Different Temperaments on digital pianos

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Just got my new piano, http://www.kawai.co.uk/ca95.htm ;

It allows the selection of different temperaments, and I am struck by how much difference there is when using a pure temperament
I'm wondering whether to just make a note of this curiosity, or to actively use this feature in future

My scale gurus are @viz and @octatonic - do you guys have any thoughts on this?
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  • vizviz Frets: 4769
    Yes! What do you mean by “pure” temperament btw? Do you mean a just temperament?
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  • Phil_aka_PipPhil_aka_Pip Frets: 8779
    Depending on which temperament you use, fretted instruments, tuned percussion, and wind instruments that have holes in (clarinets etc but not trombones or swanee whistles) will sound out of tune if you try to record them with your keyboard. I really did like the "natural" tuning (the one based on Pythagoras, I guess @Viz will remember what it's called) for a tune I played in A Aeolian, but I couldn't put the guitar with it until I switched the keyboard back into equal temperament.
    "Working" software has only unobserved bugs. (Parroty Error: Pieces of Nine! Pieces of Nine!)
    Seriously: If you value it, take/fetch it yourself
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  • vizviz Frets: 4769
    edited March 2
    Well the pythagorean tuning is in perfect 5ths which goes horrendously out after 6-7 stacks so it’s really really limited in what you can play. ‘Just’ tuning is gorgeous so long as you don’t modulate and you avoid certain intervals (and you’re in the right key to start with!) and meantone systems like 1/4 comma are brilliant for classical music like Bach (who wrote with it in mind). It’s more flexible than Just. 1/4 comma is especially good for major 3rds and minor 6ths. I love it, and 1/6th comma. Then you get 12tet which is our normal system - highly flexible but full of compromises. Nothing apart from the octave is ‘just’. 

    Phil I think you will have used 1/4 comma for your aeolian piece. It’s a fascinating tuning system and really clever if you know what it is and how it works. 
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  • Phil_aka_PipPhil_aka_Pip Frets: 8779
    I just did a quick google and found this
    "Working" software has only unobserved bugs. (Parroty Error: Pieces of Nine! Pieces of Nine!)
    Seriously: If you value it, take/fetch it yourself
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  • vizviz Frets: 4769
    edited March 2
    Yes, exactly. That’s a good summary of the main tuning systems. I did a graph of them once, below. Note how they all get good results for the perfect 4th and 5th, but some of the sharp notes are wildly out. 

    http://i.imgur.com/703V5s7.jpg
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  • ToneControlToneControl Frets: 4057
    viz said:
    Yes! What do you mean by “pure” temperament btw? Do you mean a just temperament?
    the manual says

    Pure Temperament
    (Pure Major/Pure Minor)

    This temperament, which eliminates dissonances for thirds and fifths, is still popular in choral music
    because of its perfect harmony. Any key modulation will result in dissonances.
    * The key of the temperament, and major/minor setting must be correctly matched.
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  • ToneControlToneControl Frets: 4057
    it also has

    Pythagorean
    Meantone
    Werckmeister III
    Equal Temperament (flat)
    Equal Temperament (Equal Stretch)

    but default is
    Equal Temperament (piano)
    (Equal P.only)
    "When a piano sound is selected, the tuning will be stretched like an
    acoustic piano (equal temperament).
    * If any other type of sound is selected, the tuning will be set to equal temperament (flat)."
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  • vizviz Frets: 4769
    edited March 5
    Ok so by pure temperament, they mean simple fractions - what I call ‘just’

    9/8 or 10/9 for a tone,
    6/5 for a minor 3rd
    5/4 major 3rd
    4/3 perfect 4th
    3/2 for a perfect 5th. 
    8/5 for a major 6th
    either 16/9 for a 7th or 9/5

    you probably have to select the key, or it will do it all off 440 hz or 261 hz. 

