if [[176/175]], valinorsmic, if [[385/384]], keenanismic, and if [[441/440]], werckismic. Chords which require any two of 121/120, 176/175 or 385/384 are labeled zeus, if they require any two of 126/125, 176/175 or 441/440, they are labeled thrush. Finally, if they require any three independent commas among those discussed above, it is labeled valentine.

Valentine has MOS of size 15, 16, 31 and 46. It is readily observed from the list below that even the smallest of these is well-supplied with chords. Because [[Carlos Alpha]] is the generator chain of valentine in the tuning with pure 3/2's, the list below is also a list of chords of Carlos Alpha, so long as the transversals are adjusted so that the notes are in the correct octave. This means that a number in a chord listed under "chord" less than 16 corresponds to a note in the transversal which should be left unaltered, whereas the notes from 16 to 21 correspond to transversal notes which should be adjusted up an octave. Hence, tetrad 8, the 0-2-5-9 chord with transversal 1-6/5-11/8-3/2, is an essentially zeus chord of Carlos Alpha as well as valentine. On the other hand, tetrad 76, 0-10-13-18 with transversal 1-11/7-9/5-9/8, corresponds to the werckismic 1-11/7-9/5-9/4 chord of Carlos Alpha.

== Triads ==

Example 1: Chord #13 is generators 0-5-9 and is a traditional five-limit major chord, 1/1-5/4-3/2. It occurs for the first time on the ninth generation, and will therefore occur six times (15-9=6) in valentine[15].  

Example 2: Chord #38 is generators 0-8-13, which is 1/1-5/4-7/5, occurs for the first time on the thirteenth generation, and therefore appears only twice (15-13=2) in valentine[15].

Each of the triads generated has three "inversions", i.e., can be written starting on any one of the three tones in the triad. The first chord is based on the number of generator steps for each tone. This ordering makes it easy to see how often it will occur in a given MOS, as noted in the examples above, but it may seem surprising if you're new to it: For example, chord #8 is 1/1-8/7-10/7, but it might seem more "natural" to use 1/1-5/4-7/4, which is listed as the second inversion. Unlike in traditional music theory, there is nothing canonical about these orderings and inversions.

{| class="wikitable"

! Number

| 1/1-8/7-20/11

| 1/1-8/5-20/11

| 1/1-5/4-20/11

| 1-12/11-3/2

| 1/1-12/11-3/2

| 1/1-41/31-11/6

| 1/1-68/53-7/5

| 1-12/11-18/11

| 1/1-12/11-18/11

| 1/1-97/80-11/6

| 1-12/11-12/7

| 1/1-12/11-12/7

| 1/1-12/11-14/11

| 1/1-7/6-146/79

| 1/1-18/11-20/11

 

{| class="wikitable"

! Number

| 1-12/11-6/5-3/2

| 1-12/11-3/2-18/11

| 1-12/11-6/5-12/7

| 1-12/11-3/2-12/7

 

{| class="wikitable"

! Number

| 1-12/11-6/5-3/2-12/7