Families of scales: Difference between revisions
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*****''see [[Tour of regular temperaments]]'' | *****''see [[Tour of regular temperaments]]'' | ||
*** [[Equal-step tuning|Rank-1 temperaments / Equal-step tunings]] | *** [[Equal-step tuning|Rank-1 temperaments / Equal-step tunings]] | ||
****Equal multiplications | |||
*****[[Ambitonal sequence|Ambitonal sequences (AS) / Equal multiplications of a rational interval]] | |||
*****[[Arithmetic pitch sequence|Arithmetic pitch sequences (APS) / Equal multiplications of an irrational interval]] | |||
****Equal divisions | ****Equal divisions | ||
*****[[EDO|Equal divisions of the octave (EDOs or ED2s)]] | *****[[EDO|Equal divisions of the octave (EDOs or ED2s)]] | ||
*****[[The Riemann zeta function and tuning|Zeta-stretched equal divisions]] | *****[[The Riemann zeta function and tuning|Zeta-stretched equal divisions]] | ||
**** Equal | *****[[Edonoi|Edonois]] | ||
*****[[ | ******[[EDT|Equal divisions of the third harmonic (EDTs or ED3s)]] | ||
*****[[ | ******[[Ed4|Equal divisions of the fourth harmonic (ED4s)]] | ||
******[[Ed5|Equal divisions of the fifth harmonic (ED5s)]] | |||
******[[Ed6|Equal divisions of the sixth harmonic (ED6s)]] | |||
******[[Ed7|Equal divisions of the seventh harmonic (ED7s)]] | |||
******[[Ed8|Equal divisions of the eighth harmonic (ED8s)]] | |||
******[[Ed9|Equal divisions of the ninth harmonic (ED9s)]] | |||
******[[Ed10|Equal divisions of the tenth harmonic (ED10s)]] | |||
******[[Ed11|Equal divisions of the eleventh harmonic (ED11s)]] | |||
******... | |||
******[[Ed3/2|Equal divisions of the perfect fifth (EDFs or ED3/2s)]] | |||
******[[Ed4/3|Equal divisions of the perfect fourth (ED4/3s)]] | |||
******[[Ed5/3|Equal divisions of the major sixth (ED5/3s)]] | |||
******[[Ed5/4|Equal divisions of the major third (ED5/4s)]] | |||
******... | |||
******[[Ed5/2|Equal divisions of 5/2 (EDXs or ED5/2s)]] | |||
******[[Ed7/2|Equal divisions of 7/2 (ED7/2s)]] | |||
******... | |||
******[[Ed7/3|Equal divisions of 7/3 (ED7/3s)]] | |||
******[[Ed8/3|Equal divisions of 8/3 (ED8/3s)]] | |||
******[[Ed10/3|Equal divisions of 10/3 (ED10/3s)]] | |||
******... | |||
******[[Ed11/5|Equal divisions of 11/5 (ED11/5s)]] | |||
******[[Edφ|Equal divisions of Phi (Edφs)]] | |||
=== Fokker blocks === | === Fokker blocks === | ||
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******Modes of the [[triangulharmonic series]] | ******Modes of the [[triangulharmonic series]] | ||
****Equal pitch step tunings | ****Equal pitch step tunings | ||
*****[[Equal-step tuning|Equal-step tunings]] | *****[[Equal-step tuning|Rank-1 temperaments / Equal-step tunings]] | ||
******Equal multiplications | |||
*******[[Ambitonal sequence|Ambitonal sequences (AS) / Equal multiplications of a rational interval]] | |||
*******[[Arithmetic pitch sequence|Arithmetic pitch sequences (APS) / Equal multiplications of an irrational interval]] | |||
******Equal divisions | ******Equal divisions | ||
*******[[EDO|Equal divisions of the octave (EDOs or ED2s)]] | *******[[EDO|Equal divisions of the octave (EDOs or ED2s)]] | ||
*******[[The Riemann zeta function and tuning|Zeta-stretched equal divisions]] | *******[[The Riemann zeta function and tuning|Zeta-stretched equal divisions]] | ||
****** Equal | *******[[Edonoi|Edonois]] | ||
*******[[ | ********[[EDT|Equal divisions of the third harmonic (EDTs or ED3s)]] | ||
*******[[ | ********[[Ed4|Equal divisions of the fourth harmonic (ED4s)]] | ||
********[[Ed5|Equal divisions of the fifth harmonic (ED5s)]] | |||
********[[Ed6|Equal divisions of the sixth harmonic (ED6s)]] | |||
********[[Ed7|Equal divisions of the seventh harmonic (ED7s)]] | |||
********[[Ed8|Equal divisions of the eighth harmonic (ED8s)]] | |||
********[[Ed9|Equal divisions of the ninth harmonic (ED9s)]] | |||
********[[Ed10|Equal divisions of the tenth harmonic (ED10s)]] | |||
********[[Ed11|Equal divisions of the eleventh harmonic (ED11s)]] | |||
********... | |||
********[[Ed3/2|Equal divisions of the perfect fifth (EDFs or ED3/2s)]] | |||
********[[Ed4/3|Equal divisions of the perfect fourth (ED4/3s)]] | |||
********[[Ed5/3|Equal divisions of the major sixth (ED5/3s)]] | |||
********[[Ed5/4|Equal divisions of the major third (ED5/4s)]] | |||
********... | |||
********[[Ed5/2|Equal divisions of 5/2 (EDXs or ED5/2s)]] | |||
********[[Ed7/2|Equal divisions of 7/2 (ED7/2s)]] | |||
********... | |||
********[[Ed7/3|Equal divisions of 7/3 (ED7/3s)]] | |||
********[[Ed8/3|Equal divisions of 8/3 (ED8/3s)]] | |||
********[[Ed10/3|Equal divisions of 10/3 (ED10/3s)]] | |||
********... | |||
********[[Ed11/5|Equal divisions of 11/5 (ED11/5s)]] | |||
********[[Edφ|Equal divisions of Phi (Edφs)]] | |||
****Equal length step tunings | ****Equal length step tunings | ||
*****[[Subharmonic series|Aliquot scales (modes of the subharmonic series)]] / [[EDL|EDLs]] | *****[[Subharmonic series|Aliquot scales (modes of the subharmonic series)]] / [[EDL|EDLs]] | ||