    The werckmeister and Meantone systems are “well-tempered systems”, in other words they are not as fanatical and inflexible as Just Intonation, they have some compromises but still have the occasional Just Interva. I’m pretty sure ‘Meantone’ in this case will most likely mean quarter-comma meantone, where 4 stacked 5ths are tempered to be the same as a pure major 3rd and 2 octaves (5/4 x 2 x 2 = 5. Instead of 3/2 ^ 4 = 81/16 so the 81/16 is tempered down to 80/16. The error difference (1/80) is called the comma, which is quartered and distributed over the four 5ths. The way you tune a piano to quarter comma is quite amazing. 

    Equal temperament (stretched) will be 12-TET (each semitone is 1.059 x the one below, like the distance between frets on a fretboard - except that’s 1/1.059)

    the equal temperament (flat) - I’m not really sure what that means. 
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  • ToneControlToneControl Frets: 4057
    viz said:
    Ok so by pure temperament, they mean simple fractions - what I call ‘just’

    9/8 or 10/9 for a tone,
    6/5 for a minor 3rd
    5/4 major 3rd
    4/3 perfect 4th
    3/2 for a perfect 5th. 
    8/5 for a major 6th
    either 16/9 for a 7th or 9/5

    you probably have to select the key, or it will do it all off 440 hz or 291 hz. 

    The werckmeister and Meantone systems are “well-tempered systems”, in other words they are not as fanatical and inflexible as Just Intonation, they have some compromises but still have the occasional Just Interva. I’m pretty sure ‘Meantone’ in this case will most likely mean quarter-comma meantone, where 4 stacked 5ths are tempered to be the same as a pure major 3rd and 2 octaves (5/4 x 2 x 2 = 5. Instead of 3/2 ^ 4 = 81/16 so the 81/16 is tempered down to 80/16. The error difference (1/80) is called the comma, which is quartered and distributed over the four 5ths. The way you tune a piano to quarter comma is quite amazing. 

    Equal temperament (stretched) will be 12-TET (each semitone is 1.059 x the one below, like the distance between frets on a fretboard - except that’s 1/1.059)

    the equal temperament (flat) - I’m not really sure what that means. 
    I think flat means not stretched (so only stretched when only piano tones are present)
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  • vizviz Frets: 4769
    But if it’s not “stretched” - ie 12TET, which would be the default on any keyboard - then it would have to be something else, and I can’t imagine what that would be. Most odd. And 12-TET would be the only system you don’t need to specify the key for.

    Anyway I bet it sounds nice, especially 1/4 meantone on harpsichord or organ setting. 
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  • ToneControlToneControl Frets: 4057
    viz said:
    But if it’s not “stretched” - ie 12TET, which would be the default on any keyboard - then it would have to be something else, and I can’t imagine what that would be. Most odd. And 12-TET would be the only system you don’t need to specify the key for.

    Anyway I bet it sounds nice, especially 1/4 meantone on harpsichord or organ setting. 
    they must mean 12TET with a stretched tuning as the default

    I just read about Inharmonicity (is that an album title?), which was news to me, and affects guitars: https://en.wikipedia.org/wiki/Inharmonicity ;
    Also: mode locking


    Wow, there is a huge amount of stuff down this rabbit hole, e.g. https://en.wikipedia.org/wiki/Xenharmonic_music
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  • vizviz Frets: 4769
    edited March 3
    Yes, I think so. It’s still a bit of an odd term because 12-TET IS always stretched; you can’t have an unstretched equal temperament. (Well, the 4ths are stretched. The 5ths are tempered (ie compressed), so a 4th plus a 5th still equals a precise octave.)

    Absolutely, it’s very cool stuff. Inharmonics is why you can’t rely on guitar tuners, apart from tuning one of the strings to an absolute pitch (if you don’t have perfect pitch). It’s much better imo, if you’ve got good relative pitch, to use your ear and try the method of getting your top string right, then getting the B string by fretting it at the 5th fret (not using harmonics); then fretting the G string at the 9th fret, always comparing to the top E. That way you take 12-TET and inharmonics into account. 
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  • jpfampsjpfamps Frets: 1363

    Conventional piano tuning is "stretched" as it gets sharper up the dusty end, and flatter down the bass end.

