Talk:936/935: Difference between revisions

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::: > Perhaps most interestingly for me- 117/64 with 935/512.

::: It's nothing special: any interval can be decomposed into a difference of two overtones.

::: The comma is an essential tempering comma so there should be some essentially tempered chords. We might focus on that. [[User:FloraC|FloraC]] ([[User talk:FloraC|talk]]) 06:31, 29 December 2020 (UTC)

:::: It maybe true that any interval can be decomposed into a difference of two overtones or two undertones, but the fact that one of the two overtones in this case was 117/64 is what I found interesting in light of the potential for cultural references. At any rate, it's good to know that this comma leads to essentially tempered chords. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 08:38, 29 December 2020 (UTC)

:::: These are the triads:

::::* 1-17/16-13/11 with steps 17/16-10/9-22/13, and its inversions;

::::* 1-10/9-13/11 with steps 10/9-17/16-22/13, and its inversions;

::::* 1-13/11-24/17 with steps 13/11-6/5-24/17, and its inversions;

::::* 1-6/5-24/17 with steps 6/5-13/11-24/17, and its inversions;

::::* 1-18/17-5/4 with steps 18/17-13/11-8/5, and its inversions;

::::* 1-13/11-5/4 with steps 13/11-18/17-8/5, and its inversions.

:::: There should be numerous tetrads, pentads, etc. which I don't bother to find. [[User:FloraC|FloraC]] ([[User talk:FloraC|talk]]) 07:00, 29 December 2020 (UTC)

::::: This list is good to have on hand. Perhaps I should make note of the the fact that this comma leads to essentially tempered chords- "ainic chords" in this case, and then make an article showing off some of these chords. Unfortunately, however I don't seem to have a good way of finding all the essentially tempered chords. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 08:38, 29 December 2020 (UTC)

== Forms of 17-limit Temperaments ==

Hey, Flora, what exactly do you mean when you say that we "don't know what form a 17-limit temperament should take"? --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 07:11, 31 December 2020 (UTC)

: Note it's not that we don't know what a 17-limit temperament is; it's that we haven't got examples of such pages for temperaments of a 17-limit comma. Quoting:

<pre>

If X is a 3- or 5-limit comma,

"X family" is for rank-2 temperaments that temper it out.

If X is a 7-limit comma,

"X family" is for rank-3 temperaments that temper it out, and "X temperaments" is for rank-2 temperaments that temper it out ("X clan" if the comma is a subgroup comma). See: Marvel family, Marvel temperaments.

If X is an 11-limit comma,

"X family" is for rank-4 temperaments that temper it out, and "X temperaments" is for rank-3 temperaments that temper it out. If the "X family" page isn't there (as it doesn't have many 13-limit branches), in "X temperaments" there is a brief of the rank-4 temperaments. See: Keenanismic family, Valinorsmic temperaments, Kalismic temperaments.

If X is an 13-limit comma,

there are only three such pages: The Archipelago, The Biosphere, Marveltwin, which list temperaments of various ranks.

</pre>

: So we haven't got "X temperaments" for 13-limit commas nor have we determined if there will be, let alone 17-limit. I suggest a discussion in [[Xenharmonic Wiki:Things to do]] if you feel like initiating that project. [[User:FloraC|FloraC]] ([[User talk:FloraC|talk]]) 08:24, 31 December 2020 (UTC)

@@ Line 15: / Line 15: @@
 ::: > Perhaps most interestingly for me- 117/64 with 935/512.
 ::: It's nothing special: any interval can be decomposed into a difference of two overtones.
 ::: The comma is an essential tempering comma so there should be some essentially tempered chords. We might focus on that. [[User:FloraC|FloraC]] ([[User talk:FloraC|talk]]) 06:31, 29 December 2020 (UTC)
+:::: It maybe true that any interval can be decomposed into a difference of two overtones or two undertones, but the fact that one of the two overtones in this case was 117/64 is what I found interesting in light of the potential for cultural references.  At any rate, it's good to know that this comma leads to essentially tempered chords. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 08:38, 29 December 2020 (UTC)
+:::: These are the triads:
+::::* 1-17/16-13/11 with steps 17/16-10/9-22/13, and its inversions;
+::::* 1-10/9-13/11 with steps 10/9-17/16-22/13, and its inversions;
+::::* 1-13/11-24/17 with steps 13/11-6/5-24/17, and its inversions;
+::::* 1-6/5-24/17 with steps 6/5-13/11-24/17, and its inversions;
+::::* 1-18/17-5/4 with steps 18/17-13/11-8/5, and its inversions;
+::::* 1-13/11-5/4 with steps 13/11-18/17-8/5, and its inversions.
+:::: There should be numerous tetrads, pentads, etc. which I don't bother to find. [[User:FloraC|FloraC]] ([[User talk:FloraC|talk]]) 07:00, 29 December 2020 (UTC)
+::::: This list is good to have on hand.  Perhaps I should make note of the the fact that this comma leads to essentially tempered chords- "ainic chords" in this case, and then make an article showing off some of these chords.  Unfortunately, however I don't seem to have a good way of finding all the essentially tempered chords. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 08:38, 29 December 2020 (UTC)
+== Forms of 17-limit Temperaments ==
+Hey, Flora, what exactly do you mean when you say that we "don't know what form a 17-limit temperament should take"? --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 07:11, 31 December 2020 (UTC)
+: Note it's not that we don't know what a 17-limit temperament is; it's that we haven't got examples of such pages for temperaments of a 17-limit comma. Quoting:
+<pre>
+If X is a 3- or 5-limit comma,
+"X family" is for rank-2 temperaments that temper it out.
+If X is a 7-limit comma,
+"X family" is for rank-3 temperaments that temper it out, and "X temperaments" is for rank-2 temperaments that temper it out ("X clan" if the comma is a subgroup comma). See: Marvel family, Marvel temperaments.
+If X is an 11-limit comma,
+"X family" is for rank-4 temperaments that temper it out, and "X temperaments" is for rank-3 temperaments that temper it out. If the "X family" page isn't there (as it doesn't have many 13-limit branches), in "X temperaments" there is a brief of the rank-4 temperaments. See: Keenanismic family, Valinorsmic temperaments, Kalismic temperaments.
+If X is an 13-limit comma,
+there are only three such pages: The Archipelago, The Biosphere, Marveltwin, which list temperaments of various ranks.
+</pre>
+: So we haven't got "X temperaments" for 13-limit commas nor have we determined if there will be, let alone 17-limit. I suggest a discussion in [[Xenharmonic Wiki:Things to do]] if you feel like initiating that project. [[User:FloraC|FloraC]] ([[User talk:FloraC|talk]]) 08:24, 31 December 2020 (UTC)