New Works

Meantone Suites

Meantone Suite I
(1984,2015) Harpsichord

Three decades ago I wrote a Prelude, Siciliana and Sarabande which became the "Little Suite in A Minor". I thought it would be nice to complete the suite. I have now added a Corrente, Fuga and Gigue. The Suite follows the traditional order of movements except with a Siciliana in place of the Allemande and a Fuga in place of the gallanteries.

Originally I wrote the Meantone Suite I in A minor but then realized my harpsichord only goes up to a D so I have transposed the suite into G minor. Both Meantone Suites I and II are written for a harpsichord with 56 notes from G1 to D6. The harpsichord is tuned to A=415 and the Meantone Suite I to a temperament of my own making called the "Puhm Ultra Harmonic Meantone Temperament 65" or "PUHMT65" for short. It is a temperament that is in part very close to "1/6 Holdrian Comma Equal Meantone Temperament" (a Holdrian Comma is 1/53 of an octave), and in part close to "1/4 Syntonic Comma Equal Meantone Temperament"! I am just staring to upload chapters of my Compendium Musica where eventually all will be explained!

The wolf for the G minor key is between C# and Ab. This is equivalent to tuning the temperament starting on F instead of C. All the Meantone Suites will follow this format. Centering the meantone temperament in such a way allows one to freely modulate between the six closely related keys of G minor (G-, Bb+, D-, F+, C-, Eb+) without hitting wolf intervals and chords. The wolf for the A minor key would then have to be between D# and Bb.

For the A minor key I have chosen as example a very extreme Equal Meantone Temperament that I call "Equal Harmony 1 EMT". The fifth here is a little more than 6 cents flat from Just and you can really hear as things start becoming somewhat wonky! As well the major third is tempered flat instead of sharp. More details of all these Equal Meantone Temperaments can be found in the Compendium Musica.

As the "Equal Harmony 1 EMT" is really not at all successful, I have as well realized the Suite in the standard "1/4 Syntonic Comma EMT". Slightly better but still odd. Why so? The reason is that these meantone temperaments do not support chromaticism and diminished intervals and chords well.

The Meantone Suite I was written with our regular equal temperament and then realized with the meantone temperament that allows one to modulate freely among the six closely related keys; the wolf between C# and Ab for G minor and between D# and Bb for A minor. There are no other options possible to be able to modulate among the six closely related keys without hitting wolf intervals and triads.

Only when the fifth is tempered less and less extremely does the chromatic scale begin to even out and the diminished intervals and chords become usable in a way that we are used to. And so as we transition from the Renaissance to the Baroque periods, we move from mainly major and minor triads to the dramatic usage of diminshed intervals and chords and greater chromaticism. This is only so, whether in Meantone or Well Temperaments, because the fifth is getting closer to our common temperament with the subsequent sharpening of the major thirds/sixths and flattening of the minor thirds/sixths. The less then the temper of the fifth in a meantone temperament, the more the music is able to bear diminished intervals and chords and chromaticism. Quite interesting understanding stylistic evolution by the degree of temper of the fifth and subsequent evenness of the chromatic scale!

Meantone Suite I in G minor
(Puhm Ultra Harmonic Meantone Temperament 65):
Mp3 (15:10) (20.8MB) ~ Score ~ YT

Meantone Suite I in A minor
(Equal Harmony 1 Equal Meantone Temperament):
Mp3 (15:11) (20.8MB) ~ Score

Meantone Suite I in A minor
(1/4 Syntonic Comma Equal Meantone Temperament):
Mp3 (15:11) (20.8MB) ~ Score

Meantone Suite II
(2016) Harpsichord

The Meantone Suite II was written directly using "2/9 Syntonic Comma Equal Meantone Temperament". The fifth here is only slightly less tempered than "1/4 Syntonic Comma EMT" so the major thirds / minor sixths are excellent being only 2.39 cents sharp/flat from Just.

It is a very interesting and different experience composing directly in a meantone temperament. The purity of the intervals really compels one to the purity and consonance of the harmony. On the other hand the diminished intervals and triads are harsh and so either are avoided or used with extreme care mainly through separation of register. This changes the drama of the music and using purer intervals and harmonies means a music where it is harder to create tension. Everything sounds equally in tune and dissonances are harsh and so for the most part avoided. This is in contrast to temperaments with fifths closer to our common temperament where everything is somewhat out of tune and resolving a dissonance is only a matter of degree. As the intervals and chords of equal temperament are not as well in tune there is less contrast between consonance and dissonance, unlike "1/4 and 2/9 Syntonic Comma EMT" where the difference is extreme and jarring.

