Talk:Dyadic chord: Difference between revisions

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~~= ARCHIVED WIKISPACES DISCUSSION BELOW =~~

~~'''All discussion below is archived from the Wikispaces export in its original unaltered form.'''~~

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== ~~Equal Beating Tunings~~ of ~~Essentially Tempered Chords~~ ==

== Query on mention of 36/35 -- is 36/25 meant? ==

~~I've been recently spending quite a bit of time listening~~ to ~~these chords with~~ the ~~woodwinds section available in the latest Logic Express~~. ~~When I reached the essentially tempered chords~~, ~~realizing that they can't be tuned beatless~~, wondered if they could be tuned such that each interval has the same beat. Turns out in many cases they can, and have rational solutions. In my opinion they sound better this way. There's a fairly straightforward way of solving this for an arbitrary number of notes. Some of you probably already know of it.

There are references to 36/35 and 10/7 differing by 126/125, the starling comma. Could this mean 36/25, or (6/5)^2? [[User:Mschulter1325|Mschulter1325]] 07:31, 26 January 2023 (UTC)

~~As a concrete example~~, ~~the Marvel chord 1~~/~~1-5~~/4-7/~~5-14/9 can be tempered as 1/1~~-~~121/97~~-~~136/97-151/97. With 220 Hz as 1/1, all intervals will beat at about 2.3 Hz. That's calculated based on the idea that the ratio of each pair of fractions approximates 5/4, 9/8, 10/9~~, ~~and 9/7 respectively.~~

: Yeah, 36/25 and 10/7 differ by 126/125. I just checked in Wolfram Alpha. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 07:42, 26 January 2023 (UTC)

~~Is there already~~ a ~~page for an idea like this? If not, would someone please direct me to the best place to start one?~~

== Move to "dyadically consonant chord" ==

To me, "dyadic chord" most intuitively means "chord that is a dyad".

- '''~~BryceHathaway''' November 06, 2015, 03:31:13 PM UTC-0800~~

== On anomalous saturated suspensions ==

~~----~~

I can't keep a straight face whilst looking at this section, I'm too childish I may admit, but it's kind of an unfortunate acronym. I propose it to be renamed to something like AnSaS or related.

~~== battaglia chord ==~~

: <s>I don't share that feeling but maybe that's becuz English isn't my first language.</s> I use ''saturated suspension'', omitting ''anomalous'' cuz I don't think it conveys anything. —[[User:FloraC|FloraC]] ([[User talk:FloraC|talk]]) 06:40, 14 December 2025 (UTC) (Updated [[User:FloraC|FloraC]] ([[User talk:FloraC|talk]]) 10:51, 9 May 2026 (UTC))

~~15-limit or 19-limit?~~

~~- '''xenwolf''' October 19, 2011, 12~~:~~32:32 AM UTC-0700~~

: <small>P.S. plz remember to sign your comment with <code><nowiki>~~~~</nowiki></code>.</small>

~~----~~

== ~~hendrix chord~~ ==

== Chord classification ==

is ~~it 7~~-~~limit~~ or 19-~~limit?~~

Some temperaments temper out commas that lead chords which otherwise come in otonal-utonal pairs to become neutralized, such as 7:8:9 and 9:10:11 in superpyth. In [[Chords of huygens]], the neutralized 8:9:10 and 11:14:18 chords are both classified as otonal, while in [[Chords of mohajira]], the neutralized 10:11:12 chord is classified as utonal. I believe this is based on the transversal, as the 8:9:10, 11:14:18, and 10:11:12 chords are generated as 1-9/8-5/4, 1-14/9-11/9, and 1-20/11-5/3 respectively. However, classifying these chords as otonal or utonal is misleading, so there should be a convention; perhaps ambitonal, or another term entirely.--[[User:Overthink|Overthink]] ([[User talk:Overthink|talk]]) 23:17, 13 December 2025 (UTC)

- '~~''xenwolf''' October 19~~, ~~2011, 12~~:30:~~09 AM~~ UTC~~-0700~~

: These are actually plurichords that change their o/u-tonality on different interpretations. I would suggest marking them as both otonal/utonal, which is a meaningful distinction to make from ambitonal. Perhaps it's also good to explicitly mark their plurichord nature and the associated temperaments, if we can find a way to do so. —[[User:FloraC|FloraC]] ([[User talk:FloraC|talk]]) 06:40, 14 December 2025 (UTC)

~~----~~

== ~~interesting overview~~ ==

== Det chord vs innate comma chord ==

~~thank you~~, ~~Gene :-)~~

For cataloguing chords of specific temperaments, this distinction is pointless. I have no idea why it was made in these tables in the first place.

~~- ''~~'~~xenwolf~~'~~'' October 19, 2011, 12:21:49 AM UTC-0700~~

The definition of innate comma chords seems problematic, as it's not clear how it's more specific than ordinary high-odd-limit chords.

