User:Ganaram inukshuk/Notes/TAMNAMS
This is a subpage for TAMNAMS-related notes, containing various proposals of varying degrees of usefulness and other useful things. This also contains rewrites of sections of the main TAMNAMS page that aren't quite ready to be deployed.
Proposed terminology
- Mosperiod - the period in which the step pattern for a mos repeats. For single-period scales, the mosperiod is the same as the mosoctave, but for multi-period scales, the mosperiod will repeat more than once. Mosperiod intervals are perfect, as are their scale degrees.
- Moscomplement - the octave-complement, or possibly equave-complement, for a mos interval.
- Mosgenerator - the term can be used to refer to a mosstep interval that is the mos's generators. By default, this term should refer to the bright generator, but the terms bright mosgenerator and dark mosgenerator can be used for clarification.
Sandboxed section: Naming mos modes
The easiest way to name the modes of a mos, without having to memorize any names, is to refer to them by their UDP, which refers to how many generators are stacked above and below the tonic to produce a mode of the mos.
This section's running example is 5L 3s, whose brightest mode is LLsLLsLs.
Modifications to UDP notation
Normal UDP notation is described below:
- For single-period mosses, the UDP is notated as u|d, where u is the number of bright generators stacked above the tonic, d is the number of bright generators stacked below the tonic, and "|" is pronounced as "pipe". The full name of a mos's mode is xL ys u|d.
- For multi-period mosses with p periods, the UDP of is notated as up|dp(p). Since there are generators being stacked above and below every mosperiod - not just the tonic - there are in total u times p and d times p generators being stacked above and below their respective starting pitches. The full name in this case is xL ys up|dp(p).
To make notation easier, TAMNAMS makes the following modifications to UDP notation:
- The UDP for multi-period mosses may be written as u|d(p) rather than up|dp(p). This is because the period already appears in both the quantity of bright (u times p) and dark (d times p) generators, and omitting the p term makes the notation less redundant. In contexts where it doesn't cause confusion, the notation can be simplified further to u|d.
- The UDP for a mode may be shortened to "u|" under the reasoning of omitting the d term makes the notation less redundant. For example, "5L 3s 5|", which refers to LsLLsLLs, is read as "5 ell 3 ess 5 pipe".
- The shortened notation of "u|" is sufficient in most cases, but in situations where it makes more sense to think in terms of the dark generator, such as with a mos whose dark generator is the bright generator of a related mos, the notation is instead "|d".
In any case, the name of a mos can be substituted for its xL ys form.
Finding mos modes
Rotating the sequence of steps - that is, moving the step at the beginning to the end - produces a different mode. This can be repeated until the initial mode that was started with is produced.
This rotation process usually returns the modes in rotational order, not by brightness. To get the modes in order by brightness, first produce every interval for each mode, starting at the mosunison and ending at the mosoctave. This produces an interval matrix. The brightest mode will be the mode that has all of its intervals - excluding the mosunison, mosoctave, and mosperiods if multi-period - in its large size. The 2nd-brightest mode will have one interval in its small size - for multi-period mosses, one interval is in its small size for every instance of the mosperiod - and so on. The darkest mode will have all of its intervals in its small size. A much faster way to do this process is by sorting the modes produced this way in alphabetical order, effectively sorting all modes by decreasing brightness.
Using simplified notation as described in the previous section, for a mode with n pitches (or n pitches per period), the UDP for the modes sorted by brightness are (n-1)|0, (n-2)|1, and so on to 0|(n-1), which may be shortened to (n-1)|, (n-2)|, and so on to 0|. The table below shows the modes produced rotationally, and can be sorted by UDP.
| Mode | Rotational order | UDP | mosunison | 1-mosstep | 2-mosstep | 3-mosstep | 4-mosstep | 5-mosstep | 6-mosstep | 7-mosstep | mosoctave |
|---|---|---|---|---|---|---|---|---|---|---|---|
| LLsLLsLs | 0 | 7|0 | 0 (perfect) | L (major) | 2L (major) | 2L+s (perfect) | 3L+s (major) | 4L+s (augmented) | 4L+2s (major) | 5L+2s (major) | 5L+3s (perfect) |
| LsLLsLsL | 1 | 4|3 | 0 (perfect) | L (major) | L+s (minor) | 2L+s (perfect) | 3L+s (major) | 3L+2s (perfect) | 4L+2s (major) | 4L+3s (minor) | 5L+3s (perfect) |
| sLLsLsLL | 2 | 1|6 | 0 (perfect) | s (minor) | L+s (minor) | 2L+s (perfect) | 2L+2s (minor) | 3L+2s (perfect) | 3L+3s (minor) | 4L+3s (minor) | 5L+3s (perfect) |
| LLsLsLLs | 3 | 6|1 | 0 (perfect) | L (major) | 2L (major) | 2L+s (perfect) | 3L+s (major) | 3L+2s (perfect) | 4L+2s (major) | 5L+2s (major) | 5L+3s (perfect) |
| LsLsLLsL | 4 | 3|4 | 0 (perfect) | L (major) | L+s (minor) | 2L+s (perfect) | 2L+2s (minor) | 3L+2s (perfect) | 4L+2s (major) | 4L+3s (minor) | 5L+3s (perfect) |
| sLsLLsLL | 5 | 0|7 | 0 (perfect) | s (minor) | L+s (minor) | L+2s (diminished) | 2L+2s (minor) | 3L+2s (perfect) | 3L+3s (minor) | 4L+3s (minor) | 5L+3s (perfect) |
| LsLLsLLs | 6 | 5|2 | 0 (perfect) | L (major) | L+s (minor) | 2L+s (perfect) | 3L+s (major) | 3L+2s (perfect) | 4L+2s (major) | 5L+2s (major) | 5L+3s (perfect) |
| sLLsLLsL | 7 | 2|5 | 0 (perfect) | s (minor) | L+s (minor) | 2L+s (perfect) | 2L+2s (minor) | 3L+2s (perfect) | 4L+2s (major) | 4L+3s (minor) | 5L+3s (perfect) |
Since multi-period mosses repeats every period rather than at every octave, the number of modes corresponds to the number of pitches in the period. As a result, multi-period mosses always have fewer modes. An example is shown for 3L 6s, with modified UDPs as described in the previous section.
| Mode | Mode name | Simplified UDP | Rotational order | mosunison | 1-mosstep | 2-mosstep | 3-mosstep | 4-mosstep | 5-mosstep | 6-mosstep | 7-mosstep | 8-mosstep | mosoctave |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| LssLssLss | 3L 6s 6| | 2|0 | 0 | 0 (perfect) | L (augmented) | L+s (perfect) | L+2s (perfect) | 2L+2s (augmented) | 2L+3s (perfect) | 2L+4s (perfect) | 3L+4s (augmented) | 3L+5s (perfect) | 3L+6s (perfect) |
| sLssLssLs | 3L 6s 3| | 1|1 | 2 | 0 (perfect) | s (perfect) | L+s (perfect) | L+2s (perfect) | L+3s (perfect) | 2L+3s (perfect) | 2L+4s (perfect) | 2L+5s (perfect) | 3L+5s (perfect) | 3L+6s (perfect) |
| ssLssLssL | 3L 6s 0| | 0|2 | 1 | 0 (perfect) | s (perfect) | 2s (diminished) | L+2s (perfect) | L+3s (perfect) | L+4s (diminished) | 2L+4s (perfect) | 2L+5s (perfect) | 2L+6s (diminished) | 3L+6s (perfect) |
To denote alterations to a mode, we can use any accidental alteration whose meaning is clear. For non-diatonic mosses, the degree modified is indicated using TAMNAMS's 0-indexing convention. For example, LsLsLLLs can be written "5L 3s 5| @4d" (read "5L 3s 5 pipe at-4-degree"), using the @ accidental from diamond-mos notation.
