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Encyclopedia > Semiditono

In harmony, the semiditonus is the ratio 6:5 (sesquiquintum) between a pair of frequencies or, equivalently, the ratio 5:6 between a pair of wavelengths. It is the harmonic mean of unison and diapente:

It is equal to diapente divided by ditonus:

This means that diapente is equal to a ditonus and a semiditonus, put together.

The semiditonus is 1.00110011001100110011... in binary, and it is the inversion of the exadem maius (major sixth) (5:3), viz.

The exadem maius is the sum of the first five reciprocals of triangular numbers:

The semiditonus is also called the minor third.

Results from FactBites:

 ODAREG TEXT (2167 words) Tercia differentia est, eo quod cantus quidem a finali semiditono incipiatur et statim tono intendatur, ut antiphonie:. Prima autem variatio est, ubi cantus a sua principali semitonio inchoatur et semiditono deponitur, ut antiphonie:. Quinta autem variatio est, ubi cantns a finali semiditono inchoatur, ut antiphonie G: Prima differentia est, ubi cantus a sua principali tono inferius inchoatur et gradatim intenditur, ut antiphonie:.
 TINCPT2 TEXT (5143 words) Sed videtur quod discordantiae ex duabus concordantiis compositae potius concordantiae sint, ut diapente cum semiditono vel cum ditono, namque [-93-] si Boethio credendum est, dicenti ut superiori libro retulimus, quod concordantiae concordantiis suppositae alias quasdam concordantias efficiunt, quotienscumque una concordantia alteri coniungitur ex tali compositione non discordantia sed concordantia generatur. [-94-] Diciturque diapente cum semiditono, eo quo diapente et semiditono constituatur, et quia discordantia haec quatuor tonos duoque semitonia tantum continet, communiter septima imperfecta nominatur. Diciturque diapente cum semiditono supra diapason, eo quod ex diapente cum semiditono supra diapason assumpto confectum sit; et quia, ut saepe [-96-] dictum est, diapason quinque tonos ac duo semitonia, diapente vero cum semiditono quatuor tonos ac duo etiam semitonia contineat, discordantia haec novem tonis et quatuor semitoniis tantummodo constat.
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