Porcupine temperament modal harmony: Difference between revisions
→The Porcupine[7] MOS: clarify when tonic is half diminished vs fully diminished |
→Single-alteration MODMOS's: cleaned up explanation somewhat, corrected one of the modes' names, added clarification about half diminished |
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Porcupine remains the "best" such temperament even if the maximum error is relaxed somewhat, until eventually being superceded by [[mavila]] temperament, which is simpler but much less accurate than porcupine temperament (using standard harmonic timbres). | Porcupine remains the "best" such temperament even if the maximum error is relaxed somewhat, until eventually being superceded by [[mavila]] temperament, which is simpler but much less accurate than porcupine temperament (using standard harmonic timbres). | ||
=Brief Intro to Modal Harmony and MODMOSes= | =Brief Intro to Modal Harmony and MODMOSes= | ||
Porcupine is a temperament completely capable of diverse harmony. Using it's MOS in conjunction with its modmos will allow for some very diverse chordal movement that will still be tonally solid | Porcupine is a temperament completely capable of diverse harmony. Using it's MOS in conjunction with its modmos will allow for some very diverse chordal movement that will still be tonally solid. | ||
Because the generator of porcupine is simultaneously 10/9, 11/10, and 12/11, a chord made up of consecutive generators approximates 9:10:11:12; since -6 generators approximates 9/8, the chord 8:9:10:11:12 can be approximated by a series of consecutive 2nds in the 7-note MOS. William Lynch considers varying subsets of 8:9:10:11:12 to work really well for building harmonic movement in porcupine. In addition, the second inversion which produces chords of stacked sevenths of varying sizes, also works well as an additional sonority to create better voice leading and variety. If the mode position of porcupine contains no 3/2 from the root, then a chord without 3/2 is played on the root. | Because the generator of porcupine is simultaneously 10/9, 11/10, and 12/11, a chord made up of consecutive generators approximates 9:10:11:12; since -6 generators approximates 9/8, the chord 8:9:10:11:12 can be approximated by a series of consecutive 2nds in the 7-note MOS. William Lynch considers varying subsets of 8:9:10:11:12 to work really well for building harmonic movement in porcupine. In addition, the second inversion which produces chords of stacked sevenths of varying sizes, also works well as an additional sonority to create better voice leading and variety. If the mode position of porcupine contains no 3/2 from the root, then a chord without 3/2 is played on the root. | ||
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The 7-note MOS of porcupine is great, but it lumps all the consonant chords together at one end of the scale (see below). It also fails to contain a complete 11-limit otonal hexad (4:5:6:7:9:11), even though porcupine is not excessively complex in the 11-limit. Thankfully, unlike in meantone[7] where the MODMOSs all reduce the number of consonant triads available, there are several MODMOSs of porcupine that contain an equal or greater number of consonant triads to the MOS (these are highlighted in blue text below). These MODMOSs also conveniently alter the distribution of triads within the scale, providing much-needed variety of possible chord progressions. Even better, some single-alteration MODMOSs make at least one full 11-limit hexad available, meaning 6 of the 7 notes of the scale can be sounded simultaneously and produce a consonant otonal harmony. The fact that porcupine temperament provides not just one 7-note scale but several that are equally-rich in harmonic resources makes it extremely fertile for modal harmony. | The 7-note MOS of porcupine is great, but it lumps all the consonant chords together at one end of the scale (see below). It also fails to contain a complete 11-limit otonal hexad (4:5:6:7:9:11), even though porcupine is not excessively complex in the 11-limit. Thankfully, unlike in meantone[7] where the MODMOSs all reduce the number of consonant triads available, there are several MODMOSs of porcupine that contain an equal or greater number of consonant triads to the MOS (these are highlighted in blue text below). These MODMOSs also conveniently alter the distribution of triads within the scale, providing much-needed variety of possible chord progressions. Even better, some single-alteration MODMOSs make at least one full 11-limit hexad available, meaning 6 of the 7 notes of the scale can be sounded simultaneously and produce a consonant otonal harmony. The fact that porcupine temperament provides not just one 7-note scale but several that are equally-rich in harmonic resources makes it extremely fertile for modal harmony. | ||
=Porcupine[7] and its MODMOSs= | |||
The below mode names are given in [[Modal UDP Notation|UDP notation]]. For porcupine[7], the bright generator is the 9/5, or the 11/6 if you prefer. All generators below refer to this generator, NOT the 10/9 one. For an explanation of the spellings, see [[Porcupine Notation]]. | |||
