Musical questions and answers thread

[jean]

Well, there's something in what you say. The Western scale is one of the great achievements...

...but I am rather keen on the modes, myself!...

Throughout this discussion we have focussed on the octave. Even the modes, even varieties of pentatonic scale are perceived as different ways of dividing the octave.

But I had forgotten, and was only reminded on listening my way through the COTW on Josquin*, that the ut, re, mi, fa, sol, la... which sounds so comfortingly like the diatonic major is not so at all, lacking the link to the upper ut in which it is not interested, and to which it provides no link. It is in fact a hexachord, and if the composer aspires to go beyond la, they enter a new hexachord.

Or something.

What does this mean?

*About five minutes in.

[ferneyhoughgeliebte]

A Heaxachord is a collection of six different pitches - the "chord" bit doesn't mean that they are to be played together as a chord, but how many strings (that sort of "chords"*) it would take on a harp (for example) to play. (Similarly, a tetrachord is a collection of four notes, and the pentatonic scale is a pentachord, the diatonic scale an octachord etc etc.)

Scales which miss out "steps" aren't uncommon - the pentatonic scale (which is what you hear when you just play the black keys on a piano) "misses out" the fourth and seventh degrees of a diatonic major scale (if you start on the F#)

F# G# A# (misses out B) C# D# (misses out E/E#)

or the second and seventh degrees (if you start on Eb)

Eb (misses out F) Gb Ab Bb (misses out D/Db)

- and all sorts of other degrees if you start on any of the other three notes (Ab, Bb, C#).

The seventh degree of the scale in most of the Church modes is "flattened" - perhaps a misleading term, as it suggests that it should be something else: it just means that it's a minor seventh from the Tonic. (So Bb [rather than B natural] from a Tonic of C; D natural [rather than D#] from E etc). Only the Lydian and Ionian modes have "sharpened" (ie Major) Seventh degrees of the scale - and the Ionian Mode is just the diatonic Major scale before it had a change of identity under the Equal Temperament witness protection scheme. This sort of ambiguity about whether the seventh degree should be major or minor is probably what led Josquin and his contemporaries to leave it out of the scale/hexachord - not because they couldn't make up their minds, but because it wasn't fixed, like the other pitches, and they could "freely" use both as the context allowed.


[* - the two types of "chord" - "string/rope" and "notes played together" - come from the same root of the strings of an instrument like a harp or lyre, in that if people were in "accord" (ie, if they agreed with each other) it was like when different strings of an instrument were played at the same time to create a pleasing sound. I believe (solely from Debussy's Etudes) that the French call chords "accords"? ]

[ferneyhoughgeliebte]

Throughout this discussion we have focussed on the octave.
- - -
if the composer aspires to go beyond la, they enter a new hexachord.

Just to clarify this bit - in Josquin's case it isn't a "new hexachord" in the sense of a different collection of six notes, but the same hexachord an octave higher than the first.

[Pabmusic]

Throughout this discussion we have focussed on the octave. Even the modes, even varieties of pentatonic scale are perceived as different ways of dividing the octave.

But I had forgotten, and was only reminded on listening my way through the COTW on Josquin*, that the ut, re, mi, fa, sol, la... which sounds so comfortingly like the diatonic major is not so at all, lacking the link to the upper ut in which it is not interested, and to which it provides no link. It is in fact a hexachord, and if the composer aspires to go beyond la, they enter a new hexachord.

Or something.

What does this mean?

I would not dare question Ferney's knowledge of Josquin or hexachords. :) But an 'octave' is only a label based upon the (overwhelming?) convention of division into eight basic tones. In reality we're talking about one tone and that arising from the halving of the length of the source. In other words, a ratio of 2:1.

If (say) we take one A as 440 Hz, then the octave higher will be 880 Hz, implying an 'octave' of 439 possible tones (or is it 440?). Likewise, the 'octave' lower will have 219 (or 220) possible tones.

[MrGongGong]

I would not dare question Ferney's knowledge of Josquin or hexachords. :) But an 'octave' is only a label based upon the (overwhelming?) convention of division into eight basic tones. In reality we're talking about one tone and that arising from the halving of the length of the source. In other words, a ratio of 2:1.

If (say) we take one A as 440 Hz, then the octave higher will be 880 Hz, implying an 'octave' of 439 possible tones (or is it 440?). Likewise, the 'octave' lower will have 219 (or 220) possible tones.