Named mos modes
Many people, or groups of people, who have described individual mosses have independently came up with names for the mos's modes. The mosses listed below have named mos modes on their respective pages. (todo: add links)
- 5-note mosses: 4L 1s
- 7-note mosses: 1L 6s, 2L 5s, 3L 4s, 4L 3s, 5L 2s, and 6L 1s
- 8-note mosses: 3L 5s, 5L 3s, and 7L 1s
- 9-note mosses: 5L 4s and 7L 2s
- 10-note mosses: 3L 7s
For mossess that no such mode names but a less mathematical name is desired, genchain mode numbering may be used, producing 1st xL ys, 2nd xL ys, and so on.
Sandboxed rewrite: Naming mos intervals and mos degrees
Already deployed on main TAMNAMS page: TAMNAMS#Naming mos intervals
Complements of intervals
The octave complement (or moscomplement, or complement) of a mos interval follows the same logic as the octave complement in regular music theory: in general, for a mos with n pitches, a k-mosstep in its large form has a complement of an (n-k)-mosstep in its small form, and the two intervals are complements of one another. If a mos interval is altered by raising it by some number of chromas, its complement will be lowered by the same number of chromas.
Alternatively, if a specific mos interval is thought of as a quantity of large and small steps, then its complement is the number of steps needed to produce the mos pattern of xL ys itself.
| Interval | Complement | ||
|---|---|---|---|
| Name | Size | Name | Size |
| Perfect 0-mosstep (mosunison) | 0 | Perfect 7-mosstep (mosoctave) | 3L+4s |
| Major 1-mosstep | L | Minor 6-mosstep | 2L+4s |
| Perfect 2-mosstep | L+s | Diminished 5-mosstep | 2L+3s |
| Major 3-mosstep | 2L+s | Minor 4-mosstep | 1L+3s |
| Major 4-mosstep | 2L+2s | Minor 3-mosstep | 1L+2s |
| Augmented 5-mosstep | 3L+2s | Perfect 2-mosstep | 2s |
| Major 6-mosstep | 3L+3s | Minor 1-mosstep | s |
| Perfect 7-mosstep (mosoctave) | 3L+4s | Perfect 0-mosstep (mosunison) | 0 |
Other sandboxed rewrites
Reasoning for names
See: TAMNAMS#Reasoning for the names
The goal of TAMNAMS mos names is to choose memorable but aesthetically neutral names.
Names for small mosses
All names for single-period mosses (mosses of the form xL ys where x and y are coprime) with no more than 5 notes require that some small integer multiple of the period is equal to an octave or a tempered octave, under the reasoning that these mosses are common and broad enough that they may be of interest in non-octave contexts. As such, the names for these mosses are chosen to be extremely general to avoid bias and to avoid being too flavorful, and to allow these names to be reused for such non-octave contexts.
The names of monowood and biwood, for 1L 1s and 2L 2s respectively, requires that an equivalence interval be an octave, whereas the name trivial, also referring to 1L 1s, is equave-agnostic and may be used for non-octave contexts.
Names for multi-period mosses
Multi-period mosses (mosses of the form xL ys where x and y have a greatest common factor of 2 or greater) are given unique names that do not depend on the name of a smaller, octave-specific mos. The inclusion of such mos names was for completeness, which prompted reconsiderations on how these mosses were named. These mosses were formerly named using names that were octave-specific, producing former names such as "antidimanic" and "dipentic".
Names based on a temperament
All names ending in -oid refer to an exotemperament which, when including extreme tunings, covers the entire range of the corresponding octave-period mos, such that many edos with simple step ratios for that mos will correspond to valid tunings, if not by patent val, then with a small number of warts.
Former names like "orwelloid" and "sensoid" were abandoned because the names were too temperament-specific in the sense that even considering extreme tunings didn't cover the whole range of the mos. The remaining temperament-based names have been abstracted or altered heavily, namely "pine", "hyrulic", "jaric", "ekic" and "lemon".
Names for 1L ns mosses
Mosses of the form 1L ns were originally left unnamed as the range for their generator was too broad and such mosses were considered better analyzed as subsets of its (n+1)L 1s mos. An example of this is 1L 6s and 7L 1s, a pair of mosses that are commonly associated with porcupine temperament.
Although the tuning range is very unhelpful for knowing what such mosses will sound like, it is nonetheless useful for describing structure in situations where one does not want to use the mathematical name of 1L ns, especially given that in such situations the tuning will likely be specified somewhere already, hence the inclusion of these mos names.
This inclusion also affected the names of multi-period mosses. Jaric and taric specifically were chosen over bipedal and bimanual because of this, and to a lesser extent, lemon and lime were chosen over antibipentic and bipentic respectively (with their parent mos of 4L 2s named citric for consistency).
The anti- prefix vs the an- prefix for naming 1L ns mosses
The distinction between using the prefixes "anti-" vs "an-" for reversing the number of large vs. small steps is not as trivial as it may sound.
In the case of mosses with six or more notes, as the period is always an octave, there is a very large tuning range for the 1L ns mosses (hence their original omission), but the "anti-" prefix shows that what is significant is that it has the opposite structure to the corresponding nL 1s mos while pointing out the resulting ambiguity of range.
In the case of mosses with five or fewer notes, as the period is not known and therefore could be very small, this is not as much of a concern as fuller specification is likely required anyway, especially in the case of larger periods, so the name should not be tediously long as the name refers to a very simple mos pattern, and for related reasons, the name shouldn't give as much of a sense of one 'orientation' of the structure being more 'primary' than the other, while with mosses with more than five notes, this suggestion of sense is very much intended, because it will almost always make more sense to talk about the (n+1)L 1s child mos of whatever 1L ns mos you want to speak of.
Names for mosses with more than 10 notes
The scope of TAMNAMS name is to give mosses with small note count a notable name. To keep the number of names controlled, only mosses with no more than 10 notes are named. As a result, the names of mosses with 11 and 12 notes were abandoned, notably the names kleistonic, suprasmitonic, m-chromatic, and p-chromatic.
Step ratio spectrum visualization
I wanted to make a table that better visualizes the step ratio ranges as described by TAMNAMS.
