tetrachords

[jancivil]

The enharmonic was considered the most noble and difficult tetrachord, and was already rare at the time of the ancient documents we have.

well, one thing I'm sure of is that kind of statement reads differently for me than it must for you.

[Aroused by JarJar]

The enharmonic was considered the most noble and difficult tetrachord, and was already rare at the time of the ancient documents we have.

well, one thing I'm sure of is that kind of statement reads differently for me than it must for you.

What I'm saying is common knowledge, as far as these things go.

"By the late fourth century (BCE) enharmonic had lost a good deal of ground. Aristoxenus upheld it as being the most sophisticated and beautiful of the genera, but lamented the fact that it was now largely neglected in favour of the chromatic, which people found easier to appreciate and more ingratiating." ML West, Ancient Greek Music, page 164

Later, Greek music was mixed chromatic and diatonic genera, then mostly diatonic under Roman rule. This stuff is amazingly well documented, considering how much time has passed in the interim.

I just realized that you might not be aware that "enharmonic" meant something completely different in those days than it does now. It meant a tetrachord divided into two quartertones and major third-sized interval. If you have a fretless bass I can give you a bearing plan for Didymus' enharmonic, it's easy as pie to finger.

You mentioned scala files but in my opinion that's backwards for tuning- first work it out with acoustic instruments, then make or find your scala file.

[jancivil]

The enharmonic was considered the most noble and difficult tetrachord, and was already rare at the time of the ancient documents we have.

well, one thing I'm sure of is that kind of statement reads differently for me than it must for you.

What I'm saying is common knowledge, as far as these things go.
"By the late fourth century (BCE) enharmonic had lost a good deal of ground. Aristoxenus upheld it as being the most sophisticated and beautiful of the genera, but lamented the fact that it was now largely neglected in favour of the chromatic, which people found easier to appreciate and more ingratiating." ML West, Ancient Greek Music, page 164

What I'm saying is that this has some moment in your life, and good for you, but it's speculative writing to me. Pretty sure ML West was not there.

I said, seems to me like giving two intervals in a row that are so minutely different, who knows what music it's based in, which apparently goes against something you want to believe in (even though you seem to understand they'd be two flavors of one thing in practice).

I just realized that you might not be aware that "enharmonic" meant something completely different in those days than it does now.

No, this is not news to me at all.

You mentioned scala files but in my opinion that's backwards for tuning- first work it out with acoustic instruments, then make or find your scala file.

I said that I went into this into more depth in consideration of what it would take to construct fretted instruments; that would seem to be out of being somewhat aware of intonation.

As far as scala, for me it's trial and error like everything else. I can do that in the virtual instrument just fine, and frankly I don't have space or money for instruments. I do it because there are things I'd like to hear. I'm a practical musician, I don't ask the cart to pull the horse.

[stringtapper]

The enharmonic was considered the most noble and difficult tetrachord, and was already rare at the time of the ancient documents we have.

well, one thing I'm sure of is that kind of statement reads differently for me than it must for you.

What I'm saying is common knowledge, as far as these things go.
"By the late fourth century (BCE) enharmonic had lost a good deal of ground. Aristoxenus upheld it as being the most sophisticated and beautiful of the genera, but lamented the fact that it was now largely neglected in favour of the chromatic, which people found easier to appreciate and more ingratiating." ML West, Ancient Greek Music, page 164

What I'm saying is that this has some moment in your life, and good for you, but it's speculative writing to me. Pretty sure ML West was not there.

Speculative writing? He's citing Aristoxenus. There are translations of his writing on music you can read for yourself.

Some sources readings:

Greek Musical Writings: Volume 1, The Musician and his Art by Andrew Barker

Greek Musical Writings: Volume 2, Harmonic and Acoustic Theory by Andrew Barker

Another good text on the subject:

Apollo's Lyre: Greek Music and Music Theory in Antiquity and the Middle Ages by Thomas J. Mathiesen

[Aroused by JarJar]

The enharmonic was considered the most noble and difficult tetrachord, and was already rare at the time of the ancient documents we have.

well, one thing I'm sure of is that kind of statement reads differently for me than it must for you.

What I'm saying is common knowledge, as far as these things go.
"By the late fourth century (BCE) enharmonic had lost a good deal of ground. Aristoxenus upheld it as being the most sophisticated and beautiful of the genera, but lamented the fact that it was now largely neglected in favour of the chromatic, which people found easier to appreciate and more ingratiating." ML West, Ancient Greek Music, page 164

What I'm saying is that this has some moment in your life, and good for you, but it's speculative writing to me. Pretty sure ML West was not there.

I said, seems to me like giving two intervals in a row that are so minutely different, who knows what music it's based in, which apparently goes against something you want to believe in (even though you seem to understand they'd be two flavors of one thing in practice).

I just realized that you might not be aware that "enharmonic" meant something completely different in those days than it does now.

No, this is not news to me at all.

You mentioned scala files but in my opinion that's backwards for tuning- first work it out with acoustic instruments, then make or find your scala file.

