What is the difference between just intonation and Pythagorean tuning?

What is the difference between just intonation and Pythagorean tuning?

Pythagorean tuning provides uniformity but not the chords. Just tuning, based on the simpler ratios of the overtone series, provides the chords but suffers from inequality of intervals.

What was before equal temperament?

Before Meantone temperament became widely used in the Renaissance, the most commonly used tuning system was Pythagorean tuning. Pythagorean tuning was a system of just intonation that tuned every note in a scale from a progression of pure perfect fifths.

Why does just intonation not work?

Just intonation is extremely impractical for instruments that play chords (guitar or piano), or any instrument with fixed pitches which cannot bend, such as vibraphone or marimba. How many keys do you want in an octave on your keyboard? In the Baroque period, 12-tone equal temperament had not yet been invented.

Where is just intonation used?

Supposedly used in medieval monophonic music (melody only, without harmony) and considerably discussed by theorists, just intonation proved impractical for polyphonic (multipart) music and was replaced at least by the year 1500 by meantone temperament.

Which is the correct definition of the term meantone?

The term “meantone” refers to both a specific tuning, and an abstract familyof temperaments, of which that tuning is a member. 1. meantone = a specific tuning

How is the meantone temperament of a tone specified?

Meantone temperaments can be specified in various ways: by what fraction (logarithmically) of a syntonic comma the fifth is being flattened (as above), what equal temperament has the meantone fifth in question, the width of the tempered perfect fifth in cents, or the ratio of the whole tone to the diatonic semitone.

Which is the equal temperament of meantone tuning?

Equal temperament is roughly the same as 1/11 comma meantone tuning. Quarter-comma meantone, which tempers the fifths by 1/4 comma, is the best known type of meantone temperament, and the term meantone temperament is often used to refer to it specifically.

Why are meantones always considered to be octave equivalent?

During the late 1900s most tuning theorists accepted “meantone” to describe the whole family of temperaments — that is, all temperaments in which the syntonic-comma vanishes. Meantones are always considered to be octave-equivalent– thus, the latticeessentially ignores prime-factor2, requiring only axes for 3 and 5.