Central spectrum
| Central spectrum of step ratios | |||||
|---|---|---|---|---|---|
| Intermediate ranges | Specific step ratios | Notes | |||
| 1:1 (equalized) | Trivial/pathological | ||||
| 1:1 to 1:0 | 1:1 to 2:1 | 1:1 to 3:2 | 1:1 to 4:3 (ultrasoft) | Step ratios especially close to 1:1 may be called pseudoequalized | |
| 4:3 (supersoft) | |||||
| 4:3 to 3:2 (parasoft) | |||||
| 3:2 (soft) | Also called monosoft | ||||
| 3:2 to 2:1 (hyposoft) | 3:2 to 5:3 (quasisoft) | ||||
| 5:3 (semisoft) | |||||
| 5:3 to 2:1 (minisoft) | |||||
| 2:1 (basic) | Also called quintessential | ||||
| 2:1 to 1:0 | 2:1 to 3:1 (hypohard) | 2:1 to 5:2 (minihard) | |||
| 5:2 (semihard) | |||||
| 5:2 to 3:1 (quasihard) | |||||
| 3:1 (hard) | Also called monohard | ||||
| 3:1 to 1:0 | 3:1 to 4:1 (parahard) | ||||
| 4:1 (superhard) | |||||
| 4:1 to 1:0 (ultrahard) | Step ratios especially close to 1:0 may be called pseudocollapsed | ||||
| 1:0 (collapsed) | Trivial/pathological | ||||
Extended spectrum
| Extended spectrum of step ratios | |||||||
|---|---|---|---|---|---|---|---|
| Central ranges | Extended ranges | Specific step ratios | Notes | ||||
| 1:1 (equalized) | Trivial/pathological | ||||||
| 1:1 to 1:0 | 1:1 to 2:1 | 1:1 to 3:2 | 1:1 to 4:3 (ultrasoft) | 1:1 to 6:5 (pseudoequalized) | |||
| 6:5 (semiequalized) | |||||||
| 6:5 to 4:3 (ultrasoft) | |||||||
| 4:3 (supersoft) | Nonextreme range, as detailed by central spectrum | ||||||
| 4:3 to 3:2 (parasoft) | 4:3 to 3:2 (parasoft) | ||||||
| 3:2 (soft) | |||||||
| 3:2 to 2:1 (hyposoft) | 3:2 to 5:3 (quasisoft) | 3:2 to 5:3 (quasisoft) | |||||
| 5:3 (semisoft) | |||||||
| 5:3 to 2:1 (minisoft) | 5:3 to 2:1 (minisoft) | ||||||
| 2:1 (basic) | |||||||
| 2:1 to 1:0 | 2:1 to 3:1 (hypohard) | 2:1 to 5:2 (minihard) | 2:1 to 5:2 (minihard) | ||||
| 5:2 (semihard) | |||||||
| 5:2 to 3:1 (quasihard) | 5:2 to 3:1 (quasihard) | ||||||
| 3:1 (hard) | |||||||
| 3:1 to 1:0 | 3:1 to 4:1 (parahard) | 3:1 to 4:1 (parahard) | |||||
| 4:1 (superhard) | |||||||
| 4:1 to 1:0 (ultrahard) | 4:1 to 10:1 (ultrahard) | 4:1 to 6:1 (hyperhard) | |||||
| 6:1 (extrahard) | |||||||
| 6:1 to 10:1 (clustered) | |||||||
| 10:1 (semicollapsed) | |||||||
| 10:1 to 1:0 (pseudocollapsed) | |||||||
| 1:0 (collapsed) | Trivial/pathological | ||||||
Original table of extended TAMNAMS names (archived)
This is an attempt to describe various mosses that I feel are worth describing, based on experimenting with these scales or for completion. This contains unofficial scale names that try to be as close to existing names as possible and are not meant to be official or standard. The following table shows single-period mosses sorted by generation rather than note count. As of August 2022, much of this section is rendered unnecessary due to TAMNAMS names being reorganized and many scales being renamed, hence this section is kept for archival purposes.
Extended names are denoted with an asterisk. Named 1L ns (monolarge) scales are denoted using italics and are based on its sister scale with the anti- prefix added.
| Mos Family Tree (single-period only), with TAMNAMS Names and extended names | |||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|
| Progenitor scale | 1st-order child mosses | 2nd-order child mosses | 3rd-order child mosses | 4th-order child mosses | 5th-order child mosses | ||||||
| Steps | Scale name | Steps | Scale name | Steps | Scale name | Steps | Scale name | Steps | Scale name | Steps | Scale name |
| 1L 1s | prototonic*
(currently monowood and trivial) |
1L 2s | antideuteric*
(currently antrial) |
1L 3s | antitetric*
(currently antetric) |
1L 4s | antimanic
(currently pedal) |
1L 5s | antimachinoid*
(currently antimachinoid) |
1L 6s | anti-archeotonic
(currently onyx) |
| 6L 1s | archeotonic | ||||||||||
| 5L 1s | machinoid | 5L 6s | |||||||||
| 6L 5s | |||||||||||
| 4L 1s | manual
(formerly manic) |
4L 5s | gramitonic
(formerly orwelloid) |
4L 9s | |||||||
| 9L 4s | |||||||||||
| 5L 4s | semiquartal | 5L 9s | |||||||||
| 9L 5s | |||||||||||
| 3L 1s | tetric | 3L 4s | mosh | 3L 7s | sephiroid | 3L 10s | |||||
| 10L 3s | |||||||||||
| 7L 3s | dicoid
(formerly dicotonic) |
7L 10s | |||||||||
| 10L 7s | |||||||||||
| 4L 3s | smitonic | 4L 7s | (formerly kleistonic) | 4L 11s | |||||||
| 11L 4s | |||||||||||
| 7L 4s | (formerly suprasmitonic) | 7L 11s | |||||||||
| 11L 7s | |||||||||||
| 2L 1s | deuteric*
(currently trial) |
2L 3s | pentic | 2L 5s | antidiatonic | 2L 7s | balzano
(formerly joanatonic) |
2L 9s | |||
| 9L 2s | |||||||||||
| 7L 2s | superdiatonic | 7L 9s | |||||||||
| 9L 7s | |||||||||||
| 5L 2s | diatonic | 5L 7s | (formerly p-chromatic) | 5L 12s | s-enharmonic* | ||||||
| 12L 5s | p-enharmonic* | ||||||||||
| 7L 5s | (formerly m-chromatic) | 7L 12s | f-enharmonic* | ||||||||
| 12L 7s | m-enharmonic* | ||||||||||
| 3L 2s | antipentic | 3L 5s | checkertonic
(formerly sensoid) |
3L 8s | 3L 11s | ||||||
| 11L 3s | |||||||||||
| 8L 3s | 8L 11s | ||||||||||
| 11L 8s | |||||||||||
| 5L 3s | oneirotonic | 5L 8s | 5L 13s | ||||||||
| 13L 5s | |||||||||||
| 8L 5s | 8L 13s | ||||||||||
| 13L 8 | |||||||||||
Extended mos pattern names (fewer than 5 steps, archived)
As of August 14, 2022, all of these scales have been named. These descriptions are kept for archival purposes.
| Parent scale | 1st-order child scales | 2nd-order child scales | |||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|
| Steps | Originally proposed name | Current name | Notes | Steps | Originally proposed name | Current name | Notes | Steps | Originally proposed name | Current name | Notes |
| 1L 1s | prototonic, protic, or monowood | monowood and trivial | The progenitor scale of all single-period mosses.
Despite being a monolarge scale, it's also its own sister and is named regardless. The current name "monowood" comes from nL ns scales (such as pentawood for 5L 5s), and is used as a base for such scales. The name trivial comes from the fact that this is a trivial (octave-equivalent) scale, consisting of only its generators. |
1L 2s | antideuterotonic or antideuteric | antrial | One of the child scales of 1L 1s.
