Tunings and temperaments

viz

If anyone's interested in the deviations between the 1/4 comma meantone system, pythagorean stacked 5ths system (with added wolf), and our good ole 12-TET system, I just stumbled across the most fantastic resource here: it's definitely the most accurate, user-friendly and comprehensive site I've found anywhere.  http://www.ppexpressivo.co.uk/

Phil_aka_Pip

On the bottom of P1, I disagree with 3 of the relative minors:

the relative minors of the major keys F#, B, E are D#, G#, and C# respectively, not Eb, Ab, and Db, although I agree that the notes Eb Ab and Db are (in equal temperament) the enharmonic equivalents of D# G# and C#

I can see why they've done it that way but it looks wrong

viz

Yep, I thought it was strange at first but, as you say, it's clear why they've done it like that, because the left hand side is arranged in sequence of circle of 5ths, and the right hand side is an offset replication of that. So they've done it like that to keep consistency. Good isn't it though? As a collection of all the important temperaments.

Roland

IMO this link needs to be indexed under Theory & Technique

Phil_aka_Pip

viz said:

Yep, I thought it was strange at first but, as you say, it's clear why they've done it like that, because the left hand side is arranged in sequence of circle of 5ths, and the right hand side is an offset replication of that. So they've done it like that to keep consistency. Good isn't it though? As a collection of all the important temperaments.

It is an awesome site. One thing that I'd have liked it to have made even clearer/more explicit, is the subject of "the octave". First, to define diapason as the phenomenon of doubling frequency when string or pipe length is halved. Second, to introduce octave as the commonly used word for that phenomenon but as it means 8 notes it really only applies in the western european diatonic system. Third, to explain that the diatonic system divides the diapason up into 12 semitones, some of which are given greater emphasis than others when constructing 8-note scales. The use of the word octave, to define, er the "octave", is IMO unhelpful because pupils will see it as 8 notes not as the physical phenomenon of string length halving/frequency doubling.

viz

Absolutely! And what's more, why don't we call it the tredectave for the chromaticists among us? Besides it's not only the diatonic family that have 8 notes, but 65 other scale families, and as you say, the 12 notes are not the only possible notes. I normally listen to music with 31 notes in the diapason anyway, so I call the octave a trigintaduotave.

Phil_aka_Pip

wowsers

12 semitones is enuff for me

viz