7L 1s: Difference between revisions

{{Infobox MOS

| Name = pine

| Periods = 1

| nLargeSteps = 7

| nSmallSteps = 1

| Equalized = 1

| Collapsed = 1

| Pattern = LLLLLLLs

There are three notable [[Harmonic_Entropy|harmonic entropy]] minima with this [[MOSScales|MOS]] pattern. The lowest accuracy one is [[Porcupine_family|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 [[Chromatic_pairs#Greeley|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 [[4000/3993|S10/S11]] so that ([[4/3]])/([[11/10]])³ is tempered results in an unusually high accuracy & efficient rank 2 temperament in the 2.3.11/10 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 [[Porcupine family#2.3.5.11 subgroup .28porkypine.29|porkypine]] can be seen as a trivial tuning of [[4000/3993|pine]] tempering [[100/99]] = S10 and [[121/120]] = S11.)

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.

|-

|<nowiki>6|1</nowiki>

|<nowiki>5|2</nowiki>

|-

|LLLLsLLL

|<nowiki>4|3</nowiki>

|-

|<nowiki>3|4</nowiki>

|-

|<nowiki>2|5</nowiki>

|salmon

|Bright minor

|-

|<nowiki>1|6</nowiki>

|starfish

|<nowiki>0|7</nowiki>

|}

 

{| class="wikitable"

| |

| |162.5

| style="text-align:center;" |<span style="display: block; text-align: center;">13 13 13 13 13 13 13 5</span>

| style="text-align:center;" |5 5 5 5 5 5 5 2

| style="text-align:center;" |Porcupine is in this general region

| |2\15

| style="text-align:center;" |2 2 2 2 2 2 2 1

| style="text-align:center;" |Optimum rank range (L/s=2/1) porcupine

|-

| style="text-align:center;" |<span style="background-color: #ffffff;">√3 √3 √3 √3 √3 √3 √3 1</span>

| style="text-align:center;" |13 13 13 13 13 13 13 8

| style="text-align:center;" |Golden porcupine / golden hemikleismic

|-

| style="text-align:center;" |<span style="display: block; text-align: center;">11 11 11 11 11 11 11 7 </span><span style="display: block; text-align: center;">π π π π π π π 2</span>

| style="text-align:center;" |10 10 10 10 10 10 10 7

| style="text-align:center;" |Greeley is around here

|}