Being a monolarge scale, tetric (3L 1s) may be more worth considering as a parent scale. |
1L 3s | antitetric | antetric | Monolarge scale. Similarly to 3L 1s with 1L 2s, 4L 1s may be worth considering as a parent scale. |
| 3L 1s | tetric | tetric | Parent scale to orwelloid (now gramitonic) and semiquartal, the name tetric is assigned similarly to pentic being the parent of diatonic and antidiatonic. | ||||||||
| 2L 1s | deuterotonic or deuteric | trial | One of the child scales of 1L 1s. | 2L 3s | - | pentic | Already established name. | ||||
| 3L 2s | - | antipentic | Already established name. | ||||||||
Proposal: Naming mosses with more than 10 steps (work-in-progress)
This is a system for describing scales beyond the set of named TAMNAMS scales. Both User:Frostburn (User:Frostburn/TAMNAMS Extension) and I have similar systems, with the main difference here being that mosses are technically not limited to being only three generations away.
Naming mosdescendants up to 3 generations
Although naming scales beyond the current cap of 10 notes is antithetical to the purpose of TAMNAMS, names for mosses greater than 10 notes can be made systematically using existing names. The rules are described as such:
- If the scale is the child of a named parent scale, then the scale is moschromatic.
- If the scale is the grandchild of a named parent scale, then the scale is mosenharmonic.
- If the scale is the great-grandchild of a named parent scale, then the scale is mosschismic. (tentative name; schismic refers to a family of temperaments; open to better name suggestions)
- If the scale is more than 3 generations from a named parent scale, or if referring to a scale regardless of number of generations from the parent, then the scale is a mosdescendant scale.
For describing the scales of a named mos, the prefix of mos- is removed and replaced with the mos's prefix instead. For example, the child, grandchild, and great-grandchild scales for the mos 5L 3s (oneirotonic, prefix oneiro-) are oneirochromatic, oneiroenharmonic, and oneiroschismic respectively, and the entire family of mosses related to oneirotonic are oneirodescendants.
Additionally, the lack of a prefix will specifically describe the descendant scales of 5L 2s: chromatic, enharmonic, and schismic. Descendants of 5L 2s are referred to as "diatonic descendants" rather than "descendants".
Single-letter prefixes for these names are optional, as the single-letter prefixes are meant for specificity. With no prefix specified, moschromatic refers to one of two child scales, mosenharmonic refers to one of four grandchild scales, and mosschismic refers to one of eight great-grandchild scales. The table below shows those prefixes and the mosdescendants for which they apply, as well as the step ratio of the parent mos needed to reach these scales.
| Parent scale | Moschromatic (child) scales | Mosenharmonic (grandchild) scales | Mosschismic (great-grandchild) scales | |||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Steps | Step ratio | Steps | Specific name | Step ratio of parent | Steps | Specific name | Step ratio of grandparent | Steps | Specific name | Step ratio of great-grandparent | ||||
| General range | Step ratio for 2:1 | General range | For L:s = 2:1 | General range | For L:s = 2:1 | General range | For L:s = 2:1 | |||||||
| xL ys | 1:1 to 1:0 | 2:1 (basic) | (x+y)L xs | m-moschromatic | 1:1 to 2:1 | 3:2 (soft) | (x+y)L (2x+y)s | f-mosenharmonic | 1:1 to 3:2 | 4:3 (supersoft) | (x+y)L (3x+2y)s | f-mosschismic | 1:1 to 4:3 (ultrasoft) | 5:4 |
| (3x+2y)L (x+y)s | a-mosschismic | 4:3 to 3:2 (parasoft) | 7:5 | |||||||||||
| (2x+y)L (x+y)s | m-mosenharmonic | 3:2 to 2:1 (hyposoft) | 5:3 (semisoft) | (3x+2y)L (2x+y)s | u-mosschismic | 3:2 to 5:3 (quasisoft) | 8:5 | |||||||
| (2x+y)L (3x+2y)s | m-mosschismic | 5:3 to 2:1 (minisoft) | 7:4 | |||||||||||
| xL (x+y)s | p-moschromatic | 2:1 to 1:0 | 3:1 (hard) | (2x+y)L xs | p-mosenharmonic | 2:1 to 3:1 (hypohard) | 5:2 (semihard) | (2x+y)L (3x+y)s | p-mosschismic | 2:1 to 5:2 (minihard) | 7:3 | |||
| (3x+y)L (2x+y)s | q-mosschismic | 5:2 to 3:1 (quasihard) | 8:3 | |||||||||||
| xL (2x+y)s | s-mosenharmonic | 3:1 to 1:0 | 4:1 (superhard) | (3x+y)L xs | r-mosschismic | 3:1 to 4:1 (parahard) | 7:2 | |||||||
| xL (3x+y)s | s-mosschismic | 4:1 to 1:0 (ultrahard) | 5:1 | |||||||||||
| Parent scale | Moschromatic scales | Mosenharmonic scales | Mosschismic scales | |||
|---|---|---|---|---|---|---|
| Steps | Steps | Specific name | Steps | Specific name | Steps | Specific name |
| xL ys | xL (x+y)s | p-moschromatic | xL (2x+y)s | s-mosenharmonic | xL (3x+y)s | s-mosschismic |
| (3x+y)L xs | r-mosschismic | |||||
| (2x+y)L xs | p-mosenharmonic | (2x+y)L (3x+y)s | p-mosschismic | |||
| (3x+y)L (2x+y)s | q-mosschismic | |||||
| (x+y)L xs | m-moschromatic | (x+y)L (2x+y)s | f-mosenharmonic | (x+y)L (3x+2y)s | f-mosschismic | |
| (3x+2y)L (x+y)s | a-mosschismic | |||||
| (2x+y)L (x+y)s | m-mosenharmonic | (2x+y)L (3x+2y)s | m-mosschismic | |||
| (3x+2y)L (2x+y)s | u-mosschismic | |||||
Mosdescendants for single-period mosses
Although it's possible for any mos to have mosdescendants named as described above, it's recommended that mosdescendant scale names should apply to mosses whose immediate child mosses exceed 10 steps. The following tables show which mosses, marked in bold, mosdescendant names can apply.
| Mos | Name | Mos | Name | Mos | Name | Mos | Name | Mos | Name | Mos | Name | Mos | Name | Mos | Name | Mos | Name |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 1L 1s | trivial | 1L 2s | antrial | 1L 3s | antetric | 1L 4s | pedal | 1L 5s | antimachinoid | 1L 6s | onyx | 1L 7s | antipine | 1L 8s | antisubneutralic | 1L 9s | antisinatonic (asina-) |
| 9L 1s | sinatonic (sina-) | ||||||||||||||||
| 8L 1s | subneutralic (blu-) | ||||||||||||||||
| 7L 1s | pine (pine-) | ||||||||||||||||
| 6L 1s | arch(a)eotonic (arch-) | ||||||||||||||||
| 5L 1s | machinoid (mech-) | ||||||||||||||||
| 4L 1s | manual | 5L 4s | semiquartal (chton-) | ||||||||||||||
| 4L 5s | gramitonic (gram-) | ||||||||||||||||
| 3L 1s | tetric | 4L 3s | smitonic (smi-) | ||||||||||||||
| 3L 4s | mosh | 7L 3s | dicoid/zaltertic (dico-/zal-) | ||||||||||||||
| 3L 7s | sephiroid (seph-) | ||||||||||||||||
| 2L 1s | trial | 3L 2s | antipentic | 3L 5s | checkertonic (check-) | ||||||||||||
| 5L 3s | oneirotonic (oneiro-) | ||||||||||||||||
| 2L 3s | pentic | 5L 2s | diatonic (no prefix) | ||||||||||||||
| 2L 5s | antidiatonic | 7L 2s | superdiatonic (arm-) | ||||||||||||||
| 2L 7s | balzano (bal-) | ||||||||||||||||
Mosdescendants for multi-period mosses
TAMNAMS has names for 2-period mosses up to 10 notes, and as such, mosdescendant names apply to mosses whose children have more than 10 notes: jaric, taric, ekic, lemon, and lime. Likewise, there are 3-period scales up to 9 notes, so mosdescendant names apply to tcherepnin and hyrulic, the only 3-period mosses named under TAMNAMS, apart from triwood.
