1729/1728: Difference between revisions

Line 4:

| Monzo = -6 -3 0 1 0 1 0 1

| Cents = 1.00158

| Name = ~~lesser massma, ~~ramanujanisma~~, dodecentisma~~

| Name = ramanujanisma

| Color name =

| Color name = nothozo comma

| FJS name =

| Sound =

}}

'''1729/1728''' is a [[19-limit]] (more accurately, 2.3.7.13.19 subgroup) [[superparticular]] interval and an [[unnoticeable comma]]~~. '''Lesser massma'''<ref>referring~~ to ~~number 1728 being known as the ''Maß''~~ in ~~German. </ref>, '''ramanujanisma'''<ref>referring to the anecdotal story of [[Wikipedia: Ramanujan|Ramanujan]] finding 1729 an interesting number. </ref>, and '''dodecentisma'''<ref>referring to the~~ size being close to the relative '''cent''' of '''12'''edo ('''dodeca''') (12 * 100 = 1200 and this comma is a low [[prime limit]] superparticular approximating 1/1200 of an octave) and referring to 1728 being a power of 12 (dodeca). </ref> have been proposed as the name. ~~The comma~~ forms the difference between the [[octave]] and a stack of [[7/6]], [[13/12]] and [[19/12]], and less likely, the difference between [[19/18]] and [[96/91]].

'''1729/1728''', known as the '''ramanujanisma''', is a [[19-limit]] (more accurately, 2.3.7.13.19 subgroup) [[superparticular]] interval and an [[unnoticeable comma]] that is remarkably close to one cent in size. It forms the difference between the [[octave]] and a stack of [[7/6]], [[13/12]] and [[19/12]], and less likely, the difference between [[19/18]] and [[96/91]].

Both the numerator and denominator of this interval are famous in mathematics. [[Wikipedia: 1728 (number)|1728]], being 12 to the 3rd power, is also known as mass. [[Wikipedia:1729 (number)|1729]] is known for being Ramanujan's number and the first number that can be expressed as the sum of two cubes in two different ways (1729 = 13 + 123 = 93 + 103).

~~Remarkably,~~ this comma ~~is very close to one cent~~.

Tempering out this comma enables the '''ramanujanismic chords''', the [[essentially tempered chord]]s in the 19-odd-limit, a basic form of which comprises the steps of 7/6-13/12-19/12 closing at the octave.

~~Tempering out this comma enables~~ the ~~related essentially tempered chords~~ in the ~~19-odd-~~limit.

== Terminology ==

The name ''ramanujanisma'' was first proposed by [[User:Fredg999|Frédéric Gagné]] in reference to the anecdotal story of [[Wikipedia: Ramanujan|Ramanujan]] finding 1729 an interesting number. Alternative names include '''lesser massma''', proposed by [[User:Eliora|Eliora]], in reference to the number 1728 being known as the ''Maß'' in German, and '''dodecentisma''', proposed by [[User:Godtone|Godtone]], in reference to the size being close to the relative ''cent'' of ''12''edo (''dodeca'') (12 × 100 = 1200 and this comma is a low [[prime limit]] superparticular approximating 1/1200 of an octave) and in reference to 1728 being a power of 12 (''dodeca'').

== See also ==

* [[List of superparticular intervals]]

* [[Unnoticeable comma]]

~~== Notes ==~~

[[Category:19-limit]]

[[Category:Unnoticeable comma]]

[[Category:Superparticular]]

[[Category:Ramanujanismic]]

@@ Line 4: / Line 4: @@
 | Monzo = -6 -3 0 1 0 1 0 1
 | Cents = 1.00158
-| Name = lesser massma, <br>ramanujanisma, <br>dodecentisma
+| Name = ramanujanisma
-| Color name =
+| Color name = nothozo comma
 | FJS name =
 | Sound =
 }}
-'''1729/1728''' is a [[19-limit]] (more accurately, 2.3.7.13.19 subgroup) [[superparticular]] interval and an [[unnoticeable comma]]. '''Lesser massma'''<ref>referring to number 1728 being known as the ''Maß'' in German. </ref>, '''ramanujanisma'''<ref>referring to the anecdotal story of [[Wikipedia: Ramanujan|Ramanujan]] finding 1729 an interesting number. </ref>, and '''dodecentisma'''<ref>referring to the size being close to the relative '''cent''' of '''12'''edo ('''dodeca''') (12 * 100 = 1200 and this comma is a low [[prime limit]] superparticular approximating 1/1200 of an octave) and referring to 1728 being a power of 12 (dodeca). </ref> have been proposed as the name. The comma forms the difference between the [[octave]] and a stack of [[7/6]], [[13/12]] and [[19/12]], and less likely, the difference between [[19/18]] and [[96/91]].
+'''1729/1728''', known as the '''ramanujanisma''', is a [[19-limit]] (more accurately, 2.3.7.13.19 subgroup) [[superparticular]] interval and an [[unnoticeable comma]] that is remarkably close to one cent in size. It forms the difference between the [[octave]] and a stack of [[7/6]], [[13/12]] and [[19/12]], and less likely, the difference between [[19/18]] and [[96/91]].
 Both the numerator and denominator of this interval are famous in mathematics. [[Wikipedia: 1728 (number)|1728]], being 12 to the 3rd power, is also known as mass. [[Wikipedia:1729 (number)|1729]] is known for being Ramanujan's number and the first number that can be expressed as the sum of two cubes in two different ways (1729 = 1<sup>3</sup> + 12<sup>3</sup> = 9<sup>3</sup> + 10<sup>3</sup>).
-Remarkably, this comma is very close to one cent.
+Tempering out this comma enables the '''ramanujanismic chords''', the [[essentially tempered chord]]s in the 19-odd-limit, a basic form of which comprises the steps of 7/6-13/12-19/12 closing at the octave.
-Tempering out this comma enables the related essentially tempered chords in the 19-odd-limit.
+== Terminology ==
+The name ''ramanujanisma'' was first proposed by [[User:Fredg999|Frédéric Gagné]] in reference to the anecdotal story of [[Wikipedia: Ramanujan|Ramanujan]] finding 1729 an interesting number. Alternative names include '''lesser massma''', proposed by [[User:Eliora|Eliora]], in reference to the number 1728 being known as the ''Maß'' in German, and '''dodecentisma''', proposed by [[User:Godtone|Godtone]], in reference to the size being close to the relative ''cent'' of ''12''edo (''dodeca'') (12 × 100 = 1200 and this comma is a low [[prime limit]] superparticular approximating 1/1200 of an octave) and in reference to 1728 being a power of 12 (''dodeca'').
 == See also ==
 * [[List of superparticular intervals]]
 * [[Unnoticeable comma]]
-== Notes ==
 [[Category:19-limit]]
 [[Category:Unnoticeable comma]]
 [[Category:Superparticular]]
+[[Category:Ramanujanismic]]