User:BudjarnLambeth/Substitute harmonic
A substitute harmonic[idiosyncratic term] is a more complex harmonic which is used to substitute for a simpler one.
For example, you could substitute the 3rd harmonic for the very similar 769th harmonic. By doing this, you could convert a 2.3.5 subgroup temperament into a 2.769.5 subgroup temperament. Or, you could convert a 3.5.7 combination product set into a 769.5.7 combination product set.
Why do this? It could allow for a whole array of subtly different harmonic flavours of existing tunings, while preserving their basic melodic and harmonic structure.
You can also substitute a simpler harmonic n for two more complex harmonics, to make a dual-substitute-n temperament[idiosyncratic term], with similar aims (but different tactics) to a dual-fifth temperament.
List of substitute harmonics
Each harmonic is given in octave-reduced cents. This list is not exhaustive.
Substitutes for the 3rd harmonic (~702)
- the 381st harmonic (~688)
- the 763rd harmonic (~691)
- the 191st harmonic (~693)
- the 765th harmonic (~695)
- the 383rd harmonic (~697)
- the 767th harmonic (~700)
- the 769th harmonic (~704)
- the 385th harmonic (~706)
- the 771st harmonic (~709)
- the 193rd harmonic (~711)
- the 773rd harmonic (~713)
- the 387th harmonic (~715)
Substitutes for the 5th harmonic (~386)
- the 317th harmonic (~370)
- the 635th harmonic (~373)
- the 159th harmonic (~375)
- the 637th harmonic (~378)
- the 319th harmonic (~381)
- the 639th harmonic (~384)
- the 641st harmonic (~389)
- the 321st harmonic (~392)
- the 643rd harmonic (~394)
- the 161st harmonic (~397)
- the 645th harmonic (~400)
- the 323rd harmonic (~402)
Substitutes for the 7th harmonic (~969)
- the 111th harmonic (~953)
- the 889th harmonic (~955)
- the 445th harmonic (~957)
- the 891st harmonic (~959)
- the 223rd harmonic (~961)
- the 893rd harmonic (~963)
- the 447th harmonic (~965)
- the 895th harmonic (~967)
- the 897th harmonic (~971)
- the 449th harmonic (~973)
- the 899th harmonic (~975)
- the 225th harmonic (~977)
- the 901st harmonic (~978)
- the 451st harmonic (~980)
- the 903rd harmonic (~982)
- the 113th harmonic (~984)
Substitutes for the 11th harmonic (~551)
- the 349th harmonic (~537)
- the 699th harmonic (~539)
- the 175th harmonic (~541)
- the 701st harmonic (~544)
- the 351st harmonic (~546)
- the 703rd harmonic (~549)
- the 705th harmonic (~554)
- the 353rd harmonic (~556)
- the 707th harmonic (~559)
- the 177th harmonic (~561)
- the 709th harmonic (~564)
- the 355th harmonic (~566)