We present Bach's Air from 3rd Orchestral suite, tuned into Vicentino adaptive just intonation, arranged for Baroque Ensemble (Recorder, Oboe, Clarinet, Bassoon, Cello, Violone). The intonation system is quarter-comma meantone, but ascending fifths minor 3ds are tuned a quarter comma higher (hence just). Anyway, diminished chords have been left tuned into quarter-comma meantone without modifications.
We present Bach's Air from 3rd Orchestral suite, tuned into Vicentino adaptive just intonation, arranged for Baroque Ensemble (Recorder, Oboe, Clarinet, Bassoon, Cello, Violone). The intonation system is quarter-comma meantone, but ascending fifths minor 3ds are tuned a quarter comma higher (hence just). Anyway, diminished chords have been left tuned into quarter-comma meantone without modifications.
We present Bach's Air from 3rd Orchestral suite, tuned into Vicentino adaptive just intonation, arranged for Baroque Ensemble (Recorder, Oboe, Clarinet, Bassoon, Cello, Violone). The intonation system is quarter-comma meantone, but ascending fifths minor 3ds are tuned a quarter comma higher (hence just). Anyway, diminished chords have been left tuned into quarter-comma meantone without modifications.
557 Decimal Digits of Pi, rendered in 10-equal division of the octave, and split into two voices (baroque oboe and baroque bassoon). Both oboe and bassoon play the integer part 3, then bassoon plays the odd-numbered digits, oboe the even-numbered ones. A little bit of swing effect has been applied. Repeating numbers (in the above schema) have been rendered as tied notes. 10-equal division of the octave has been notated in the customary way: C = 0¢ C# = 120¢ D = 240¢ D# = 360¢ F = 480¢ F# = 600¢ G = 720¢ G# = 840¢ A = 960¢ A# = 1080¢ Octave correction has been implemented in the following way:
.... 'cause 50 is generated by a fifth G=969 ¢ i.e. 29 steps out of 50, and 29 is coprime with 50 (in fact, 29 is a prime number); hence everything is concatenated. Also, by an aestæthical point of view, it creates kind of an ancient sounding general setting (it's in fact a meantone tuning, with a generator slightly flatter than it would be in quarter-comma meantone, G = 696.578 ¢). 60edo is fine, but it consists of five chains of 12 fifths each, so it's rather different in its overall philosophy (the most important issue = in 60edo, 5/4 = 390 ¢ ≠ 4 fifths = 400 ¢). Of course, both require a computer to be implemented, unless you choose 12 tones out of each one of them (this would cause wolf fifths to appear, at least in 50 edo).
Interesting! What type of program do you use to implement? I’ve got Logic Pro but I haven’t seen any options for that type of thing. I would love to experiment…
A chord progression raising by a fifth of an octave (+240 cents), repeated five times, thus spanning a whole octave. Tuning is 50-equal division of the octave (note that 50 is divisible by 5). The basic chord progression consists of two major triads and a septimal dominant chord: F-C-F-A E-C-G-C Gb-Ebb-Bbb-C This progression resolves to Abb major, at +240 cents from F in 50edo. Note that 240 x 5 = 1200 cents = 1 octave, hence the progression iterated five times goes back to the original starting tone, i.e. F. This is alike Giant Steps, but it's ascending rahter than descending, and features division by 5 rather than by 3; in particular, it cannot be carried out in 12edo, since 12 is not divisible by 5.
We present the first movement from Beethoven's Moonlight Sonata, arranged for baroque oboe, clavichord, bassoon, viola da gamba, sackbut. Tuning is Rameau Tempérament Ordinaire, generated by 7 meantone fifths (as large as 697 ¢) and five sharp fifths (as large as 704.2 ¢), then rounded to integer values. The Scala file of the tuning is: 101.0 194.0 295.0 388.0 496.0 596.0 697.0 798.0 891.0 992.0 1092.0 2/1.
This is Mozart's Gigue KV 574, arranged for harpsichord (midi rendition) and tuned into Golden Meantone, the meantone system defined by setting the relation between the whole tone and diatonic semitone intervals to be the Golden Ratio φ=1/2*(51/2+1)≈1.6180… This makes the Golden fifth exactly (8−φ)/11 octaves, or (9600−1200φ)/11 cents, approximately 696.214 cents. This in turn implies that the ratio between the diatonic semitone and the chromatic semitone is the Golden Ratio as well.
We present Bach's Air from 3rd Orchestral suite, tuned into Vicentino adaptive just intonation, arranged for Baroque Ensemble (Recorder, Oboe, Clarinet, Bassoon, Cello, Violone). The intonation system is quarter-comma meantone, but ascending fifths minor 3ds are tuned a quarter comma higher (hence just). Anyway, diminished chords have been left tuned into quarter-comma meantone without modifications.
How do major 2nds/ whole tones work in the 'Vicentino' tuning? Are they always meantone?