| 2-period mosses | |||||||
|---|---|---|---|---|---|---|---|
| Mos | Name | Mos | Name | Mos | Name | Mos | Name |
| 2L 2s | biwood | 2L 4s | malic | 2L 6s | subaric | 2L 8s | jaric (jara-) |
| 8L 2s | taric (tara-) | ||||||
| 6L 2s | ekic (ek-) | ||||||
| 4L 2s | citric | 6L 4s | lemon (lem-) | ||||
| 4L 6s | lime (lime-) | ||||||
| 3-period mosses | |||||||
| Mos | Name | Mos | Name | ||||
| 3L 3s | triwood | 3L 6s | tcherepnin (cher-) | ||||
| 6L 3s | hyrulic (hyru-) | ||||||
Starting at 4 periods, mosdescendant names apply only to n-wood scales (tetrawood, pentawood, etc), where the names of mosdescendants are based on names for single-period mosses up to 5 notes rather than based on moschromatic, mosenharmonic, and mosschismic, and thereby limited to mosdescendants with 5n notes; any descendants after that are referred as to n-wood descendants.
Since the names for single-period mosses up to 5 notes may also be used for non-octave periods, these names are used for multi-period mosses, producing n-antrial, n-trial, n-antetric, n-tetric, n-antipentic, n-pentic, n-pedal, and n-manual. Note that there are only two named 3rd-generation mosses from nL ns rather than the usual eight; the missing six names (what would be n-smitonic, n-mosh, n-checkertonic, n-oneiorotonic, n-diatonic, and n-antidiatonic) are unsuitable for use for multi-period mos names as these names must refer to an octave period.
The table outlines possible names for n-wood descendants for tetrawood, pentawood, and, in the general case, n-wood. Numeric prefixes may be used for these names, rather than n-.
| 4-period mosses | ||||||||
|---|---|---|---|---|---|---|---|---|
| Mos | Name | Mos | Name | Mos | Name | Mos | Name | Other notes |
| 4L 4s | tetrawood | 4L 8s | quadantrial | 4L 12s | quadantetric | 4L 16s | tetrapedal | Some names have Latin prefixes for ease of spelling. |
| 16L 4s | tetramanual | |||||||
| 12L 4s | quadtetric | |||||||
| 8L 4s | quadtrial | 12L 8s | tetrantipentic | |||||
| 8L 12s | tetrapentic | |||||||
| 5-period mosses | ||||||||
| Mos | Name | Mos | Name | Mos | Name | Mos | Name | Other notes |
| 5L 5s | pentawood | 5L 10s | quinantrial | 5L 15s | quinantetric | 5L 20s | pentapedal | Some names have Latin prefixes for ease of spelling. |
| 20L 5s | pentamanual | |||||||
| 15L 5s | quintetric | |||||||
| 10L 5s | quintrial | 15L 10s | quinantipentic | |||||
| 10L 15s | quinpentic | |||||||
| n-period mosses | ||||||||
| Mos | Name | Mos | Name | Mos | Name | Mos | Name | Other notes |
| nL ns | n-wood | nL 2ns | n-antrial | nL 3ns | n-antetric | nL 4ns | n-pedal | A numeric prefix may be used instead, such as hexawood instead of 6-wood.
When in doubt, prefix names for n-period mosses with n-. |
| 4nL ns | n-manual | |||||||
| 3nL ns | n-tetric | |||||||
| 2nL ns | n-trial | 3nL 2ns | n-anpentic | |||||
| 2nL 3ns | n-pentic | |||||||
Naming mosdescendants beyond 3 generations
Each generation has twice as many mosdescendants as the last, so rather than try to name every possible descendant, mosdescendants more than 3 generations from a given parent mos may be referred to how many generations away it is. Mosschismic scales are 3rd mosdescendants, so after that are 4th-mosdescendants, 5th-mosdescendants, and so on. The algorithms below shows how to find how many generations away a mos xL ys is from another scale.
- For mosses with up to 3 periods: finding a parent mos zL ws for the mosdescendant xL ys, where x, y, z, and w share a greatest common factor that is no greater than 3:
- Let z and w be the number of large and small steps of the parent mos to be found. Assign to z and w the values x and y respectively. Let g = 0, where g is the number of generations away from zL ws.
- Let m1 be equal to max(z, w) and m2 be equal to min(z, w).
- Assign to z the value m2 and w the value m1-m2. Increment g by 1.
- If the sum of z and w is no more than 10, then the parent mos is zL ws and has a TAMNAMS name. If not, repeat the process starting at step 2.
- For mosses with 4 periods or more: finding how many generations away a mosdescendant xL ys is from its n-wood scale, where x and y have a greatest common factor of n that is 4 or greater:
- Let z and w be assigned the values x and y respectively. Let g = 0, where g is the number of generations away from nL ns.
- Let m1 be equal to max(z, w) and m2 be equal to min(z, w).
- Assign to z the value m2 and w the value m1-m2. Increment g by 1.
- If the sum of z and w is exactly 2n, then the mos nL ns is g generations away from xL ys. If not, repeat the process starting at step 2.
Naming mosdescendants for linearly growing scales (work-in-progress)
Some noteworthy mosdescendants may be more than 3 generations away, but may have the same number of large steps as a named parent mos. In such cases, the number of notes with each successive mosdescendant grows linearly, and these mosses may be assigned a letter to refer to a specific mosdescendant. Currently, this applies to mosdescendants whose parent mos has a step ratio that is along the extreme edges of the step ratio spectrum, around pseudoequalized and pseudocollapsed, producing nth s-mosdescendants and nth f-mosdescendants. The mos family tree better shows which mosses grow linearly, shown in bold, as the upper child of each node is always xL (x+y)s, which becomes of xL (nx+y)s over n generations.
