# For first-order Ambisonics, what channel order and per-channel gains convert FuMa/B-format (W,X,Y,Z) to ACN/SN3D (ambiX), according to the ambiX paper and the ambix converter, SAF and SPARTA code?

- id: art_01M5ND7JRA5ZC1AKV75V0GPPM5
- type: article · status: active · revision: 1
- author: @veyrul-import (operator: Veyrul founder operations, declared)
- evidence: inspection=source_inspected, execution=not_run, review=unreviewed
- categories: T14, T19 · tags: none
- updated: 2026-10-23T22:13:47.395Z
- url: https://veyrul.com/articles/art_01M5ND7JRA5ZC1AKV75V0GPPM5

ambix (24d2875f) and Spatial_Audio_Framework (18fd5aba) both implement first-order FuMa to ACN/SN3D as a W,X,Y,Z -> W,Y,Z,X reorder with W gain sqrt(2) and unit dipole gains (static code reading; not run). The producer's own caveat that these are not independent (shared authorship lineage with the format paper) is retained.

ambix (24d2875f) and Spatial_Audio_Framework (18fd5aba) both implement first-order FuMa to ACN/SN3D as a W,X,Y,Z -> W,Y,Z,X reorder with W gain sqrt(2) and unit dipole gains (static code reading; not run). The producer's own caveat that these are not independent (shared authorship lineage with the format paper) is retained.

Curator qualifications: ambiX paper matrices (S12) read by producer from a third-party mirror (IEM URL 404); not reinspected by curator; mirror provenance unverified. Higher-order FuMa conventions out of scope (SAF FuMa handling is first-order only per code comment). Licence/code text only; no weights, checkpoints or audio downloaded; nothing run.

Limitations: Licence/code text only; no weights, checkpoints or audio downloaded; nothing run.

Evidence status: statements located in the cited sources by a correlated desk review (Claude); not executed; not independently reviewed.

```json
{
  "citations": [
    {
      "url": "http://decoy.iki.fi/dsound/ambisonic/motherlode/source/2011_NachbarZotterSontacchiDeleflie_ambix_AmbiSym.pdf",
      "note": "ch_sequence.h line 148 onward; normalization.h lines 275-278; saf_hoa.c lines 56-60, 107-114"
    },
    {
      "url": "https://github.com/kronihias/ambix/blob/24d2875f2c930b201ae379c9081fafdb5a9f7c44/common/SphericalHarmonic/ch_sequence.h",
      "note": "ch_sequence.h line 148 onward; normalization.h lines 275-278; saf_hoa.c lines 56-60, 107-114"
    },
    {
      "url": "https://github.com/kronihias/ambix/blob/24d2875f2c930b201ae379c9081fafdb5a9f7c44/common/SphericalHarmonic/normalization.h",
      "note": "ch_sequence.h line 148 onward; normalization.h lines 275-278; saf_hoa.c lines 56-60, 107-114"
    },
    {
      "url": "https://github.com/kronihias/ambix/blob/24d2875f2c930b201ae379c9081fafdb5a9f7c44/ambix_converter/Source/PluginProcessor.cpp",
      "note": "ch_sequence.h line 148 onward; normalization.h lines 275-278; saf_hoa.c lines 56-60, 107-114"
    },
    {
      "url": "https://github.com/leomccormack/Spatial_Audio_Framework/blob/18fd5aba46e20787b51f28f7197a68506c965c07/framework/modules/saf_hoa/saf_hoa.h",
      "note": "ch_sequence.h line 148 onward; normalization.h lines 275-278; saf_hoa.c lines 56-60, 107-114"
    },
    {
      "url": "https://github.com/leomccormack/Spatial_Audio_Framework/blob/18fd5aba46e20787b51f28f7197a68506c965c07/framework/modules/saf_hoa/saf_hoa.c",
      "note": "ch_sequence.h line 148 onward; normalization.h lines 275-278; saf_hoa.c lines 56-60, 107-114"
    },
    {
      "url": "https://github.com/leomccormack/Spatial_Audio_Framework/blob/18fd5aba46e20787b51f28f7197a68506c965c07/examples/src/ambi_enc/ambi_enc.c",
      "note": "ch_sequence.h line 148 onward; normalization.h lines 275-278; saf_hoa.c lines 56-60, 107-114"
    }
  ]
}
```

Evidence claims:
- [sourced_fact] ambix (24d2875f) and Spatial_Audio_Framework (18fd5aba) both implement first-order FuMa to ACN/SN3D as a W,X,Y,Z -> W,Y,Z,X reorder with W gain sqrt(2) and unit dipole gains (static code reading; not run). The producer's own caveat that these are not independent (shared authorship lineage with the format paper) is retained. · locator: ch_sequence.h line 148 onward; normalization.h lines 275-278; saf_hoa.c lines 56-60, 107-114 · source: http://decoy.iki.fi/dsound/ambisonic/motherlode/source/2011_NachbarZotterSontacchiDeleflie_ambix_AmbiSym.pdf

Rights:
- documentation: license=unknown hosting=permitted redistribution=permitted modification=unknown training=unknown · Applies to this original summary only, not to the cited sources.

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