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Posted By: FrankCox Temperament - 11/03/20 08:02 PM
My piano (Casio AP-650) has sixteen different temperament settings, as follows:

00: Equal / 01: Pure Major /
02: Pure Minor /
03: Pythagorean /
04: Kirnberger 3 /
05: Werckmeister /
06: Mean-Tone / 07: Rast /
08: Bayati / 09: Hijaz /
10: Saba / 11: Dashti /
12: Chahargah /
13: Segah /
14: Gurjari Todi /
15: Chandrakauns /
16: Charukeshi

Could any of you much-smarter-than-me folks shed some light on what, exactly, these are and where and why one might want to adjust it?

I've read up a bit on temperament on Wikipedia and I even tried switching to a different setting to see what would happen. Yup, it sounds different.

Somehow I'm missing the point here. Based on the names, I'm guessing some of those settings might be for playing Arabic music or something like that. What about the others? Historical pianoforte pieces or something?

I'm thinking this might be a fun thing to play around with if I could just get a start on exactly what it's supposed to be doing for me.
Posted By: Sidokar Re: Temperament - 11/03/20 08:26 PM
Well in the modern tuning the octave is divided in 12 equal half tone. Thus any given interval will sound exactly the same whatever is the starting note. In non equal temperament, that is not the case, so depending on the tuning method, intervals will sound differently in different keys. There is a more mathematical way to explain this by saying that the pythogore comma is spread evenly. There are different ways to tune the various fifth, circular and non circular. Some tuning systems would be less balanced than others and some keys would not be usable in those.

The non equal temperaments gives a specific color to each key, but in the same time they are less practical to use, and if you play with other people, they would need to know how to tune their instrument.
Posted By: Sweelinck Re: Temperament - 11/03/20 09:11 PM
00: Equal

Current common tuning method.

01: Pure Major
02: Pure Minor
03: Pythagorean

Pure major, pure minor, and Pythagorean temperaments can be used for Medieval music (other than maybe that of John Dunstable). This is music that was modal to avoid notes outside the key signatures, and often had limited harmony (octaves and fifths) or was in unison (Gregorian chant).

04: Kirnberger

Kirnberger could be used for historically accurate late baroque, riccoco, and early, and mid classical era music, and a moderate amount of (some will say all) late classical era music.

05: Werckmeister

Werckmeister tunings were early well temperaments that were not as successful as others, but still appropriate for late Baroque music.

06: Mean-Tone

Mean-tone would be used for historically accurate performance of Renaissance and Baroque music.

The ones below are not temperaments but scale designs used for eastern music. A number of them, if not all of them, have quarter-tone intervals.

07: Rast /
08: Bayati /
09: Hijaz /
10: Saba /
11: Dashti /
12: Chahargah /
13: Segah /
14: Gurjari Todi /
15: Chandrakauns /
16: Charukeshi

----------

On a digital instrument, you typically can choose the root of the temperament. A piece in B major may not work in Kirnberger rooted on C but may be just fine in Kirnberger rooted on B.
Posted By: FrankCox Re: Temperament - 11/03/20 09:37 PM
Fantastic! This is just exactly the answer I was hoping to receive!

Thank you ever so much for taking the time to educate me on this.

Now I feel ever so much smarter....
Posted By: trooplewis Re: Temperament - 11/03/20 09:49 PM
Really interesting thread, glad this question came up.
Posted By: WeakLeftHand Re: Temperament - 11/03/20 10:26 PM
Some really smart people here!
Posted By: bennevis Re: Temperament - 11/03/20 10:48 PM
Most digitals come with a range of selectable temperament settings, which are fun to play with if you're playing Baroque and some Classical music, for example Bach's Inventions.

Make sure you select the right key (i.e. the key of your piece). The music sounds amazingly 'purer' than in ET (equal temperament). But if you play a piece in D major with, say, Werckmeister temperament set to C, you'll think your piano is badly out of tune.

BTW, string players playing by themselves (and singers singing a cappella) will not generally be using ET: they naturally gravitate towards pure fifths, possibly also pure thirds. I sing occasionally in a choir, and used to play with a violinist: with some music (like Bach motets), we can sing a cappella or with organ accompaniment. Our tuning 'choices' depends on whether the organist turns up.......
Posted By: Sweelinck Re: Temperament - 11/03/20 10:53 PM
Most welcome. I should mention that mean-tone is actually a family of temperaments, not a single one. Kirnberger and Werckmeister also produced more than one temperament. My guess would be that Casio used Kirnberger III and Werckmeister III, but Werckmeister II is also a possibility.