    I think the theory behind this is to minimize beat notes with overtones from the strings.

    Interestingly I've seen several people tuning a piano, and none of them used a reference pitch, but tuned by ear.
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  • vizviz Frets: 4769
    jpfamps said:

    Conventional piano tuning is "stretched" as it gets sharper up the dusty end, and flatter down the bass end.

    Well blow me I never knew that!
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  • ToneControlToneControl Frets: 4057
    viz said:
    jpfamps said:

    Conventional piano tuning is "stretched" as it gets sharper up the dusty end, and flatter down the bass end.

    Well blow me I never knew that!
    ahh, I assumed you'd heard of that
    that's why my piano switches off the stretch when you layer it with strings or whatever

    I suppose a piano in a band should also avoid stretched tuning for the same reason?
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  • vizviz Frets: 4769
    edited March 6
    Edit: cool, this is really fascinating. Thanks!
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  • jpfampsjpfamps Frets: 1363
    viz said:
    jpfamps said:

    Conventional piano tuning is "stretched" as it gets sharper up the dusty end, and flatter down the bass end.

    Well blow me I never knew that!
    ahh, I assumed you'd heard of that
    that's why my piano switches off the stretch when you layer it with strings or whatever

    I suppose a piano in a band should also avoid stretched tuning for the same reason?
    Well, you would only really have the choice if you had an electronic keyboard......

    I expect a lot of the tonality of various instruments is down to the compromises in tuning.

    Interestingly I play in a band where the piano player has perfect pitch and says he can hear the differences in tuning across the keyboard.
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  • vizviz Frets: 4769
    jpfamps said:
    viz said:
    jpfamps said:

    Conventional piano tuning is "stretched" as it gets sharper up the dusty end, and flatter down the bass end.

    Well blow me I never knew that!
    ahh, I assumed you'd heard of that
    that's why my piano switches off the stretch when you layer it with strings or whatever

    I suppose a piano in a band should also avoid stretched tuning for the same reason?
    Well, you would only really have the choice if you had an electronic keyboard......

    I expect a lot of the tonality of various instruments is down to the compromises in tuning.

    Interestingly I play in a band where the piano player has perfect pitch and says he can hear the differences in tuning across the keyboard. 

    Oh absolutely. I’m sure he (indeed any musician) can hear the differences between temperaments on a keyboard - the intervals sound massively different. That’s why the well-tempered clavier is so brilliant when played on a 1/4 comma meantone instrument, because the flavours of each key are so distinctive. (Check out Schubart’s writings on it - if anyone’s interested)

    However I wonder whether others with PP can hear the difference between middle C’s 12-TET 261.6, the Just 264 and the 1/4 comma’s 263.2 when C is played in isolation. I certainly can’t. 
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  • ToneControlToneControl Frets: 4057
    jpfamps said:
    viz said:
    jpfamps said:

    Conventional piano tuning is "stretched" as it gets sharper up the dusty end, and flatter down the bass end.

    Well blow me I never knew that!
    ahh, I assumed you'd heard of that
    that's why my piano switches off the stretch when you layer it with strings or whatever

    I suppose a piano in a band should also avoid stretched tuning for the same reason?
    Well, you would only really have the choice if you had an electronic keyboard......

    I expect a lot of the tonality of various instruments is down to the compromises in tuning.

    Interestingly I play in a band where the piano player has perfect pitch and says he can hear the differences in tuning across the keyboard.
    the higher keys do sound sharp to me as well in normal stretched setting
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  • jpfampsjpfamps Frets: 1363
    viz said:
    jpfamps said:
    viz said:
    jpfamps said:

    Conventional piano tuning is "stretched" as it gets sharper up the dusty end, and flatter down the bass end.