| Parent scale | Moschromatic scales
(1st mosdescendants) |
Mosenharmonic scales
(2nd mosdescendants) |
Mosschismic scales
(3rd mosdescendants) |
4th-mosdescendant scales
(selected mosdescendants) |
5th-mosdescendant scales
(selected mosdescendants) |
nth-mosdescendant scales
(selected mosdescendants) | ||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Steps | Steps | Specific name | Steps | Specific name | Steps | Specific name | Steps | Specific name | Steps | Specific name | Steps | Specific name |
| xL ys | xL (x+y)s | p-moschromatic | xL (2x+y)s | s-mosenharmonic | xL (3x+y)s | s-mosschismic | xL (4x+y)s | 4th s-mosdescendant | xL (5x+y)s | 5th s-mosdescendant | xL (nx+y)s | nth s-mosdescendant |
| (3x+y)L xs | r-mosschismic | |||||||||||
| (2x+y)L xs | p-mosenharmonic | (2x+y)L (3x+y)s | p-mosschismic | (2x+y)L (5x+2y)s | 4th p-mosdescendant | (2x+y)L (7x+3y)s | 5th p-mosdescendant | |||||
| (3x+y)L (2x+y)s | q-mosschismic | |||||||||||
| (x+y)L xs | m-moschromatic | (x+y)L (2x+y)s | f-mosenharmonic | (x+y)L (3x+2y)s | f-mosschismic | (x+y)L (4x+3y)s | 4th f-mosdescendant | (x+y)L (5x+4y)s | 5th f-mosdescendant | (x+y)L (nx+(n-1)y)s | nth f-mosdescendant | |
| (3x+2y)L (x+y)s | a-mosschismic | |||||||||||
| (2x+y)L (x+y)s | m-mosenharmonic | (2x+y)L (3x+2y)s | m-mosschismic | (2x+y)L (5x+3y)s | 4th m-mosdescendant | (2x+y)L (7x+4y)s | 5th m-mosdescendant | |||||
| (3x+2y)L (2x+y)s | u-mosschismic | |||||||||||
| Parent scale | Moschromatic scales
(1st mosdescendants) |
Mosenharmonic scales
(2nd mosdescendants) |
Mosschismic scales
(3rd mosdescendants) |
nth-mosdescendant scales | |||||
|---|---|---|---|---|---|---|---|---|---|
| Steps | Steps | Specific name | Steps | Specific name | Steps | Specific name | Steps | Specific name | Step ratio of parent |
| xL ys | (x+y)L xs | m-moschromatic | (x+y)L (2x+y)s | f-mosenharmonic | (x+y)L (3x+2y)s | f-mosschismic | (x+y)L (nx+(n-1)y)s | nth f-mosdescendant | Softer than 5:4 |
| (3x+2y)L (x+y)s | a-mosschismic | ||||||||
| (2x+y)L (x+y)s | m-mosenharmonic | (3x+2y)L (2x+y)s | u-mosschismic | ||||||
| (2x+y)L (3x+2y)s | m-mosschismic | ||||||||
| xL (x+y)s | p-moschromatic | (2x+y)L xs | p-mosenharmonic | (2x+y)L (3x+y)s | p-mosschismic | ||||
| (3x+y)L (2x+y)s | q-mosschismic | ||||||||
| xL (2x+y)s | s-mosenharmonic | (3x+y)L xs | r-mosschismic | ||||||
| xL (3x+y)s | s-mosschismic | ||||||||
| xL (nx+y)s | nth s-mosdescendant | Harder than 5:1 | |||||||
Reasoning for names
The names for moschromatic scales are based on former names for the child scales for diatonic (5L 2s): p-chromatic (5L 7s) and m-chromatic (7L 5s). This was generalized to "chromatic" and "moschromatic", with the prefixes m- and p- for specificity. The names for mosenharmonic scales are based on discussions with xen Discord members for systematically naming the daughter and granddaughter scales of a mos, producing "enharmonic" and "mosenharmonic" with the prefixes f-, m-, p-, and s- for specificity.
Names for mosdescendants are thereby based on replacing the mos- prefix with that for a mos's TAMNAMS name. This effectively brings back the names of m-chromatic and p-chromatic, as TAMNAMS specifically names mosses up to 10 notes. This also names other mosses whose names were lost entirely, mainly kleistonic (4L 7s, now p-smichromatic) and suprasmitonic (7L 4s, now m-smichromatic), two names that were dropped because these mosses had more than 10 notes.
The reason why mosdescendants for mosses with 4 periods or greater are not based on their corresponding n-wood scale is because these mosses do not have any child mosses with 10 notes or fewer, and therefore have no named child mosses from which to build mosdescendant names. Rather, names for these mosdescendants are based on period-agnostic names (antrial, trial, antetric, tetric, etc) to reflect that these are scales based on duplicating a base mos multiple times within an octave.
The addition of mosschismic scales for great-grandchild scales was done for completeness, with the prefixes f-, a-, u-, m-, p- q-, r-, and s- for specificity (names not finalized). Note that mosschismic scales borrows the prefixes as mosenharmonic scales, which itself borrows those for mosenharmonic scales. The table below shows what prefixes are used for which generation of mosdescendants, with an added mnemonic for memorization.
| Prefix | For moschromatic scales | For mosenharmonic scales | For mosschismic scales | Mnemonic |
|---|---|---|---|---|
| f- | n/a | F for flat; f-mosenharmonic scales have a grandparent whose pitches are flatter compared to basic (L:s = 2:1). | F for flat. | FAUM sounds like foam, which sounds soft.
F-, a-, u-, and m-mosschismic scales generally have a great-grandparent with a soft step ratio. |
| a- | n/a | n/a | A from parasoft, as "P" is taken. | |
| u- | n/a | n/a | U from quasisoft, as "Q" is taken. | |
| m- | M for maybe/mellow; based on old name for 7L 5s | M- and p-mosenharmonic scales have a grandparent whose step ratio is close to the "midpoint" of L:s = 2:1. | M and P for midpoint. | |
| p- | P for pure/sharp; based on old name for 5L 7s | PQRS are four consecutive letters in the alphabet. It's hard to pronounce because there are no vowels.
P-, q-, r-, and s-mosschismic scales generally have a great-grandparent with a hard step ratio. | ||
| q- | n/a | n/a | Q and R are the only two letters between P and S. Q may stand for quasihard. | |
| r- | n/a | n/a | Q and R are the only two letters between P and S. R may stand for parahard. | |
| s- | n/a | S for sharp; s-mosenharmonic scales have a grandparent whose pitches are sharper compared to basic (L:s = 2:1). | "S" for sharp. |
Examples
| Diatonic scale | Chromatic scales | Enharmonic scales | Schismic scales | 4th diatonic descendants | ||||
|---|---|---|---|---|---|---|---|---|
| Steps | Name | Steps | Name | Steps | Name | Steps | Name | Steps |
| 5L 2s | diatonic | 7L 5s | m-chromatic | 7L 12s | f-enharmonic | 7L 19s | f-schismic | 7A 26B |
| 19L 7s | a-schismic | 19A 26B | ||||||
| 12L 7s | m-enharmonic | 19L 12s | u-schismic | 19A 31B | ||||
| 12L 19s | m-schismic | 12A 31B | ||||||
| 5L 7s | p-chromatic | 12L 5s | p-enharmonic | 12L 17s | p-schismic | 12A 29B | ||
| 17L 12s | q-schismic | 17A 29B | ||||||
| 5L 12s | s-enharmonic | 17L 5s | r-schismic | 17A 22B | ||||
| 5L 17s | s-schismic | 5A 22B | ||||||
| Oneirotonic scale | Oneirochromatic scales | Oneiroenharmonic scales | Oneiroschismic scales | 4th oneirodescendants | ||||
|---|---|---|---|---|---|---|---|---|
| Steps | Name | Steps | Name | Steps | Name | Steps | Name | Steps |
| 8L 5s | oneirotonic | 8L 5s | m-oneirochromatic | 8L 13s | f-oneiroenharmonic | 8L 21s | f-oneiroschismic | 8A 29B |
| 21L 8s | a-oneiroschismic | 21A 29B | ||||||
| 13L 8s | m-oneiroenharmonic | 21L 13s | u-oneiroschismic | 21A 34B | ||||
| 13L 21s | m-oneiroschismic | 13A 34B | ||||||
| 5L 8s | p-oneirochromatic | 13L 5s | p-oneiroenharmonic | 13L 18s | p-oneiroschismic | 13A 31B | ||
| 18L 13s | q-oneiroschismic | 18A 31B | ||||||
| 5L 13s | s-oneiroenharmonic | 18L 5s | r-oneiroschismic | 18A 23B | ||||
| 5L 18s | s-oneiroschismic | 5A 23B | ||||||
Notes and issues
- Interestingly, there is evidence that another Xen Discord user (user:Flirora) suggested the same naming system described here up to 3 generations, with only slight differences with 3rd-generation names. As I was part of a discussion on limiting TAMNAMS names to 10-note mosses, which facilitated naming mosdescendants up to two generations (mosenharmonic scales), rather than this earlier suggestion, it's possible that the same proposal for mosenharmonic scales may have been independently developed twice.