Out of interest I have also realized the Meantone Suite II in "1/5 Ditonic Comma EMT". The major thirds / minor sixths here being only 2.80 cents sharp/flat from Just. This is an excellent temperament in its own right with equal beating major triads as compared to the equal beating minor triads of "2/9 Syntonic Comma EMT". "1/5 Ditonic Comma EMT" is just the smallest bit brighter due to slightly sharper major thirds and a very small amount less consonant than "2/9 Syntonic Comma EMT". The choice of temperament and instrument directly reflects how the music is composed which makes complete sense!

At the outset I wanted the wolf to be the same for both Meantone Suites I and II so that if only one particular meantone temperament was chosen, they could still be played together without retuning the instrument. I as well decided to utilize all the modulation possibilities of the meantone temperament here instead of just the six closely related keys. Beforehand I wanted to be able to modulate to the minor I, IV and V keys and so I chose to compose in C major with, as above, the wolf between C# and Ab. This however precluded the relative key of A minor being complete, missing its dominant chord!

Meantone Suite II in C Major
(2/9 Syntonic Comma Equal Meantone Temperament):
Mp3 (21:59) (30.1MB) ~ Score ~ YT

Meantone Suite II in C Major
(1/5 Ditonic Comma Equal Meantone Temperament):
Mp3 (21:59) (30.2MB) ~ Score

Meantone Suite III
(2016) Organ

Meantone Suite III was composed directly in "31Et Equal Meantone Temperament". The major third / minor sixth is less than 1 cent sharp/flat from Just. The minor third / major sixth is a little more than 5 cents flat/sharp from Just, as is the perfect fifth / perfect fourth. "31Et EMT" is almost the same as "1/4 Syntonic Comma EMT" yet I find "31Et EMT" much better in tune. There may be a number of reasons for this.

Firstly, most individual notes of any instrument are slightly enharmonic with the overtones bearing slightly sharp. There would then be a better alignment between the overtones of the tempered major intervals to the overtones of the individual notes of that interval. In "1/4 Syntonic Comma EMT" where the major third is pure the overtones would then actually be less in alignment. We as well prefer our major intervals to tend slightly sharp and brighter and our minor intervals to tend flat and duller. It makes sense then when writing in a minor key to use a temperament with flatter minor thirds. Conversely, when writing in a major key to use a temperament with sharper major thirds.

Secondly, the octave is evenly divided into 31 parts by the fifth of "31Et EMT". This would then seem to bring a deep seated balance overall to the temperament. 31Et (along with 43Et) are as well the only viable equal temperaments to move beyond 12Et until the almost 5 Limit perfection of 53Et. 31Et also gives the best approximation to the 7 and 11 limit ratios available if we choose to move in that direction. 12Et gives the worst approximation of any equal temperament to 7, 11 and 13 limit ratios hence the reason we don't use them and their complete unfamiliarity to our ear.

"31Et EMT" has two possible harmonic seventh chords available which are very usable even though they clip wildly with a very distinct sound. The pitch center of "31Et EMT" though is lopsided which can clearly be heard moving between remote chords.

Meantone Suite III is composed for a single manual chamber organ without pedals, tuned to A=415 with a range of 49 notes between C2 and C6. Tuning a chamber organ to a Meantone Temperament is viable whereas retuning a large organ certainly would not be!

Meantone Suite III in C Minor
(31Et Equal Meantone Temperament):
Mp3 (28:19) (38.9MB) ~ Score ~ YT

Meantone Suite IV
(2016) Organ

The Meantone Suite IV for Organ follows immediately the Meantone Suite III. It is as well written for a single manual chamber organ without pedals, tuned to A=415 with a range of 49 notes between C2 and C6. I initially wanted to compose this work using a different Meantone Temperament than the 31Et EMT of the Meantone Suite III. I also wanted to make the work more concise. On neither of these two points did I succeed! In F Major the Meantone Suite IV is much lighter than the C Minor of the Meantone Suite III.