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~~== Orwell ==~~

—[[User:FloraC|FloraC]] ([[User talk:FloraC|talk]]) 10:51, 9 May 2026 (UTC)

~~Are we sticking to only codimension 1 here? Because if not, 1/1-7/6-11/8-8/5 deserves a shoutout, perhaps even 1/1-7/6-11/8-8/5-15/8-11/~~10~~-9/7-3/2.~~

~~Maybe in the future it would be nice to have a 2D table organizing everything by limit and codimension.~~

~~- '''mbattaglia1''' September 17, 2011, 01:46~~:~~26 AM UTC-0700~~

~~----~~

~~I forgot to add "orwell tetrad" to the list~~, ~~though the page around for while.~~

~~- '''genewardsmith''' September 17, 2011, 02:13:05 PM~~ UTC~~-0700~~

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-= ARCHIVED WIKISPACES DISCUSSION BELOW =
+{{WSArchiveLink}}
-'''All discussion below is archived from the Wikispaces export in its original unaltered form.'''
-----
-== Equal Beating Tunings of Essentially Tempered Chords ==
+== Query on mention of 36/35 -- is 36/25 meant? ==
-I've been recently spending quite a bit of time listening to these chords with the woodwinds section available in the latest Logic Express. When I reached the essentially tempered chords, realizing that they can't be tuned beatless, wondered if they could be tuned such that each interval has the same beat. Turns out in many cases they can, and have rational solutions. In my opinion they sound better this way. There's a fairly straightforward way of solving this for an arbitrary number of notes. Some of you probably already know of it.
+There are references to 36/35 and 10/7 differing by 126/125, the starling comma. Could this mean 36/25, or (6/5)^2? [[User:Mschulter1325|Mschulter1325]] 07:31, 26 January 2023 (UTC)
-As a concrete example, the Marvel chord 1/1-5/4-7/5-14/9 can be tempered as 1/1-121/97-136/97-151/97. With 220 Hz as 1/1, all intervals will beat at about 2.3 Hz. That's calculated based on the idea that the ratio of each pair of fractions approximates 5/4, 9/8, 10/9, and 9/7 respectively.
+: Yeah, 36/25 and 10/7 differ by 126/125.  I just checked in Wolfram Alpha. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 07:42, 26 January 2023 (UTC)
-Is there already a page for an idea like this? If not, would someone please direct me to the best place to start one?
+== Move to "dyadically consonant chord" ==
+To me, "dyadic chord" most intuitively means "chord that is a dyad".
-- '''BryceHathaway''' November 06, 2015, 03:31:13 PM UTC-0800
+== On anomalous saturated suspensions ==
-----
+I can't keep a straight face whilst looking at this section, I'm too childish I may admit, but it's kind of an unfortunate acronym. I propose it to be renamed to something like AnSaS or related.
-== battaglia chord ==
+: <s>I don't share that feeling but maybe that's becuz English isn't my first language.</s> I use ''saturated suspension'', omitting ''anomalous'' cuz I don't think it conveys anything. —[[User:FloraC|FloraC]] ([[User talk:FloraC|talk]]) 06:40, 14 December 2025 (UTC) (Updated [[User:FloraC|FloraC]] ([[User talk:FloraC|talk]]) 10:51, 9 May 2026 (UTC))
--limit or 19-limit?
-- '''xenwolf''' October 19, 2011, 12:32:32 AM UTC-0700
+: <small>P.S. plz remember to sign your comment with <code><nowiki>~~~~</nowiki></code>.</small>
-----
-== hendrix chord ==
+== Chord classification ==
-is it 7-limit or 19-limit?
+Some temperaments temper out commas that lead chords which otherwise come in otonal-utonal pairs to become neutralized, such as 7:8:9 and 9:10:11 in superpyth. In [[Chords of huygens]], the neutralized 8:9:10 and 11:14:18 chords are both classified as otonal, while in [[Chords of mohajira]], the neutralized 10:11:12 chord is classified as utonal. I believe this is based on the transversal, as the 8:9:10, 11:14:18, and 10:11:12 chords are generated as 1-9/8-5/4, 1-14/9-11/9, and 1-20/11-5/3 respectively. However, classifying these chords as otonal or utonal is misleading, so there should be a convention; perhaps ambitonal, or another term entirely.--[[User:Overthink|Overthink]] ([[User talk:Overthink|talk]]) 23:17, 13 December 2025 (UTC)
-- '''xenwolf''' October 19, 2011, 12:30:09 AM UTC-0700
+: These are actually plurichords that change their o/u-tonality on different interpretations. I would suggest marking them as both otonal/utonal, which is a meaningful distinction to make from ambitonal. Perhaps it's also good to explicitly mark their plurichord nature and the associated temperaments, if we can find a way to do so. —[[User:FloraC|FloraC]] ([[User talk:FloraC|talk]]) 06:40, 14 December 2025 (UTC)
-----
-== interesting overview ==
+== Det chord vs innate comma chord ==
-thank you, Gene :-)
+For cataloguing chords of specific temperaments, this distinction is pointless. I have no idea why it was made in these tables in the first place.
-- '''xenwolf''' October 19, 2011, 12:21:49 AM UTC-0700
+The definition of innate comma chords seems problematic, as it's not clear how it's more specific than ordinary high-odd-limit chords.
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-== Orwell ==
+—[[User:FloraC|FloraC]] ([[User talk:FloraC|talk]]) 10:51, 9 May 2026 (UTC)
-Are we sticking to only codimension 1 here? Because if not, 1/1-7/6-11/8-8/5 deserves a shoutout, perhaps even 1/1-7/6-11/8-8/5-15/8-11/10-9/7-3/2.
-Maybe in the future it would be nice to have a 2D table organizing everything by limit and codimension.
-- '''mbattaglia1''' September 17, 2011, 01:46:26 AM UTC-0700
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-I forgot to add "orwell tetrad" to the list, though the page around for while.
-- '''genewardsmith''' September 17, 2011, 02:13:05 PM UTC-0700
-----