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 2.5.769 subgroup temperament or a 2.5.769/512 subgroup temperament. Or, you could convert a 3.5.7 combination product set into a 769.5.7 combination product set.

You could also substitute a simpler harmonic n in a dual-n temperament for two more complex harmonics, to make a dual-substitute-n temperament^{[idiosyncratic term]}. For example, you could convert a 2.3-.3+.5 subgroup temperament into a 2.5.767.769 subgroup temperament, or a 2.5.767/512.769/512 subgroup temperament.

List of substitute harmonics

Substitutes for the 2nd harmonic (1200)

Each harmonic is given in octave-reduced cents. This list is not exhaustive.

• the 1017th harmonic (~1188)
• the 509th harmonic (~1190)
• the 1019th harmonic (~1192)
• the 255th harmonic (~1193)
• the 1021st harmonic (~1195)
• the 511th harmonic (~1197)
• the 1023rd harmonic (~1198)
• the 1025th harmonic (~2)
• the 513th harmonic (~3)
• the 1027th harmonic (~5)
• the 257th harmonic (~7)
• the 1029th harmonic (~8)
• the 515th harmonic (~10)
• the 1031st harmonic (~12)

Substitutes for the 3rd harmonic (~702)

Each harmonic is given in octave-reduced cents. This list is not exhaustive.

• 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)

Each harmonic is given in octave-reduced cents. This list is not exhaustive.

• 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)

Each harmonic is given in octave-reduced cents. This list is not exhaustive.

• 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)

Each harmonic is given in octave-reduced cents. This list is not exhaustive.

• 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)

Dual-substitute-n temperaments

Dual-substitute-3 temperaments

a.k.a. dual-substitute-fifth temperaments^{[idiosyncratic term]}.

Other temperaments with substitute harmonics

See also

• List of octave-reduced harmonics
• Naughty and nice harmonics