Yes indeed... they are always meantone 🙂 Only minor thirds and fifths happen to be fine-tuned.
We present Bach's Air from 3rd Orchestral suite, tuned into Vicentino adaptive just intonation, arranged for Baroque Ensemble (Recorder, Oboe, Clarinet, Bassoon, Cello, Violone). The intonation system is quarter-comma meantone, but ascending fifths minor 3ds are tuned a quarter comma higher (hence just). Anyway, diminished chords have been left tuned into quarter-comma meantone without modifications.
We present Bach's Air from 3rd Orchestral suite, tuned into Vicentino adaptive just intonation, arranged for Baroque Ensemble (Recorder, Oboe, Clarinet, Bassoon, Cello, Violone). The intonation system is quarter-comma meantone, but ascending fifths minor 3ds are tuned a quarter comma higher (hence just). Anyway, diminished chords have been left tuned into quarter-comma meantone without modifications.
Pretty cool!
Thank you ! 🙂
557 Decimal Digits of Pi, rendered in 10-equal division of the octave, and split into two voices (baroque oboe and baroque bassoon). Both oboe and bassoon play the integer part 3, then bassoon plays the odd-numbered digits, oboe the even-numbered ones. A little bit of swing effect has been applied. Repeating numbers (in the above schema) have been rendered as tied notes. 10-equal division of the octave has been notated in the customary way: C = 0¢ C# = 120¢ D = 240¢ D# = 360¢ F = 480¢ F# = 600¢ G = 720¢ G# = 840¢ A = 960¢ A# = 1080¢ Octave correction has been implemented in the following way:
Why not just use duodecimal?
I have tried it... but still with unsatisfactory results 🤔 I guess it'll be one of the next productions, anyway 🙂
Here's another example: this one shows instead that you can carry to extremes the role of 13edo diminished fifth 7/13 = 646.154 cents:
Thanks! I like the music you've written in this tuning ☺️
Thanks to you for your appreciation 🙂
50 is a lot. If you are doing that many why not go to 60? Then you get all the “benefits“ of 12 and 5.
.... 'cause 50 is generated by a fifth G=969 ¢ i.e. 29 steps out of 50, and 29 is coprime with 50 (in fact, 29 is a prime number); hence everything is concatenated. Also, by an aestæthical point of view, it creates kind of an ancient sounding general setting (it's in fact a meantone tuning, with a generator slightly flatter than it would be in quarter-comma meantone, G = 696.578 ¢). 60edo is fine, but it consists of five chains of 12 fifths each, so it's rather different in its overall philosophy (the most important issue = in 60edo, 5/4 = 390 ¢ ≠ 4 fifths = 400 ¢). Of course, both require a computer to be implemented, unless you choose 12 tones out of each one of them (this would cause wolf fifths to appear, at least in 50 edo).
Interesting! What type of program do you use to implement? I’ve got Logic Pro but I haven’t seen any options for that type of thing. I would love to experiment…
Thank you so much for your appreciation ! I'm planning a blog post about that... but, meanwhile: I use the following free software:
A chord progression raising by a fifth of an octave (+240 cents), repeated five times, thus spanning a whole octave. Tuning is 50-equal division of the octave (note that 50 is divisible by 5). The basic chord progression consists of two major triads and a septimal dominant chord: F-C-F-A E-C-G-C Gb-Ebb-Bbb-C This progression resolves to Abb major, at +240 cents from F in 50edo. Note that 240 x 5 = 1200 cents = 1 octave, hence the progression iterated five times goes back to the original starting tone, i.e. F. This is alike Giant Steps, but it's ascending rahter than descending, and features division by 5 rather than by 3; in particular, it cannot be carried out in 12edo, since 12 is not divisible by 5.
The first 256 digits of the Golden Ratio φ=1/2*(51/2+1) rendered as sounds in the following way:
We present the first movement from Beethoven's Moonlight Sonata, arranged for baroque oboe, clavichord, bassoon, viola da gamba, sackbut. Tuning is Rameau Tempérament Ordinaire, generated by 7 meantone fifths (as large as 697 ¢) and five sharp fifths (as large as 704.2 ¢), then rounded to integer values. The Scala file of the tuning is: 101.0 194.0 295.0 388.0 496.0 596.0 697.0 798.0 891.0 992.0 1092.0 2/1.
This is Mozart's Gigue KV 574, arranged for harpsichord (midi rendition) and tuned into Golden Meantone, the meantone system defined by setting the relation between the whole tone and diatonic semitone intervals to be the Golden Ratio φ=1/2*(51/2+1)≈1.6180… This makes the Golden fifth exactly (8−φ)/11 octaves, or (9600−1200φ)/11 cents, approximately 696.214 cents. This in turn implies that the ratio between the diatonic semitone and the chromatic semitone is the Golden Ratio as well.