7777/7776: Difference between revisions

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{{Infobox Interval

| ~~Ratio~~ = ~~7777/7776~~

| Name = pulsar comma

| ~~Monzo~~ = ~~-5 -5 0 1 1 020 1~~

| Comma = yes

| ~~Cents = 0.223~~

| Color name = 101o1oz2, Fifiwolozo comma

~~| Name~~ = ~~power of 6 repdigit~~ comma

}}

'''7777/7776''', the '''power of 6 repdigit comma''' is an unnoticeable comma of 223 ~~millicents~~, and it is a part of 101-limit just intonation.

'''7777/7776''', the '''pulsar comma''' or '''power of six repdigit comma''' is an unnoticeable comma of 0.223 cents, and it is a part of 101-limit [[just intonation]].

The comma derives from the resemblance of a perfect power of 6, 7776, to a repdigit number 7777. It is the difference between a stack of 5 [[6/1~~|hexataves~~]] and 7, 11, and 101 harmonics stacked, or when octave-reduced, between 7/4, 11/8, and 101/64 and the Pythagorean major seventh, [[243/128]]. It is also the difference between 404/243 and 128/77.

The comma derives from the resemblance of a perfect power of 6, 7776, to a decimal repdigit number 7777. It is the difference between a stack of five [[6/1]]'s and 7, 11, and 101 harmonics stacked, or when octave-reduced, between 7/4, 11/8, and 101/64 and the Pythagorean major seventh, [[243/128]]. It is also the difference between 404/243 and 128/77.

The name origin is the following: power of six repdigit – ''psr'', which is the astronomical shortening for pulsars.

== Temperaments ==

[[~~135edo]] [[support~~]]~~s a large amount~~ of temperaments ~~when it comes to this comma~~. ~~Other EDOs~~ which ~~temper it out~~ are {{EDOs|342, 207, 1012, 477, 1147, 971, 270, 836, 877}}. Note that 270edo is a multiple of 135edo.

Tempering it out leads to the [[stellar remnants]] collection of temperaments, the core of which is the 2.3.7.11.101 subgroup. Some of the edos which support pulsar temperaments are [[135edo|135]], {{EDOs|342, 207, 1012, 477, 1147, 971, 270, 836, 877}}. Note that 270edo is a multiple of 135edo.

~~=== 135 & 836 ===~~

~~Subgroup: 2.3.7.11.101~~

~~Mapping: {{Wedgie|1 -4 3 5 -23}}, {{Wedgie|0 29 -1 -8 154}}~~

~~POTE Generator~~: ~~231.1022c ~8/7~~

[[Category:Pulsar]]

[[Category:~~Superparticular~~]]

[[Category:Commas named for their regular temperament properties]]

@@ Line 1: / Line 1: @@
+{{Novelty}}
 {{Infobox Interval
-| Ratio = 7777/7776
+| Name = pulsar comma
-| Monzo = -5 -5 0 1 1 0<sup>20</sup> 1
+| Comma = yes
-| Cents = 0.223
+| Color name = 101o1oz2, Fifiwolozo comma
-| Name = power of 6 repdigit comma
 }}
-'''7777/7776''', the '''power of 6 repdigit comma''' is an unnoticeable comma of 223 millicents, and it is a part of 101-limit just intonation.
+'''7777/7776''', the '''pulsar comma''' or '''power of six repdigit comma''' is an unnoticeable comma of 0.223 cents, and it is a part of 101-limit [[just intonation]].
-The comma derives from the resemblance of a perfect power of 6, 7776, to a repdigit number 7777. It is the difference between a stack of 5 [[6/1|hexataves]] and 7, 11, and 101 harmonics stacked, or when octave-reduced, between 7/4, 11/8, and 101/64 and the Pythagorean major seventh, [[243/128]]. It is also the difference between 404/243 and 128/77.
+The comma derives from the resemblance of a perfect power of 6, 7776, to a decimal repdigit number 7777. It is the difference between a stack of five [[6/1]]'s and 7, 11, and 101 harmonics stacked, or when octave-reduced, between 7/4, 11/8, and 101/64 and the Pythagorean major seventh, [[243/128]]. It is also the difference between 404/243 and 128/77.
+The name origin is the following: <u>p</u>ower of <u>s</u>ix <u>r</u>epdigit – ''psr'', which is the astronomical shortening for pulsars.
 == Temperaments ==
-[[135edo]] [[support]]s a large amount of temperaments when it comes to this comma. Other EDOs which temper it out are {{EDOs|342, 207, 1012, 477, 1147, 971, 270, 836, 877}}. Note that 270edo is a multiple of 135edo.
+Tempering it out leads to the [[stellar remnants]] collection of temperaments, the core of which is the 2.3.7.11.101 subgroup. Some of the edos which support pulsar temperaments are [[135edo|135]], {{EDOs|342, 207, 1012, 477, 1147, 971, 270, 836, 877}}. Note that 270edo is a multiple of 135edo.
-=== 135 & 836 ===
-Subgroup: 2.3.7.11.101
-Mapping: {{Wedgie|1 -4 3 5 -23}}, {{Wedgie|0 29 -1 -8 154}}
-POTE Generator: 231.1022c ~8/7
+[[Category:Pulsar]]
-[[Category:Superparticular]]
+[[Category:Commas named for their regular temperament properties]]