7L 1s: Difference between revisions

==== Proposed names ====

Mode names are from [[Porcupine Temperament Modal Harmony|Porcupine temperament modal harmony]]. Descriptive mode names are based on using 1-4-7, i.e. 3+3 triads as a basis for harmony.

{| class="wikitable"

|<nowiki>7|0</nowiki>

|octopus

|Bright quartal

|Dark quartal

|Bright major

|Middle major

|Dark major

|Bright minor

|Middle minor

|Dark minor

|}

There are three notable [[harmonic entropy]] minima with this [[mos]] pattern. The lowest accuracy one is [[porcupine]], in which two generators make a [[6/5]] and three make a [[4/3]]. The range of porcupine tunings is about 2\15 to 3\22. Less well-known and more accurate is [[greeley]], in which two generators are still 6/5 but three fall quite short of a 4/3, but the scale happens to closely approximate a lot of higher-complexity intervals like [[10/7]], [[11/7]], etc. Thirdly and finally, [[tempering out]] [[4000/3993|S10/S11]] so that ([[4/3]])/([[11/10]])³ is tempered out results in an unusually high accuracy and efficient rank-2 temperament in the 2.3.11/5 subgroup for which interpretation as a rank-3 temperament in 2.3.5.11 (the no-7's [[11-limit]]) is natural, making [[10/9]] and [[12/11]] [[square superparticular|equidistant from 11/10]] and offering many fruitful tempering opportunities. Note therefore that [[porkypine]] can be seen as a trivial tuning of [[4000/3993|pine]] tempering out [[100/99]] = S10 and [[121/120]] = S11.