Equal vrs. Just tuning

[Mitch]

<snigger> I also regard OXX XXX as the beginner's middle D - it's a fake so's you can not physically drop into the low D - and for those who lerve non-whistly instruments (such as hyper timbre-corrected sampler piano widgets), if you don't like the different timbre in the second octave .. there's a ton of software available to sanitise your favourite machine .. just download midi files and sit back.

There will always be an energy difference between 1st register middle D and second register middle D - it will be expressed in timbre or tone. if it's tone - well, I have no idea what your tonsils are used to, a musician will use whatever gets the job done - a good one will find the sensitivity to go further..

For real musicians: IF it's there - use it. These are whistles for god's sake .. not computers. The salt of the earth? - Seasoning's a matter of taste .. but if it's your salary .. it better be able to walk on the sabath while everyone else is sitting on their "salt"

[hans]

The modes of any just-tuned instrument will be as "in-tune" as as the root Ionian.

Mitch - what do you think of the difference between a just-intoned 10/9 E (just minor tone, -18cents of ET full tone) and 9/8 E (just major tone, +4cents of ET full tone)? The Ionian mode on D will sound best with the 9/8 E, whereas the Dorian mode will sound best with a much flatter 10/9 E. To me the Dorian mode with a 'sharp' 9/8 E sounds not in tune. We cannot assume the modes are all in tune just-intonated with a just-intonated Ionian (major) mode.

[Mitch]

The modes of any just-tuned instrument will be as "in-tune" as as the root Ionian.

Mitch - what do you think of the difference between a just-intoned 10/9 E (just minor tone, -18cents of ET full tone) and 9/8 E (just major tone, +4cents of ET full tone)? The Ionian mode on D will sound best with the 9/8 E, whereas the Dorian mode will sound best with a much flatter 10/9 E. To me the Dorian mode with a 'sharp' 9/8 E sounds not in tune. We cannot assume the modes are all in tune just-intonated with a just-intonated Ionian (major) mode.

Yes, but it would seem to depend on what drone is in play. To me the modes are an inference of the places visited in the scale's journey and where the tune considers itself "home" - in a lot of traditional musics, the "home" is relative to the drone - not necessarily on it. In that sense, the Ionian is inferred. If your ear prefers the tonic to be "at-rest" (on the drone) then the intervals of the scale are absolute to the drone - to my ear that is not modal. In such cases, it might be better to use separate terms for the scales.

[Carey]

Perhaps I've not thought about it enough, but I understand the modes of a key to be made up of the same notes. If the Ionian is C then to get Dorian wouldn't you play the same notes but start on D rather than C, thus moving the 1/2 steps a note lower in the scale? I wouldn't think it would be cricket (hurley?) to diddle with the freq of the notes. If you do you are doing more than just playing a mode of your selected key. Or have I missed something?

[benhall.1]

I think - mind, I'm getting just a bit stretched here - that the modes are actually different. For instance, to put it (realtively!) simply, if you play in Dorian mode starting on D, you will need a perfect fifth for the A. But a correct sixth from C in just intonation won't produce a perfect fifth from the D (or at least, I don't think it will). I'm not so good on the maths of this ... yet ... sounds as if Hans might be able to expand on this ...

[jemtheflute]

Ben, you should have borrowed those books on temperament I was reading when you were up at New Year! I ploughed through all the ones I had! Mind you, the maths were mostly way beyond me: I can comprehend the concepts and to a fair degree the practical implications when well explained in text, but real meaningful comprehension, let alone serious application of or expression with the numbers is beyond me! I've still got the books, though.....

[benhall.1]

Yes, I meant to ask you what those books were - especially the one I was in the middle of. What were they? I can cope with the maths ...

Meanwhile, the book I really want is Dr Richard Henebry's discussion of temperament and modality as applied to Irish music. I still haven't got it, so if anyone knows where I can get it ... ?

[MTGuru]

Carey, what you're describing is the case for ET, where all given intervals are the same, regardless of key, and only the interval structure varies from mode to mode. But I think Ben has got the essence of what happens in JI or unequal temperaments.

When you change keys/modes from the root you used to set your tuning, the equivalent intervals are no longer necessarily the same from key to key. When you stay within the keys a temperament was designed to handle, the differences are perceived as "coloration". Beyond that, they're likely to be perceived as discordant. That is why baroque keyboards were often retuned before playing a specific piece, in order to handle the keys and modulations of that piece.

For example, a JI major 3rd is exactly 5:4 = 1.25. But if you tune to JI in C, then play a major 3rd on D (D-F#), the interval is 7:5/9:8 = 1.2444, around 8 cents flat. So D major chords on a C-tuned instrument may be perceived as being darker, sadder, more tense. That sort of thing.

[hans]

I think the statement "modes use the same notes as the major scale, but use a different note as the tonic" is only true if you use equal temperament, where all semi tones have the same value. If we move back to just intonation, then whole tone intervals are not double of an equal tempered semitone, and in fact vary quite a bit. In fact there are a lot more musical interval ratios than the twelve we know from ET. So a Dorian mode will use different intervals than the related Ionian major mode. Specifically the Second of the major scale needs to be flat to be the tonic of the Dorian mode, or the tonic of the Minor mode, using a diminished sixth (Cnat on a D whistle or flute).