I said that I went into this into more depth in consideration of what it would take to construct fretted instruments; that would seem to be out of being somewhat aware of intonation.

As far as scala, for me it's trial and error like everything else. I can do that in the virtual instrument just fine, and frankly I don't have space or money for instruments. I do it because there are things I'd like to hear. I'm a practical musician, I don't ask the cart to pull the horse.

What you are calling "two intervals in a row that are slightly different" are two intervals that are the same size interval in practice. Without cents (logarithmic), you either write two very similar ratios or you use some imprecisely defined unit that has the same function, such as "parts of a whole tone".

The exact tuning of the intervals was a matter of taste. As long as there were two tiny intervals and one big one within the tetrachord, it was the enharmonic genus. Usually the two small intervals were thought of as "the same size". You could play the enharmonic genus in 24-tone equal temperament and it's indistinguishable from the Pythagorean versions of the genus.

In the case of Archytas, the two small intervals were not the same size. In his tuning of the enharmonic, there's a very small "semitone" and a very small "quartertone". Archytas based his tunings on reed instrument playing. That's an iffy proposition as far as accuracy- did anyone ever really play those exact intervals? On the other hand, the shape of his genera may give a very good picture of what was played in his time and place, eg, NOT equal "quartertones", one distinctly larger than the other. And the auloi were played in pairs, which means drones and other "non-functional" harmony (there's even an extant notated piece with the drones marked). If you use his tunings with reed instruments, you get diads that are oddly similar to those of some ancient Mediterranean and Balkan folk musics that still exist in little pockets, like the vocal trios of Sardigna, where they'll sustain a 7:6 for example.


In the case of Didymus, the two small intervals are both quartertones that sound the same size and are the same size on a string length. If you play these things on an acoustic instrument, it is clear that he based his tuning on practice.

What's important here is not the exact tunings. The beauty of the enharmonic genera is in the shape of it. It's the same kind of thing as still exists with the maqams- the same tetrachord in the same maqam is intoned slightly differently in different regions.

And I disagree strongly about which is the cart and which is the horse here. It's only by playing acoustic instruments that you can determine which historical tunings are theoretical and which reflect practice. You can't say, for example, oh those numbers are way too complex, that must be a purely theoretical tuning, because sometimes complex numbers reflect very simple real-life practice. Some of the medieval Islamic tunings look absurd on paper, until you tune them on a baglama and realize that it's "tune this and this by pure fifths, then tie a fret halfway between". Extremely simple real-life musician stuff, not numerology.

But we should get back to the original post.

[Aroused by JarJar]

The enharmonic was considered the most noble and difficult tetrachord, and was already rare at the time of the ancient documents we have.

well, one thing I'm sure of is that kind of statement reads differently for me than it must for you.

What I'm saying is common knowledge, as far as these things go.
"By the late fourth century (BCE) enharmonic had lost a good deal of ground. Aristoxenus upheld it as being the most sophisticated and beautiful of the genera, but lamented the fact that it was now largely neglected in favour of the chromatic, which people found easier to appreciate and more ingratiating." ML West, Ancient Greek Music, page 164

What I'm saying is that this has some moment in your life, and good for you, but it's speculative writing to me. Pretty sure ML West was not there.

Speculative writing? He's citing Aristoxenus. There are translations of his writing on music you can read for yourself.

Some sources readings:

Greek Musical Writings: Volume 1, The Musician and his Art by Andrew Barker

Greek Musical Writings: Volume 2, Harmonic and Acoustic Theory by Andrew Barker

Another good text on the subject:

Apollo's Lyre: Greek Music and Music Theory in Antiquity and the Middle Ages by Thomas J. Mathiesen

Ancient Greek Music by ML West is also great, and has transcriptions of extant notation.

I already linked to Divisions of the Tetrachord. There's also Chris Forster's Musical Mathematics

http://www.chrysalis-foundation.org/mus ... matics.htm

which is aimed at instrument tuners and builders.

ML West makes some mistakes because he did not work with these things hands-on. He brushes off Didymus' ratios as fancy math and give cents instead. This is just plain wrong, and an insult to Didymus, because Didymus' ratios are based on simple practicalities: they literally show you how to tune up if you understand them. They're the polar opposite of fancy math.

[Aroused by JarJar]

In response to the original post:

The guitar in standard tuning is set up for conjunct tetrachords.

Play E-A-D on the open strings. That's the skeleton of conjunct tetrachords, two conjunct pure fourths.

Barre a "box" with fifth and octave. For example F-C-F. That's the skeleton of a pentachord with a conjunct tetrachord. Drop the fifth but retain the barre. That's the frame of a tetrachord with a conjunct pentachord. Play the tonic, the fourth, then fret the fifth back in and play it, then play the octave. That's the octave in two disjunct tetrachords.

This is much easier to play and demonstrate than to describe.

[Aroused by JarJar]

[quote="jancivil"] What I'm saying is that this has some moment in your life, and good for you, but it's speculative writing to me. Pretty sure ML West was not there.

what has "moment in my life" is playing these things.