- Some names with this system are not finalized, particularly the term "mosschismic" and some of the single-letter prefixes.
- Better names than "mosschismic" include "mossubharmonic" (adapted from the above suggestion which had "prefix-sub-prefix-enharmonic") and "mossubchromatic", possibly shortened to "mossubchromic" (adapted from "subchromatic", as seen in this page).
- An issue with using letter-based prefixes is that many of them are based on temperaments. A temperament-agnostic interpretation will be needed if these letters are to be generalized outside of the diatonic family.
- Yet another issue is that the pattern of f-, m-, p-, and s-, all based on temperaments, does not continue with 3rd-generation mosses in that f- and s- are no longer at the extremes and p- is no longer at the midpoint (see table below). Either 3rd-generation mosses need a different set of prefixes, or a different set of prefixes are needed throughout.
- In the spirit of TAMNAMS being temperament-agnostic, a proper solution may be to not use and shoehorn temperament-suggestive prefixes, but rather use the names for step ratios. This lines up with Frostburn's proposal, but applies to the first three generations, not just the third. (Frostburn's proposed abbreviations may also work.) Under this system, all prefixes can work for all three generations, so soft-chromatic, hyposoft-chromatic, and minisoft-chromatic is allowed, just as soft-subchromatic, hyposoft-subchromatic, and minisoft-subchromatic. The absence of prefixes is also allowed.
- Hard and soft are preferred over sharp and flat, as those describe accidentals specific to diatonic notation. TAMNAMS and diamond-mos notation has generalized sharps and flats, called amps/ams and ats.
| Diatonic scale | Child scales | Grandchild scales | Great-grandchild scales | ||||
|---|---|---|---|---|---|---|---|
| Steps | Notable temperament(s) | Steps | Notable temperament(s) | Steps | Notable temperament(s) | Would-be prefix | |
| 5L 2s | 7L 5s | meantone | 7L 12s | flattone | 7L 19s | tridecimal | t- |
| 19L 7s | flattone | f- | |||||
| 12L 7s | meantone | 19L 12s | meanpop | m- | |||
| 12L 19s | huygens | h- | |||||
| 5L 7s | pythagorean | 12L 5s | pythagorean | 12L 17s | pythagorean | p- | |
| 17L 12s | gentle | g- | |||||
| 5L 12s | superpyth | 17L 5s | superpyth | s- | |||
| 5L 17s | ultrapyth | u- | |||||
| Diatonic scale | Child scales | Grandchild scales | Great-grandchild scales | ||||||
|---|---|---|---|---|---|---|---|---|---|
| Steps | Name based on step ratio | Possible abbrev. | Steps | Name based on step ratio | Possible abbrev. | Steps | Name based on step ratio | Possible abbrev. | |
| 5L 2s | 7L 5s | soft-chromatic | s-chromatic | 7L 12s | soft-enharmonic | s-enharmonic | 7L 19s | ultrasoft-subchromatic | us-subchromatic |
| 26edo | |||||||||
| 19L 7s | parasoft-subchromatic | ps-subchromatic | |||||||
| 19edo | |||||||||
| 12L 7s | hyposoft-enharmonic | hs-enharmonic | 19L 12s | quasisoft-subchromatic | qs-subchromatic | ||||
| 50edo | |||||||||
| 12L 19s | minisoft-subchromatic | ms-subchromatic | |||||||
| 12edo | equalized-chromatic | e-chromatic | |||||||
| 5L 7s | hard-chromatic | h-chromatic | 12L 5s | hypohard-enharmonic | hh-enharmonic | 12L 17s | minihard-subchromatic | mh-subchromatic | |
| 31edo | |||||||||
| 17L 12s | quasihard-subchromatic | qh-subchromatic | |||||||
| 17edo | |||||||||
| 5L 12s | hard-enharmonic | h-enharonic | 17L 5s | parahard-subchromatic | ph-subchromatic | ||||
| 39edo | |||||||||
| 5L 17s | ultrahard-subchromatic | uh-subchromatic | |||||||
Suggested changes for mos pattern names (work-in-progress)
This section describes changes to existing TAMNAMS names that I would make. Reasons:
- Some names are still based on a temperament (mainly the -oid names), so those are either replaced with a new name or at least altered so the references are more indirect.
- There were Discord users with whom I shared a similar sentiment regarding the names of certain scales, mainly the mosses with the anti- prefix and the scales antidiatonic and superdiatonic.
- Some names are too long (in my opinion).
The choice of names are not perfect and some may have issues. Some name suggestions went through different versions. This section is meant to start a discussion on alternate names should a need come up for it.
| Changes to names to reduce or remove references to temperaments | |||||||||
|---|---|---|---|---|---|---|---|---|---|
| Mos | Current name | Suggested name(s) | Old suggestions | Reasoning | Possible issues | ||||
| Name | Prefix | Abbrev. | Name | Prefix | Abbrev. | ||||
| 5L 1s | machinoid | mech- | mech | mechatonic | unchagned | unchagned | A more indirect reference to machine temperament. | Still references machine temperament. May also reference mechanism temperament. | |
| 3L 7s | sephiroid | seph- | seph | sephirotonic or sephiratonic | unchagned | unchagned | septonic | Rather than alluding to sephiroth temperament, the name should allude to Peter Kosmorsky's Tractatum de Modi Sephiratorum (A Treatise on the Modes of the Sephirates), whose name ultimately comes from the sefirot. The document describes several edos that are said to contain the "modi sephiratorum" (sephirate modes). Therefore, instead of the name "sephiroid", suggesting that the mos pattern resembles the modi sephiratorum, the mos pattern is the modi sephiratorum, hence the mosname "sephirotonic". | May still reference sephiroth temperament. For a more indirect reference, an alternate transliteration of סְפִירוֹת (sefirot) may be used instead.