It is really worthwhile to experiment with this, to try to hear the differences.
If you have an equally tuned whistle, you could flatten the Second, Third and Sixth by using a bit of Scotch tape on holes 2,5,6 ( L2, R2 and R3). If you are into whistle making, it may be worth it to try the following tuning, with differences in cents from ET:
(first row associated whistle holes)

Code: Select all

   6   5    4   3   2    1
I  II  III  IV  V   VI   VII  VIII
D  E   F#   G   A   B    C#   D'
0  -8  -14  -2  +2  -16  -12  0

This is a just intonated scale with exception of the E, which is a compromise between the -18 cents flat 'minor Second' and +4 cents sharp 'major Second', and will allow to play both.

I also would use a thumb hole for the Cnat and tune it -4 cents to ET C:

Code: Select all

   6   5    4   3   2   T    1
I  II  III  IV  V   VI  VII- VII  VIII
D  E   F#   G   A   B   C    C#   D'
0  -8  -14  -2  +2  -16 -4   -12  0

The result is a very sweetly intoned whistle, especially lovely to play in minor modes.

[david_h]

I read somewhere on one of the articles on JI that in the past (medieval times ?) string instruments where sometimes tuned to the just scale of the lowest note of the tune, not neccessarily the 'home note' (is that plagal modes ? Ben ?). So that would be like most irish tunes in G being played over a D drone or in a D scale.

A question I keep asking and maybe those gathered above can answer - do pipers play E dorian tunes over the D drone (or do they stop the drones for those tunes). If so does that have an effect on what irish E dorian tunes are 'supposed to sound like'.

[benhall.1]

That is why baroque keyboards were often retuned before playing a specific piece, in order to handle the keys and modulations of that piece.

Also bear in mind the use, in the baroque and, inded later, of 'split key' keyboards, with more than one key for each individual note, tuned slightly differently so as to enable better intonation in various keys and to differentiate between, for instance, G# and Ab.

You did point out that this was a huge topic, MTGuru!



[PS David_h I'm not ignoring your comment/question - just thinking about it ... I may be some time ...]
[PPS Sorry, that line above should of course read "... was a huge topic, Mr Guru Sir" ]

[pancelticpiper]

About the position/size of the top finger-hole, it's usually the mark of a whistle or flute maker who is not coming from the tradition if they attempt to make the hole large/high enough to get C# in tune. Because if the C# hole is large/high enough to get at in-tune C# at normal pressue 1) the C natural will be too sharp using the normal traditional C natural fingerings 2) the vented middle D will be spoiled (at least on flute).

Anyone accustomed to traditional playing will want that C# to be a bit flat anyhow- it almost always is on the uilleann pipes, at the Just Intonation C# is supposed to be flatter than the Equal Temp C#, whether it's the sharp 7th in the key of C or the Major 3rd in the key of A, around 14 cents flat is correct.

I've come across many a neo-Irish flute over the years made by American newbie flutemakers who do this. The vented middle D breaks/squawks and the C natural is hopeless. Such instruments are pretty much useless for traditional Irish fluteplaying.

[jemtheflute]

Yes, I meant to ask you what those books were - especially the one I was in the middle of. What were they? I can cope with the maths ...

Right then. My Spring reading was:

Tuning and Temperament, A Historical Survey J Murray Barbour, Michigan 1951 (Dover pb edition 2004 ISBN 0486434060) - the root modern study and base reference for just about everything since - somewhat ET biased but comprehensive.

How Equal Temperament Ruined Harmony (and Why You Should Care) Ross W Duffin, New York 2007 (W W Norton pb edition 2008 ISBN 9780393334203) - reviews of which turned me on to the topic (as well as C&F discussions) and which is interesting but ultimately a bit disappointing. I think it's the one you were browsing?

Temperament - How Music Became a Battleground for the Great Minds of Western Civilization Stuart Isacoff, New York 2001 (Vintage pb edition 2003 ISBN 0375703306) which kind of bridges areas the previous two titles don't address....


Come up for a sesh and borrow them!

[pancelticpiper]

a Bach peice on a just tempered keyboard compared with an equal tempered keyboard

There can be no such thing as a "just tempered" keyboard. It's a confusion, a contradiction, in terms.

"Just" is from "just intonation", a scale based on the harmonic series.

"Tempered" is by definition a departure from "just".

We nowadays are used to Equal Temperament which is the arbitrary division of the octave into 12 equal units. It was attacked at the time of its introduction:
"Equal in what way? In that it allows one to play in every key equally out of tune?"

Bach's Well-Tempered Clavier was not written for Equal Temperament, which wasn't used at the time, but rather for one of the numerous tempered scales coming into vogue. Musicologies are not in agreement as to which scale was intended. All the various tempered scales represented an attempt at compromise between Just Intonation (which is what sounded "in tune" at the time) and Equal Temperament (which was judged to be to out of tune to be usable).

[Carey]

Carey, what you're describing is the case for ET, where all given intervals are the same, regardless of key, and only the interval structure varies from mode to mode. But I think Ben has got the essence of what happens in JI or unequal temperaments.

Well, that's the crux of it then. And maybe a point of refinement of my thinking. I don't consider changing modes to be changing keys. I understand that changing "key" when using just intonation requires one to re-tune, but I still am not convinced (or am still confused) about changing modes within a "key." Maybe that concept is the one that has to go, that you can change modes without changing keys. According to my mental model (which I'm sure looks pretty scary were one to peer into it) the "key" and the tuning determine the frequency of the individual notes, and if one plays Dorian or Mix or Minor, one doesn't change the notes, just the way they are mixed together to get a scale.

E Dorian in my mind is the same "key" as D Ionian, and (again, I'm speaking from a reference of how my current mental model is formed) should not need retuning from D Ionian. The perfect fifth would be with respect to the D in both cases.

Said another way, anytime the key is D, any mode of the key of D should sound fine played over a D drone.

No? Maybe?

(Edited for spelling)