The wiki entry for John Dunstable is worth reading. Apparently Dunstaple is an alternate spelling. His music is some of, if not the earliest known keyboard music to use 3rds, 6ths, and triads in harmony. I have played his Agincourt Hymn, but am not very familiar with his vocal and choral music.

https://en.m.wikipedia.org/wiki/John_Dunstaple

One feature of early and baroque and much classical era keyboard music is it rarely if ever requires big reaches. In fact, for a long time it was thought that thumbs should not be used, and finger crossings were used to play scales.
Posted By: Sidokar Re: Temperament - 11/04/20 10:36 AM
The Agincourt hymn is a song in 2 parts composed by an unknown composer (It is actually Azincourt from the name of a french small town where a famous battle occurred in 1415). The organ version you played is likely an arrangement done by somebody else and attributed to Dunstable. Most of the compositions by Dunstable that have survived are vocal and a very few could be for organ though with no certainty either on the composer or for what sort of instrument (if instrumental).

The harmonisation technic used by Dunstable is the faburden, an english version of the french fauxbourdon where the upper and tenor voice move in parallel sixth. A third voice is added a fourth below. Thats how the Azincourt carol is mostly harmonized in the style of the 15th century. There is a debate as to who is the initial creator, of this new technic, either the english by influence of the gymel or the french school of Dufay. To be noted though that the resulting 3rd interval between the lower voice and the middle voice is the result of adding the third voice a fourth below the soprano, thus creating a mix between the usage of a sixth and the older fourth interval predominant in the free organum.

The 3 voices compositions for organ are usually intabulations which start to appear in the 15th century. We have very little sources, if any, extent for certain solo organ music in Italy, France, England. Compositions with organ are supporting songs. The only sources known that are formerly solo organ are mainly in various german manuscripts such as the Berlin, Hamburg or the Conrad Paumann Fundamentum Organisandi.
Posted By: zrtf90 Re: Temperament - 11/04/20 05:23 PM
FWIW, Bradley Lehman wrote an article about Bach's Well Tempered tuning (it's on on larips.com). I started using it around 2013 on my digital and although I can't tell the difference in an AB comparison I do find the Lehman temperament gives me some glorious harmonies in certain pieces that I don't get with any other temperament except Stephen Hammer's alteration to Lehman's (StephenHammer.com), which I currently use on Pianoteq.

I find ET quite boring now and probably wouldn't choose to use it again.
Posted By: Sweelinck Re: Temperament - 11/04/20 05:48 PM
Originally Posted by Sidokar
The Agincourt hymn is a song in 2 parts composed by an unknown composer (It is actually Azincourt from the name of a french small town where a famous battle occurred in 1415). The organ version you played is likely an arrangement done by somebody else and attributed to Dunstable. Most of the compositions by Dunstable that have survived are vocal and a very few could be for organ though with no certainty either on the composer or for what sort of instrument (if instrumental).

The harmonisation technic used by Dunstable is the faburden, an english version of the french fauxbourdon where the upper and tenor voice move in parallel sixth. A third voice is added a fourth below. Thats how the Azincourt carol is mostly harmonized in the style of the 15th century. There is a debate as to who is the initial creator, of this new technic, either the english by influence of the gymel or the french school of Dufay. To be noted though that the resulting 3rd interval between the lower voice and the middle voice is the result of adding the third voice a fourth below the soprano, thus creating a mix between the usage of a sixth and the older fourth interval predominant in the free organum.

The 3 voices compositions for organ are usually intabulations which start to appear in the 15th century. We have very little sources, if any, extent for certain solo organ music in Italy, France, England. Compositions with organ are supporting songs. The only sources known that are formerly solo organ are mainly in various german manuscripts such as the Berlin, Hamburg or the Conrad Paumann Fundamentum Organisandi.

Agincourt is a standard English spelling. E. Power Biggs, who did the organ arrangement of the Agincourt Hymn writes, "It is believed that Dunstable was in the service of the Chapel Royal, and that he was the author of the famous hymn celebrating the victory of Henry V at the Battle of Agincourt in France, on St. Crispian's Day, October 25th, 1415."
Posted By: Sidokar Re: Temperament - 11/04/20 06:51 PM
Originally Posted by Sweelinck
Agincourt is a standard English spelling. E. Power Biggs, who did the organ arrangement of the Agincourt Hymn writes, "It is believed that Dunstable was in the service of the Chapel Royal, and that he was the author of the famous hymn celebrating the victory of Henry V at the Battle of Agincourt in France, on St. Crispian's Day, October 25th, 1415."

Yes, I know for both points. Though Azincourt being a name does not need to be spell corrected, but indeed that is how it is done in England.

For what Biggs wrote and it is how indeed how he published the hymn, it is a false assumption. There is no evidence that Dunstable composed it. It is in fact a 2 parts carol song and not an organ composition. Biggs made an organ arrangement out of it which is not by Dunstable. There are a handful of compositions (intabulation of songs), which may be for organ or for another instrument or for voice that could be by Dunstable and published in his complete set of works by Bukofzer, and this one not being part of it. For example the arrangement of O Rosa Bella that was attributed to him but eventally recognized to be by John Bedyngham.

That said, indeed Dunstable is known for his panconsonant music, which is supposed to have influenced Dufay. In return Dunstable adopted the french technique of the isorythmic motet.
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