The | The functional names are pretty straightforward: there are two major modes, one bright and one dark (differing in the second scale degree), two similarly-named minor modes (differing in the fourth scale degree), and then three modes with a diminished triad on the tonic (differing in the sixth and seventh scale degrees). The brightest two of these diminished modes both have a half-diminished tetrad on the tonic, and so they are named the bright and dark half-diminished modes, whereas the darkest has a fully diminished (or [[magical seventh chord|magical seventh]] tetrad) instead. These are sometimes just written bright/dark diminished and magical seventh modes when clear. | ||
William Lynch proposed the fun idea of naming modes of porcupine by various animal names, which are listed as "William's Name" below. | === William Lynch's System === | ||
William Lynch proposed the fun idea of naming modes and MODMOS's of porcupine by various animal names, which are listed as "William's Name" below. He has named these scales as such as he views none of them to be remotely similar to any existing mode name from anywhere. The initial four modes: Porcupine, Chinchilla, Zebra, and Dingo all contain 3/2 from the root while the latter three: Gazelle, Lemur, and Panda lack 3/2 and instead have a triad similar to a diminished triad on the root. In order to remedy this problem, it may be fruitful to use other methods than triadic tertian harmony to build tonal frameworks in porcupine. | |||
The scale's nominals can be named by the normal 7-tone alphabet starting on G. This has become somewhat of a standard. Some feel however that given Superpyth uses the same nominals in a contrasting way, it may be beneficial to use an entirely different set of letters for Porcupine. William Lynch's suggestion involves using the old-English alphabet, allowing for both porcupine[8] and porcupine[7] to be notated by leaving out "ð" from the scale. | The scale's nominals can be named by the normal 7-tone alphabet starting on G. This has become somewhat of a standard. Some feel however that given Superpyth uses the same nominals in a contrasting way, it may be beneficial to use an entirely different set of letters for Porcupine. William Lynch's suggestion involves using the old-English alphabet, allowing for both porcupine[8] and porcupine[7] to be notated by leaving out "ð" from the scale. | ||
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{| class="wikitable" | {| class="wikitable" | ||
|- | |- | ||
! | Functional | ! | Functional Name | ||
! | William's Name (repltiles) | ! | William's Name (repltiles) | ||
! style="text-align:center;" | 22edo Steps | ! style="text-align:center;" | 22edo Steps | ||
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and suggests it as a candidate for "default major" | and suggests it as a candidate for "default major" | ||
|- | |- | ||
| | |Dark (half-)diminished v2 | ||
| | Crocodile | | | Crocodile | ||
| style="text-align:center;" | 2433343 | | style="text-align:center;" | 2433343 | ||
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| style="text-align:center;" | | | style="text-align:center;" | | ||
|- | |- | ||
| | |Magical seventh v3 | ||
| | Turtle | | | Turtle | ||
| style="text-align:center;" | 3243334 | | style="text-align:center;" | 3243334 | ||
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Major with major IV chord | Major with major IV chord | ||
|- | |- | ||
|Symmetric diminished | |Symmetric half-diminished | ||
| | Llama | | | Llama | ||
| style="text-align:center;" | 3342433 | | style="text-align:center;" | 3342433 | ||
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and suggest it as a candidate for default "minor" | and suggest it as a candidate for default "minor" | ||
|- | |- | ||
|Bright diminished ^3 | |Bright (half-)diminished ^3 | ||
| | Cheetian | | | Cheetian | ||
| style="text-align:center;" | 3423433 | | style="text-align:center;" | 3423433 | ||
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| style="text-align:center;" | | | style="text-align:center;" | | ||
|- | |- | ||
|Dark diminished ^4 | |Dark (half-)diminished ^4 | ||
| | Jaguarian | | | Jaguarian | ||
| style="text-align:center;" | 3342343 | | style="text-align:center;" | 3342343 | ||
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=Porcupine[8] and its MODMOS's= | =Porcupine[8] and its MODMOS's= | ||
All generators below refer to the porcupine[8] | All generators below refer to the porcupine[8] bright generator (the 10/9~11/10~whatever). | ||
Similarly to Porcupine[7], William Lynch has proposed naming the modes off of sea creatures, with Octopus being relevant to the number eight. | Similarly to Porcupine[7], William Lynch has proposed naming the modes off of sea creatures, with Octopus being relevant to the number eight. | ||
Functional mode names are proposed based on the 3-step triads, which may be augmented (~9:12:16), major (~3:4:5) or minor (~12:15:20). | Functional mode names are proposed based on the 3-step triads, which may be augmented (~9:12:16), major (~3:4:5) or minor (~12:15:20). However, it can also useful to look at a different functional system in which the octatonic MOS modes extend the heptatonic ones by adding one extra note. | ||
==The Porcupine[8] MOS== | ==The Porcupine[8] MOS== | ||