I don't think we agree on what mambo means. In Cuba it's a different dance, in NY it's what people call salsa on 2, and in Sweden it's a guy over 25 yrs old who still lives with his mother

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In NY, Mambo has generational distinctions.
There's my dad's generation who were in their teensteens and early 20s circa the 1950s that, if still alive, are dancing or approaching the music as they did 70+ years ago. Either through dance instruction or via osmosis. Then there's the Eddie Torres generation. The post-'80s to the present, who religiously and exclusively employ the dance studio technique developed by Eddie Torres, Sr. It's the latter who define "Mambo" as Salsa On2 and dance to Mambo the exact same way, each and every time. Partnerwork throughout the entire dance with repetitive cross body leads. That's not how the old school danced to Mambo 75 years ago. That would include that era's dance studio crowd who, by and large, emulated the non-studio honed dancers who did not employ any established technique, and went back to the studio to systemize it and offer instruction. Which is exactly what Eddie Torres Sr. did upon he establishing a dance instruction operation.
I've also heard of mambo as a segment in a salsa song, but doesn't that derive from the dance? many songs call 'mambo!', and then you can dance a short part of mambo to it.
It's as a result OF dance culture, but not necessarily to engage in "Mambo" dance action or deployment of moves. As a musical section the term "Mambo" is also found in Merengue and even in some Mexican music. It is traditionally a call for the horn or wind section to begin playing a repetitive pattern of notes. You hear it in Perez Prado or Benny More music. You hear it in modern day "Salsa." You hear it in some Mexican corridos. In Merengues by Oro Solido, Ramon Orlando, Kinito Mendez, Wilfrido Vargas, etc. All of it is a product of pianist/composer Orestes Lopez having established a section in the Danzon that picked up the pace and became more progressive within an area of a chart. The signal was he shouting "Mambo." Everyone has followed suit since then. Only now the conceptual "section," aka the "Mambo," became the entire song structure itself. And the horns were implemented and conducted in a way (thanks to both Arsenio Rodriguez AND *especially* Luis Griñan "Lili" Martinez) that the repetitive musical notes the horns would play became the standard design or approach for all "Mambos" within any genre.
If someone calls out "Mambo!" in Merengue, that's intended for the horn section in the band to begin playing repetitive notes over the uptempo rhythm being played, sans vocals/choral refrain. Not for the dancer to stop dancing Merengue and go into exhibiting dance steps or motion associated with Mambo as a musical form.
Mambo is a conceptual device employed in uptempo Afro Cuban dance music, adopted by other musical cultures. It is also the name that was applied to the way people danced to
Guaracha and
Son Montuno in the 1930s and 1940s. In the same role "
Salsa" is used today.
Anyway, a guaganco is the slowest form of rumba. The difference with mambo and rumba is that they have different claves. Not more complicated than that.
Yambu would be the slowest, with
Columbia being the fastest.
Guaguancó is smack in the middle.
The African
clave rhythm is what
Mambo and
Rumba are founded upon. But, as you alluded, one form
(Rumba) has a pause or is mute prior to the 3rd pulse on the 3-side emanating immediately thereafter seguing to the 2-bar pattern on the 2-side. No matter which side a
Rumba begins on. In
Mambo-Son there is no pause or mute on the 3rd pulse. The 3-side of the
clave is played straight forward until reaching the 2-side.
3-2 Rumba: X-X--X -- XX
3-2 Son/Mambo: X-X-X -- XX
And vice versa when starting on the 2-side.