31Et EMT is the most harmonious meantone temperament there is for major and minor triadic harmony which is why both suites for organ are written in this temperament. The major thirds are less than one cent pure from just. The fifths and fourths are around 5 cents flat and sharp from just which is more than twice what we are used to in 12Et but they are still excellent. The minor thirds are as well around 6 cents flat which is a little more than a third of what they are tempered in 12Et. Such purity of intonation is excellent for the sustained notes of an organ whereas 12Et is always very grinding on an organ. This is one reason why organ music (besides excessive reverberation bleeding all the sounds together) at times can be very unpleasant to listen to and enjoy. Again diminished chords and intervals are out of tune compared to the purity of the rest of the harmony and so aren't as easily incorporated which makes it much more difficult to create and release tension.

After listening to much music in 31Et I am pretty much on the verge of abandoning this temperament. Any form of extended harmony beyond the basic major / minor triads and the harmonic seventh chord is sour. There is a distinct lack of blending which gives for starters, extremely unpleasant and dissonant diminished and augmented triads. Composers always try to plum the depths of what is possible with their instruments and tunings. If most Renaissance keyboards were tuned to 1/4 Syntonic Meantone (which is almost the same as 31Et EMT) we can readily understand why the music from this period is largely written using only major and minor triads. The ear of the composers from this time of course avoided any unpleasant harmonic combinations, a dissonance which was further heightened by how excellent the major and minor triads sound! In order to bring the diminished chords and intervals more freely into play, a Meantone Temperament that doesn't temper the fifth as much must be used. It is only when the fifth becomes less tempered that the diminished triad becomes listenable, hence the dramtic usage of diminished seventh chords in the Baroque era and beyond.

Much more information can be found in the Equal Meantone Temperaments chapter in the Compendium Musica.

Meantone Suite IV in F Major
(31Et Equal Meantone Temperament):
Mp3 (41:49) (57.4MB) ~ Score ~ YT

Meantone Suite V
(2017) Fortepiano

The Meantone Suite V is written for a classical fortepiano tuned to A=415 with a range of 61 notes from F1 to F6. The only thing is, in the end I find most fortepianos to have a very clunky clangy sound and I much prefer the beautiful resonant and sustained sound of a concert grand.

The Meantone Suite V is written in 43Et EMT. I can't praise this temperament highly enough. The problems of extended harmony in 31Et EMT are almost completely overcome. Triadic major / minor harmony is still amazing and resonant and the harmonic seventh chords are stunning and balanced. In 43Et EMT extended harmony chords blend wonderfully together. There is an overall balance in the harmony of this temperament. This makes sense as the major thirds are tuned sharp almost as much as the perfect fifths are tuned flat. The major thirds are 4.38 cents sharp from just which is three times better than the major thirds in 12Et. The fifths and fourths are 4.28 cents flat and sharp from just which is more than twice what we are used to in 12Et but they are still excellent. The minor thirds are 8.66 cents flat from just which is a little more than half of what they are tempered in 12ET.

In 43Et EMT we can write dramatically again but still enjoy the beauty of it's superior harmony. As well the major seventh (and minor second) intervals are almost pure. The harmonic seventh 7/4 ratio is 7.92 cents sharp from just but it still retains its character. Not only does it retain it's character but being slightly tempered it actually blends and sounds better than the wildly clipping harmonic seventh chord in 31Et! If I had a choice of one Meantone Temperament it would be 43Et EMT. All of our common Meantone, Well and Equal Temperaments (12Et) temper the 10/9 and 9/8 major seconds to a single pitch. That means that all of these temperaments consist of a major second that is some sort of mean between 10/9 and 9/8. Only when we move to 53Et or Just Intonation do we untemper the major second into two distinct pitches.

On two final notes it is understood that fortepianos historically were tuned in a Well Temperament. The second note deals with touch when playing a keyboard instrument that has the ability to play dynamics. When playing in a superior tuning like 43Et EMT the performer does not have to force the sound into tune. The ear and playing is always relaxed as the notes combine beautifully. This is in stark contrast to playing in 12Et where one is always playing harder trying to force the ear to dynamically retune what it hears to not be in tune and resonant.

Meantone Suite V in D Minor
(43Et Equal Meantone Temperament):
Mp3 (49:21) (67.7.4MB) ~ Score ~ YT