New name is longer than the old name. |
| 7L 3s | dicoid and zaltertic | dico- and zal- | dico and zal | zaltertic | zal- | zal | As of writing, there are two names. I would favor zaltertic over dicoid in that it removes a name that suggests a temperament. | Central zalzalian thirds (another name for neutral thirds) are not the scale's bright generator, but are produced by the scale. | |
| Changes to names that bear the anti- prefix | |||||||||
| Mos | Current name | Suggested name(s) | Old suggestions | Reasoning | Possible issues | ||||
| Name | Prefix | Abbrev. | Name | Prefix | Abbrev. | ||||
| 1L 5s | antimachinoid | amech- | amech | selenite | sel- | sel | selenic | Shorter name. An indirect reference to luna temperament; "selene" is Greek for "moon". The name "selenite" follows the same pattern of 1L 6s being named after a type of gemstone. | Pun. |
| 1L 7s | antipine | apine- | apine | spinel | spin- | spin | alpine, stelanic | Shorter names. These names follow in the same spirit as "onyx" for 1L 6s in the following ways:
|
Pun. The names suggested don't typically rhyme with the words they're trying to rhyme with or reference, ruining the joke. |
| 1L 8s | antisubneutralic | ablu- | ablu | agate | aga- or agat- | aga | mineric | ||
| 1L 9s | antisinatonic | asina- | asi | olivine | oliv- | oliv | parivalic, alentic | ||
| Changes to names that bear other prefixes | |||||||||
| Mos | Current name | Suggested name(s) | Old suggestions | Reasoning | Possible issues | ||||
| Name | Prefix | Abbrev. | Name | Prefix | Abbrev. | ||||
| 2L 5s | antidiatonic | pel- | pel | pelotonic | unchagned | unchagned | pelic | From "pelog" and "armodue". The proposed names are to make both scales more distinct from diatonic. These names must be changed together. | The connection to diatonic may be beneficial to some musicians. Additionally, the mode names commonly used for both mosses are those from diatonic (lydian, ionian, etc) with the anti- and super- prefixes added.
New names reference pelog tuning and armodue theory. |
| 7L 2s | superdiatonic | arm- | arm | armotonic | unchagned | unchagned | armic | ||
| 8L 1s | subneutralic | blu- | blu | azurtonic | azu- or unchanged | azu or unchanged | azuric | An indirect reference to bleu temperament; azure is a specific shade of blue. Simplified name. Also, the sub- prefix may falsely suggest another scale called "(prefix)neutralic", similar to how subaric (2L 6s) is the parent to both jaric (2L 8s) and taric (8L 2s). | New name is referencing a temperament, albeit indirectly. The sub- prefix reasoning may be a stretch, since subaric, jaric, and taric are the only mosses related this way. |
| 2L 6s | subaric | subar- | subar | baric | bara- | bar | Rhymes perfectly with jaric and taric. May also mean "basic -aric", as this mos with a basic step ratio (L:s=2:1) cannot produce jaric or taric, or rather, produces both but equalized. | Too minor of a modification. The use of "bar" as an abbreviation may be problematic ("bar" may also mean "measure" in sheet music). | |
Aesthetic rules
These are the rules that attempt to justify the logic behind much of the name suggestions. There are, of course, exceptions to these rules, as some names are arguably too memorable to change.
- Names for single-period mosses with 5 or fewer notes are the most general names in the sense that they're not limited to an octave period and end with -ic or -al. These should be the only mosses that contain the anti- prefix, shortened to an-. (Exception: monowood is octave-specific and does not end with -ic or -al.)
- An extreme alternative to rule 1 is to say that all mosses named under rule 1 should end with -al, but this requires renaming more mosses (antetral, tetral, pental, anpental) for arguably little gain.
- Names for single-period mosses not of the form 1L ns end with -tonic, suggesting that these are octave-specific and reference a specific interval, a notable pre-TAMNAMS or other temperament-agnostic name, or indirectly reference a temperament if all other options are exhausted. (Exceptions: mosh, semiquartal, zaltertic, balzano, and pine don't end with -tonic.)
- Names for mosses of the form 1L ns with 6 or more notes are named after gemstones and minerals, following the spirit of 1L 6s being named onyx. These are named differently than those named using the previous rule as these mosses have too broad a tuning range to even suggest a single temperament.
- Names for multi-period mosses end with -ic and always refer to an octave-equivalent scale. (Execptions: lemon, lime, tcherepnin, and all the -wood scales don't end with -ic.)
- With the exception of mosses named under rule 1, no mosses should be named in a way that they contain additional prefixes such as anti-, sub-, or super-. (Exception: semiquartal bears the semi- prefix, but its mosprefix is chton-).
Other name changes:
- Antipentic -> anpentic; follows names of other small mosses where an- is used as a shortened form of anti-.
| Single-period mosses | |||||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Mos | Name | Mos | Name | Mos | Name | Mos | Name | Mos | Name | Mos | Name | Mos | Name | Mos | Name | Mos | Name |
| 1L 1s | trivial
monowood |
1L 2s | antrial | 1L 3s | antetric | 1L 4s | pedal | 1L 5s | selenite | 1L 6s | onyx | 1L 7s | spinel | 1L 8s | agate | 1L 9s | olivine |
| 9L 1s | sinatonic | ||||||||||||||||
| 8L 1s | azurtonic | ||||||||||||||||
| 7L 1s | pine | ||||||||||||||||
| 6L 1s | arch(a)eotonic | ||||||||||||||||
| 5L 1s | mechatonic | ||||||||||||||||
| 4L 1s | manual | 5L 4s | semiquartal | ||||||||||||||
| 4L 5s | gramitonic | ||||||||||||||||
| 3L 1s | tetric | 4L 3s | smitonic | ||||||||||||||
| 3L 4s | mosh | 7L 3s | zaltertic | ||||||||||||||
| 3L 7s | sephiratonic | ||||||||||||||||
| 2L 1s | trial | 3L 2s | anpentic | 3L 5s | checkertonic | ||||||||||||
| 5L 3s | oneirotonic | ||||||||||||||||
| 2L 3s | pentic | 5L 2s | diatonic | ||||||||||||||
| 2L 5s | pelotonic | 7L 2s | armotonic | ||||||||||||||
| 2L 7s | balzano | ||||||||||||||||
| 2-period mosses | |||||||||||||||||
| Mos | Name | Mos | Name | Mos | Name | Mos | Name | ||||||||||
| 2L 2s | biwood | 2L 4s | malic | 2L 6s | baric | 2L 8s | jaric | ||||||||||
| 8L 2s | taric | ||||||||||||||||
| 6L 2s | ekic | ||||||||||||||||
| 4L 2s | citric | 6L 4s | lemon | ||||||||||||||
| 4L 6s | lime | ||||||||||||||||
| 3-period mosses | |||||||||||||||||
| Mos | Name | Mos | Name | ||||||||||||||
| 3L 3s | triwood | 3L 6s | tcherepnin | ||||||||||||||
| 6L 3s | hyrulic | ||||||||||||||||
| 4-period mosses | |||||||||||||||||
| Mos | Name | ||||||||||||||||
| 4L 4s | tetrawood | ||||||||||||||||
| 5-period mosses | |||||||||||||||||
| Mos | Name | ||||||||||||||||
| 5L 5s | pentawood | ||||||||||||||||