    Well blow me I never knew that!
    ahh, I assumed you'd heard of that
    that's why my piano switches off the stretch when you layer it with strings or whatever

    I suppose a piano in a band should also avoid stretched tuning for the same reason?
    Well, you would only really have the choice if you had an electronic keyboard......

    I expect a lot of the tonality of various instruments is down to the compromises in tuning.

    Interestingly I play in a band where the piano player has perfect pitch and says he can hear the differences in tuning across the keyboard. 

    Oh absolutely. I’m sure he (indeed any musician) can hear the differences between temperaments on a keyboard - the intervals sound massively different. That’s why the well-tempered clavier is so brilliant when played on a 1/4 comma meantone instrument, because the flavours of each key are so distinctive. (Check out Schubart’s writings on it - if anyone’s interested)

    However I wonder whether others with PP can hear the difference between middle C’s 12-TET 261.6, the Just 264 and the 1/4 comma’s 263.2 when C is played in isolation. I certainly can’t. 

    Presumably there are different levels of perfect pitch, in so far as the absolute accuracy of pitch determination.

    To recognize individual notes wouldn't actually require that level of accuracy compared to being able to tell the difference between C 262.6 and C 264.

    A friend of mine can hear the difference between A440 and A443, which is what many european orchestras tune to with no external reference.

    Stevie Wonder, who has perfect pitch, also tunes to A443.

    Another friend of mine was playing guitar with an artist who was recording with the Metropole Orchestra. They tune to A443, and the conductor (who was the youngest conductor of a major orchestra in Europe), has perfect pitch, but recognizes A443.

    Interestingly my friend, who has an excellent ear and can tune the top string of his guitar to E by ear but does not perfect pitch, after a week of recording at A443 then adjusted and with no external reference would tune his top E sharper to A443.


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  • vizviz Frets: 4769
    jpfamps said:
    viz said:
    jpfamps said:
    viz said:
    jpfamps said:

    Conventional piano tuning is "stretched" as it gets sharper up the dusty end, and flatter down the bass end.

    Well blow me I never knew that!
    ahh, I assumed you'd heard of that
    that's why my piano switches off the stretch when you layer it with strings or whatever

    I suppose a piano in a band should also avoid stretched tuning for the same reason?
    Well, you would only really have the choice if you had an electronic keyboard......

    I expect a lot of the tonality of various instruments is down to the compromises in tuning.

    Interestingly I play in a band where the piano player has perfect pitch and says he can hear the differences in tuning across the keyboard. 

    Oh absolutely. I’m sure he (indeed any musician) can hear the differences between temperaments on a keyboard - the intervals sound massively different. That’s why the well-tempered clavier is so brilliant when played on a 1/4 comma meantone instrument, because the flavours of each key are so distinctive. (Check out Schubart’s writings on it - if anyone’s interested)

    However I wonder whether others with PP can hear the difference between middle C’s 12-TET 261.6, the Just 264 and the 1/4 comma’s 263.2 when C is played in isolation. I certainly can’t. 

    Presumably there are different levels of perfect pitch, in so far as the absolute accuracy of pitch determination.

    To recognize individual notes wouldn't actually require that level of accuracy compared to being able to tell the difference between C 262.6 and C 264.

    A friend of mine can hear the difference between A440 and A443, which is what many european orchestras tune to with no external reference.

    Stevie Wonder, who has perfect pitch, also tunes to A443.

    Another friend of mine was playing guitar with an artist who was recording with the Metropole Orchestra. They tune to A443, and the conductor (who was the youngest conductor of a major orchestra in Europe), has perfect pitch, but recognizes A443.

    Interestingly my friend, who has an excellent ear and can tune the top string of his guitar to E by ear but does not perfect pitch, after a week of recording at A443 then adjusted and with no external reference would tune his top E sharper to A443.


    That’s amazing! I’m definitely not in that camp! I will always sing / recognise the right note though, plus or minus about quarter of a semitone or so. 
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