It is, of course, sometimes important to make the distinction between

Note, pitch and frequency

[ahinton]

A Heaxachord is a collection of six different pitches - the "chord" bit doesn't mean that they are to be played together as a chord, but how many strings (that sort of "chords"*) it would take on a harp (for example) to play. (Similarly, a tetrachord is a collection of four notes, and the pentatonic scale is a pentachord, the diatonic scale an octachord etc etc.)

Scales which miss out "steps" aren't uncommon - the pentatonic scale (which is what you hear when you just play the black keys on a piano) "misses out" the fourth and seventh degrees of a diatonic major scale (if you start on the F#)

F# G# A# (misses out B) C# D# (misses out E/E#)

or the second and seventh degrees (if you start on Eb)

Eb (misses out F) Gb Ab Bb (misses out D/Db)

- and all sorts of other degrees if you start on any of the other three notes (Ab, Bb, C#).

The seventh degree of the scale in most of the Church modes is "flattened" - perhaps a misleading term, as it suggests that it should be something else: it just means that it's a minor seventh from the Tonic. (So Bb [rather than B natural] from a Tonic of C; D natural [rather than D#] from E etc). Only the Lydian and Ionian modes have "sharpened" (ie Major) Seventh degrees of the scale - and the Ionian Mode is just the diatonic Major scale before it had a change of identity under the Equal Temperament witness protection scheme. This sort of ambiguity about whether the seventh degree should be major or minor is probably what led Josquin and his contemporaries to leave it out of the scale/hexachord - not because they couldn't make up their minds, but because it wasn't fixed, like the other pitches, and they could "freely" use both as the context allowed.


[* - the two types of "chord" - "string/rope" and "notes played together" - come from the same root of the strings of an instrument like a harp or lyre, in that if people were in "accord" (ie, if they agreed with each other) it was like when different strings of an instrument were played at the same time to create a pleasing sound. I believe (solely from Debussy's Etudes) that the French call chords "accords"? ]

Sur le même accord, n'est-ce pas?(!).

All excellent points eloquently expressed and I love especially the notion of "a change of identity under the Equal Temperament witness protection scheme"!...

[ferneyhoughgeliebte]

It is, of course, sometimes important to make the distinction between
Note, pitch and frequency

- and the difference between "pitch" (a specific pitch, such as middle C - or c') and "pitch class" (a named pitch whatever octave it appears in). So the lowest note of both the 'cello and viola has the pitch class C, but the pitch of the 'cello is specifically that C two octaves below middle C, and the pitch on the viola is specifically an octave below middle C.

And, as Pabs rightly points out, "octave" is a term of convenience here, used because everybody knows what we mean by it. Speaking chromatically, it could be called a Tridecatave?! (Or, with Octatonic scales, a "Nonave"????!!!!! )

[ferneyhoughgeliebte]

I love especially the notion of "a change of identity under the Equal Temperament witness protection scheme"!...

I try to put such witticismettes at the end of my long posts as a sort of "reward" for anybody who's stayed with it that long. (In the tradition of Bede's "Good luck to the reader!")

[Serial_Apologist]

I believe (solely from Debussy's Etudes) that the French call chords "accords"?

Nous sommes d'accord.

[jean]

Just to clarify this bit - in Josquin's case it isn't a "new hexachord" in the sense of a different collection of six notes, but the same hexachord an octave higher than the first.

I was thinking more of overlapping hexachords, possibly a meaningless notion.

I wonder sometimes if Guido d'Arezzo (or whoever it was) had happened upon a piece of plainsong where the sequence of notes to which the initial syllables of each line of text had continued an upward trajectory instead of dropping back again, as it does at Sancte Johannes, the history of music might have been a bit less complicated.

[ahinton]

I try to put such witticismettes at the end of my long posts as a sort of "reward" for anybody who's stayed with it that long. (In the tradition of Bede's "Good luck to the reader!")

Well, please be assured that they're much appreciated!

[ferneyhoughgeliebte]

I was thinking more of overlapping hexachords, possibly a meaningless notion.

Not at all "meaningless" - the "all-interval" Note Row that Berg uses in his Lyric Suite is based on two overlapping versions of Josquin's hexachord, a tritone apart - but not really for Josquin's time. (Although, now that I've written that, I wouldn't be surprised to be now inundated with examples of Mediaeval Music that uses oerlapping hexachords!)

[Pianoman]

oerlapping hexachords!)

Eee, lad, ah can tell tha's frum t'north...))

[ferneyhoughgeliebte]

Eee, lad, ah can tell tha's frum t'north...))

- aye, but posh "North": I didn't drop t'aitch!

[gradus]

I find piano tuning interesting and I wondered if others might also enjoy this video:

https://www.youtube.com/watch?v=PPVgDm9x8kk